Download An Overview of Fee Structures in Real Estate Funds and Their

An Overview of Fee Structures in Real Estate
Funds and Their Implications for Investors
Joseph L. Pagliari, Jr.
October, 2013
{Do not quote without permission}

University of Chicago Booth School of Business; [email protected]
The author thanks the Pension Real Estate Association for its funding of this study and in
particular thanks Mike Caron, Joe D’Alesandro, Jeff Fisher, David Geltner, Jacques Gordon, Jeff
Havsy, Steve Kaplan, Ted Leary, Fred Lieblich, David Lewandowski, Derek Lopez, Greg
MacKinnon, Paul Mouchakkaa, Randy Mundt, Devon Olson, Stavros Panageas, Martha Peyton,
Tim Riddiough, Jack Rodman, Kevin Scherer, Roy Schneiderman, Jim Valente and Nathan Zinn
for their helpful comments. Additionally, the author thanks Camilo Varela for his excellent
research assistance. However, all errors and omissions are the author’s responsibility.
Upon his recent 80th birthday, it seems appropriate to dedicate this study to Blake Eagle.
More than any other person, his vision and efforts have made such studies possible.
TABLE OF CONTENTS
I.
Introduction ................................................................................................................... 3
II.
Base Fees & Costs.......................................................................................................... 3
II.A.
Types of Base Fees & Costs ............................................................................................. 3
II.B.
The Market: Fees ≈ f(Complexity, Size, Experience) ......................................................... 5
II.C.
Management Fees & Differing Methodologies ................................................................. 6
II.D.
An Aside: Public-Market Benchmarks for Fees................................................................. 9
II.E.
Base Fees Act as a Drag on Returns ≈ f(Holding Period) ................................................ 11
II.F.
Fees on Committed v. Contributed Capital ..................................................................... 16
III.
Incentive Fees – Rationale, Mechanics and Effects .................................................... 17
III.A. The Rationale for Incentive Management Fees ............................................................... 17
III.B. The Mechanics: A Simple Example ................................................................................ 22
III.C. Variations on the Simple Example .................................................................................. 41
III.D. Co-Investment Capital ................................................................................................... 64
IV.
The Use of Double-Bogey Benchmarks ...................................................................... 65
IV.A. A Sketch of the the Plan’s Incentive Fee ........................................................................ 66
IV.B. Quantifying the Likely Incentive Fee .............................................................................. 71
IV.C. Additional Commentary: Beating the “Market” .............................................................. 82
V.
Principal/Agent Issues ................................................................................................ 83
V.A.
Building Blocks: Utility, Effort & Likelihood .................................................................. 84
V.B.
In-the-Money Promote ← Behavioral Effects ................................................................ 87
V.C.
Out-of-the-Money Promote ← Behavioral Effects ......................................................... 91
V.D.
Lowering Prefs & Promotes ← Improving Alignment of Interests? ............................... 95
VI.
An Empirical Illustration ............................................................................................. 98
VI.A. The Performance Data ................................................................................................... 99
VI.B. Assessing Risk-Adjusted Performance .......................................................................... 105
VI.C. Caveats Regarding Risk-Adjusted Performance ............................................................ 119
VII.
Conclusions ................................................................................................................. 131
VIII. Appendix 1: Notation Glossary ...................................................................................135
IX.
Appendix 2: Further Thoughts on Risk ......................................................................136
IX.A. Implications Regarding the Law of One Price .............................................................. 136
IX.B. Volatility Differences: Index v. Average of All Funds ................................................... 138
2
An Overview of Fee Structures in Real Estate Funds
and Their Implications for Investors
I.
Introduction
This study provides a conceptual framework by which investors can assess the implications
of various investment management fees and costs on the net returns of their investments.
For ease of discussion, this study will classify investment management fees as belonging to
one of two broad categories: base fees and incentive fees. Additionally, this study will
consider fees paid to investment managers differently from third-party costs incurred by
investment managers in the course of conducting the investment fund’s business. Whereas
investment managers may be keenly motivated1 to minimize the latter; the same disciplining
market forces are somewhat less keen with regard to the former – the investment
management fees may not only sustain the manager’s business platform but they may also
provide significant profits. With regard to these investment management fees, investors need
to understand both the static effects of such fees on returns and the behavioral effects of
such fees – particularly incentive fees – on investment managers’ decision making.
The balance of the paper is organized as follows: Section II examines base investment
management fees, with a particular emphasis on the types, methodologies and rationales for
such fees as well as how such fees alter the net return as the investment horizon lengthens.
Section III examines the static effects of incentive management fees. Section IV examines
the impacts of extending incentive management fees when the manager must beat two
hurdles (the so-called “double-bogey” benchmark). Section V examines the principal/agent
issues or behavioral impacts of particular incentive management fees. Section VI presents
with some empirical analyses of core and non-core returns as illustrations of the conceptual
issues raised earlier. Section VII concludes
II.
Base Fees & Costs
For purposes of this study, base investment management fees are distinguished from
incentive fees (i.e., those fees paid to the investment manager based on the fund’s and/or
property’s return). 2 To facilitate this discussion, the terms “fund,” “property” and “venture”
will be viewed as essentially equivalent. (Said another way, a fund may include a single
property or venture.) However, the term “fund” will be used in most instances. 3
II.A. Types of Base Fees & Costs
The base fees and costs generally relate to the three stages of a fund’s life cycle: inception,
operations and dissolution. Clearly, there may be some overlap and/or ambiguity with regard
In a competitive marketplace, differentials of a few basis points often matter in terms of investment
manager selection/retention.
1
These incentive fees include a manager’s promoted or carried interest, which – as a technical matter
– do not typically flow through the fund’s income statement; yet, they are fees in a larger sense.
2
The use of this term also ignores the distinctions between open- and closed-end commingled funds
and separate accounts.
3
3
to a particular fee’s classification. However, for discussion purposes, we can think of these
fund-level 4 fees and costs as shown below in Exhibit 1:
Exhibit 1: Various Types of Base Fees & Costs
Inception
Investment
Management
Fees
Third-Party
Costs:


Acquisition
Financing
Operations
Dissolution

Disposition

Asset/Portfolio Mgmt
Leasing
Property Mgmt
Construction Mgmt




Organizational

Legal

Professional Fees

Offering
“Dead” Deal(s)

Accounting
Valuations

Transaction Costs


Of course, not every fund has all of these fees and costs, while others have additional fees
and/or costs. Putting aside annual investment management fees (see §II.C) for now,
investment vehicles charge investors a host of other fees and costs – as shown below 5, 6 in
Exhibit 2:
4 By focusing on fund-level expenses, we are ignoring property-level expenses (i.e., those expenses
which would be incurred irrespective of the nature of the fund’s formation) – including those
generally associated with acquisition (e.g., environmental studies) and disposition (e.g., transfer taxes).
Unfortunately, the study reports these fees and costs by type of investment vehicle, rather than by
investment strategy. So, as a supplement to the PREA-provided table, the author has included as
supplemental information (Exhibit 3) the number of fund strategies per investment vehicle.
5
While a 2012 PREA report available, it does not provide the same level of detail as the 2011 report
on the matter of these fees.
6
4
Exhibit 2: Other Fees and Costs Charged Separately
Commingled
Commingled
Separate account
Joint Venture
Total
closed-end fund
open-end fund
# Vehicles % of type # Vehicles % of type # Vehicles % of type # Vehicles % of type # Vehicles % of type
Fees and Costs
Accounting fees
Acquisition fees paid to manager
Asset management fees
Bank Charges
Debt arrangement fees
Development management fees
Disposal fees paid to manager
Leasing fees
Legal fees
Overhead
Property management fees
Setup costs
Total of funds in the account category
17
57
16
22
13
47
13
15
23
71
60
34
184
Core
Value-Added
Opportunistic
Total of funds in the account category
12
92
80
184
9
31
9
12
7
26
7
8
13
39
33
18
2
7
1
2
4
3
2
7
2
7
7
2
31
6
23
3
6
13
10
6
23
6
23
23
6
6
23
3
4
3
5
5
3
3
6
18
2
35
17
66
9
11
9
14
14
9
9
17
51
6
3
8
1
2
0
3
4
0
5
8
10
1
14
21
57
7
14
0
21
29
0
36
57
71
7
28
95
21
30
20
58
24
25
33
92
95
39
264
Number of Vehicles by Investment Strategy
27
4
0
31
19
13
3
35
8
6
0
14
66
115
83
264
Source: PREA 2011 Management Fees & Terms Study | Tables 3 and 30 and author's calculations.
II.B. The Market: Fees ≈ f(Complexity, Size, Experience)
In perfectly competitive markets with commodity products, market forces are such that
prices (or, in our case, fees) evolve towards “normal” profits in which producers (or, in our
case, investment managers) cover their costs plus a “fair” profit. However, real estate
markets are often thought to fall short of the competitive market ideals; 7 moreover, such
products can be highly differentiated which, in turn, makes it more difficult for consumers to
discern the prices of such fees and costs. Accordingly, a brief discussion of the market for
base fees seems warranted.
As indicated above, the fees charged by investment managers theoretically ought to reflect
the underlying costs (plus a “fair” profit) to provide their services. These costs reflect the
costs of existing and new technologies as well as the complexities of the property type(s) and
strategies to be implemented. For example, the complexities and, therefore, the costs to
manage a portfolio of industrial properties – leased on a long-term, triple-net basis to credit
tenants – differ from the costs to manage the turnaround of a portfolio of under-performing
hotel properties. However, there is often some sense that costs as a percentage of invested
assets ought to decline as the size 8 of the portfolio increases; that is, the scalable nature of
the investment management business lends itself to the belief that increasing economies of
scale are realized as assets under management (AUM) grow. When looking at the fees for
large “core” funds, we see both of these effects at work: As compared to non-core funds,
managers of core funds are thought to engage in less complexity and the assets under
Characterized by perfect information, absence of pricing power, free entry/exit and equal access to
production technologies. See Debreu (1972).
7
There are two dimensions to size: a) dollar amount of AUM and b) number of properties (e.g., a $1
billion apartment portfolio typically has far more properties than a $1 billion mall portfolio). Not
surprisingly, investment managers find more scalability with properties having higher price points.
8
5
11
36
8
11
8
2
9
9
13
35
36
15
management of most core funds are significantly larger; consequently, (base) fees and costs
for core funds tend to be significantly lower than those found in non-core funds.
Another dimension is the experience of the investment manager. Because the ex ante
selection of an investment manager is fraught with uncertainty about the manager’s ability to
outperform its competitors, less-experienced firms often discount their fees (relative to
market averages) in order to offset investors’ natural skepticism about the less-experienced
firm’s capabilities. An extension of this line of reasoning is to observe that more-experienced
and -successful firms are able to source investor capital even though their fees are higher
than market averages.
II.C. Management Fees & Differing Methodologies
In terms of this evolution of fees and costs, Table 10 of PREA’s 2011 Management Fees
& Terms Study indicates that there are a host of rates and methodologies by which annual
asset/portfolio management fees are computed, as shown in Exhibit 3:
Exhibit 3: Annual Management Fee Rates by Investment Style
Core
Value-Added
Opportunistic
Total
Fee Basis
# Vehicles Average (%) # Vehicles Average (%) # Vehicles Average (%) # Vehicles Average (%)
Commitment
0
16
1.14%
4
1.28%
20
1.17%
Drawn commitment
5
1.19%
10
1.45%
11
1.23%
26
1.31%
Gross asset value
9
0.55%
7
NA
3
19
0.55%
Invested equity
7
1.17%
48
1.26%
47
1.39%
102
1.32%
Net asset value
15
0.90%
5
0.98%
5
1.70%
25
1.08%
Net operating income
9
6.31%
8
0
17
6.59%
Cash flow
0
3
0
3
Rental income
1
0
0
1
Two or more bases
4
4
1
9
Other
16
14
12
42
Total
66
115
83
264
Source: PREA 2011 Management Fees & Terms Study | Table 10 and author's calculations.
When looking at the array of rates and methodologies, 9 there are two broad points to be
made concerning: 1) the mathematical equivalence between fee methodologies and 2) the
underlying rationale for the methodology. First, there is a simple mathematical equivalence
between most of these fee methodologies, such that investors can easily convert the fee
under one methodology to the equivalent fee under another methodology. For example,
some funds charge their annual management fee based on gross asset value (GAV) while
others charge on net asset value (NAV). So long as the fund’s leverage ratio (LTV) is
9
Here too, there 2011 report provides more detail than 2012 report – for our purposes.
6
known (or can be reasonably estimated), then investors can convert 10 the fee payable under
one methodology to the other:
=
FeeGAV FeeNAV (1 − LTV )
For the reader’s convenience, a glossary of pertinent notation is provided in Appendix 1.
Likewise, a fee based on net operating income provides a similar equivalence assuming that
the fund’s capitalization rate is known (or can be reasonably estimated):
FeeGAV = FeeNOI ( Capitalization Rate )
Clearly, extensions can be easily drawn to fees based on cash flow or rental income.
Furthermore, extensions can be made to other methodologies (e.g., commitment, drawn
commitment, invested equity, etc.) however, the assumptions (e.g., the rate at which
committed capital is drawn) may become more tenuous.
Second and perhaps more importantly, the varying methodologies also speak to various
rationales – which can involve clarity, motivation(s) and/or the passage of time – which
attempt to produce some level of fairness between the investor and the fund manager. As
examples of these rationales, consider the following:
•
Committed v. Invested (or Drawn) Capital – Those funds which charge annual
management fees on committed capital are almost always non-core funds. The rationale
for investors paying such management fees seems to rest on the notion(s) that:
o to do otherwise may encourage fund managers to hurriedly deploy capital (thereby
potentially missing better risk-adjusted return possibilities had they invested more
deliberately and possibly increasing vintage-year risk),
o investing in non-core assets is a more time-consuming and intensive process (as
compared to investing in core properties) requiring (not only the level of fees to be
higher but also) that fees be paid sooner (to cover these higher costs), and/or
Given any two of these three parameters (Fee GAV, Fee NAV and LTV), investors can solve for the
third parameter – including the leverage ratio that produces an identical fee amount under both
10
methodologies: LTV = 1 −
FeeGAV
. As an example using the table above, the annual management
FeeNAV
fee for core funds averages 55 basis points of GAV and 90 basis points of NAV; this implies a
leverage ratio of approximately 40% in order to equate the annual management fee under the two
methodologies. If the fund’s leverage ratio is more than approximately 40%, than the management
fee would be lower under the NAV methodology (and the converse is also true).
7
o there are significant start-up costs associated with non-core funds whereas many core
funds (particularly, open-end commingled funds) are ongoing investment vehicles –
well beyond their start-up periods.
•
Gross v. Net Asset Value – As indicated above, there is a mathematical equivalence
between management fees based on GAV and those based on NAV, provided the
leverage ratio is known or can be estimated with reasonable precision. And, therein lies
the potential rub: Depending on the nature of the fund, the fund’s “targeted” leverage
ratio may represent a wide range of potential outcomes and the leverage ratio may
change over time (e.g., a combination of asset growth and principal amortization). When
significant uncertainty surrounds the leverage ratio, the mathematical equivalence is little
more than an interesting algebraic exercise.
•
Net Asset Value v. Invested Equity – Initially, (fair market value-based) NAV and
invested equity essentially denote the same item on the balance sheet. However, NAV is
a dynamic concept (meaning that the then-current value of NAV varies with changing
market conditions and with portfolio/balance sheet management) while initial equity is a
static concept (meaning that the amount of initially contributed equity is unchanging
with market conditions and portfolio/balance sheet management). Within the context of
a fund that is relatively short-lived, these methodologies produce similar fees. However,
when the fund has a long-term orientation, then there may be significant divergences
between the results produced by the two methodologies and issues of fairness; let’s
consider a few long-term issues:
o Fluctuating Capitalization Rates – Fluctuations in market-wide capitalization rates
clearly impact the asset valuation in the NAV-based calculation. For example, a
decrease in market-wide capitalization rates increases the value of the asset(s) –
possibly without any particular skill and effort of the manager – and, therefore,
invites the question as to whether an NAV-based methodology unfairly enriches the
fund manager in such instances. Of course, the converse is also true: an increase in
market-wide capitalization rates may unfairly impoverish the fund manager. 11
Meanwhile, a fee based on invested equity is a static number; so, it neither rewards
skill (e.g., increasing property values by more than that attributable to market-wide
decreases in capitalization rates) nor rewards good luck (e.g., market-wide decreases
in capitalization rates) [nor punishes bad luck (e.g., market-wide increases in
capitalization rates)].
o Portfolio v. Balance Sheet Management – Active fund managers engage in portfolio
management and/or balance sheet management which, in turn, may alter NAV. For
example, consider a portfolio-management practice such as harvesting mature
properties through asset sales and/or a balance sheet-management practice such as
increasing the leverage on remaining assets; further assume that in both instances the
Fluctuations in interest rates have a similar effect, but in the opposite direction, with regard to the
debt valuation: A decrease in interest rates increases the fair market value of the liabilities and,
therefore, decreases market-based NAV. Here too, the converse is true: An increase in interest rates
decreases the fair market value of the liabilities and, therefore, increases market-based NAV.
11
8
fund returns the cash proceeds to investors. In both cases, there is a shrinking of
NAV and, accordingly, an NAV-based management fee reduces payments to the
fund manager (or, alternatively stated, a management fee based on initial equity
would see the fee unchanged). However, in the (first) case of a shrinking asset base,
payment of an annual management fee based on initial equity – rather than NAV –
would seem to overly compensate the fund manager (as the manager presumably has
less work to do going forward as the number of assets managed is now reduced). On
the other hand, in the (second) case of increasing the leverage of the balance sheet,
payment of an annual management fee based on initial equity – rather than NAV –
would seem to fairly compensate the fund manager (as the manager presumably has
the same work to do going forward as the number of assets managed is unchanged).
o Unanticipated Inflation – A fee tied to NAV may, for example, more fairly
compensate the fund manager for unanticipated changes in inflation 12 (presumably,
the manager’s costs are tied to inflation) as it is generally assumed that real assets
provide (an imperfect) hedge against unanticipated inflation.
•
Asset Value v. Income – Because estimates of the current fair market value of the fund’s
assets (and potentially its liabilities) are inherently imprecise, some investors prefer that
the methodology by which annual management fees is calculated be tied to a metric that
is observable: for example, net operating income, cash flow and/or rental revenues. 13
Such metrics may also have the benefit that these are metrics that the investor would like
to see maximized. Additionally, such metrics also largely avoid the earlier-cited dilemma
of compensating investment managers based on fluctuations in market-wide
capitalization rates.
As a result of the potential ambiguities and sometimes conflicting motivations of the effects
relating to various methodologies used to compute annual portfolio/asset management fees,
it seems unlikely that one methodology is superior to all others. Accordingly, some investors
have begun to use a blend of two or more methodologies to compute such fees.
II.D. An Aside: Public-Market Benchmarks for Fees
Another perspective is to consider the level of general and administrative (“G&A) expenses
incurred by public REITs. Spanning the last five years, Exhibit 4 below displays the
(capitalization-weighted) average G&A expense by type of (equity) REIT:
At least in theory, it is the unanticipated component of inflation that matters – because investors
and managers can incorporate anticipated inflation into their negotiations over fee arrangements.
12
However, it would be naïve to assume that such measures cannot be manipulated – to some degree
– by the investment manager.
13
9
Exhibit 4: Average G&A Ratios for the Years 2008 through 2012
Property Type
Total Enterprise
Rental
Revenue
Gross Property
Value
Equity Market
Capitalization
8.07%
0.70%
0.73%
Health Care
Value *
0.50%
Industrial
0.99%
13.82%
1.16%
2.55%
Lodging
0.74%
N/M
0.64%
1.65%
Malls
0.32%
3.93%
0.49%
0.99%
Manufactured Homes
1.46%
6.82%
1.09%
2.25%
Multi-family
0.42%
4.59%
0.52%
0.89%
Net Lease
0.63%
8.23%
0.77%
1.30%
Office
0.63%
6.51%
0.84%
1.49%
Self-Storage
0.45%
5.63%
0.81%
0.62%
Shopping Centers
0.79%
10.16%
1.14%
1.75%
Total
0.55%
6.41%
0.73%
1.21%
Source: SNL Financial, as of December 31, 2012, and author's calculations.
* Includes pro-rata share of JV Debt.
The comparison to the public REIT market is imperfect. Among other considerations:
•
There are additional costs (e.g., SEC reporting, Sarbanes-Oxley compliance, analyst
calls, etc.) of a publicly traded corporation (REITs or otherwise). 14
•
The total compensation of REIT management is reported in G&A. To the extent
that “bonus” (and other deferred) compensation represents payments more akin to
the promoted interests of private real estate, then these G&A ratios are not directly
comparable to the base fees charged in private real estate funds.
•
Most institutional investors pay investment management fees (in addition to the
G&A charges) to a fund manager who assembles and monitors a portfolio of REIT
stocks.
Notwithstanding these imperfections, large institutional investors have the opportunity to
aggressively invest in both the private 15 and public real estate markets. Consequently, both of
these markets have a disciplining effect on one another, thereby pushing fees (and costs)
towards the “normal” profits envisioned for perfectly competitive markets. Said another
Despite REITs becoming larger over time, Kirby and Rothemund (2012) assert that the continued
rise over the last 10-15 years in REITs’ G&A expense as a percentage of total assets – a rise by more
than can be explained by increases in costs due to Sarbanes-Oxley, increases in executive
compensation, more complex business models, etc. – may be an attempt by some REIT managers to
allocate borderline costs to G&A as a means of boosting net operating income and, therefore,
estimated net asset values.
14
15
Sometimes also referred to as direct or unsecuritized (v. indirect or securitized) real estate.
10
way, the differences in fees is thought to mainly represent differences in the costs of
managing different property types, different strategies, etc. in different markets (private v.
public, domestic v. foreign, etc.).
II.E. Base Fees Act as a Drag on Returns ≈ f(Holding Period)
Irrespective of the “fairness” and/or necessity of the base fees and costs (and the
methodology by which they are computed), these fees and costs reduce the investor’s net
return. 16 The clearest examples of which are the fees relating to asset/portfolio management
and the annual professional fees and costs necessary to operate the fund; these fees and
costs directly reduce the investor’s net return. Meanwhile, the drag of the acquisition and
dissolution fees and costs fade as the investor’s holding period increases.
Perhaps a simple example best illustrates the issue. As a starting point, first consider a
hypothetical fund in which the unlevered real estate produces a (gross) return of 8.0% per
annum; further assume that the fund is 40% levered, where the interest rate is 5.0% per
annum with loan origination fees and costs of 1.5%. Because the loan fees increase the
effective interest rate 17 and increasingly do so as the holding period 18 shortens, the (gross)
levered returns 19 decreases as the holding period shortens – as illustrated below in Exhibit 5
(which assumes a constant leverage ratio over the holding period):
When cash returns are less than property returns, cash holdings also act as a drag on fund-level
returns.
16
The effective interest rate (ε ) can be approximated as the loan’s contract interest rate (i ) plus the
loan fees and costs, often referred to as “points,” (Pts) divided by the investor’s anticipated holding
17
period (T ) with respect to the loan: ε ≈ i +
Pts
.
T
18
To simplify, it is assumed that the holding period coincides with the loan-maturity date.
19
The return on levered equity (ke) can be thought of as the following function of the unlevered asset
return (ka), the cost of indebtedness (kd = ε) and the leverage ratio (LTV): ke =
is a version of Modigliani and Miller (1954).
11
ka − kd LTV
, which
1 − LTV
Exhibit 5: Illustration of Gross Levered Real Estate Returns
as a Function of the Holding Period
Major
Assumptions:
12%
10%
Unlevered Real Estate Return = 8.00%
Leverage Ratio = 40%
Interest Rate = 5.00%
Loan Origination Fees = 1.50%
Gross Levered Real Estate Return
Approximated Annual Return
Leverage Effects
8%
6%
Unlevered Real Estate
Return
4%
2%
0%
1
2
3
4
5
6
7
8
9
Holding Period (Years)
10
11
12
13
14
The region in light blue illustrates the annual return (8%) of the unlevered real estate; as
earlier noted, the return is assumed constant across time. The region in dark blue illustrates
the impact of leverage – given our earlier assumptions – for holding periods of 1 to 15 years,
as indicated on the horizontal axis. As also earlier noted, the leverage effect declines as the
holding period shortens, because the effective interest rate is higher when the holding period
is shorter. The sum of the light- and dark-blue regions represents the gross levered return
per annum, as a function of the holding period.
Second, let’s extend the illustration to further contemplate the fees and costs relating to the
inception, operation and dissolution of the fund. At inception, assume that the fund’s
sponsor charges an acquisition fee of 0.5% of asset value – which, because the fund is 40%
levered, equates to a fee of 0.833% on initial equity – and that the (third-party)
organizational and offering (“O&O) costs equal 1.0% of initial equity. On an operational
basis, assume that the fund’s sponsor charges an asset/portfolio management fee equal to
1.0% of equity and that on-going, third-party professional fees equal 0.25% of asset value –
which, because the fund is 40% levered, equates to a fee of 0.417% on initial equity. And
upon dissolution, assume that the fund’s sponsor charges a disposition fee of 0.25% of asset
value – which, because the fund is 40% levered, equates to a fee of 0.417% on initial equity –
and that the (third-party) disposition costs equal 0.75% of initial equity.
12
15
As noted at outset of this subsection, the asset/portfolio management and the annual
professional fees and costs directly reduce the investor’s net return, while the drag of the
acquisition and dissolution fees and costs fade as the investor’s holding period lengthens 20
(or, equivalently, the drag increases as the holding period shortens). The impact of these fees
and costs, as function of the investor’s holding period, is illustrated below in Exhibit 6:
Exhibit 6: Illustration of Net Levered Real Estate Returns
as a Function of the Holding Period
Major
Assumptions:
12%
10%
Unlevered Real Estate Return = 8.00%
Leverage Ratio = 40%
Interest Rate = 5.00%
Loan Origination Fees = 1.50%
Acquisition and O&O Costs = 1.83%
Asset Management & Professional Fees = 1.67%
Disposition Fees & Costs = 0.75%
Gross Levered Real Estate Return
Approximated Annual Return
Asset Management & Professional Fees
8%
Loan Origination Fees & Costs
Acquisition and O&O Costs
6%
Disposition Fees & Costs
4%
Investor's Net Return
2%
0%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Holding Period (Years)
Beginning with same yearly gross returns of the previous graph, the blue-shaded area
illustrates the drag on returns attributable to loan origination fees and costs (as implied by
Exhibit 5) while the gray-shaded areas illustrate the drag on returns attributable to various
fund-level fees and costs. The darkest-gray region illustrates the impact of the acquisition fee
and the organizational and offering costs – given our earlier assumptions – for holding
periods of 1 to 15 years (as indicated on the horizontal axis). Their combined effect21 is, as
As a first approximation, the drag on investor’s return attributable to the combined acquisition fee
and “O&O” costs (I) is roughly equal to their percentage of initial equity divided by the holding
period: I/T; the drag on investor’s return attributable to the combined disposition fee and dissolution
20
costs (D) is roughly equal to nth root of their percentage of initial equity:
T
1+ D −1 .
In terms of the impact on net returns and the composition of the total inception costs, both the
acquisition fee and the O&O costs have the same effect. (However, fees on committed capital – as
opposed to contributed capital – would worsen these effects.) Similar reasoning is true with regard to
the composition of the dissolution costs.
21
13
15
earlier noted, to reduce the investor’s return more significantly as the holding period
shortens. Meanwhile, the lightest-gray region illustrates the impact of the disposition fee and
the dissolution costs; here too, their effect is to reduce the investor’s return more
significantly as the holding period shortens. (But, because the disposition and dissolution
fees are not incurred until the end of the investment period, they have a smaller effect than
do the acquisition fees and O&O costs incurred at the beginning of the investment period.)
On the other hand, the annual asset/portfolio management costs plus on-going professional
fees and costs are – by assumption – a constant percentage of equity. As such, their
combined effect is a constant drag on investor returns – as indicated by the middle region of
these three gray areas. The sum of these three gray-shaded regions represents the drag on
returns, as a function of the holding period, with the remainder – indicated by the greenshaded region – representing the investor’s net return. All else being equal, longer holding
periods are preferable to shorter holding periods – such that, in the long run, the impact of
start-up and wind-up fees and costs fades nearly to zero and thereby maximizing the
investor’s net return. 22 Perhaps unsurprisingly, there is a tendency for investors to display
greater tolerance for these fees and costs when returns are high (and the opposite tendency
when returns are low).
Thirdly, this discussion about holding periods matters because such periods are typically a
byproduct of fund strategy. To oversimplify the point, assume that opportunistic strategies
generally have a fund life of 3 to 5 years, value-added strategies generally have a fund life of
5 to 7 years, and, while core funds generally have infinite lives, investors often remain in
such funds for 7 to 10 years. Consequently, Exhibit 6 can be inverted to solve for the gross
return that provides the investors with higher increasing net returns 23 – continuing with all
of our earlier assumptions – as holding period shortens, as shown in Exhibit 7:
In this regard, the acquisition fee and O&O costs act similarly to those situations in which
investors acquire an interest in a REIT which is trading at a premium to its underlying net asset value:
Investors are best served – all else being equal – by lengthening their holding period to effectively
amortize these costs which are spent on something other than the underlying real estate.
22
The analysis arbitrarily assumes higher net returns in the non-core strategies than in the core
strategies – as compensation for the higher risk generally attributable to these non-core strategies. (A
different slope could be easily shown.) Finally, these calculations ignore the promoted interests most
typically associated with non-core funds. Both topics (risk and promoted interests) are subsequently
explored.
23
14
Exhibit 7: Illustration of Net Levered Real Estate Returns
as a Function of the Holding Period
Major
Assumptions:
16%
Acquisition and O&O Costs = 1.83%
Asset Management & Professional Fees = 1.67%
Leverage Ratio = 40%
Interest Rate = 5.00%
Loan Origination Fees = 1.50%
Disposition Fees & Costs = 0.75%
Loan Origination Fees & Costs
Acquisition and O&O Costs
12%
Approximated Annual Return
Gross Levered Real Estate Return
Disposition Fees & Costs
8%
Asset Management & Professional Fees
Opportunistic
Funds
4%
0%
1
2
3
4
Value-Added
Funds
5
6
Core
Funds
7
8
Investor's Net Return
9
10
11
12
13
14
Holding Period (Years)
Finally, several caveats should be noted, including:
•
While the assumptions (e.g., real estate return, leverage ratio, fees, etc.) have been held
constant across holding periods in Exhibits 5 and 6, it is often the case that varying
strategies (e.g.,
core,
value-added
and opportunistic) invoke
varying
assumptions/characteristics and, therefore, different strategies offer differing expected
returns (and risks) as illustrated in Exhibit 7.
•
To simplify the illustration, the effects of various fees and costs have been
approximated. As such, compounding effects, certain non-linearities, joint effects
amongst factors, potential differences between income and appreciation returns,
differences between interest-only and amortizing loans, etc. have been ignored.
These simplifications, however, have the benefit of focusing on the main effects: The drag
of fees and costs on returns is lessened as the holding period lengthens. If investors believe
that they (and/or their consultants 24) have little ability to select those investment managers
which will prospectively outperform the market, then these investors ought to minimize
In the arena of general investment consulting, Jenkinson, et al. (2013) find no evidence that the
consultants’ recommendations improve, on average, the performance of plan sponsors’ allocation to
U.S. equities.
24
15
15
investment management fees – lengthening the holding period is one form of minimizing
fees (as is, of course, lowering the fees themselves). As Kahn, et al. (2006) have pointed out,
“Of the three dimensions of investment management – return, risk and costs – investors
have direct control over only costs.” Of course, the investor’s goal should be to maximize
risk-adjusted net returns; investment management fees are just one part of that calculus.
II.F. Fees on Committed v. Contributed Capital
Let us return to the issue of fees on committed v. contributed (or drawn) capital. While the
earlier subsections addressed issues of mathematical equivalence and the possible rationale
justifying such fees, let us also acknowledge another possibility: The investment manager
uses the unfunded portion of the capital commitment to effectively increase the fund’s
leverage ratio. 25 As noted earlier, the payment of management fees on committed (as
opposed to contributed or drawn) capital is most closely associated with the non-core funds,
which also tend to operate with higher degrees of financial leverage. As to be discussed later,
while leverage increases the expected return of the fund (whether this expectation proves
true depends on evolving events), leverage unambiguously increases the volatility and
riskiness of the fund. Provided full disclosure and investors understand 26 the effects, there is
nothing inherently imprudent about increasing the leverage ratio of the fund.
How should investors think about the future returns likely produced by funds which, initially
at least, require only a partial drawdown on the investors’ equity commitment? To make
things starkly simple, let’s assume that there are only two future states: 1) the “good” state in
which the fund does well and, therefore, the unfunded portion of the equity commitment is
never drawn, and 2) the “poor” state in which the fund does poorly and, therefore, the
unfunded portion of the equity commitment is entirely drawn. On an ex ante basis, there are
three ways to view the initially unfunded portion of the investor’s equity commitment: 1)
ignore it (and merely note the higher leverage ratio as described above), 2) acknowledge the
unfunded portion by assuming that this (potential) future investment will earn the “market”
rate of return from, say, REITs (or some other real estate vehicle offering sufficient liquidity
to fund the remaining equity commitment if and when called), or 3) acknowledge the
When committing capital to a particular fund, the investor signs a subscription agreement and a
note for the portion of the capital commitment not immediately funded. Assuming the investor is
creditworthy, the fund manager can secure a loan (with full recourse to the investor to the extent of
unpaid committed capital) against the unfunded commitment and use the proceeds to acquire
additional assets for the fund, thereby effectively increasing the leverage of the fund. Because not all
investors are equally creditworthy (and/or some investors are prohibited by their governing
documents from using subscription lines) and because the fund uses the entirety of the unfunded
commitment to finance the subscription line, all investors share pari passu in the interest rate of
whatever subscription line is procured. Hence, there is also a (relatively small) "free rider" problem
associated with subscription lines for the less-creditworthy investor(s).
25
These effects may be substantial. For example, assume that the use of a “subscription line”
increases the fund’s leverage from 66.7% to 75%; this increases the volatility of levered equity by
33.3%. Similarly, an increase in the fund’s leverage from 75% to 85% increases the volatility of
levered equity by 66.7%. As subsequently discussed, the volatility of levered equity (σe) is a function
26
of the asset-level volatility (σa) and leverage: σ e =
σa
1 − LTV
16
(assuming fixed-rate, default-free debt).
unfunded portion by assuming that this (potential) future investment will earn the “safe” rate
of return from money-market instruments (again, with sufficient liquidity to fund the
remaining equity commitment if and when called). The first of these three approaches
assumes that the bad state will never occur, while the second and third approaches assume
that there is some possibility that the bad state will occur. In all three approaches, the fund’s
expected return is then a weighted average of the fund’s returns under the good and bad
states – where the weighting is predicated on the investor’s perceptions about the likelihood
of these future states. Of course, actual returns from such funds represent the realizations of
these future states. More broadly, investors in such cases (i.e., partial draw downs of their
committed capital) have an embedded assumption about how much of their committed
capital will be ultimately invested. If the undrawn capital is held in a liquid low-return form,
investors are foregoing the higher expected returns in less-liquid, longer-duration
investments; this has a cost in the sense that the manager is forcing investors to provide the
fund with liquidity at no charge.
III. Incentive Fees – Rationale, Mechanics and Effects
This section examines the rationale for utilizing incentive clauses (which are more prevalent
among non-core funds) in investment management contracts and how the mechanics of
typical structuring techniques influence investor returns. 27 To be clear, this section will
examine the static effects of such structures; that is, we will take the fund’s risk and (gross)
return characteristics as given (or, in the words of the economists, these risk/return
characteristics will be “exogenous” to the structuring techniques). A subsequent section (§V)
will consider the interplay between structuring techniques and the fund’s risk and (gross)
return characteristics (i.e., the “endogenous” relationship between structure and the fund’s
risk/return characteristics). For now, let’s begin by addressing the basics.
III.A.
The Rationale for Incentive Management Fees
The underlying rationale for utilizing incentive fees within investment-management contracts
is (or, at least, ought to be) to motivate and compensate investment managers for producing
favorable risk-adjusted returns. In so doing, institutional investors often attempt to
differentiate “alpha” (α) and “beta” (β ), where the latter represents market-wide or
systematic risk/return characteristics and the former represents the residual return and,
therefore, an estimate of fund manager’s ability to produce risk-adjusted returns. These
concepts are illustrated below in Exhibit 8:
In the context of non-real estate private equity – predominately leveraged-buyout and venturecapital funds – Metrick and Yasada (2010) estimate that approximately two-thirds of the fund
managers’ revenues come from base fees and, therefore, approximately one-third comes from carried
interests.
27
17
Fund and Market Returns
Exhibit 8: Illustration of Fund Alphas and Market Beta
Market
Return
rf
Market Risk (β = 1)
Fund and Market Risk (β)
In this form of the market model (the blue line), there is a linear relationship between the
risk-free rate (rf) and the (benchmark or) “market” portfolio. Investments – or, in our case,
funds – which lie above the market line provided positive alpha; for convenience, they are
shown as green dots. Conversely, investments (or funds) which lie below the market line
provided negative alpha; for convenience, they are shown as red dots. Given the fund’s beta,
the distance from the fund’s return to the market line represents the extent to which the
fund produced (positive or negative) alpha.
At least in principle, sophisticated investors loathe paying incentive fees for “beta” (i.e.,
exposure to broad market forces) as they can gain this exposure through a passive
investment vehicle; consequently, the payment of an incentive fee ought to be tied to
producing positive alpha. Consider this statement (Douvas (2003)) as generally reflecting
investor views (italics in the original):
A cornerstone of the private equity fund philosophy is that fees should reflect performance
and interest between GPs and LPs are aligned via the compensation arrangement. There
should be a continuum along the risk and return spectrum of fees paid for performance.
Managers should only be rewarded with outsized fees for exceptional performance. … No manager should be
rewarded with outsized fees just for utilizing leverage.
In practice, this separation of alpha and beta is more difficult to achieve. Let’s briefly
consider some of the reasons why.
18
III.A.1. Passive Investment Vehicle(s)?
While the stock and bond markets offer a plethora of passive investment vehicles (e.g.,
indexed mutual funds, exchange-traded funds, etc.) designed to provide low-cost access to
broad market forces, the same cannot be said of private real estate. Strictly speaking, when
providing such access to private-market real estate investors, two possibilities come to mind:
NCREIF swap contracts 28 and/or an index fund of (equity) REITs. 29 However, these
approaches have – so far at least – not gained significant allocations with regard to the real
estate portfolios of large pension (endowment and sovereign wealth) funds. Though the
reasons for this lack of traction are beyond the scope of this study, the basic dilemma
remains: institutional private-market real estate investors have few low-cost options.
Moreover, the dilemma intensifies as investors move to non-core real estate investments.
That said, many investors view the open-end core funds as providing systematic exposure
(or “beta”) to institutional real estate investors with non-core funds providing excess riskadjusted returns (or “alpha”) – e.g., see Fairchild, et al. (2012).
III.A.2. The “Market”?
What is the proper market index? While the appropriate selection may be clear in the stock
and bond markets, the selection is often hazy in private-market (or alternative) investments –
here too the effect intensifies as investors move to non-core real estate investments. For
domestic “core” funds, a reasonable argument can be made for NCREIF’s ODCE (OpenEnd Diversified Core) Index or the PREA | IPD U.S. Property Fund Index. But, even here,
differences in leverage ratios can – if not properly controlled – can account for significant
differences in performance.
III.A.3. Which Measure of Risk?
In addition to the difficulty associated with defining the “market,” the definition of risk is
also equivocal. In the classic single-factor market model of Sharpe (1964), the risk measure is
the investment’s beta (β ): a measure of systematic risk, based on how returns co-vary with
σ
the market. More technically: βi = ρi , Mkt i , where: ρi,Mkt = the correlation between the
σ Mkt
returns of the ith security (investment or fund) and the market (Mkt), σi = the volatility
(standard deviation) of the ith security’s returns and σMkt = the volatility of the market’s
returns. Notice that the beta of a particular security is the product of its correlation with the
market and its volatility (then scaled by the inverse of the market’s volatility). Whether right
For example, see: http://www.markit.com/en/products/data/indices/structured-financeindices/ncreif/ncreif.page. Additionally, FTSE NAREIT has introduced PureProperty ® indices, see:
http://www.ftse.com/Indices/FTSE_NAREIT_PureProperty_Index_Series/index.jsp.
28
29 Pagliari, et al. (2005), Oikarinen, et al. (2009) and Horrigan, et al. (2009) suggest, from varying
perspectives, that institutionally oriented public- and private-market real estate investments are near
substitutes for one another – provided that care is taken to control for the substantive differences
(e.g., leverage, property-type composition, etc.) in the respective market indices. However, there are
also issues of liquidity and control which may tip a large institutional investor in one direction or the
other.
19
or wrong, this is not how many real estate investors think about risk; instead, they often
think in terms of total risk (σi ). 30 So, this difference in approach calls into question the
separation of alpha and beta – at least in comparison to how their counterparts in the public
equity markets perceive risk. 31, 32
There is, however, a more insidious problem when it comes to risk measures: using the
volatility of realized returns may not fully communicate the risks borne by investors in a
particular fund. This is particularly true when the fund is either short-lived and/or has not
experienced a full market cycle. The former problem – a short time series – can often mask
significant risks not yet realized. 33 And the latter problem – lack of a full market cycle – can
often make bumblers look like geniuses (and vice verse). In both cases, it is difficult to
distinguish luck from skill. 34
III.A.4. An Aside: The Misstatement of Alpha
When discussing alpha, many practitioners misuse the concept. It is, for example, not
uncommon for practitioners to state that a non-core fund produced a positive alpha because
it produced a larger return than, say, the NCREIF Index over the same time period. This is
an abuse of the concept of alpha because such comparisons fail to incorporate risk into the
analysis. Using our earlier example, let’s identify two funds (call them funds i and j ) such that
one produced positive alpha and the other negative alpha, as shown in Exhibit 9:
For purposes of this study, we will assume that risk can be represented by the volatility of returns.
This somewhat controversial assumption is examined elsewhere, e.g. see: Holton (2004). Instead,
many investors prefer some measure of “downside” risk (e.g., semi-variance).
30
This is not a purely theoretical problem. If private-market real estate investors tend to focus on
total risk, they therefore may not fully capture the possible diversification benefits of investments or
funds with low correlation to the market returns. So, thoughtful real estate investors often utilize
approaches involving modern portfolio theory to create diversification strategies.
31
Underlying Sharpe’s capital-asset pricing model (CAPM) are assumptions which may be difficult to
abide by in the private real estate market. These problematic assumptions include: lending and
borrowing at the same rate, costless trading, investors unable to influence returns, and all information
is always freely available to all investors.
32
The academic term often used is the “peso problem” – meaning low-probability but significant
events that do not occur in the sample (it is taken from the unanticipated devaluation of the Mexican
peso in 1994). I prefer a more gruesome analogy to illustrate the small-sample problem: If you play
Russian roulette and are not killed when you pulled the trigger, it does not mean that you did not
take a significant risk.
33
While a robust discussion of the issues involved with distinguishing luck from skill are beyond the
scope of this study, the interested reader is referred to Fama and French (2010), Grinold (1989) and
Sharpe (1991) among others.
34
20
Fund and Market Returns
Exhibit 9: Illustration of Fund Alphas and Market Beta
-α
Fund j
Market
Return
Fund i
+α
rf
Market Risk (β = 1)
Fund and Market Risk (β)
In the hypothetical above, Fundi (shown on the left half of the graph) provides a lower
return than the “market” yet provides a positive alpha because its risk-adjusted return is
higher than that produced by the passive index (of the same risk); meanwhile, Fundj (shown
on the right half of the graph) provides a higher return than the “market” yet provides a
negative alpha because its risk-adjusted return is lower than that produced by the passive
index. Because, as earlier noted, the private real estate market is not replete with passive
indices, investors have two practical (but imperfect) choices: 1) better identify (or customize)
benchmarks 35 when assessing the risk-adjusted performance of non-core funds or 2) use
leverage to synthetically create a risk/return continuum for non-core funds (and
investments). This latter approach will be the tact taken later in this study when comparing
the net-return performance of non-core and core funds – as an illustration of these
principles in practice.
When considering customized benchmarks, it is important to acknowledge that some investment
managers attempt to produce “allocation” alphas (i.e., portfolio rebalancing) while others attempt to
produce skill-based alphas (i.e., positive risk-adjusted performance within a certain sector); some
attempt to produce both. See, for example, Bailey (1990) and Leibowitz (2005).
35
21
III.B.
The Mechanics: A Simple Example
Like the evolving market with regard to base fees and costs, so too is true of incentive fees.
This evolution has been particularly stark after the 2007-2008 financial crisis, with investors
simultaneously demanding more transparency 36 – particularly with regard to aspects of
financial leverage.
Let’s begin with a simple example regarding incentive fees: Assume that an investor and an
investment manager agree to first allocate the fund’s profits such that the investor receives
its capital plus 12% per annum – the “preferred” return (or the “pref”) – and that excess
profits (if any) are to be allocated 80% to the investor and 20% to the investment manager.
In the vernacular of the industry, the investment manager’s participation in the excess profits
would be referred to as promoted interest 37 of 20%. Moreover, the conventional wisdom
generally believes that the investor is thereby defining alpha as emerging at or near the
preferred return. (However, as illustrated in §V, such a view ignores the link between the
preference and the manager’s efforts; consequently, §V argues for a more integrated view
than the received wisdom.)
To continue with our example, assume that the fund is also expected to produce a 12%
return and that the standard deviation of that return is 15%. And to keep matters simple,
let’s assume the fund’s life is one year and that its returns are normally distributed. 38, 39 An
With regard to the transparency and consistency of reporting, several domestic initiatives have
been quite helpful: a) the Real Estate Information Standards: http://www.reisus.org/index.html
(REIS), jointly sponsored by NCREIF and PREA, has – since 1995 – provided standards for
calculating, presenting and reporting investment results to the domestic institutional real estate
investment community, and b) the Institutional Limited Partners Association: http://ilpa.org/
(ILPA) has – since 2009 – provided its Principles, to establish best practices between limited and
general partners. Internationally, c) INREV, https://www.inrev.org/, is the European association for
investors in non-listed real estate vehicles and d) ANREV, http://www.anrev.org/ , is its counterpart
in Asia.
36
In practice, the promoted interest is referred to in a variety of ways, including as the carried
interest, residual-profits participation, back-end split and the “scrape.”
37
Young and Graff (1995) dispute the notion that real estate returns are normally distributed.
Nevertheless, any symmetrical distribution of gross returns will have similar effects on net returns –
as described herein. The normal distribution is a special case of the symmetrical distributions, which
simplifies much of the mathematics (including the fact that the standard deviation (σ ) completely
describes the distribution’s volatility). Perhaps a more interesting consideration is the case of nonsymmetrical distributions; here the degree and direction of the skewness may alter the conclusions
reached herein using the normal distribution. Ultimately, this is an empirical question beyond the
scope of this paper.
38
In layman’s terms, you are unsure about the fund’s future return. Your best guess (i.e., your
expectation) is a 12% return, although the final result could be higher or lower with equal likelihood.
The 15% standard deviation implies that you expect roughly two-thirds of the outcomes will be
found at 12% ± 15% (i.e., a range from -3% to 27%).These numbers – like all other illustrations in
this section – are only used for purposes of demonstrating these concepts; they are not the result of
an empirical analysis.
39
22
illustration of the fund’s expected return and investment manager’s participation in the
excess profits are shown below in Exhibit 10:
Manager's Promoted Interest
Manager's Promoted Interest
Estimated Frequency of Fund-Level Returns
Exhibit 10: Illustration of Expected Fund-Level Returns
with Investment Manager's Promoted Interest
Distribution of Expected
Fund-Level Returns
-33%-29%-25%-21% -17% -13% -9% -5% -1% 3% 7% 11% 15% 19% 23% 27% 31% 35% 39% 43% 46% 50% 54%
Likely Returns
The blue bell-shaped curve represents the distribution of the fund’s likely returns before the
investment manager’s promoted interest, which is shown as the red kinked line. The
horizontal axis represents the likely range of fund-level returns (given our assumptions) –
centered at the assumed mean (12%) – while the left-hand vertical axis represents the
frequency with which these returns are expected to occur and the right-hand vertical axis
represents the scale of the manager’s promoted interest.
The impact of the promoted interest is to truncate the investor’s upside return (i.e., returns in
excess of the preferred return are shared between the investor and the investment manager),
as shown below in Exhibit 11. For example and given our assumptions: If the fund-level
return is 12%, then the investor’s return is 12% and the manager’s promoted interest is
worth zero. If the fund-level return is 22%, then the investor’s return is 20% and the
manager’s return is 2% of the 22% (i.e., the investment manager receives 20% of the fund’s
profits in excess of 12%). If the fund-level return is 32%, then the investor’s return is 28%
and the manager’s return is 4% of the 32%. These and other likely possibilities are shown
below in Exhibit 11 by comparing the blue curve to the green curve (for returns in excess of
the mean (the white dashed line)). The blue-shaded area represents the manager’s promoted
interest, while the green-shaded area represents the investor’s net return.
23
Exhibit 11: Illustration of Fund-Level and Investor-Level Returns
when Investment Manager Receives a Promoted Interest
Estimated Frequency
Likely Returns
before Promote
Likely Returns
after Promote
-33%
-28%
-23%
-18%
-13%
-8%
-3%
2%
7%
12%
17%
22%
27%
32%
37%
42%
47%
52%
57%
Likely Returns
As is visually apparent from the graph above, the investor’s net return is reduced and,
therefore, so is the investor’s expected net return – as compared to the fund-level (or gross)
return. While treated at greater depth in the next section, it is important to note intuitively
that this simple graph communicates two crucial results (which, to many, may be
counterintuitive):
1. The investor’s expected net return is lower than the fund’s expected gross return,
even when the preferred return is set equal to the fund’s expected gross return.
2. The calculated standard deviation of the investor’s net return is lower than the
standard deviation of the fund’s gross return. This result is, for all intents and
purposes, a statistical illusion – because the investor’s downside risk is unchanged.
Specific to our example, the manager’s carried interest serves to reshape the distribution of
returns 40 as shown in Exhibit 12:
As noted earlier, any symmetrical distribution will produce similar results. Consider, as an extreme
example of this assertion, the uniform distribution – in which every value in the relevant rage is
equally likely – as a symmetrical, but fat-tailed, distribution. When utilizing the uniform distribution,
the expected value of the manager’s promoted interest increases to 1.3% (as compared to the 1.2%
result shown in Exhibit 12 utilizing the normal distribution) and the volatility of the expected
40
24
Exhibit 12: Fund- and Investor-Level Expected Performance
Likely Returns:
Fund-Level Returns before Investment Manager's Promoted Interest
Reduction in Return Attributable to Investment Manager's Promoted Interest
Investor's Net Return
12.0%
1.2%
10.8%
Volatility (Standard Deviation):
Fund-Level Volatility of Expected Return
Reduction in Volatility Attributable to Investment Manager's Promoted Interest
Standard Deviation of Investor's Expected Net Return
15.0%
1.5%
13.5%
Though these effects have been described in Kritzman (2012) and Pagliari (2007) in other
but similar contexts, let’s examine these effects in greater detail:
III.B.1. A Lower Expected Return ← Often Misunderstood
As indicated above, the impact of the convexity of the manager’s promoted interest (in this
case, the convexity 41 is generated by the asymmetric nature of the carried or promoted
interest) is to reduce the investor’s expected return – because the manager’s promote serves
to truncate the upside of the investor’s return. See Exhibit 13 below:
promoted interest increases to 1.7% (as compared to the 1.5% result shown in Exhibit 12 utilizing
the normal distribution).
Convexity is a mathematical term, describing the orientation of a curve relative to the horizontal
axis. Mathematical finance has adopted the term to describe, among other things, the orientation of
bond prices relative to interest rates, the payoff to the purchase of a call option and, in our case, the
payoff to incentive-compensation fee schedules.
41
25
Exhibit 13: Illustration of Fund-Level and Investor-Level Returns
when Investment Manager Receives a Promoted Interest
Estimated Frequency
Likely Returns
before Promote
Likely Returns
after Promote
Manager's
Promoted
Interest
-33%
-28%
-23%
-18%
-13%
-8%
-3%
2%
7%
12%
17%
22%
27%
32%
37%
42%
47%
52%
57%
Likely Returns
Surely, sophisticated investors appreciate that their upside is truncated in such arrangements;
however, they also believe that such arrangements produce incentives in the investment
manager that leads, on average, to higher risk-adjusted outcomes. Whether or not this
truncation (and, therefore, lowered expected return) is offset by the investment manager’s
ability to generate positive alpha is partly an empirical question (i.e., what do the data tell
us?); as noted earlier, the last section of this study will attempt to illustrate how this empirical
question might be evaluated.
While the mathematics of the expectation are somewhat complicated (as shown next), a
simple two-outcome example will serve to illustrate how the asymmetric nature of the
promote serves to lower the investor’s (net) expected return below the fund’s expected gross
return – even when the preferred return is set equal to the fund’s expected return. So,
assume that there are only two possibilities: either the fund produces a 24% return or a 0%
return, each with equal probability. Specific to our example, the manager’s carried interest
serves to reduce the investor’s expected return to 10.8%; see Exhibit 14:
26
Exhibit 14: Simple, Two-Outcome Illustration of Asymmetric Payoffs
Outcomes
Probability
Gross
Returns
Outcome1
50%
24.0%
2.4%
21.6%
Outcome2
50%
0.0%
0.0%
0.0%
12.0%
1.2%
10.8%
Average
Promote
Net
Returns
As with the earlier assumptions, this two-outcome example assumes an average (gross)
return of 12% per annum. However, in the first outcome, 2.4 percentage points of the 24%
return is allocated to the investment manager, with the investor receiving the remainder
(21.6%); in the second outcome, all of the 0% return is allocated to the investor. Since both
outcomes are equally likely, the investor’s average or expected (net) return is 10.8%.
[Author’s note: The balance of this subsection can be safely skipped by the uninterested reader.]
The underlying mathematics require that the promoted interest and the investor’s net return
be calculated for each outcome and then multiplied by the probability of that outcome
occurring. For example, the expected value of the investment manager’s carried interest
( E [π ]) can be written as:
=
E [π ]
N
∑ P ( k ) ϕ max ( 0, k
n =1
n
n
−ψ ) 
(1)
where: P ( kn ) = the probability of kn, kn = the fund-level return in the nth outcome, with n
= 1,…, N possible outcomes, ϕ = the manager’s profit-participation percentage (or the
“promote”) and ψ = the investor’s preferred return. And, in the same manner, the investor’s
expected (net) return ( E [ν ]) is merely the fund’s expected (gross) return ( E [ k ]) less the
expected value of the investment manager’s carried interest:
E=
[ν ] E [ k ] − E [π ]
(2)
N
N
=
∑ P ( kn ) kn −∑ P ( kn ) ϕ max ( 0, kn −ψ )
=
n 1=
n 1
It is always true that the expected value of the investment manager’s carried interest is
greater than zero. 42 In turn, then it is also always true that the expected value of the
investor’s (net) return is less than the expected value of the fund’s (gross) return. 43, 44
The only exception – in which case, the expected value equals zero – is when the investor’s
preferred return is set higher than highest possible fund-level return. If so, this would defeat the
purpose(s) of having an incentive-fee arrangement.
42
27
III.B.2. A Lower Standard Deviation ← Statistical Illusion
Because the impact of the fund’s promoted interest is to reduce the investor’s expected
return, the blue-shaded area representing the investor’s net return is smaller than the entire
distribution. For convenience, Exhibit 11 is replicated below:
43
The earlier bell-shaped curves presume that fund-level returns are normally distributed. So, the
continuous version of the return-generating function is appropriate: f ( k ) =
1
σ k 2π
In which case, the expected value of the fund-level return can be written as: E [ k ] =
e
 1  k − µk 
− 

 2  σ k 
2
.
∞
∫ ( k ) f ( k )dk ;
−∞
similarly, the expected value of the investment manager’s promote can be expressed as:
E=
[π ]
∞
∫ψ ϕ ( k −ψ ) f ( k ) dk and, therefore, the expected value of the investor’s net return can be
expressed as:=
E [ν ]
44
∞
∞
−∞
ψ
∫ ( k ) f ( k )dk − ∫ ϕ ( k −ψ ) f ( k ) dk .
Said another way, the average expectation of the carried interest is greater than the expectation of
∞
(
)
the carried interest vis-à-vis the fund’s average return: E [π ] =ϕ ( k −ψ ) f ( k ) dk > ϕ E [ k ] −ψ .
∫
ψ
This was better said by Savage (2009), who referred to a form of this differential as “the flaw of
averages.”
28
Exhibit 11: Illustration of Fund-Level and Investor-Level Returns
when Investment Manager Receives a Promoted Interest
Estimated Frequency
Likely Returns
before Promote
Likely Returns
after Promote
-33%
-28%
-23%
-18%
-13%
-8%
-3%
2%
7%
12%
17%
22%
27%
32%
37%
42%
47%
52%
57%
Likely Returns
From purely a mathematical perspective, the calculated standard deviation of the investor’s
net return is smaller than the standard deviation of the fund’s (gross) return because the
dispersion of the investor’s (net) return is narrower. However, this result is a statistical
illusion in the sense that the investor’s downside risk remains unchanged (and that
distribution of net returns is no longer symmetrical). 45 And while we could resort to
measures such as semi-variance 46 to better describe the riskiness of the investor’s net return,
it seems more pragmatic to simply use the standard deviation of fund-level gross returns as
the metric by which the volatility of one investment can be compared to another.
III.B.3. Expectations v. Realizations
The illustrations above are discussed in the context of expectations about future returns.
Clearly, we cannot know with absolute certainty the future outcome at the time we make our
investment and, therefore, it is far more appropriate to think about future returns as some
range of likely outcomes. This is particularly important – indeed, imperative – when dealing
45 When the likely returns are normally distributed, the mean and the standard deviation completely
describe the distribution. When the returns are not, additional parameters are needed. See, for
example, Fama (1963).
A statistical measure of the dispersion of all observations that fall below the target value, using the
average of the squared deviations of such values (e.g., see: Nantell and Price (1979)).
46
29
with investments in which there are asymmetries, such as the convexity of the investment
manager’s promoted interest. These asymmetries render the fund’s average (gross) return a
misleading statistic of the investor’s (net) return. That these distributions of future returns
are inherently unknowable does not make their estimation any less important. Consequently,
investors are well advised to weigh not only the expected return but also the likelihood of
higher and lower outcomes.
There is, however, another way to think of the dispersion in returns. Consider, as an
example, an investor who has invested in a large number of funds of the type (i.e., a 12%
preferred return to the investor and a 20% promoted interest to the manager) described at
the beginning of this section and further assume that the aggregated realized performance of
these funds can also be fairly described as before (i.e., normally distributed with a 12% mean
and a 15% standard deviation). 47 Then, all of the previous points made about the dilution
caused by the convexity of the manager’s promoted interest are equally applicable to this
pool of realized returns: the investor’s net return is lower than the fund’s gross return and
the standard deviation of the investor’s net return understates the riskiness of the investor’s
return.
III.B.4. Which Parameters Matter?
Let’s further consider the expected value of the manager’s promoted interest (and, therefore,
the dilution of the investor’s net return). The expected value of the investment manager’s
promoted interest is analogous to a call option in which the manager has a contingent claim
on the fund’s future profitability; therefore, three relationships are important:
•
the level of the promoted interest (ϕ ) ,
•
the fund’s expected return less the investor’s preferred return ( E [ k ] −ψ ) , and
•
the volatility of fund-level returns (σ k ) .
Let’s examine each of these three relationships separately.
III.B.4.a. The Level of the Promoted Interest
The impact of changing the level of the promoted interest (ϕ ) is intuitive and
straightforward. A percentage increase (or decrease) in the level of the promoted interest
has an equal effect on the expected value of the promoted interest. Using our example, let’s
assume that we were to double the promote from 20% to 40% (i.e., an increase of 100%); in
turn, this would increase the expected value of the promoted interest from 1.2% to 2.4% (of
the fund’s expected 12% return).
III.B.4.b. The Spread between the Return and the “Pref”
The impact of changing the spread between the fund’s expected return and the investor’s
preferred return ( E [ k ] −ψ ) is intuitive, but not necessarily straightforward. So, Exhibit 15
In more mathematical/statistical terms, this is nothing more than suggesting that the distribution
of expected (or ex ante) returns and the distribution of realized (or ex post) returns are identical.
47
30
examines a range of outcomes in which we fix the preferred return (ψ = 12%) and let the
fund-level expected return (E[k]) vary:
Exhibit 15: Illustration of Manager's Expected Profit Participation as the
Spread Between the Fund's Expected Return and Investor's "Pref" Varies
22.5%
18.5%
Gross & Net Returns
Fund's Expected Gross Return
14.5%
10.5%
Investor's Expected Net Return
6.5%
2.5%
-7%
-6%
-5%
-4%
-3%
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
Spread between the Fund's Expected Return and Investor's Preference
To help orient the reader: The horizontal axis displays the spread between the expected
fund-level returns (E[k]) and the investor’s preferred return (ψ), ranging from -7% to +10%.
The vertical axis displays the expected returns to the fund, the investor and the investment
manager. Because the investor’s preferred return (ψ) is held constant (at 12%) across all
spread possibilities, the expected fund-level returns vary from 5% to 22%. Meanwhile, the
blue-shaded area represents the expected value of the investment manager’s promoted
interest and the green-shaded area represents the expected value of the investor’s (net) return
– across all spread possibilities. Finally, the dashed vertical line highlights the 0% spread (i.e.,
E[k] = ψ = 12%) of our earlier examples and the ellipse highlights that 1.2% of the expected
fund-level return is the expected value of the manager’s promoted interest, when the spread
between the fund’s expected return and the investor’s preference equals zero (and all of our
earlier assumptions are met). Notice that the expected value of the manager’s promoted
interest increases substantially as the spread widens in a positive manner (i.e., to the right of
the dashed line). In non-core funds, it is typical that spread between the expected fund-level
returns (E[k]) and the investor’s preferred return (ψ) is significantly greater than zero and, in
fact, the 10% spread illustrated above may not capture the expected spread of many of the
opportunistic funds (e.g., E[k] = 20% and ψ = 8%).
31
Here, it is imperative to reiterate the earlier point that, because of the asymmetric and
convex nature of the investment manager’s participation in fund-level profits, the expected
value of the manager’s promoted interest is greater than simply estimating the spread
between the fund’s expected profit and the investor’s preferred return then multiplied by the
manager’s share of fund-level profits. Given our earlier examples and assumptions, we know
that even when the spread is zero the expected value of the manager’s promoted interest is
1.2% of the fund’s expected return of 12%. To illustrate the option-like value of the
manager’s promoted interest, 48 the earlier graph has been amended to include a red dashed
line which indicates the value of the investment manager’s promoted interest in the absence
of this optionality (e.g., if E[k] = 17%, ψ = 12% and ϕ = 20%, then the expected value of
the promote (E[π]) equals 1.0% (i.e., (.17-.12)*.2) – ignoring optionality. 49 See Exhibit 16:
Exhibit 16: Illustration of Manager's Expected Profit Participation as the
Spread Between the Fund's Expected Return and Investor's "Pref" Varies
22.5%
18.5%
Gross & Net Returns
Fund's Expected Gross Return
14.5%
10.5%
Investor's Expected Net Return
6.5%
2.5%
-7%
-6%
-5%
-4%
-3%
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
Spread between the Fund's Expected Return and Investor's Preference
Clearly, the expected promoted interest can be a significant component of the valuation of the
investment manager’s company. When the investment manager is publicly traded (e.g., Apollo,
Blackstone, Carlyle, Fortress, KKR, Oaktree and Och-Ziff), the optionality value is often more
transparently discussed; for example, see: Grant (2013) and Irizarry, et al. (2013).
48
As the next section shows, ignoring optionality is equivalent to assuming the volatility of expected
fund-level returns equals zero (σk = 0).
49
32
The area in dark blue that lies below the red dashed line represents the optionality portion of
the expected value of the promoted interest, while the light blue area that lies above
represents the expected value of the promoted interest assuming no optionality.
Exhibit 17 merely isolates the expected value of the manager’s promoted interest, as shown
in Exhibit 16. That is, Exhibit 17 utilizes the blue-shaded regions of Exhibit 16 to isolate the
changing valuation of the expected value of the investment manager’s carried interest as the
spread (i.e., expected fund-level profits less the investor’s preference) varies. Exhibit 17
captures the optionality of the promote by contrasting its expected value assuming the full
distribution of expected fund-level returns (i.e., uncertain fund-level returns) with its
expected value assuming a single outcome of expected fund-level returns (i.e., certain fundlevel returns).
Exhibit 17: Illustration of the Optionality Embedded
in the Investment Manager's Promoted Interest
Expected Value of Manager's Promoted Interest
3.0%
2.5%
2.0%
Total Expected
Value of the
Promoted Interest
1.5%
1.0%
Optionality
0.5%
0.0%
-7%
-6%
-5%
-4%
-3%
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
Spread between Fund's Expected Return and Investor's Preference
As shown in Exhibits 16 and 17, the option value of the manager’s promoted interest is
highest when the spread (i.e., expected fund-level profits less the investor’s preference)
equals zero. This result is entirely consistent with the pricing of options and other contingent
claims. 50
In general, the difference between the option’s value at inception (t = 0) and at expiration (t = T) is
greatest when the spread between the price of the underlying asset and the option’s strike price
equals zero (or, in our case, when the fund’s expected return equals the investor’s preference). At
50
33
III.B.4.c. The Volatility of Fund-Level Returns
To many of us, the impact of changing the estimated volatility of fund-level returns (σ k ) on
the expected value of the promoted interest is neither intuitive nor straightforward. 51
Accordingly, it may be the most important parameter to explore here. As noted above, the
expected value of the investment manager’s promoted interest is analogous to a call option.
Like any option, its value increases (decreases) as the volatility of the underlying security
increases (decreases). One perspective on this relationship is to revisit Exhibit 10; however,
this time let’s show two distributions of possible fund-level returns (one riskier than the
other, but with the identical expected returns) against the backdrop of the investment
manager’s convex and asymmetric participation (the red kinked line shown below) in the
fund’s profits. See Exhibit 18:
Exhibit 18: Illustration of Increasing Expected Value of the Promote
as the Volatility of Fund-Level Returns Increases
25%
Estimated Frequency of Fund-Level Returns
σFund 2 > σFund 1
Investment Manager's Promoted Interest
20%
15%
Fund 1
Manager's Promoted Interest
10%
Fund 2
5%
-60%
-40%
-20%
0%
20%
40%
60%
0%
80%
Likely Returns
Exhibit 18 illustrates that the expected value of the investment manager’s promoted interest
is higher (and, therefore, the dilution to the investor’s net return is greater) for the riskier
green bell-shaped curve than it is for the less risky blue bell-shaped curve. To understand
inception (t = 0), the ending price of the underlying asset is unknown. At expiration (t = T), the
ending price of the underlying asset is known with certainty.
Notwithstanding the impact of the change, one could further argue that merely estimating future
volatility (which involves the likelihood and magnitude of higher and lower returns) is an
uncomfortable exercise.
51
34
that the expected value of the investment manager’s promoted interest is higher (and,
therefore, the dilution to the investor’s net return is greater) with the more-volatile return
distribution, it is imperative to observe that as the investment manager’s promoted interest
becomes more deeply “in the money” (to continue our earlier option-pricing analogy) it
happens with greater frequency with the more-volatile distribution of fund-level returns (i.e.,
the green bell-shaped curve displays more dispersion or volatility than the blue bell-shaped
curve). Because the expected value is the product of the likelihood (or frequency) and the
level of profitability, the expected value of the promoted interest is greater with the morevolatile distribution.
Another perspective is to consider a range of volatility estimates for fund-level returns
against our backdrop of the assumed preferred return (ψ = 12%) and promoted interest (ϕ
= 20%), while maintaining the fund’s expected return (E[k] = 12%). See Exhibit 19:
Exhibit 19: Illustration of Manager's Increasing Expected Participation
as the Volatility of Fund-Level Returns Increases
14%
Fund's Expected Gross Return
12%
Manager's Expected Promote
Gross & Net Returns
10%
8%
6%
Investor's Expected Net Return
4%
2%
0%
0%
3%
5%
8%
10%
13%
15%
18%
20%
23%
25%
28%
30%
Fund Volatility
To help orient the reader: The horizontal axis displays fund-level volatility ranging from 0%
to 30%. The vertical axis displays the expected returns to the fund, the investor and the
investment manager. The expected fund-level return is constant (at 12%) across all volatility
possibilities. Meanwhile, the blue-shaded area represents the expected value of the
investment manager’s promoted interest and the green-shaded area represents the expected
value of the investor’s (net) return – across all volatility possibilities. As indicated earlier, the
option value of the promoted interest equals zero when the volatility of fund-level returns is
also zero – an unrealistic assumption for commercial real estate investments. Finally, the
dashed vertical line highlights the 15% volatility of our earlier examples and the ellipse
35
highlights that 1.2% of the expected fund-level return is the expected value of the manager’s
promoted interest.
The graph above illustrates that the volatility of fund-level returns can dramatically impact
the expected value of the manager’s promoted interest: greater volatility 52 increases the
expected value of the promoted interest and decreases the expected value of the investor’s
(net) return. In turn, this stimulates a discussion about the factors contributing to the
volatility of fund-level returns; they include:
•
•
•
•
property effects (i.e., type, geography and life-cycle considerations), 53
capital-market effects (e.g., shifting market-wide capitalization rates),
investment manager’s track record and expertise, 54 and
financial leverage.
Of these effects, financial leverage may be the most impactful – particularly, when one
considers funds using fairly high degrees of leverage – for long-term investors. Therefore,
let’s take a moment to consider more fully the impact of leverage.
III.B.4.d. Leverage vis-à-vis the Promote
Consider the following formula 55 for identifying the impacts of financial leverage on the
volatility of fund-level returns:
σe =
σa
(3)
1 − LTV
where: σe = the volatility of the fund-level return on equity, σa = the volatility of the fundlevel (unlevered) return on assets and LTV = the fund’s leverage ratio. The impact of
52
Provided that the distributions have the same mean.
53 As has been well documented elsewhere, these effects can be considerable. Hark back to our earlier
example: a portfolio of industrial properties, leased on a long-term (triple-net) basis to credit tenants,
differs from a portfolio of under-performing hotel properties.
For example, consider the differences between a well-established investment manager sticking to
its expertise versus either a well-established manager entering a new business area or the inception of
a start-up firm entering a business area in which the firm’s principals have had prior experience.
54
This is a one-period model assuming fixed-rate, default-free financing. If multiple periods are
involved, then the average leverage ratio over the holding period can be used. If floating-rate
financing and/or defaultable debt is utilized, then the impact of financial leverage is: σ e =
55
2
2
LTV
 1  2  LTV  2
σ aσ d ρ a ,d , which incorporates the volatility

 σa + 
 σd − 2
2
 1 − LTV 
 1 − LTV 
(1 − LTV )
of floating-rate and/or defaultable debt (σ d ) and its correlation
Equation (3) is a special case in which: =
σ d ρ=
0.
a ,d
36
( ρ ) with asset-level returns;
a ,d
relatively high leverage ratios on the volatility of fund-level returns (σ k ) can be deceiving, as
displayed below in Exhibit 20:
Exhibit 20: Illustration of the Volatility of Levered Equity Returns
5.0x
Volatility of the Levered Equity Returns (σe)
Volatility quintuples at 80% Leverage
4.0x
Volatility quadruples at 75% Leverage
3.0x
Volatility triples at 66.7% Leverage
2.0x
Volatility doubles at 50% Leverage
1.0x
0.0x
0%
10%
20%
30%
40%
50%
60%
70%
80%
Leverage Ratio (LTV)
The volatility of fund-level returns doubles as the fund goes from 0% to 50% leverage, but
also doubles as the fund goes from 50% to 75% leverage or from 60% to 80% leverage.
These latter two examples (50% → 75% and 60% → 80%) are meant to illustrate the
dramatic gearing effects of higher leverage ratios. Moreover, these gearing effects should be
considered in light of the earlier discussion about the expected value of the manager’s
promote vis-à-vis the volatility of expected fund-level gross returns. Changing nothing from
our earlier example but the doubling the volatility of expected fund-level returns, we find
that the expected value of the promoted interest also doubles – as indicated earlier and
shown in Exhibit 21:
37
Exhibit 21: Illustration of Manager's Increasing Expected Participation
as the Volatility of Fund-Level Returns Increases
14%
Fund's Expected Gross Return
12%
Manager's Expected Promote
Gross & Net Returns
10%
8%
Investor's Expected Net Return
6%
4%
2%
0%
0%
3%
5%
8%
10%
15%
13%
18%
20%
23%
25%
28%
30%
Project Volatility (σ k )
Of course, the use of leverage also impacts the fund’s expected return:
ke =
ka − kd LTV
1 − LTV
(4)
where: ke = the fund-level return on equity, ka = the fund-level (unlevered) return on assets,
kd = the effective interest rate (ε) on fund borrowings and LTV = the fund’s leverage ratio. 56
This result seems much better understood by real estate practitioners than is the volatility
aspect of leverage. That is, positive leverage 57 occurs in instances when ka > kd and negative
leverage occurs when ka < kd , growing in a geometric way with increases in the leverage
ratio, as shown in Exhibit 22:
56 This is also a one-period model. If multiple periods are involved, then – as also noted before – the
average leverage ratio over the holding period can be used. If floating-rate financing is utilized, then
estimation of kd must incorporate an expectation about the evolution of short-term interest rates
over the fund’s anticipated holding period.
Irrespective of whether leverage is positive or negative, the use of leverage increases the volatility
of the levered equity return – see equation (3).
57
38
Exhibit 22: Illustration of Levered Equity Returns
Return on Levered Equity (k e)
ka > kd
ka = kd
ka < kd
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
55%
60%
65%
70%
75%
80%
Leverage Ratio (LTV)
As result, positive leverage increases the investment’s expected (gross) return and, in turn,
increases the spread between the fund’s expected (levered) equity returns and a given
preferred return, thereby increasing the expected value of the manager’s promoted interest.
Whether the increase in expected (gross) return (due to leverage) offsets the further dilution
of the investor’s net return (due to the increase in the expected value of the promote) is a
function of the actual values involved, but tends to heavily depend on a significant spread
between asset-level returns (ka ) and debt costs (kd ). 58
The conclusion of this discussion is not that leverage is bad (or good). There are plenty of
valid reasons as to why investors prefer the use of leverage. Instead, the conclusion is that
investors need to understand the effects of leverage on expected fund-level returns and
volatility and trace these effects through the “pref” and promote structure to assess their
likely net returns. Moreover, investors ought to recognize the need to modify the “pref” and
promote structure as fund-level characteristics differ between funds and/or managers.
58
A sketch of the tradeoff between the increase in expected returns and the growing expected value of the
promote involves three relationships (assuming fixed-rate, default-free debt): a) ke =
σe =
σa
1 − LTV
, and c)
E [π ] = f ( ke , σ e ,ψ , ϕ ) .
39
ka − kd LTV
, b)
1 − LTV
Continuing with our earlier examples, consider two identical funds (E[k1] = E[k2] = 12%, ψ1
= ψ2 = 12% and ϕ1 = ϕ2 = 20%) with only one difference – the volatility of one fund is
twice the other (σ1 = 15% and σ2 = 30%). We have already shown that, in such cases, the
expected value of the promote is 1.2% and 2.4%, respectively (i.e., E[π1] = 1.2% and E[π2] =
2.4%) – see Exhibit 21. What is the prudent investor to do? A first step is to consider cutting
in half the investment manager’s promoted interest in the second fund (i.e., ϕ1 = 20% and
ϕ2* = 10%), such that the expected value of the promote is now identical (i.e., E[π1] = E[π2*]
= 1.2%). However, this only a first step as, even though both funds now have the same
expected (net) return to the investor, the second fund comes with twice the volatility of the
first. So, a second step – which is beyond the scope of this study – is to consider the
appropriate pricing of the risk (i.e., the market’s risk/return tradeoff and the investor’s utility
function). The third step is consider any behavioral implications of revising the “pref”
and/or promote. These behavioral considerations will be discussed in §V (Principal/Agent
Issues).
The preceding paragraph implicitly assumes that the equivalence in levered returns is merely
a function of the lender’s requirement for a larger interest rate given a high leverage ratio –
“leverage neutral” returns. In such cases, the performance of the underlying assets is
identical between the two funds and it is only the leverage that accounts for the difference in
their expected returns and volatilities. There is, of course, another case in which the
differences in leverage masks the under-performance of one of the funds – “leverage
enhanced” returns. 59 Consider the two examples below in Exhibit 23:
Exhibit 23: Illustration of Leverage-Neutral Returns v. Leverage-Enhanced Returns
Leverage-Neutral Returns
Parameters
Leverage-Enhanced Returns
Fund 1
Fund 2
Fund 3
Fund 4
Asset-Level Return (k a )
8.4%
8.4%
8.4%
8.0%
Debt Cost (k d )
Leverage Ratio (LTV )
6.0%
60.0%
6.0%
7.5%
80.0%
6.0%
6.0%
60.0%
7.0%
80.0%
6.0%
6.0%
12.0%
15.0%
12.0%
30.0%
12.0%
15.0%
12.0%
30.0%
Asset-Level Volatility (σ a )
Observed Returns:
Fund-Level Return (k e )
Fund-Level Volatility (σ e )
Let’s first consider the case of leverage-neutral funds: Here, the asset-level performance of
the two funds is identical (i.e., E[k1] = E[k2] = 8.4% and σ1 = σ2 = 6.0%) and the difference
in fund-level performance is solely attributable to differences in leverage (i.e., LTV1 = 60%
and kd 1 = 6.0%, while LTV2 = 80% and kd 2 = 7.5%). 60 Absent other considerations (as
59 In this usage, “leverage-neutral” funds describe two or more funds which when de-levered are
shown to have identical asset-level risk/return characteristics, whereas “leverage-advantaged” funds
describe two or more funds which when de-levered are shown to have differing asset-level
risk/return characteristics, such that one fund underperforms the other.
The higher interest rate for the more highly levered fund reflects the lender’s requirement of a
higher interest rate as the leverage ratio increases. We can think of increasing the leverage ratio from
60
40
noted above), it seems sensible for the investor to cut the promoted interest in half (i.e., ψ1 =
20% and ψ2* = 10%) – as a starting point – thereby treating the asset-level performance as
identical (and not penalizing or benefiting one fund over the other), as in the preceding
paragraph. (In the alternative, the preferred return could be increased or some combination
of the two.)
Now consider the case of leverage-enhanced funds: Here, the asset-level return performance
of the two funds differs (i.e., E[k3] = 8.4%, but E[k4] = 8.0%, while σ3 = σ4 = 6.0%) and the
identical fund-level return performance is solely attributable to differences in leverage (i.e.,
LTV3 = 60% and kd 3 = 6.0%, while LTV4 = 80% and kd 4 = 7.0%). 61 However, in this
instance, it seems unfair to treat these two funds as producing the same asset-level
performance; clearly, the investment manager of Fund 4 has underperformed the manager of
Fund 3. Accordingly, it seems sensible for the investor to consider basing the “pref” and
promote structure on each fund’s unlevered returns. 62
III.C.
Variations on the Simple Example
The simple example of the previous section has many variations in practice. Here too, the
capital markets have evolved – particularly after the 2007-2008 financial crisis. The variations
noted below swing to and fro given the ease/difficulty of fund raising. Not each of these
variations is currently in vogue; however, “what is old may become new again.”
Two of the most significant variations are the use of a) a “waterfall” structure and b) a
“catch-up” structure. Let’s take a moment to examine each.
III.C.1. The Use of “Waterfalls”
The earlier example of a preferred return of 12% with a 20% promote may be viewed by
either the investor or the manager as too “rich” to the other party. So, it is often the case
that, as an accommodation to reaching an agreement, both parties will agree to step or
increase the promoted interest as certain minimum-return thresholds are surpassed –
creating a hierarchy of sequential distributions (to the extent of available profits). 63 There is
nothing sacrosanct about either the number of tiers or the selection of the preference and
the profits allocation. Investors and their investment managers are bound only by their
60% to 80% as if Fund 2 secured a mezzanine loan (for the 20% of additional leverage) at a rate of
12% – such that the fund’s blended cost of debt financing is 7.5%.
In this instance, we can think of Fund 4 securing a mezzanine loan (for the 20% of additional
leverage) at a rate of 10% – such that the fund’s blended cost of debt financing is 7.0%.
61
A related frustration is the difficulty of determining whether the manager of Fund 4 provided value
through its ability to secure a below-market rate of interest. This argues for a lending-market
inefficiency which may or may not exist. Moreover, the market-clearing interest rate on mezzanine
debt is very difficult to observe – as the rate can vary widely with the level of subordination, leverage,
sponsor risk, asset quality, etc.
62
In practice, the term “waterfall” is used in a variety of manners; therefore and in order to avoid
potential confusion, this section is intended to examine multi-tier promoted interests (as opposed to
the single-tier promoted interests examined earlier).
63
41
imagination, the expectations of both parties and the practicalities of finding a balance
between complexity and anticipated results.
III.C.1.a An Example of a “Waterfall” Approach
For purposes of illustration, let’s assume that the investment manager successfully persuades
the investor to accept a waterfall structure which is more favorable to the investment
manager. Accordingly, one variation of our earlier example is the following:
Fund-Level Returns:
Preference #1
Preference #2
Thereafter
9%
12%
Allocation to
Manager
Investor
100%
0%
90%
10%
80%
20%
This is a relatively simple, two-tiered preference-and-promote structure. In this instance,
100% of the fund’s profits are allocated to the investor until the investor has received a
return of 9% per annum; fund-level returns between 9% and 12% (of invested capital) are
allocated 90% to the investor and 10% to the investment manager; and excess profits are
allocated 80% to the investor and 20% to the investment manager (i.e., an 80/20 “split”).
If we run this structuring mechanism through our earlier presumed fund-level returns (i.e., an
expected return of 12% with volatility of 15%), we have the following effects (shown in
comparison to our earlier structure without a waterfall), as shown in Exhibit 24:
Exhibit 24: Fund- and Investor-Level Expected Performance
Current Example
with Waterfall
Previous Example
without Waterfall
Likely Returns:
Fund-Level Returns before Investment Manager's Promoted Interest
Reduction in Return Attributable to Investment Manager's Promoted Interest
Investor's Net Return
12.0%
1.4%
10.6%
12.0%
1.2%
10.8%
Volatility (Standard Deviation):
Fund-Level Volatility of Expected Return
Reduction in Volatility Attributable to Investment Manager's Promoted Interest
Standard Deviation of Investor's Expected Net Return
15.0%
1.6%
13.4%
15.0%
1.5%
13.5%
Notice that the two-tiered preference-and-promote structure, as envisioned above, increases
the investment manager’s expected profits interest by approximately 17% (i.e., 1.4%/1.2% 1). Whether the additional dilution of twenty basis points in the investor’s expected return is
material – in light of the possible enhanced motivations of the investment manager – is a
topic examined in §V. (Again, the reduction in the standard deviation of the expected return
is a statistical illusion in the sense that the investor’s downside risk remains unchanged.)
The example above is meant to illustrate the use of the waterfall technique – not to make
assertions about the “correct” manner in which the technique ought to be utilized. Of
course, we could have just as easily illustrated a waterfall structure that decreased (by an
amount equal to the increase identified above) the investment manager’s participation in the
fund’s profitability (e.g., Preference #1 equals 12%, Preference #2 equals 15.5% and the
42
manager’s promoted interest remains at 90% and 80%). Or, we could have also illustrated
yet another waterfall structure in which the results were essentially equivalent before and
after inclusion of the waterfall (e.g., Preference #1 equals 10.5%, Preference #2 equals 13.5%
and the manager’s promoted interest remains at 90% and 80%).
III.C.1.b Contrasting “Waterfall” Approaches
Waterfall structures create an intermediate hierarchy that can introduce ambiguity into the
distribution of returns. To illustrate this ambiguity, let’s return to our waterfall example. For
the first tier in the hierarchy of preferences (e.g., the 9% Preference #1 in the immediate
example above), there is no ambiguity about its economic interpretation and the same can be
said for the last item in the hierarchy or waterfall (e.g., the 80/20 allocation in the immediate
example above). However, there is an element of ambiguity for any intermediate hierarchy.
Fund-Level Returns:
Preference #1
Preference #2
Thereafter
9%
12%
Allocation to
Investor
Manager
100%
0%
90%
10%
80%
20%
To help illustrate the distinction, assume that fund consists of $100 million of equity (entirely
contributed by the investor). There are two possible economic interpretations (and, hence,
the ambiguity) of the intermediate priority: 64
1. the return of up to 12% is to be computed on the fund’s equity before any
consideration of the 90/10 split, or
2. the return of up to 12% is to be computed on the fund’s equity after any
consideration of the 90/10 split.
In the first method, the intermediate preference equals the difference between the first and
second preferences times the contributed capital. Given our particular assumptions, this
equates to an intermediate preference of $3 million per year (i.e., (.12-.09)*$100). Notice that
this method requires an intermediate distribution of $3 million; from which, the investor
receives $2.7 million (and the manager receives $0.3 million) – implying that the investor
receive a 11.7% return (i.e., 100% of the first 9% and 90% of next 3%) before residual
profits are split 80/20.
In the second method, the intermediate preference equals the difference between the first
and second preferences divided by the investor’s allocation of these intermediate profits
times the contributed capital. Given our particular assumptions, this equates to an
intermediate preference of approximately $3.33 million per year (i.e., (.12-.09)÷.9*$100); from
which, the investor receives 90% or $3 million (and the manager receives approximately
$0.33 million) – permitting the investor to receive a 12% return before residual profits are
split 80/20.
The first method has sometimes been referred to as “investment-centric” and the second method
as “investor-centric” – see Schneiderman and Altshuler (2011).
64
43
In the grand scheme of things, the foregoing difference is a fairly small economic point.
Continuing with our example, assume that there are approximately $12.33 million of profits
to distribute. The first method produces a distribution of approximately $11.97 million to
the investor (i.e., 100% of the first $9 million, 90% of next $3 million and 80% of the
remaining (approximate) $0.33 million), while the second method produces a distribution of
$12.0 million to the investor (i.e., 100% of the first $9 million and 90% of the remaining
(approximate) $3.33 million). This approximate $0.03 million (or 3 basis points) remains the
maximum (annual) difference between the two methodologies – because any further profits
are split 80/20. (Naturally, the ongoing difference is larger when the final tier of the
promoted interest is larger; this is of often the case, for example, with joint ventures in
which the operating partner receives a 50% interest in residual profits.)
III.C.2. The Use of a “Catch-Up” Provision
On the other hand, the use of a “catch-up” provision often involves a significant economic
re-allocation of profits. A catch-up provision is another intermediate allocation of profits;
however, it is generally designed to allocate all or a majority of those intermediate profits to
the investment manager until such a point that the manager’s allocation of total fund profits
(to the extent available) equals the final sharing ratio. Most typically, such a provision is used
with non-core funds. In fact, the technique is generally similar to that found in (non-real
estate) private-equity funds (e.g., venture capital, leveraged buyouts, “arb” funds, etc.).
III.C.2.a A Simple Example of a “Catch-Up” Provision
Like many of these concepts, they seem more easily understood when illustrated via an
example. So, let’s reintroduce our initial example (without a catch-up provision): The
investment manager receives 20% of the profits in excess of a 12% preferred return to the
investor; let’s also again assume that the fund consists of $100 million of equity (entirely
contributed by the investor). To begin, assume that there are $15 million of profits to be
distributed. Exhibit 25 illustrates the allocation of profits:
Exhibit 25: Allocation of Profits without a Catch-Up Provision
Investor
Manager
Total
1st $12,000
Next $3,000
Total
Share of Profits
$12,000
2,400
$14,400
96%
$0
600
$600
4%
$12,000
3,000
$15,000
100%
Now assume the same fact pattern as above, except that the investment management
agreement provides for a (100%) catch-up provision. As noted earlier, there is then an
intermediate level of profit allocation designed to raise the investment manager’s share of
total profits such that the manager now enjoys a participation rate in the fund’s profitability
equal to the final tier of profit allocations (i.e., 20% in our example). So, the assumed $15
million of profits would be distributed as follows as shown in Exhibit 26:
44
Exhibit 26: Allocation of Profits with a 100% Catch-Up Provision
Investor
Manager
Total
Next $3,000
$12,000
0
$0
3,000
$12,000
3,000
Total
$12,000
$3,000
$15,000
80%
20%
100%
1st $12,000
Share of Profits
While the investor first receives an allocation of profits (to the extent available) such that its
preferred return is satisfied in both instances, the allocation of the remaining profits is where
the differences occur. Notice that the catch-up provision raises the investment manager’s
share of overall fund profitability to the 20% level and that every subsequent dollar of profit
maintains this allocation of profit sharing. (Whereas the investment manager in the fund
without the catch-up provision never receives 20% of the fund’s total profits; it is only in the
limit that the manager’s share of profits approaches this ratio.)
More broadly, the investor’s share of profits can be viewed across a wide range of fund-level
profitability as shown below (given our assumptions) in Exhibit 27:
Exhibit 27: Illustration of Investor's Share of Fund-Level Profits
with and without a Catch-up Provision for the Investment Manager
using a Range of Potential Fund Profitability
100%
without a Catch-up Provision
90%
with a Catch-up Provision
70%
Investor's Preferred Return
Investor's Share of Fund-Level Profits
80%
60%
50%
40%
30%
20%
10%
0%
0%
5%
10%
15%
20%
25%
30%
Fund-Level Profitability per Annum
45
35%
40%
45%
50%
As indicated above, the investor receives 100% of the profits until its preferred return (in
this case, 12%) is fully paid; thereafter, the investment manager begins to participate in
excess profits. When the investment management contract has a catch-up provision, then
the investor’s share of fund-level profits declines more rapidly than were the contract to
have no such provision (as indicated by the spread between the graph’s red and blue lines).
If we overlay the two possibilities – an investment management contract that contains a
catch-up provision and another that does not – over the earlier-presumed distribution of
fund-level returns (i.e., E[k] = 12% and σ = 15%), then we can view these two possibilities
in a probabilistic sense as shown in Exhibit 28:
Exhibit 28: Illustration of Fund- and Investor-Level Returns
when Investment Manager Receives a Promoted Interest
with and without a Catch-Up Provision
Estimated Frequency
Likely Returns
before Promote
Likely Returns
after Promote
without Catch-Up
Likely Returns
after Promote
with Catch-Up
-40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
60%
70%
Likely Returns
Moreover, this probabilistic perspective can be translated into the summary statistics
displayed in Exhibit 29:
46
Exhibit 29: Fund- and Investor-Level Expected Performance
Current Example
with Catch-Up
Likely Returns:
Fund-Level Returns before Investment Manager's Promoted Interest
Reduction in Return Attributable to Investment Manager's Promoted Interest
(a)
Previous Example
without Catch-Up
Investor's Net Return
12.0%
2.3%
9.7%
12.0%
1.2%
10.8%
Volatility (Standard Deviation):
Fund-Level Volatility of Expected Return
Reduction in Volatility Attributable to Investment Manager's Promoted Interest
Standard Deviation of Investor's Expected Net Return
15.0%
2.4%
12.6%
15.0%
1.5%
13.5%
(a)
(b)
(b)
A 12% preferred return to the investor and a 20% promoted interest to the manager, with a (100%) catch-up provision.
A 12% preferred return to the investor and a 20% promoted interest to the manager, without a catch-up provision.
Perhaps not surprisingly, the inclusion of a catch-up provision (while leaving all other
parameters unchanged) creates significant dilution with respect to the investor’s net return.
In our specific case, the additional dilution is 110 basis points (i.e., 9.7% - 10.8%) or roughly
twice the initial dilution (i.e., 2.3% v. 1.2%). While these results are naturally dependent on
the parameters we’ve assumed for purposes of these illustrations, it is undeniable that the
inclusion of a catch-up provision is likely to cause a more significant dilution to the
investor’s return, as compared to an investment management contract without such a
provision.
III.C.2.b Equating Funds with and without a “Catch-Up” Provision
Because the inclusion of a catch-up provision can create significant additional dilution to the
investor’s return, it is natural to ask how might the parameters of the preference-andpromote structure be modified such that the investor is roughly indifferent between one
fund with a catch-up provision and another without. A crude answer is to consider reducing
the manager’s promoted interest by half in the fund when the promoted interest includes a
catch-up provision.
This is an imperfect answer and, of course, is an outcome dependent upon the assumptions
we have made along the way. Nevertheless, let’s examine some of the byproducts of this
proposed revision. To be clear then, the investor can invest in one of two funds; each is
structured with a 12% preferred return to the investor while the investment manager’s
carried interest differs as follows:
1. a 20% promoted interest without a catch-up provision, or
2. a 10% promoted interest with a catch-up provision
The consequences of this modification are now that the investor’s share of the fund’s
profitability is no longer always higher when the catch-up provision is avoided; in fact, the
investor is better served at high levels of profitability (i.e., when the red line lies above the
blue line) to bear the catch-up provision while precluding the investment manager from
sharing in the excess profits at the higher participation level:
47
Exhibit 30: Illustration of Investor's Share of Fund-Level Profits
with and without a Catch-up Provision for the Investment Manager
using a Range of Potential Fund Profitability
100%
with a Catch-up Provision
90%
without a Catch-up Provision
70%
Investor's Preferred Return
Investor's Share of Fund-Level Profits
80%
60%
50%
40%
30%
20%
10%
0%
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
Fund-Level Profitability per Annum
The essential tradeoff is that the investor is better served by avoiding the (modified) catchup provision when the fund’s expected returns are likely to lie near but above the preferred
return, but better served by accepting the (modified) catch-up provision (and reducing the
manager’s participation level) when the fund’s expected returns are likely to lie significantly
above the preferred return.
Let’s run the two investment structures through our earlier-presumed distribution of fundlevel returns (i.e., E[k] = 12% and σ = 15%), which cluster about the preferred return. When
we view these two possibilities in a probabilistic sense, we see the results displayed in Exhibit
31:
48
Exhibit 31: Fund- and Investor-Level Expected Performance
Initial Example
Modified Example
Previous Example
with Catch-Up(a)
with Catch-Up(b)
without Catch-Up(c)
Fund-Level Returns before Investment Manager's Promoted Interest
Reduction in Return Attributable to Investment Manager's Promoted Interest
12.0%
12.0%
12.0%
2.3%
1.2%
1.2%
Investor's Net Return
9.7%
10.8%
10.8%
15.0%
Likely Returns:
Volatility (Standard Deviation):
→
Fund-Level Volatility of Expected Return
15.0%
15.0%
Reduction in Volatility Attributable to Investment Manager's Promoted Interest
2.4%
1.2%
1.5%
Standard Deviation of Investor's Expected Net Return
12.6%
13.8%
13.5%
(a)
A 12% preferred return to the investor and a 20% promoted interest to the manager, with a (100%) catch-up provision.
(b)
A 12% preferred return to the investor and a 10% promoted interest to the manager, with a (100%) catch-up provision.
A 12% preferred return to the investor and a 20% promoted interest to the manager, without a catch-up provision.
(c)
Given our assumptions, it turns out that halving the manager’s carried interest when a catchup provision is included produces a near-identical net return (i.e., ≈10.8%) for the investor.
To reiterate, this is result is a byproduct of our assumptions; a different set of assumptions
produces different results. Consequently, prudent investors ought to analyze these tradeoffs
in a probabilistic sense (as illustrated herein) – using their best judgments about the likely
dispersion of future returns – in order to determine the profit-sharing terms that best suit
their circumstances and objectives.
III.C.2.c Variations of the “Catch-Up” Provision
The two preceding subsections utilized a 100% catch-up provision – meaning that 100% of
the intermediate profits were allocated to the investment manager until the manager realized
an allocation of total profits whereby the manager’s participation rate in the fund’s overall
profitability equals the final tier of profit allocations.
This approach was taken mostly for illustrative purposes, as it simplifies the mathematics
and aids the intuition. However, something less than a 100% catch-up provision is most
typically used in practice. Consider the following fund structures for several large, wellknown opportunity funds as shown in Exhibit 32:
49
Exhibit 32: Catch-Up Provisions of Selected Opportunity Funds
Distribution of Profits
Actual /
Target Size
($million)
Operator / Fund
Blackstone
Blackstone Real Estate Partners Asia
Blue Vista Capital
Blue Vista Sponsor Equity Fund 3
Brookwood Financial
Brookwood U.S. Real Estat Fund
Dune Real Estate
Dune Real Estate Fund 3
Fortress Investment
Fortress Real Estate Opportunities
JMI Realty
JMI Realty Partners 4
Moonbridge Capital
Moonbridge Capital Greater China Development
Prudential Real Estate Investors
PLA Industrial Fund 4
Woodbourne Investment
Woodbourne Canada Partners 2
Net
Return
Goal (%)
Fees
GP / LP Split until
Preferred Return for GP Captures 20% of
Profits
LPs
IRR at which GP
Captures 20% of
Profits
$3,500
16+
1.5% Mgmt
(1.25% for $200 million+)
300
18
1.5% Mgmt
8.0%
100/0
10.0%
700
15-18
1.5% Mgmt
8.0%
20/80
Never
850
20
1.5% Mgmt
9.0%
60/40
13.5%
1,000
17
1.5% Mgmt
8.0%
50/50
13.3%
300
18-20
2.0% Mgmt
10.0%
70/30
14.0%
400
18-20
2.0% Mgmt
9.0%
20/80
Never
350
15-18
10.0%
80/20
13.3%
291
18
9.0%
50/50
15.0%
1-1.75% Mgmt
(1-1.25% Invested)
1.5% Mgmt
8.0%
80/20
10.7%
Source: Real Estate Alert , "Fee Scorecard for Funds," March 27, 2013, p.6.
Only one of these funds display a 100% catch-up mechanism; the rest (excluding those two
funds without a catch-up provision) range with the investment manager receiving between
50% and 80%. To illustrate the technique, let’s revisit our initial catch-up example as shown
in Exhibit 26:
Exhibit 26: Allocation of Profits with a 100% Catch-Up Provision
Investor
Manager
Total
Next $3,000
$12,000
0
$0
3,000
$12,000
3,000
Total
$12,000
$3,000
$15,000
80%
20%
100%
1st $12,000
Share of Profits
As you will recall, we assume that the fund consists of $100 million of equity (entirely
contributed by the investor). The investor first receives a preferred return of 12%; next, the
manager receives the entire catch-up allocation and any excess profits are split 80/20. With a
100% catch-up provision, the first $15 million of profits completely satisfies the “pref” and
the catch-up hierarchies.
Now, let’s assume the same fact pattern but, instead, assume that there is a 60% catch-up
provision – meaning that, in the second tier of distributions, the manager receives 60% of
the profits and investor receives 40% (until the fund’s overall sharing ratio is met). Because
the profits flow to the investment manager less quickly in this arrangement, the second-tier
distribution must be larger in order to satisfy a profits distribution that equates to the fund’s
50
overall sharing ratio. As it turns out, a total distribution of $18 million is now needed to
completely satisfy the “pref” and the catch-up hierarchies. See Exhibit 33:
Exhibit 33: Allocation of Profits with a 60% Catch-Up Provision
Investor
Manager
Total
Next $6,000
$12,000
2,400
$0
3,600
$12,000
6,000
Total
$14,400
$3,600
$18,000
80%
20%
100%
1st $12,000
Share of Profits
Clearly, lowering the rate at which the catch-up provision is applied can have a substantial
impact on the allocation of profits. In our illustrations, the second-tier distribution jumped
from $3 million to $6 million as the catch-up rate moved from 100% to 60%.
III.C.2.d Mathematics of the “Catch-Up” Provision
The foregoing illustrations were, of course, a byproduct of the assumptions made previously.
This subsection provides a more general framework for identifying the amount necessary to
have the investment manager “catch up” with the investor. To simplify our thinking about
these relationships, we will only examine structures with a single waterfall (i.e., those
structures with a single preferred return). In such cases, the amount of the catch-up
distribution (X) as a percentage of invested capital is given by:
X =ψ
ϕ
λ −ϕ
(5)
where: λ = the catch-up rate (e.g., 60% in the example above) and 1 ≥ λ > ϕ. As a special
case of equation (5), note that when the catch-up rate (λ) is twice the manager’s promote (ϕ),
then X equals the preferred return (i.e., X = ψ). 65 When the catch-up rate (λ) is more than
the twice the manager’s promote (λ > 2ϕ), then X is less than the preferred return (i.e., X <
ψ) and, conversely, when the catch-up rate (λ) is less than the twice the manager’s promote
(λ < 2ϕ), then X is more than the preferred return (i.e., X > ψ). This relationship can be
summarized as:
< ψ λ > 2ϕ

=
X  ψ=
λ 2ϕ
> ψ λ < 2ϕ

(6)
Regardless of the relationship between the catch-up rate (λ) and the manager’s promote (ϕ),
the level of fund profitability needed to have the manager “catch up” increases as the catchup rate declines; at the same time, the investor’s share of these profits is increasing.
For example, assume the catch-up rate is 40% (λ = .4) and the manager’s promote is 20% (ϕ = .2)
then the catch-up distribution (X) equals the investor’s preferred return (ψ).
65
51
III.C.3. Other Structuring Considerations
When considering incentive fees, there are a host of other structuring considerations. We
examine some of them below:
III.C.3.a. Fixed- v. Indexed-Based Preferences
So far, we have expressed the investor’s preferred return in terms of a fixed percentage over
the life of the investment. Of course, an alternative is to consider a variable percentage that
is tied to some underlying index. In so doing, there is a wide variety of choices; clearly, the
selection of the fixed spread and of one of these indices depends on the fund’s investment
strategy (i.e., its expected risk/return characteristics); investors would like to avoid paying
incentive-management fees for performance which mirrors an appropriate passive index.
Some of the more-often-used indices 66 include:
•
A fixed spread (i.e., a risk premium) over the realized inflation rate – as it is often argued
that commercial real estate acts as a hedge against (unanticipated) inflation.
•
A fixed spread over a floating interest rate – as it is often argued that equities ought to
provide a return premium over debt products.
•
A fixed spread over the NCREIF Index – the fund manager, in principle, ought to be
able to provide positive “alpha.”
•
A fixed spread over a levered NCREIF Index – a variation of the approach above, in
which the NCREIF Index is restated for leverage characteristics (i.e., leverage ratio and
cost of indebtedness) similar to the fund.
The potential mismatch between a fixed and index-based (or floating) preference is often
greatest for funds with long investment horizons. At these long horizons, the differences
between expected and realized market conditions are often greatest. These differences often
include a capital-market component (e.g., rising or falling capitalization rates) which is
beyond the control of the investment manager; to reward or penalize the investment
manager for such events is often unfair to both the manager and the investor. Accordingly,
an index-based (or floating) preference serves to remove some of the unintended
consequences of a fixed preference – particularly those relating to uncontrollable capitalmarket effects.
Let’s take a moment to explore some of the effects of index-based (or floating) preferences
in greater detail:
66
Note: the fixed spread should vary with the index and the fund’s characteristics.
52
III.C.3.a.(i ) Changing Expectations & Renegotiations
It is often the case that initial expectations about fund-level performance vary from realized
performance. With the passage of time, uncertainties about future performance may begin to
narrow (particularly with relatively short-horizon non-core funds) while the expectation of
likely performance may shift:
Exhibit 34: Fund's Evolving Expected Returns
Consistent
Conditions
Improving
Conditions
Estimated Frequency
Deteriorating
Conditions
Initial
Expectations
Likely Returns
At the risk of oversimplifying, Exhibit 34 illustrates three such possibilities with regard to
evolving market conditions: they deteriorate, remain consistent or improve vis-à-vis initial
expectations67 (which are illustrated by the blue-shaded region). If the fund manager’s carried
interest (or incentive fee) is designed with a fixed preference, then the two diverging cases
(i.e., deteriorating and improving conditions) can create significant imbalances between the
investor and the investment manager (assuming that the manager met the investor’s
expectations in all other respects).
The use of “market conditions” is meant to imply an element of returns about which the
investment manager has little to no control. As a result, the investment manager’s carried interest
may be unfairly penalized or unjustly enriched when such conditions significantly diverge from the
initial expectations: Et[k] = the expected return at time t = 0. Subsequent conditions can be thought
of as: Et+j [k] = the expected return at time t + j (where: j > 0).
67
53
In the case of improving market conditions and a fixed preference, we find that the
investment manager is unjustly rewarded and the investor unfairly penalized because
improving market conditions (e.g., falling capitalization rates) have improved fund-level
performance without commensurate effort and expertise from the investment manager. In
other words, the investor paid an incentive fee when the manager failed to outperform the
passive benchmark.
The case of deteriorating market conditions and a fixed preference is less straightforward. In
such cases, we find that the investment manager is unfairly penalized because deteriorating
market conditions (e.g., rising capitalization rates) have worsened fund-level performance due
to no fault of the investment manager. However, the story does not end there for many noncore investments. Instead, it is often the case that the manager’s effort and expertise are
integral components to the fund’s future success. It may be the case that, without a
reasonable likelihood that the manager’s carried interest will end up “in the money,” the
manager will choose to focus its effort and expertise on other funds (in which, the investor
may not be involved). 68 Provided that the investor does not find the manager dishonest,
incompetent and/or financially distressed, the investor and the manager may rationally look
to renegotiate 69 the fixed preference downward – such that there is now a reasonable
likelihood that the manager’s carried interest will end up “in the money” and, therefore, the
manager will choose to focus its effort and expertise on the investor’s fund. 70 (In turn, it
should also be pointed out – for similar reasons – that the non-core fund manager may seek
to renegotiate the pref-and-promote structure it may have previously entered into with jointventure partners.)
We will return to these behavioral arguments in §V; we only sketch them here for purposes of
motivating our discussion about fixed v. index-based preferences. Nevertheless, it is worthwhile to
note that, particularly in the case of fixed preferences, investors may actually face more risk than
originally estimated (i.e., the dispersion of returns is wider than initially expected) due to the link
between the manager’s efforts and the fund’s returns and the link between the manager’s efforts and
the likelihood of its carried interest being realized (including the possible renegotiation of the pref
and the promote).
68
69
For a robust treatment of renegotiating and, more generally, bargaining, see Schelling (1956).
Perhaps there is no greater collision of these forces than with regard to the so-called “zombie”
funds – those funds, typically non-core, which employ substantial leverage and, during the downturn
in asset prices, find themselves in multiple instances of the loan’s book value exceeding the fair
market value of the asset. Particularly when the loan is non-recourse, the fund’s equity is like a call
option on the future value of the property. As the investment manager continues to collect fees,
investors naturally ask whether the manager is merely “milking” the fund for its fees before the fund
ultimately has to “throw in the towel” (i.e., transfer the property’s deed to the creditor)? Or, in the
alternative, is the fund manager rightfully attempting to recover lost equity (perhaps employing some
of the risk-shifting practices cited later as a way to improve the odds of recovery)? In many cases, it is
extremely difficult to know the likelihood of recovery and, therefore, whether the fees paid for the
manager’s ongoing efforts are foolish or prudent. Unfortunately, it is easy to believe the worst of
intentions by the other side (i.e., investors vis-à-vis managers) in such perilous times.
70
54
We should also note that this sort of renegotiation is also found in corporations with stockoption plans for senior management. When it is determined by the corporation’s board of
directors that the company’s share price has fallen due to no (or little) fault of senior
management, then the strike price of these options is often reset to a lower value such that
senior management now expects there is a reasonable likelihood that their stock options will
end up “in the money” and, accordingly, senior management is sufficiently motivated to help
improve the fortunes of the company.
The point of examining the deviating cases coupled with a fixed preference is to point out
the “tails I win/heads you lose” circumstance it might create for the investment manager. In
case of improving conditions, the manager is unjustly enriched; in the case of the
deteriorating conditions, the manager’s carried interest (or some portion of it) is often
preserved by lowering the investor’s preference. Much of this circumstance can be avoided
by using an index-based (rather than a fixed) preference.
III.C.3.a.(ii ) Relative v. Absolute Returns
For some investors, however, the use of an index-based preference presents an untenable
possibility: When fund-level returns drop beneath some perceived unacceptable floor (e.g.,
the risk-free rate, the rate of inflation, 0% return, etc.), it may be the case that the manager’s
carried interest is “in the money” and, therefore, that investor’s unfavorable return is diluted
further due to the payment of the incentive fee. For example, assume that the indexed-based
preference is tied to the NCREIF Index and that the Index displays one or more years of
negative returns; if the investment manager sufficiently outperforms the NCREIF Index but
still produces a negative return, it may well be the case that the manager receives its incentive
fee while producing a negative return.
For those investors who feel that payment of an incentive fee in such circumstances is
unacceptable, an obvious remedy to this situation is to structure the investment management
contract (using an index-based preference) with a clause indicating that the carried interest
will only be paid in the event that fund-level returns exceed some minimum threshold. There
are, however, complications to this remedy: the introduction of this floor reduces the
likelihood that the manager’s carried interest will end up “in the money” and, if so, the
manager’s effort level may decline which further imperils fund-level returns. We will return
to these themes in §IV and §V.
III.C.3.b. Early Payment of Incentive Fees
Particularly in funds with long investment horizons, there is often a negotiation between the
investor and the manager about mechanisms in the investment management contract
designed to provide profit distributions to the investment manager in advance of the fund’s
liquidation. From the manager’s perspective, waiting until the fund’s termination date in
order to receive its carried interest (if realized) may not sufficiently motivate the firm’s senior
management to fully deploy their efforts and expertise 71 and/or the base fees provide
These interim payments may do little to aid the firm (and/or investor) resolve one of its
fundamental objectives: identifying executives who can persistently produce alpha. As suggested by
Acharya, et al, (2013): “…when projects have risks that materialize only in the long term, there may
be a dark side to competition for (senior executives)…who can exploit this dark side by taking on
71
55
insufficient profits to be redeployed in needed human and/or technological capital. As a
result, several approaches have been utilized in an attempt to accelerate profit distributions
to the investment manager. Some of the more common ones are discussed below:
III.C.3.b.(i ) Fund- v. Property-Level Returns
Rather than determining the manager’s carried interest on the fund’s overall performance
(which is unknown until the entire fund is liquidated), it has been occasionally been
proposed – typically in instances of fairly small non-core funds with longer investment
horizons – that the carried interest is computed on individual properties as they are sold.
Such proposals present several problems:
•
Losing the Portfolio Effect – In comparison to a fund-based approach, a property-based
approach separates the “winners” (i.e., properties that produce returns greater than the
investor’s preference) and the “losers” (i.e., properties that produce returns less than the
investor’s preference). Consequently, the investment manager reaps a larger carried
interest than would have otherwise been the case with a portfolio (or fund) approach. 72
•
Reluctance to Sell “Losers” – Exacerbating the problem of losing the portfolio effect, it
is well documented that managers/investors are reluctant to sell their losers (e.g., see
Odean (1998)). Consequently, the investor is left with a portfolio in which the manager
has culled the winners – leaving only the losers. This then raises behavioral questions
(discussed in §V) about the manager’s willingness to expend effort and expertise and, in
turn, the likely performance of the remaining already-underperforming properties.
Because of these obvious problems, it is often the case that, when the investment manager’s
carried interest is based on the profitability of each individual property, the promoted
interest (ϕ) is set to a lower percentage than if the carried interest were based on aggregated
fund-level profitability. Two others approaches are also worth noting:
III.C.3.b.(ii ) Interim Distributions & Claw-back Provisions
In the alternative, interim distributions of the investment manager’s promoted interest have
been utilized when these distributions are based on fund-level profitability and, as such,
avoid the obvious problems associated with promoted interests calculated on property-level
profits (as opposed to fund-level profits). A typical configuration is to disburse these interim
profits (to the extent available) to the investment manager at the midpoint of the fund’s
expected life.
projects with tail risk and using the labor market to move from firm to firm to delay the resolution of
uncertainty about their talent” (pp. 38-39).
In principle, this result is identical to the analysis found in the discussion of Exhibit 14 – assuming
the two illustrated outcomes each represent realized property performance. On a portfolio basis, the
manager’s promoted interest equals zero (because the fund’s realized performance fails to exceed the
preferred return); yet, on an individual-property basis, the manager’s promoted interest exceeds zero
(because one of the property’s realized performance exceeds the preferred return and because of the
asymmetric nature of the manager’s carried interest).
72
56
Clearly, such interim distributions are not without problems of their own. The most glaring
of these is the unfortunate outcome in which the interim profit distribution to the
investment manager exceeds the final profit distribution to the investment manager. For
example, assume that the interim profit distribution to the investment manager would have
been $10 million; however, the final profit distribution (in the absence of any interim
distribution) would have been $4 million. In this regard, no distinction is drawn between
external forces (e.g., market-wide changes in the level of capitalization rates) and internal
forces (e.g., manager’s poor decisions and/or lack of effort) which lead to the rollback in
manager’s promote. Instead, let’s focus solely on the issue that the investment manager’s
interim distribution exceeded what the manager was otherwise due.
One mechanism for dealing with such situations is the use of a “claw-back” provision in the
investment management agreement. This contractual provision enables the investor to
demand that the manager repay the excess profit distribution ($6 million in the example
above), sometimes adjusted for the time value of money. This too may be an imperfect
solution. Consider a few obstacles: The investment manager may not be in a financial
position to repay the excess. The tax consequences of receiving an interim profit distribution
and having later to repay the excess may be adverse to the investment manager. 73 To guard
against the unwanted consequences of turnover of the manager’s senior management team
and of adverse income taxes, the investment manager may hold a significant portion of the
interim distribution in reserve – thereby thwarting the interim distribution’s objective
(accelerating profit distributions as a means of motivating senior management).
Because of these and other imperfections, another approach is to forsake the claw-back
provision in return for an interim distribution based on a lower profits percentage (e.g., a
10% carried interest for purposes of the interim distribution, but a 20% carried interest for
purposes of the final distribution). A variation of this approach is to specify differing
(interim profit) percentages for those coming from realized profits (i.e., property sales) and
those based on appraised values. Lastly, it should be noted that these permutations do not
completely mitigate the earlier-cited problems involving interim distributions; they do,
however, lessen the magnitude of the interim distribution which may then make the
tradeoffs (these problems v. motivating senior management) worthwhile.
III.C.3.c. “Double” and “Triple” Promotes
It is often the case with non-core funds that investors are significantly exposed to “double”
(and sometimes “triple”) promotes; such instances occur, for example, when the manager
invests fund-level assets in one or more joint ventures. These ventures are typically aimed at
producing high risk-adjusted returns (e.g., real estate developments, condominium
conversions, etc.) and involve promoted interests payable to the operating partner (e.g.,
developers, condo converters, etc.) which are often higher than those found in the context of
these non-core funds. More specifically, it is not uncommon for the operating partner’s
promoted interest to be 25-50% of the venture’s profits; commensurately, these higher
promoted interests are also often accompanied by higher preferences (payable on the fund’s
In a similar vein, certain investment managers are looking to include a provision which permits a
renegotiation of the circumstances surrounding interim distribution should there be an adverse
change to the U.S. tax code with regard to the treatment of carried interests.
73
57
capital contributed to that particular venture). These ventures and the structuring of
promoted interests to the operating partner clearly invoke our earlier discussions about
contingent claims with asymmetric, convex payoffs and the ultimate dilution of the
investor’s expected return. So, let’s take a moment to further explore these issues. Again, the
use of illustrations seems to best present these concepts.
Let’s begin with a simple comparison. Assume investors can invest in one fund (Fund A)
that avoids investing in joint ventures and a second fund (Fund B) that exclusively invests in
joint ventures. In comparing funds with and without the double promote, let’s begin with a
set of assumptions that more or less puts the two funds on equal footing. There is, of
course, no guarantee that such rough equivalence happens in practice. Nevertheless, the
examples that follow nicely illustrate the severely truncated upside that invariably occurs in
those instances in which investors face the double promote. So, to make the comparison
worthwhile, let’s assume that the first fund is expected to produce (gross) returns consistent
with our initial assumptions (see Exhibit 10 and its accompanying text): an expected return
(E[k]) of 12%, with volatility (σk ) of 15%, and a 20% promoted interest (ϕ ) payable to the
fund’s investment manager after the investors have received a 12% preference (ψ ), as shown
in Exhibit 35:
Exhibit 35: Illustration of the Effects of the Absence of Joint Ventures
on Fund- and Investor -Level Returns
Expected Frequency
Likely Returns
before Promote
Likely Returns
After Promote
-33% -28% -23% -18% -13% -8%
-3%
2%
7%
12%
17%
22%
27%
32%
37%
42%
47%
52%
57%
Likely Returns
Let’s assume that, while our second fund invests in higher-return/higher-risk strategies, it
also produces fund-level returns (i.e., net of the operating partner’s promoted interest paid in
58
these joint ventures which are (approximately) consistent with our initial assumptions. To do
this, we further assume that the operating partner receives a promoted interest 74 of 50%
after the fund is paid a preference (on the capital it has contributed to that particular
venture) set equal to the joint venture’s expected return. Lastly, we assume that the volatility
of each venture’s return is 20% (σJV = 20%). In other words, each of these ventures
produces greater expected returns but does so with higher volatility; however, the
diversification effect 75 of combining a number of the ventures reduces the volatility of Fund
B’s gross return to 15% (i.e., the same as Fund A).
Based on the foregoing assumptions, each joint venture in Fund B is then expected to
produce a gross expected return of 16%. After a 16% preference to the fund with a 50%
promoted interest to the joint venture’s operating partner 76 is considered, each joint venture
is then expected to produce an approximate 12% return to the fund. In principle, this
difference between the joint venture’s gross and net returns is identical to our earlier
discussions (e.g., see Exhibit 13 and its accompanying text) regarding the dynamics of the
fund. The exception, of course, is that Fund B must pay each operating partner its promoted
interest (if realized) and then Fund B’s investment manager receives its promoted interest (if
realized) – based upon exceeding a 12% preference. Exhibit 36 captures these effects:
74 The promoted interest of 50% was arbitrarily chosen. If a smaller percentage is chosen, then a
smaller gross venture-level return is needed to produce a 12% net venture-level return. For example,
a 40% promoted interest to the operating partner requires a 15.25% gross venture-level return, a
33.3% promote requires a 14.75% return, etc.
The volatility of the second fund’s expected returns can be thought of as a portfolio of ventured
investments. Assuming that they are not perfectly correlated, an increase in the number (N) of
ventures in which the fund invests serves to lower the volatility of the fund’s expected return. More
broadly, the formula for the variance of a fund (or portfolio) with N-assets (or ventures) can be
=
σ P2
wi2σ i2 +
wiσ i w jσ j ρi , j ∀i ≠ j . If we assume for simplicity that all
written as:
75
∑
∑∑


ventures are equally weighted  wi =
(
1
2
2
 , have the same volatility (σ i = σ ) and have the same
N
)
correlation with one another ρi , j = ρ , then the fund-level (or portfolio-level) variance simplifies
1
N −1

to:
σ P2 σ 2  +
=
( ρ ) . Assuming this fund has invested, for example, in ten ventures (each
N
N

with volatility of 20%), then an average correlation of returns between any two ventures of
approximately 51% produces a fund-level volatility of 15%. Of course, a similar dynamic is also true
of the first fund.
To be clear, this promoted interest in the joint venture (payable to the operating partner) is quite
apart from the 20% promoted interest in the fund payable to the investment manager – hence, the
so-called “double” promote.
76
59
Exhibit 36: Illustration of the Effects of Joint Ventures
on Fund- and Investor-Level Returns
Estimated Frequency
Likely Returns
before JV
Promote
Likely Returns
after JV
Promote
Likely Returns
after
Manager's
Promote
-29%
-24%
-19%
-14%
Note: Distributions not to scale.
-9%
-4%
1%
6%
11%
16%
21%
26%
31%
36%
41%
46%
51%
56%
61%
Likely Returns
The dilution occurring when moving from gross joint venture returns to net joint venture
returns is larger than was the case when examining fund-level (gross and net) returns. Why?
The operating partner’s promote is larger than the investment manager’s because the
promoted interest is higher (ϕ JV = 50% as compared to ϕ Fund = 20%); the promoted interest
is higher because, in part, the preferred return is higher (ψJV = 16% as compared to ψFund =
12%); and the preferred return is higher because, in part, the volatility of the venture-level
returns is higher (σ JV = 20% as compared to σ Fund = 15%). Exhibit 37 summarizes the
statistical properties of the venture’s gross and net returns 77 and then the fund’s gross and
net returns:
In practice, much of the higher risk/return payoffs from joint-ventured investments often comes
from the use of leverage (see §III.B.4.d). Moreover, it is often notoriously difficult to trace the
leverage ratio(s) of these ventured investments through the financial statements of the fund (or the
REIT or REOC (real estate operating company), in the case of public real estate companies utilizing
joint ventures).
77
60
Exhibit 37: Investor's Net Returns When Fund Avoids Joint Ventures and Embraces Joint Ventures
No JVs
(Fund A)
(a)
All JVs
(Fund B)
Differences
Expected Returns
Gross Joint Venture-Level Returns
Operating Partner's Promoted Interest
16.0%
(b)
4.0%
Net Venture-Level Returns = Fund-Level Gross Returns
Investment Manager's Promoted Interest
(c)
Investor's Net Return
12.0%
12.0%
0.0%
1.2%
10.8%
0.9%
11.1%
(0.3%)
0.3%
Volatility (Standard Deviation): (d)
Gross Joint Venture-Level Returns
15.0%
Operating Partner's Promoted Interest
4.1%
Net Venture-Level Returns = Fund-Level Gross Returns
15.0%
11.4%
(3.6%)
Investment Manager's Promoted Interest
1.4%
13.6%
1.2%
10.5%
(0.2%)
(3.1%)
Investor's Net Return
(e)
Expected returns may not foot due to rounding.
(a)
(b)
(c)
(d)
(e)
Determined via Monte Carlo simulation (using 30,000 iterations).
The joint venture's operating partner is paid a promoted interest of 50% after the fund receives a preferred
return of 16%.
The investment manager is paid a promoted interest of 20% after the investors receive a preferred return
of 12%.
Unless returns are perfectly correlated, standard deviations are not additive.
Because of the promoted interest(s), the distribution is no longer symmetrical; consequently, the standard
deviation is an incomplete measure of dispersion.
Exhibit 37 is both revealing and misleading!
The revealing aspects relate to expected returns. Notice that both funds begin with the same
gross return of 12% (after having paid the operating partner’s promote in the joint ventures
of Fund B). However, somewhat counter-intuitively, investors in Fund A (which avoids all
joint ventures) suffer greater dilution than those investors in Fund B (which invests only in
joint ventures). Per Exhibit 37 (and our underlying assumptions), the additional dilution
suffered by the investors in Fund A is approximately 30 basis points. Consequently, both
funds have a gross return of 12%; yet, the investors in Fund A have a lower net return (i.e.,
10.8% v. 11.1%). How can this be (when Fund B invests in higher-volatility strategies and
volatility is directly related to the expected value of the promoted interest)? The answer lies
in the fact that Fund B’s upside returns have already been truncated by the operating
partner’s promoted interest – see Exhibit 36. Less upside means less of an expected
promote. (In other words, the expected value of the fund manager’s promoted interest is
dependent upon instances in which likely returns exceed the preference; these instances
happen with less magnitude for managers (and investors) in Fund B because the operating
partner’s promoted interest in the joint venture already cleaves off high returns.) Another
way to demonstrate this effect is to consider the so-called “three sigma” event (i.e., E[k] ±
3σ ) and the effects of the (single or double) promote on investors’ net return, as shown in
61
Exhibit 38. Notice that the upside return from the investor’s perspective is far higher with
Fund A (i.e., 48.0% v. 33.2%) because of the double promote associated with Fund B:
Exhibit 38: Illustration of "Three-Sigma" Events
Net Returns When Fund Avoids Joint Ventures and Embraces Joint Ventures
No JVs
All JVs
(Fund A)
(Fund B)
Investor's "Three-Sigma" Returns:
Differences
1. Upside Return:
Gross Venture-Level Return (E [k JV ] + 3σ )
61.0%
Operating Partner's Promote (a)
22.5%
Net Venture-Level Returns
38.5%
18.5%
Fund-Level Gross Returns (E [k ] + 3σ )
57.0%
Investment Manager's Promoted Fund Interest (b)
9.0%
5.3%
-3.7%
Investor's Net Upside Return
48.0%
33.2%
14.8%
2. Downside Return (E [k ] - 3σ )
-33.0%
-29.0%
-4.0%
(a)
The joint venture's operating partner is paid a promoted interest of 50% after the fund receives a preferred return of
16%.
(b)
The investment manager is paid a promoted interest of 20% after the investors receive a preferred return of 12%.
Represents the difference between Fund A's gross return and Fund B's gross return after having paid the operating
partner's promoted interest in the joint venture
(c)
The misleading aspects relate to the volatility of returns. Both Exhibits 37 and 38 suggest
Fund A is substantially more risky. Exhibit 37 indicates a standard deviation of expected
(net) returns equal to 13.6% for investors in Fund A, while only 10.5% for investors in Fund
B – even though both funds begin with a 15% standard deviation for expected gross returns
(and the joint ventures themselves (of Fund B) individually have standard deviations of
20%). Similarly, Exhibit 38 indicates that the “3-sigma” (downside) event is -33% for Fund
A and -29% for Fund B. How can it be that Fund A is riskier than Fund B? The answer is
twofold: First, as stated earlier (see §III.B.2), the reduction in standard deviation is an
illusion; it is a mathematical byproduct of reducing the investor’s upside while maintaining all
of the investor’s downside. Second, the lower “3-sigma” downside event associated with
Fund B is a statistical byproduct of having centered the mean of Fund B’s expected (gross)
returns at four percentage points higher than Fund A (i.e., E[kA] = 12% and E[kB] = 16%).
Because both funds are assumed to have the same volatility (i.e., σA = σB = 15%), the result
is that the three-sigma event results in a lower figure for Fund A. If we measure riskiness by
standard deviation of gross portfolio returns, then Fund A is no riskier than Fund B.
However, if we measure riskiness by the probability of failing to realize some minimum
downside hurdle, then Fund A is riskier. But, such a discussion of probabilities begs the
question on the upside: which fund is more likely to exceed some upside target? Here the
answer is Fund A – again, because of the truncated upside associated with Fund B. Said
another way, this is also a discussion about skewness (i.e., the departure from the symmetry
found in normally distributed returns). Clearly, the double promote associated with Fund B
causes its returns to have greater skewness than is found with Fund A. This stark difference
– given our assumptions – is highlighted in Exhibit 39:
62
Exhibit 39: Illustration of Investor's Likely (Net) Returns
in Funds with and without Joint Ventures
Estimated Frequency
Likely Returns
without JVs
"Fund A"
Likely Returns
with JVs
"Fund B"
-40.0%
-30.0%
Note: Distributions not to scale.
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
Likely Returns
It is apparent from Exhibit 39 that Fund A (which avoids investing in joint ventures) offers
more upside return to investors than Fund B (which invests exclusively in joint ventures) –
even though both funds offer the same expected gross fund-level return (E[k] = 12%) –
while Fund A also presents more downside risk. 78 And though the expected net return to
Fund A is 30 basis points lower than Fund B (given our assumptions), it remains an open
question as to whether reaching for these 30 additional basis points 79 by investing in Fund B
is worth forsaking the greater upside return associated with Fund A.
78 An issue not addressed until §V is the behavioral impact of the fund manager’s out-of-the-money
promoted interest. In such cases, the fund manager may exert less effort and/or “reach” for yield by
making riskier bets; however, the adverse reputational effects of less effort and/or losing such bets
(coupled with the desire to raise future funds) may dissuade the manager from such behavior.
Importantly, these reputational effects may be much less of a mitigating factor for operating partners
in “one-off” (or non-programmatic) joint ventures with the fund/manager.
An alternative presentation regarding the issue of double promotes would be to determine the level
of gross venture profitability for Fund B such that both funds offer the same expected net returns to
investors. Given our assumptions, such an approach would require reducing the (gross) expected
return on joint ventures by approximately 30 basis points (i.e., 16.0% → 15.7%). In so doing, the
earlier comments about the extreme skewness of Fund B’s returns still apply.
79
63
Finally, investors with capital allocated to (typically, non-core) fund-of-fund strategies often
face a “triple” promote; in addition to the issues described above, the sponsor of the fund of
the funds often receives a promoted interest. Such instances tend to exacerbate the
attenuated upside return as described above.
III.D.
Co-Investment Capital
It is often said the securing co-investment capital from the investment manager helps create
an “alignment of interests” between the manager and investor(s). In such cases, the
investment manager can be thought of as contributing a portion of the investor equity
capital (which we have heretofore treated as coming solely from passive investors). In these
cases, the investment manager earns a blended rate of return: a combination of the investor’s
return plus the manager’s promoted interest, as scaled by the manager’s co-investment
capital.
But, more importantly, does co-investment capital really align interests? Or, is it merely a
requirement of marketing funds in today’s environment? Unfortunately, there is precious
little evidence 80 regarding co-investment capital and real estate investment performance. See
Leary (2012) and Schneiderman (2011). In fact, anecdotal evidence often supports the
counter-argument: co-investment capital does little to deter imprudent risk-taking. Two
prominent examples come immediately to mind: First, many of the principals of Lehman
Brothers – including the company’s chairman and chief executive officer, Richard Fuld, Jr. –
reportedly had substantial percentages of their personal fortunes invested in the company.
This arrangement apparently did not lead to any better decision-making in the period leading
up to the 2008 financial crisis than other investment banks. 81 Second, many of the real estate
investment advisors who lost substantial amounts of their clients’ capital during the same
financial crisis were also the advisors who posted substantial co-investment capital at the
fund’s inception. Moreover, there does not seem to be any particular pattern with regard to
the type of investment managers (e.g., publicly traded companies, affiliates of developers,
stand-alone firms, etc.) which were undeterred by their co-investment capital contributions
from making poor investment decisions on the verge of the financial crisis.
For the investor who nevertheless insists on a co-investment requirement, what distinctions
are important? First and most obviously, the alignment of interests is generally thought to
grow as the size of the co-investment contribution 82 increases. However, let’s parse “size”
80 In the mutual-fund industry, there is some evidence that co-investment capital improves fund
performance. See Cremers, et al. (2009).
81 More broadly, Malmendier and Tate (2008) show – using a sample of nearly 500 publicly traded
companies – that overconfident CEOs, with access to internal finance, tend to overpay for
acquisition/merger opportunities. Overconfidence is measured by CEOs’ personal over-investment
(i.e., failure to exercise highly in-the-money vested, non-tradable executive options) in his/her
company (and corroborated by his/her portrayal in the financial press as more “confident” or
“optimistic” than his/her contemporaries).
For purposes of this section, we will assume that the base fees (§II) earned by the investment
manager simply cover the costs of operation plus a “fair” profit. If, however, base fees produce an
82
64
for a moment. Size can be construed as a percentage of the fund’s overall equity capital. Or,
size can be construed as relative to the investment manager’s net worth. The latter may be
far more effective at focusing the efforts and experiences of the manager’s senior
management team than the former. Second, the subordination of the manager’s coinvestment capital may be another important dimension. If the manager’s return of capital is
subordinated to the investor’s return of capital, then this may be more likely to assist with
the alignment of interests than if the manager’s co-investment capital is pari passu with the
investor’s capital. And third, whether senior management (and/or specific key employees of
the fund manager) contributed their own equity capital or, instead, borrowed it from an
affiliate (or, in some cases, a third party) is another important distinction. In those instances
where the investment manager is affiliated with a large financial organization83 and that entity
contributes the equity capital, this arrangement – from the perspective of senior
management – is similar to creating another hierarchy of preferences and promotes which
must be satisfied before senior management participates (via their (subordinated) promoted
interest) in the fund’s profits and, consequently, carries with it many of the behavioral issues
discussed in §V.
Ultimately, co-investment requirements – like many contractual provisions – are no panacea
when it comes to preventing imprudent behavior 84 on the part of certain investment
managers. Perhaps the best rationale for a co-investment requirement came from an
unnamed investor: While the co-investment requirement may not eliminate imprudent
behavior on part of the investment manager, at least investors can take some comfort in the
fact that the manager lost money as well.
IV. The Use of Double-Bogey Benchmarks
Until now, we have primarily focused on the use of a single benchmark for the investor’s
preferred rate of return (and, most often, this benchmark has typically been a fixed
percentage of invested equity capital). But as indicated in the earlier discussions (§III.C.3.a)
concerning the difficulties of determining the appropriate benchmark – particularly as the
fund’s investment horizon lengthens – it is apparent that the use of two (or more)
benchmarks may often serve to mitigate some of the potential infirmities of using a single
benchmark.
Fortunately for us, more than a decade ago a large U.S. pension plan (“the Plan”) instituted
an incentive system for many of its large “core” real estate advisors with many of these
earlier-mentioned characteristics. Therefore, we will use a stylized version of this incentivefee arrangement to analyze the use of two benchmarks – in the parlance of the industry, this
outsized profit, then the matter of the size of the manager’s co-investment capital might be better
judged in light of these profits.
83 In the alternative, there are financial firms which specialize in investing in unaffiliated investment
managers – providing “seed” capital for new funds as well as start-up capital covering the manager’s
initial cost of operations.
Or, succumbing to “animal spirits” – see Keynes (1936). However, even if co-investment does
align interests (i.e., managers act in investors’ interests), that does not mean that poor decisions will
never be made or that risks that turn out unfavorably will never be taken.
84
65
is often called a “double-bogey” benchmark – when, in both instances, the benchmarks are
tied to an underlying index (rather than a fixed percentage of equity capital).
While what follows is based on an incentive-fee arrangement introduced by an actual
investor, it is presented in a simplified and incomplete form for expositional purposes.
Further, the actual investor has altered some aspects of the arrangement since its
introduction and some of these alterations are not included here. Because the representation
here is an incomplete generalization, we refer to the investor simply as “the Plan” and the
example should be treated as a general example of this approach to incentive structures
rather than a perfectly accurate portrayal of any specific investor’s incentive fee structure.
Nevertheless, the design and its application as presented here are based on a real-world
approach and nicely illustrate many of the points discussed earlier.
IV.A.
A Sketch of the Plan’s Incentive Fee
IV.A.1.
Avoid Competing with Itself
In an attempt to pay investment management fees to only those managers who produce
positive alpha (see §III.A), the Plan tailored its investment management contracts for large
core funds such that base management fees (see §II) were reduced from market-wide levels
and, in return, the investment managers had the opportunity to earn an incentive
management fee. Moreover, the Plan required these investment managers post significant
(approximately 5% of total equity) co-investment capital (see §III.D).
Given the large size of the Plan’s real estate portfolio and the large number of real estate
investment managers working on behalf of the pension fund, it was imperative that the Plan
institute a mechanism which attempts to eliminate these managers competing with one
another to acquire the same property. One such mechanism was the adoption of a plan that
divided the country in half (east v. west) and then awarded each investment manager with
one property type in one half of the country. While this arrangement works reasonably well
for three of the four core property types, it is less efficient for the retail sector. Regional and
super-regional malls, in particular, involve highly specialized expertise, transact in very large
dollar sizes and have a commonality of tenancy not typically observed in the other property
types. Consequently, the retail sector was divided by sub-property types, malls v. shops,
rather than geography. Exhibit 40 sketches the arrangement:
66
Exhibit 40: An Example of Dividing Manager Mandates by Geography and/or Property Type
West
Apartments: Manager A
Industrial: Manager B
Office:
Manager C
East
Apartments: Manager D
Industrial: Manager E
Office:
Manager F
Retail (national):
Shopping Centers: Manager G
Regional Malls: Manager H
IV.A.2.
Beating a Real-Return Benchmark
As the first leg of earning the incentive management fee, the managers were to earn 20% of
their particular investment fund’s profits in excess of the rate of inflation plus 5% over the
holding period. Not only is this a form of a real (i.e., inflation-adjusted) return, it is also the
form of an indexed benchmark (i.e., indexed to a spread over inflation) – see §III.C.3.a.
This 5% premium was scaled upward as the investment manager assumed more risks in the
portfolio. This scaling occurred in two crucial dimensions:
1. Leverage – Based on the average leverage of the fund over the investment horizon,
increments (measured in basis points) were added to the 5% real-return requirement:
Leverage Ratio Return Premia
0-15%
25 bps
15-30%
50 bps
30-40%
75 bps
40-50%
125 bps
50-60%
200 bps
60-70%
350 bps
2. Life-Cycle Effects – Based on the mix of property strategies within the fund’s portfolio
of properties, increments were added to the 5% real-return requirement:
67
Property Subtype Return Premia
Stabilized Class A
0 bps
Pre-sale Class A
50 bps
Stabilized Class B
75 bps
Pre-sale Class B
100 bps
Renovation
200 bps
Development
250 bps
As an example, if a particular fund were to specialize in (only) development properties and
utilize leverage of 50% to do so, then that fund would be required to generate a real return
greater than 9.5% (i.e., the base return of 5.0% plus 2.0% for leverage plus 2.5% for
development) in order to have the investment manager earn the first leg of the incentive
fee. 85
If there is a criticism of these scaling adjustments, it may be twofold: First, the premia were
determined at the fund’s inception. Consider leverage: If you have perfect foresight about
future property returns and the cost of debt capital, then you would know exactly the
leverage premiums to set. However, perfect foresight is unavailable to us mere mortals. As
the spread between asset returns and debt costs widens or narrows with realized
performance, then the appropriate leverage adjustment widens or narrows accordingly. For
example, assume that is initially anticipated that asset-levels returns are 8% and the cost of
debt is 6%, for a spread of 2%. If so, the appropriate leverage adjustments are easily
determined – see equation (4). With the passage of time, assume that the portfolio actually
realized asset-levels returns of 9% and the cost of debt is 6%, for a spread of 3%. Then, the
appropriate leverage spreads ought to be 50% higher than initially set. To help illustrate this
point, Exhibit 41 provides the appropriate leverage spread (∆:ke) for varying loan-to-value
(LTV) ratios and contrasts initial expectations with actual portfolio realizations (to aid
understanding, LTV ratios of 20%, 40% and 60% have been highlighted):
There are also a host of issues with regard to competing methodologies (e.g., dollar- v. timeweighted rates of return, market- v. equal-weighted rates of return, frequency of compounding, etc.).
All of which can have a significant bearing on the reported outcomes.
85
68
Exhibit 41: lllustration of Changing Leverage Premia
as Portfolio Realizations Differ from Initial Expectations
LTV
0%
5%
10%
Initial Expectations (a)
ke
∆: k e
8.00%
0.00%
8.11%
0.11%
8.22%
0.22%
LTV
0%
5%
10%
Actual Realizations (b)
ke
∆: k e
9.00%
0.00%
9.16%
0.16%
9.33%
0.33%
∆ in ∆: k e
0.00%
0.05%
0.11%
15%
20%
8.35%
8.50%
0.35%
0.50%
15%
20%
9.53%
9.75%
0.53%
0.75%
0.18%
0.25%
25%
30%
35%
8.67%
8.86%
9.08%
9.33%
0.67%
0.86%
1.08%
1.33%
25%
30%
35%
40%
10.00%
10.29%
10.62%
0.33%
0.43%
0.54%
0.67%
9.64%
10.00%
1.64%
2.00%
45%
50%
11.00%
11.45%
12.00%
1.00%
1.29%
1.62%
2.00%
2.45%
3.00%
0.82%
10.44%
11.00%
2.44%
3.00%
3.71%
55%
60%
65%
12.67%
13.50%
14.57%
3.67%
4.50%
1.00%
1.22%
1.50%
5.57%
1.86%
4.67%
70%
16.00%
6.00%
8.00%
75%
80%
18.00%
21.00%
7.00%
9.00%
12.00%
2.33%
3.00%
4.00%
40%
45%
50%
55%
60%
65%
11.71%
12.67%
70%
75%
80%
14.00%
16.00%
(a)
(b)
Assumes asset-level returns of 8% per annum and debt costs of 6% per annum.
Assumes asset-level returns of 9% per annum and debt costs of 6% per annum.
A similar point could be made about setting life-cycle premia at the fund’s inception, rather
than waiting until the fund’s dissolution to determine the realized market-wide life-cycle
spreads. Admittedly, observing life-cycle premia may be more difficult than leverage premia.
The second criticism is that any approach which sets wide ranges potentially encourages the
investment manager to utilize, for example, a leverage ratio just below the cutoff. Consider:
leverage ratios of 30.5% and 39.5% impose the same incremental adjustment (i.e., 75 bps in
our example). We have already seen that leverage increases the volatility of returns and that
increased volatility increases the expected value of the manager’s promoted interest.
Accordingly, investment managers who are prone to “gaming” the incentive fee are likely to
utilize leverage approaching the cutoff. Naturally, the problem worsens as the width of the
leverage range widens. So, two approaches are viable: a) narrow the ranges to the extent
practical 86 or b) compute the real return after the portfolio returns have been de-levered.
The extreme version of this approach is to use equation (4) – instead of specifying ranges and
related premia. In actuality the Plan used ranges that were narrower than shown above.
86
69
A variation of this second criticism is to note that when classifications have some ambiguity,
investment managers who are prone to gaming the incentive fee are likely to utilize their
discretion in identifying properties with ambiguous/imprecise classifications (e.g., is a given
property to be classified as class B or C?) to improve the expected value of their promoted
interest.
IV.A.3.
Beating a Peer-Based Benchmark
As the second leg of earning the incentive management fee, the fund’s de-levered returns
had to exceed the NCREIF return for a given property type. In this regard, the Plan could
have created a simple dichotomous rule; for example:
•
•
beat NCREIF and earn 100% of the incentive fee, or
fail to beat NCREIF and earn 0% of the incentive fee.
Instead, the Plan used a sliding-scale mechanism in which the manager earns 100% of the
incentive fee if the particular fund outperformed NCREIF by 100 bps (the “ceiling”), earns
0% if the particular fund under-performed NCREIF (the “floor”) and earns a ratable
percentage if the fund’s performance falls between the ceiling and the floor. Exhibit 42
illustrates this approach:
Exhibit 42: Illustration of Ratable Share
Based on a Sliding-Scale for Excess Performance
100%
90%
80%
70%
Ratable Share
60%
50%
40%
30%
20%
10%
0%
-0.03
-0.02
-0.01
0
Floor (F )
0.01
Ceiling (C )
0.02
0.03
Investment Manager's Performance (P )
For example, if the investment manager’s performance (P) were to fall midway between the
ceiling (C) and the floor (F), then the manager would earn 50% of the incentive fee earned in
70
P −F
, subject to the bounds
C −F
of 0% and 100%. (Note that the ceiling and floor can be based on something other than the
NCREIF return plus 100 bps and the NCREIF return, respectively.)
the first leg. More generally, the manager’s ratable share equals
Why would the Plan adopt this sliding-scale mechanism when the dichotomous rule is so
much simpler? The answer relates to fairness. Consider the lone benchmark of a
dichotomous mechanism: If the manager under-performs the benchmark by a single basis
point, then manager earns nothing and conversely, if the manager out-performs the
benchmark by a single basis point, then manager earns all of the incentive fee. These stark
outcomes turn on two basis points of differential return, which seems inequitable to both
the manager and the investor.
IV.A.4.
Beating the Double-Bogey Benchmark
Consequently, the investment manager must beat both benchmarks in order to earn the
incentive fee. A summary of this stylized version of the Plan’s incentive fee can be shown
(where k = the fund’s return and ρ = the inflation rate) as:
S 0
=


P −F
(.2)max ( 0, (1 + k ) / (1 + .05 + ρ ) − 1) S=
 where: S
C −F

S 1
=

if P ≤ F
if F < P < C
if P ≥ C
Note that this representation ignores return premia for leverage and property-type effects.
IV.B.
Quantifying the Likely Incentive Fee
IV.B.1.
Likelihood of Beating a Real-Return Benchmark
It is important to consider quantifying the likely incentive fee for a variety of reasons. From
the investor’s perspective, it is important to understand both the likely size of the fee (e.g. are
they overpaying for investment management services?) and the potential behavioral effects
on the investment manager (see §V). From the investment manager’s perspective, the likely
fee must be viewed in light of the accompanying reduction in base fees and the substantial
co-investment requirement. And while it can certainly be argued that the book of business is
important in its own right, as being awarded business by a large institutional investor may
confer additional legitimacy upon the manager and the larger portfolio of assets under
management allows the manager to spread its fixed costs over a larger “footprint,” it would
seem that there must be a plausible likelihood of the investment manager realizing a
significant incentive fee.
The starting point for considering the likelihood of exceeding a real return of 5% per annum
is to consider the historical return properties of, say, the NCREIF Index (because, in the
case of the Plan, fund-level returns were de-levered before making a comparison to the
appropriate NCREIF sub-index). Exhibit 43 illustrates the yearly real returns generated by
the NCREIF Index for the thirty-five years ending in 2012; as shown by the maroon line, the
Index produced an average real return of approximately 5.25% per annum:
71
Exhibit 43: Historical Real Returns for the NCREIF Property Index
for the Period 1978 through 2012
20%
15%
10%
Then-Current Average
Current Average
5%
0%
-5%
-10%
-15%
-20%
However, the long-run average does not tell the entire story. For instance, the red line
represents the then-current (or trailing) average real return (e.g., this trailing average reached
its maximum in 1986, with a real return of approximately 7%) and it fluctuates about the
current average. By construction, the then-current average converges with the current (longterm) average at the end of analysis period.
Clearly, a statistical description of the dispersion of real returns is also essential. In that
regard, the standard deviation of the annual return is approximately 7.15%. While we could
extend the statistical examination to other characteristics (e.g., skewness) of the distribution,
it will be sufficient for our illustration to assume that the real return is normally distributed. 87
Consequently, we can use the average (µ ) and the standard deviation (σ ) to construct an
approximate distribution of returns – as illustrated in Exhibit 44:
In fairness, it should be pointed out that this distributional assumption represents a familiar result
found in other settings (e.g., distribution of test scores) and simplifies some of our mathematics. That
said, the reasonableness of this distributional assumption depends on the degree to which the
underlying empirical distribution diverges from normality. In certain instances, this divergence is
significant and it is potentially damaging to your financial health to assume otherwise.
87
72
30%
Exhibit 44: Historical Real Returns for the NCREIF Property Index
for the Period 1978 through 2012
Stylized Normal Distribution (given historical µ and σ).
Realized Real Returns
20%
10%
0%
-10%
-20%
Assuming that past results are a fair representation of likely future results (a questionable
assumption at times – consider, for example, real estate’s performance during and after the
2007-08 financial crisis), then we can consider the likelihood of a given investment manager
beating the 5% real-return threshold 88 in a probabilistic sense, as we have done with earlier
analyses – see Exhibit 45:
88 More accurately, we should concern ourselves with holding-period returns equal to the expected
life of the investment fund. In general, such an approach would leave the annualized (compounded
or geometric) average return unchanged but would lessen the volatility of annualized returns – as a
function of the serial correlation in the return series. However, our analysis is framed in terms of
one-year returns as a means of simplifying the discussion.
73
Exhibit 45: Illustration of Assumed Distribution of
Real Returns on the NCREIF Property Index
5%
4%
Probability of Outcomes
4%
3%
3%
2%
2%
1%
1%
0%
-16.50%
-12.15%
-7.80%
-3.45%
0.90%
5.25%
9.60%
13.95%
18.30%
22.65%
27.00%
Real Returns
From the preceding graphs and accompanying discussions, it is clear that the investment
manager is likely to generate a real return in excess of 5% slightly more than half of the
time. 89 Like earlier examples, the investment manager’s incentive fee represents a convex
payoff (whereby the manager receives nothing if the real return falls beneath 5% but receives
20% of the excess). Again, the question is: How should the investment manager (and the
investor) quantify the estimated incentive fee? The answer, like before (see §III.B.1), requires
viewing the incentive-fee calculation in the context of the expected return distribution.
Exhibit 46 does so and, in order to make the calculations more tangible, assumes that the
advisor manages a $500 million book of business on behalf of the investor:
It should also be noted that there is significant variation among the property types with regard to
their realized real returns (e.g., apartments offered the highest and suburban office the lowest). As
such, certain investment managers found the 5% real return threshold easier to beat than others.
89
74
Exhibit 46: Illustration of the Expected Value of the Manager's Incentive Fee
…
E [r ] − 1σ
…
E [r ]
…
E [r ] + 1σ
…
E [r ] + 2σ
E [r ] + 3σ
Possible Portfolio
Real Returns
(a )
Value of Manager's
Incentive Fee
(b )
Marginal
Probability
(c )
Weighted Value of
Incentive Fee
(d ) = (b ) * (c )
-2.72%
-2.00%
-1.27%
-0.55%
0.18%
0.90%
1.63%
2.35%
3.08%
3.80%
4.53%
5.25%
5.98%
6.70%
7.43%
8.15%
8.88%
9.60%
10.33%
11.05%
11.78%
12.50%
13.23%
13.95%
14.68%
15.40%
16.13%
16.85%
17.58%
18.30%
19.03%
19.75%
20.48%
21.20%
21.93%
22.65%
23.38%
24.10%
24.83%
25.55%
26.28%
27.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.05%
0.20%
0.34%
0.49%
0.63%
0.78%
0.92%
1.07%
1.21%
1.36%
1.50%
1.65%
1.79%
1.94%
2.08%
2.23%
2.37%
2.52%
2.66%
2.81%
2.95%
3.10%
3.24%
3.39%
3.53%
3.68%
3.82%
3.97%
4.11%
4.26%
4.40%
2.15%
2.40%
2.65%
2.90%
3.14%
3.37%
3.58%
3.76%
3.91%
4.03%
4.12%
4.16%
4.12%
4.03%
3.91%
3.76%
3.58%
3.37%
3.14%
2.90%
2.65%
2.40%
2.15%
1.91%
1.67%
1.46%
1.25%
1.07%
0.90%
0.75%
0.62%
0.51%
0.41%
0.33%
0.26%
0.21%
0.16%
0.12%
0.10%
0.07%
0.05%
0.04%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.01%
0.01%
0.02%
0.02%
0.03%
0.03%
0.03%
0.04%
0.04%
0.04%
0.04%
0.03%
0.03%
0.03%
0.03%
0.03%
0.02%
0.02%
0.02%
0.02%
0.01%
0.01%
0.01%
0.01%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
100.00%
0.59%
Expected Value of Manager's Incentive Fee
(a) Based on returns with mean = 5.25% and volatility = 7.25%.
(b ) Equals max[ 0, ( perforrmance - 5%)] *20%.
(c ) Computed from the normal distribution.
75
$2,937,579
To help orient the reader: Column (a) represents a range of potential real returns, beginning
with the fund-level expected real return less one standard deviation (E[r] – 1σ) and ending
with the fund-level expected real return plus three standard deviations (E[r] + 3σ). For this
purpose, the displayed returns need not be symmetrical because any real return value
beneath 5% produces no incentive fee. In the other direction, the shaded area represents
outcomes in which the fund’s real return is expected to exceed the 5% threshold; there is
virtually no possibility of generating more than a “three sigma” return on the upside.
Column (b) represents the value of the manager’s incentive fee, given the real return found in
column (a). Column (c) represents an estimate of the probability associated with the real
return found in column (a), assuming returns are normally distributed. Column (d) represents
the manager’s incentive, given a particular real return, multiplied by the likelihood of the
fund producing that real return. Finally, the sum of all the values of column (d) totals just
short of 60 basis points; this represents the annual incentive fee that investment manager is
expected to earn each year over the life of the fund. In other words, there is slightly less than
a 50% chance that the incentive fee will not be earned by the investment manager and
slightly greater than a 50% chance that the incentive fee will be earned; in the latter
instances, the magnitude of the incentive increases as the probabilities decrease. The
weighted average of all such outcomes falls just shy of 60 basis points.
If the portfolio represents $500 million of equity, then the investment manager’s expected
incentive fee is approximately $2.94 million per year. If the manager is required to contribute
5% of the equity, then the manager is expected to earn an annual incentive fee of
approximately 11.75% (i.e., $2,937,579/(.05 * 500,000,000)) – assuming that the second leg
of the incentive-fee calculation produces a sliding-scale adjustment of 100%. This rate of
return is in addition to whatever return is realized on other investor capital (assuming the
investment manager’s contributed capital is pari passu with the investor’s capital) and
whatever profit is to be earned on the base fees. 90
IV.B.2.
Likelihood of Beating a Peer-Based Benchmark
If the investment manager produced a real return exceeding 5% per annum, then second leg
of the incentive-fee calculation comes into play. As indicated above, the second leg
compares the fund’s de-levered performance to the NCREIF sub-index appropriate to the
manager’s property type. Essentially, this is a matter of relative, peer-based performance. 91
While investment managers might protest, it must be the case that the average investment
manager generates average performance. See Sharpe (1991). Said another way, the odds of
beating the market of one’s peers is 50:50. Moreover, most managers’ returns are clustered
near this average, while extreme over- or under-performance is a rare event. As a result,
Exhibit 47 is drawn in a manner that reflects these assumptions for a given investment
manager:
90 Unsurprisingly, the calculation is more complicated than portrayed here. Among the complications,
the incentive fee is paid upon the fund’s liquidation – though potentially subject to an interim
distribution and a claw-back provision (see §III.C.3.b) – and is paid based upon nominal (not real)
returns.
91
§IV.C revisits this assumption in greater detail.
76
Exhibit 47: Illustration of the Dispersion
of an Investment Manager's Relative Performance
5%
4%
Probability of Outcomes
4%
3%
3%
2%
2%
1%
1%
0%
0%
Under-perform
Performance Relative to Peers
Over-perform
Consistent with those assumptions, Exhibit 47 reflects average relative performance (i.e., the
manager’s performance less the index or market return) as equal to zero. The probabilities
associated with this relative performance then must be run through the Plan’s sliding-scale
mechanism. Because we have chosen to examine the manager’s performance relative to its
peers (as proxied by the appropriate NCREIF sub-index), the floor is equal to 0% and the
ceiling to 1%. 92 (The choice of 1% is arbitrary; any “ceiling” (above 0%) could be chosen.)
As with the likelihood of exceeding a 5% real-return threshold, we can also probabilistically
estimate the likely value of the sliding scale mechanism. Given our assumptions, 93 Exhibit 48
does so:
Given that the the Plan’s sliding-scale mechanism uses the market return as the “floor” (F), the
manager’s performance (P) can, on a relative basis, be viewed as E[P – F] = 0.
92
One additional assumption is needed: we assume the standard deviation of managers’ relative
returns equals 1% (and, therefore, approximately 67% of the managers produce returns which are ±
1% of the market’s average return).
93
77
Exhibit 48: Illustration of Manager's Likley Excess Performance
Possible
RelativePortfolio
Returns
(a )
…
E [ P − F ] − 1σ
…
E [P − F ]
…
E [ P − F ] + 1σ
…
E [ P − F ] + 2σ
E [ P − F ] + 3σ
-1.10%
-1.00%
-0.90%
-0.80%
-0.70%
-0.60%
-0.50%
-0.40%
-0.30%
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
0.60%
0.70%
0.80%
0.90%
1.00%
1.10%
1.20%
1.30%
1.40%
1.50%
1.60%
1.70%
1.80%
1.90%
2.00%
2.10%
2.20%
2.30%
2.40%
2.50%
2.60%
2.70%
2.80%
2.90%
3.00%
Value of Sliding-Scale
Mechanism
Marginal
Probability
(b )
(c )
Weighted Value of
Sliding-Scale
Mechanism
(d ) = (b ) * (c )
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
100.00%
2.15%
2.40%
2.65%
2.90%
3.14%
3.37%
3.58%
3.76%
3.91%
4.03%
4.12%
4.16%
4.12%
4.03%
3.91%
3.76%
3.58%
3.37%
3.14%
2.90%
2.65%
2.40%
2.15%
1.91%
1.67%
1.46%
1.25%
1.07%
0.90%
0.75%
0.62%
0.51%
0.41%
0.33%
0.26%
0.21%
0.16%
0.12%
0.10%
0.07%
0.05%
0.04%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.41%
0.81%
1.17%
1.50%
1.79%
2.02%
2.20%
2.32%
2.39%
2.40%
2.15%
1.91%
1.67%
1.46%
1.25%
1.07%
0.90%
0.75%
0.62%
0.51%
0.41%
0.33%
0.26%
0.21%
0.16%
0.12%
0.10%
0.07%
0.05%
0.04%
100.00%
31.07%
Expected Value of Sliding-Scale Mechanism
(a) Based on returns with mean = 0.00% and volatility = 1.00%.
(b ) Equals (P -F )/(C - F ), subject to bounds of 0% and 100%.
(c ) Computed from the normal distribution.
78
To help orient the reader: Column (a) represents a range of the manager’s potential relative
returns, beginning with the fund-level expected relative return less one standard deviation
(E[P – F] – 1σ) and ending with the fund-level expected relative return plus three standard
deviations (E[P – F] + 3σ). As before, the displayed returns need not be symmetrical
because any relative return value beneath 0% produces no incentive fee. In the other
direction, the shaded area represents outcomes in which the fund’s relative return is expected
to exceed the 0% threshold (i.e., the “floor”); there is virtually no possibility of generating
more than a “three sigma” return on the upside. Column (b) represents the value of the
sliding-scale mechanism, given the relative return found in column (a). Column (c ) represents
an estimate of the probability associated with the relative return found in column (a),
assuming that such returns are normally distributed. Column (d) represents the value of the
sliding-scale mechanism, given a particular relative return, multiplied by the likelihood of the
fund producing that relative return. Finally, the sum of all the values of column (d ) totals
approximately 31%; this represents the likely portion of the annual incentive fee that
investment manager is expected to earn each year over the life of the fund (assuming that the
manager’s real return exceeds the 5% threshold). In other words, there is a 50% chance that
the manager’s relative performance will fail to exceed the market return and a 50% chance
that the manager’s relative performance will exceed the market return; in the latter instances,
the magnitude of the over-performance increases as the probabilities decrease. The weighted
average of all such outcomes equals approximately 31%.
As before, assume the portfolio represents $500 million of equity – of which, the manager is
required to contribute 5% – and then further assume that the investment manager’s expected
incentive fee is approximately $2.94 million per year (see Exhibit 46) under the first leg of
the incentive-fee calculation. Now assuming that the manager’s relative performance
produces a sliding-scale adjustment of approximately 31%, then the manager is expected to
earn an annual incentive fee of approximately 3.65% relative to the co-investment capital
(i.e., (31.07% * $2,937,579)/(.05 * 500,000,000)). Again, this rate of return is in addition to
whatever return is realized on other investor capital (assuming the investment manager’s
contributed capital is pari passu with the investor’s capital) and whatever profit is to be earned
on the base fees.
The analysis above assumes that the likelihood of the investment manager beating the 5%
real-return threshold is independent of the likelihood of the investment manager
outperforming its peers. This assumption is examined below.
IV.B.3.
Likelihood of Beating Both Benchmarks
However, there is more to consider when estimating the likelihood of beating two
benchmarks. As an initial example, consider an investment manager who is faced with
beating two benchmarks, where the probability of beating each is 50% and the outcomes are
independent of one another. Then, as Exhibit 49 illustrates, there is a 25% chance of beating
both benchmarks (and, by extension, a 75% chance of failing to beat both): 94
More generally, describe the probability of beating the first benchmark as p1 and the probability of
beating the second as p2; then, assuming these outcomes are independent of one another, the
probability of the investment manager beating both benchmarks equals p1*p2.
94
79
More broadly, we need to understand the correlation (ρx,y ) between the likelihood of the
investment manager beating the 5% real-return threshold (x) and the likelihood of the
investment manager outperforming its peers (y). While the mathematics 95 are complicated,
the intuition is straightforward. From the investment manager’s perspective, the odds of
earning the incentive fee increase if there is a high degree of correlation (ρx,y ) between the
likelihood of the investment manager beating the 5% real-return threshold and the likelihood
of the investment manager outperforming its peers. In other spheres of investment
management, this is referred to as a “high beta” or “aggressive” strategy; when the market is
“up” (i.e., real returns exceed the long-run average of approximately 5%), the manager is also
quite likely to outperform its peers. 96 Contrast this investment strategy with a “low beta” or
“defensive” strategy: when the market is “down” (i.e., real returns fall short of the long-run
average of approximately 5%), the manager is quite likely to outperform its peers. These two
opposing investment strategies are illustrated in Exhibit 50:
Formally and assuming both underlying distributions are normal, the probability of successfully
and simultaneously beating both benchmarks  P ( r > 5% ∩ P − F > 0 ) =
P ( S )  can be expressed as:
95
P(S )
∞∞
∫ ∫ 2πσ σ
ψ 0
x
1
y
1 − ρ x2, y
(

 x − µ  2  y − µ
−1
y
x


exp
 +
 2 (1 − ρ x2, y )  σ x2   σ y2


)
(
)
2

2  x − µx
 − 2 ρ x , y 
 σx

 y − µy
 
 σ y
 
   dx dy
  
where: ψ = .05, r = x ~ N µ x , σ x2 and P − F =
y ~ N µ y , σ y2 .
Or, equivalently, instances of beating the 5% real-return threshold are typically accompanied by
instances of the investment manager out-performing its peers.
96
80
Exhibit 50: Illustration of Correlated Returns:
Investment Manager's Peer-Adjusted Performance v. Real Return
Area for which the Incentive
Fee is "In the Money"
Real Return vis-a-vis the Benchmark
Low β |
Defensive
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
High β |
Aggressive
Peer-Adjusted Performance
To help orient the reader: The vertical axis represents the fund’s real return in comparison to
the real return benchmark (which was 5% in the case of the Plan). The horizontal axis
represents the fund’s return relative to the market (which was the relevant NCREIF subindex in the case of the Plan). From the investment manager’s perspective, the upper-right
quadrant (shaded in light green) of the graph represents the intersection of the real-return
and peer-adjusted performance which results in the manager earning the incentive fee (i.e.,
the manager is “in the money”). In the graph’s other three quadrants, the fund fails to meet
one or both of the benchmarks. The upward-sloping, green-colored ellipse 97 represents a
“high beta” or “aggressive” strategy in which instances of beating the 5% real-return
threshold are typically accompanied by instances of the investment manager out-performing
its peers. The downward-sloping, blue-colored ellipse represents a “low beta” or “defensive”
strategy in which instances of failing to beat the 5% real-return threshold are typically
accompanied by instances of the investment manager outperforming its peers.
So all other considerations aside, investment managers prone to gaming the incentive fee are
likely to adopt high beta/ aggressive strategies (and shun low beta/defensive strategies) –
irrespective of how accurately the leverage and life-cycle premia have been set. In turn, the
Inside the ellipse represents a range of likely outcomes for an investment strategy which is
measured relative to two benchmarks. More technically, the ellipse represents our earlier-used bellshaped curve for a single measure of performance extended to two measures; its location depends on
the means (µx and µy) and the volatilities (σx and σy ) of the two distributions and, most importantly
for the point illustrated here, on the correlation (ρx,y ) between the two distributions.
97
81
prudent investor ought to recognize that designing an incentive fee with this sort of doublebogey hurdle induces aggressive investment behavior from the investment manager. (§V is
devoted to the behavioral implications of incentive fees.) Consequently, the astute investor
will deploy this sort of double-bogey hurdle when the investor believes that market returns
are likely to be favorable. Said another way, the use of a double-bogey benchmark (of the
sort described here) leads to over-performance in an “up” market and under-performance in
a “down” market. And, as a result, investors ought to be mindful of the likely investment
climate faced over the life of the fund. 98, 99
IV.C.
Additional Commentary: Beating the “Market”
For the sake of expediency, the preceding discussions treated instances of the investment
manager beating its peers as equivalent to the investment manager beating the “market.” In
the case of the Plan’s incentive fee, the market was represented by the NCRIEF sub-index
specific to the property typed managed by the investment advisor.
Is this fair to the investment manager? No. Indices such as NCREIF represent collections of
whole interests in fee-simple real estate holdings. While such holdings are clearly part of the
fund and its peers’ makeup, other factors – such as cash holdings and fund-level costs –
generally conspire to drag fund-level performance below the index’ return. Consequently,
these indices do not fairly represent the performance of one’s peers. 100
If unfair, what then? In practice, investment managers often use financial leverage as means
of “outperforming” the market. However, this is generally a mere contrivance – as the
increase in (expected or realized) returns is offset by an increase in volatility – as shown
earlier (§III.B.4.d). As noted previously, fund-level returns were de-levered, in the case of the
Plan, before making a comparison to the appropriate NCREIF sub-index. As a result, the
investment manager is generally left to produce outperformance in two ways: a) the manager
might truly be skillful (as opposed to lucky) 101 and/or b) the manager might “shade” to
riskier assets within a given classification (e.g., stretch the definition of “institutional quality”
As real-life examples of the importance of time-varying rates of (real) returns, consider an investor
who contributed capital to a 5-year fund in 2000 and another investor who contributed capital to a 5year fund in 2005, with each fund having a double-bogey benchmark of the sort described herein. In
the first instance, the high beta/aggressive strategy produced by having the double-bogey would
have, in all probability, performed handsomely; in the second instance, the high beta/aggressive
strategy produced by having the double-bogey would have, in all probability, performed disastrously
– largely due to the 2007-08 financial crisis. Of course, the difficulty lies in our attempts to forecast
the future.
98
99 For the period 1999-2010, Fairchild, et al. (2011) find that the betas of open-end core funds range
from .7 (defensive) to 1.3 (aggressive).
This underperformance is not confined to the real estate market. This pattern has been repeatedly
found in the stock market. For example, Fama and French (2010) report that the aggregate
performance of U.S. equity mutual funds has underperformed the passive benchmark by
approximately 100 basis points per annum, over approximately the last quarter century.
100
However, not all investment managers can posses above-average skill (just as all children cannot
be above-average).
101
82
with regard to property quality). The former meets the definition and goals of
outperformance, the latter does not.
Therefore, it seems more sensible for investors to pragmatically set the “floor” and “ceiling”
(and the real-return threshold) by recognizing the drag of cash holdings and fund-level costs
on portfolio returns. (The PREA|IPD U.S. Property Fund Index permits this type of
disaggregation.) A more attainable set of benchmarks may reduce the incentives for
investment managers to shade towards riskier assets because of the improved probability of
the manager’s promoted interest being “in the money” coupled with the adverse reputational
effects of ending up “out of the money” and, in turn, increase the incentives for investment
managers to rely on their skills. Of course, investors still need to tightly define and monitor
the fund’s property holdings.
V.
Principal/Agent Issues
This section is intended to explore some of the behavioral aspects of investment managers
as influenced by future incentive fees yet to be earned. To be clear, this section will consider
the interplay between structuring techniques and the fund’s risk and (gross) return
characteristics (as noted earlier, the “endogenous” relationship between structure and the
fund’s risk/return characteristics). Previous sections examined the static effects of such
structures; that is, we (generally) took the fund’s risk and (gross) return characteristics as
given (or, in the parlance of the economists, these risk/return characteristics were
“exogenous” to the structuring techniques). These endogenous effects can be subtle, but are
often quite powerful. Both investors and managers should understand these effects.
In this regard, there is a rich literature in economics having to do with the interactions
between principals and agents, when the relationship between the agent’s efforts and the
project’s outcomes is unobservable 102 by the principal (in the parlance of the economists, this
unobservable effort is a source of “asymmetric information.”) In one version of the classic
setup, the principal is the owner of a firm and the agent is the manager of the firm 103 – e.g.,
see Grossman and Hart (1983) and Harris and Raviv (1979) – and the firm’s profits reflect
the manager’s efforts as well as random factors (outside the manager’s control). In order to
align the interests of the principal and the agent, the typical solution involves a contract
designed to motivate the agent’s efforts; this is generally accomplished through the use of an
incentive contract with a convex payoff tied to observable performance (e.g., profits, share
price, etc.). Without such incentives, the manager would not expend costly effort; however,
notwithstanding the incentive contract, the manager still expends less effort than if the
102
In the alternative, there are significant costs to the principal when observing the agent’s efforts.
As a variation of this example, the agent has a firm in need of equity and the agent’s dilemma is to
determine how much of the firm to sell to outside equity (the principal) in order to satisfy both the
agent and the principal – which has to do with the determinants of capital structure (e.g., see Jensen
and Meckling (1976)).
103
83
manager owned the firm in its entirety. The difference in effort levels is often referred to as
an “agency cost.” 104
Clearly, it is an easy extension to delegated investment management, in which we consider
the principal as the investor and the manager as the agent. The incentive contract with a
convex payoff referred to above is analogous to the “pref and promote” structures of our
earlier discussions. As mentioned earlier, these incentive structures are largely found in noncore funds – where effort is more difficult to discern than for core funds. And, these core
funds are, in some sense, analogous to the mutual fund business; another instance of
delegated investment management in which incentive fees are unusual. Interestingly, the
finance literature – see Chevalier and Ellison (1997) and Lakonishok, et al. (1992) – suggests
that the lack of incentive fees in the mutual fund industry does not produce lower levels of
effort among active (v. passive) investment managers. The reasoning is tied to the highly
scalable nature of the investment management business (i.e., as assets under management
rise, revenues grow far more quickly than costs) and that the buildup in assets under
management is generally tied to investment performance (i.e., managers with above-average
returns typically grow AUM faster than those with below-average returns).
Finally, these (convex) incentives produce behavioral effects in the agent, which is the main
subject of this section. Again, these effects are largely found in non-core funds.
V.A. Building Blocks: Utility, Effort & Likelihood
We next need a few building blocks with which we can better appreciate the behavioral
aspects of incentive fees. First among them are the ideas of utility and prospect theory (e.g.,
see Friedman and Savage (1948) and Kahneman and Tversky (1979)). The basic premise is
quite simple: In our case, investors (principals) and managers (agents) – more broadly,
decision makers – prefer bigger gains to smaller gains but at a declining rate, which leads to
risk aversion. These concepts are illustrated in Exhibit 51:
There are other examples of utilizing incentive contracts to solve agency costs (perhaps most
notably in the area of employment contracts) – including for other alternative investments (e.g., see
Anson (2012)).
104
84
Exhibit 51: Illustration of Utility Theory and Risk Aversion
u($2,000)
u($1,000)
Utility
(.5)u($2,000) + (.5)u($0)
u($0)
($1,000)
($500)
$0
$1,000
$500
$1,500
$2,000
$2,500
Monetary Gain/(Loss) - in $ thousands
The blue curve represents the individual’s utility over a range of gains and losses. At some
point, the utility of future gains begins to slow. This decline in the marginal utility of gains
gives rise to risk-averting behavior. 105 Perhaps an example perhaps bests illustrate the point.
Consider a gamble or a prospect in which an individual will either receive $1 million with
certainty (represented by the blue dot) or will receive either $2 million or $0 (represented by
the two maroon dots) with equal probability. Exhibit 51 indicates that the utility of $2
million is less than twice the utility of $1 million and, accordingly, risking a certain $1 million
for the chance of winning $2 million but losing everything is unacceptable to this individual.
More formally, decision makers consider the probabilities 106 associated with uncertain
outcomes when evaluating these prospects; the utility of (u) each outcome is weighted by its
probability (as shown by the black square for the gamble of winning $2 million or losing
everything) and the prospect with the higher expected utility is preferred. Using our twooutcome illustration: u($1,000) > [u($2,000) + u($0)] (½).
Each individual has his/her own utility function; the curvature of which may differ from that
shown above. It is believed that individuals generally display risk-averting behavior with regard to
gains and risk-seeking behavior with regard to losses. This is reflected in the concave portion of the
blue curve gains and the convex portion for losses. If an individual were risk-neutral, then the blue
curve would become a straight line.
105
Kahneman and Tversky (1979) argue that individuals use decision weights (a tendency to overweight low-probability events and to over-weight high-probability events) – rather than probabilities
– to assess such prospects, relative to the individual’s initial wealth.
106
85
Second, let’s consider some positive relationship between the manager’s efforts and the
fund’s asset-level returns. (Unfortunately, there is little empirical research suggesting the
precise shape of this relationship.) Exhibit 52 illustrates one potential 107 relationship:
Return on Assets
Exhibit 52: Hypothetical Illustration of
Return on Assets v. Manager's Effort Level
-3.00
-2.00
-1.00
Low
0.00
Manager's Effort Level
1.00
2.00
3.00
High
The central idea is that low managerial effort leads to below-market results and high
managerial effort leads to above-market results – notwithstanding the idiosyncratic effects of
random factors on the fund’s assets – with some notion that the marginal productivity of
effort is declining at high effort levels (so, no matter how hard the manager works, there is
some inherent ceiling on returns). However, expending effort is costly to the manager;
therefore, the manager must believe it is plausible that its promoted interest will end up “in
the money.” (See §III.C.3.a.(i) regarding renegotiation issues surrounding “out of the
money” promoted interests.) Exhibit 53 presents one potential relationship (here too, there
is little empirical support) between the manager’s effort and the likelihood of the manager
realizing its promoted interest:
For purposes of simplifying this illustration, the random effects of the market’s idiosyncratic
factors have been ignored. A more complete model might look something like:
ka = min ( ka ) + Φ (W ) + e where: ka = asset-level returns, min(ka) = minimum asset-level returns,
107
Φ = the cumulative normal distribution function, W = work or effort (3 ≥ W ≥ -3) and e = a
( (
random “noise” factor ~ N 0, σ w2
)) .
86
Exhibit 53: Hypothetical Illustration of
Manager's Effort Level v. Probability that Manager's Option Is in the Money
400%
High
300%
200%
Manager's Effort Level
100%
0%
-100%
-200%
-300%
Low
-3.0000
-2.0000
Low
-1.0000
-400%
0.0000
1.0000
Probability of Manager's Option in the Money
2.0000
3.0000
High
Let’s now examine these building blocks in light of the manager’s promoted interest.
V.B. In-the-Money Promote ← Behavioral Effects
Over the life of the fund, but particularly after the midpoint of the fund’s expected life, the
investment manager partly views the fund’s performance through the prism of the likely
promoted interest. To the extent that the promoted interest is likely to end up “in the
money” (i.e., is likely to be realized), the investment manager tends to take conservative
actions (sometimes referred to as “hugging the benchmark” or, in other cases, “closet
indexing”) in order to preserve its promote.
To better understand this assertion, consider the following illustration. Assume that the
fund’s performance currently exceeds the investor’s preferred return and, accordingly, the
manager’s promoted interest is “in the money” at some interim date (t1). Further assume
that, for convenience, the manager has two choices: a) take a conservative action such that
the promoted interest remains “in the money” at the fund termination date (t1 = t2) or b) take
some risky action such that the promoted interest either doubles (t’’2) or falls to zero (t’2),
with equal probability, at the fund termination date. These concepts are illustrated in Exhibit
54:
87
Exhibit 54: Illustration of Manager's Choices
when the Promoted Interest is "in the Money"
25%
Manager's Promoted Interest
Estimated Frequency of Fund-Level Returns
20%
15%
Manager's Promoted Interest
10%
5%
t' ' 2
t1 = t2
-80%
-60%
-40%
-20%
0%
t' 2
20%
40%
60%
80%
0%
100%
Likely Returns
To help orient the reader: As before, the blue bell-shaped curve represents the fund’s
expected return before the investment manager’s promoted interest, while the red kinked
line represents the manager’s promoted interest at varying levels of fund profitability. The
blue dot on the kinked line represents the manager’s promoted interest at some interim date
(t1) which is currently “in the money.” If the investment manager takes conservative actions,
it is expected that its promoted interest will remain unchanged (t1 = t2). The two maroon dots
represent the two possible outcomes (of equal probability) if the investment manager takes
some risky action; its promoted interest either doubles (t’’2) or falls to zero (t’2) at the fund
termination date.
Assuming that the investment manager is risk-averse, the utility of maintaining the existing
(in-the-money) promote is greater than the expected utility of the gamble which results in
the promote either doubling or falling to zero, as illustrated in Exhibit 55:
88
Exhibit 55: Illustration of the Utility of Manager's Potential Actions
Assuming the Promote Is "In the Money"
Utility
u(t1 = t2)
> 1/2 u(t' 2) + 1/2 u(t"2)
u(t" 2)
u(t1 = t2)
u(t' 2)
0
Manager's Promoted Interest
Because the utility of preserving the existing promote (t1 = t2) is greater than the expected
utility of gambling on the promote either doubling (t’’2) or falling to zero (t’2) – with equal
probability – at the fund termination date for the risk-averse investment manager (i.e., a
manager for which there is declining marginal utility in further gains), the manager takes on
the conservative action of maintain the existing promote. 108
Moreover, we can think of marginal utility as encompassing more than just the profits
earned from the promoted interest in the current fund. Another aspect is, for example, the
impact of the fund’s return on the manager’s track record (see, e.g., Chung, et al. (2012)). If it
is the case that the fund’s return at the current level (which, in turn, produces a promoted
interest equal to t1 = t2) places the manager’s performance in the top tier of its competitors,
then this level of return may be sufficient for future fund-raising efforts. Similarly, if it is the
case that losing the gamble on the risky action (i.e., the promote of t’2 is realized) and, in
turn, this produces a fund-level return which is merely mediocre with regard to the
manager’s peers, then this prospect may severely damage the manager’s future fund-raising
efforts. As a stark example, assume the fund’s return is 20% per annum with conservative
A risk-neutral manager would be indifferent between the certain promote (t1 = t2) and the gamble
of the promote either doubling (t’’2) or falling to zero (t’2), with equal probability. Furthermore, Ross
(2004) reminds us, in a slightly different context, that the manager’s utility curve may change shape as
the manager experiences gains (and losses) from this fund and/or others and, accordingly, it can be
precarious to make universal statements about risk-averting v. -seeking behavior.
108
89
actions (i.e., t1 = t2); but, it is either 40% if the risky action succeeds (i.e., t’’2) or 0% if the risky
actions fails (i.e., t’2). It may well be the case that the investment manager’s future fundraising efforts are more harmed by a return of 0% than helped by a return of 40%. If so, the
investment manager concludes it is best to select the conservative action, thereby producing
a return of 20% and not jeopardizing future fund-raising efforts. 109
While the tradeoffs between conservative and risky actions can be illustrated in myriad ways,
let’s utilize a simple example. Assume that a significant amount of the fund’s properties have
leases which are about to expire at some interim date (t1) of the fund. Further assume that
the investment manager can either execute new (triple-net) leases with strong-credit tenants
at $12 per square foot or with weak-credit tenants at $14 per square foot and that the
market-clearing capitalization rate is 6% in the case of strong-credit tenants and 7% in the
case of weak-credit tenants. So, the current market value of the new lease is $200 per square
foot in either case. At the fund’s termination date (t2), the strong-credit tenants are still
expected to be valued at the market-clearing capitalization rate of 6% and, therefore, will
continue to be worth $200 per square foot – thereby preserving the manager’s promoted
interest (t1 = t2). On the other hand, the weak-credit tenants have some economic event 110
that will either be favorably or unfavorably resolved, with equal probability, before the fund’s
termination date. If the economic event is favorably resolved, the market-clearing
capitalization rate for these tenants will fall to 6% (the same as strong-credit tenants) and,
therefore, the leased space will increase in value to $233 per square foot – thereby doubling
the manager’s promoted interest (t’’2); if the economic event is unfavorably resolved, the
market-clearing capitalization rate will jump to 8.4% and, therefore, the leased space will
decrease in value to $167 per square foot – thereby erasing the manager’s promoted interest
(t’2). These tradeoffs 111 are summarized in Exhibit 56:
109 Robinson and Griffiths (2012) suggest that cash-flow distributions and liquidations also occur
earlier when the manager’s carried interest is in-the-money.
110 Here too there are myriad possibilities; however, let’s consider just a few of these events (i.e., the
resolution of): bringing a new product to market, adjudication of a major lawsuit, the final status of a
pending patent, a change in technology, etc.
This is an illustration about risk-taking – not skill (which is the persistent ability of an investment
manager to produce positive alpha). This illustration presents what is often referred to as a “fair”
gamble, wherein the certain outcome equals the expected value of the gamble: t1 = t2 = [t’’2 + t’2](½).
111
90
Exhibit 56: Illustration of Manager's Choice between Stong- and Weak-Credit Tenants
When Manager's Interim Promote Is "In the Money"
Tenant
t1
t2
Value of
Credit
Type
Lease
Rate/sq. ft.
Capitalization
Rate
Building
Value/sq. ft.
Lease
Rate/sq. ft.
Capitalization
Rate
Building
Value/sq. ft.
Promoted
Interest
Strong
$12.00
6.0%
$200.00
$12.00
6.0%
$200.00
t1 = t2
50%
$14.00
6.0%
$233.33
t' ' 2
50%
$14.00
8.4%
$166.67
t' 2
Weak
$14.00
7.0%
$200.00
In this simple example, the investment manager is best served (in the sense of maximizing
expected utility) by selecting the conservative action – as indicated by the shaded region of
Exhibit 56 – and thereby preserving its existing in-the-money promoted interest. It should
also be noted that this sort of behavior is not confined to managers with incentive fees in
their investment management contract. As noted earlier, core funds – generally operating
without an incentive fee – are still motivated to post above-average returns, as a means of
attracting greater assets under management. Consequently, a (typically, core) investment
manager without an incentive fee, which has so far realized above-average performance, is
also more likely to consider the conservative action.
V.C. Out-of-the-Money Promote ← Behavioral Effects
Assume the same fact pattern as above, except that the manager’s promoted interest is out
“of the money” at some interim date (t1). Further assume that, for convenience, the manager
has two choices: a) takes a conservative action such that the promoted interest remains out
of the money at the fund termination date (t2) or b) take some risky action such that the
expected value of the promoted interest either improves substantially (t’’2) or remains at zero
(t’2), with equal probability, at the fund termination date. These concepts are illustrated in
Exhibit 57:
91
Exhibit 57: Illustration of Manager's Choices
when the Promoted Interest is "Out of the Money"
25%
Manager's Promoted Interest
Estimated Frequency of Fund-Level Returns
20%
15%
Manager's Promoted Interest
10%
5%
t' ' 2
t' 2
-80%
-60%
-40%
-20%
0% t1 = t2 20%
40%
60%
80%
0%
100%
Likely Returns
To help orient the reader: The blue dot on the kinked line represents the manager’s
promoted interest at some interim date (t1) which is currently “out of the money.” If the
investment manager takes conservative actions, it is expected that its promoted interest will
remain unchanged (t1 = t2). The two maroon dots represent the two possible outcomes if the
investment manager takes some risky action; its promoted interest either improves
substantially (t’’2) or remains at zero (t’2) at the fund termination date.
Clearly, the utility of maintaining the existing (out-of-the-money) promote is less than the
expected utility 112 of the gamble which results in the promoted interest either improving
substantially or remaining at zero, as illustrated in Exhibit 58:
While Exhibit 58 utilizes a declining marginal utility of future gains (i.e., risk-averting) to be
consistent with the previous section, this result holds regardless of the manager’s utility function and,
therefore, whether the manager is risk-averting, -seeking or -neutral.
112
92
Exhibit 58: Illustration of the Utility of Manager's Potential Actions
Assuming the Promote Is "Out of the Money"
Utility
u(t1 = t2)
< 1/2 u(t' 2) + 1/2 u(t"2)
u(t" 2)
u(t1 = t2) = u(t'2)
0
Manager's Promoted Interest
Because the utility of preserving the existing promote (t1 = t2) is less than the expected utility
of gambling on substantially improving the promoted interest (t’’2) or remaining at zero (t’2)
– with equal probability – at the fund termination date, the investment manager takes on the
risky action of improving the promoted interest.
Assume the same fact pattern as before in terms of market rents for strong- and weak-credit
tenants. At the fund’s termination date (t2), the strong-credit tenants are still expected to be
valued at the market-clearing capitalization rate of 6% and, therefore, will continue to be
worth $200 per square foot – thereby preserving the manager’s out-of-the-money promoted
interest (t1 = t2). On the other hand, the weak-credit tenants have some economic event that
will either be favorably or unfavorably resolved, with equal probability. If the economic
event is favorably resolved, the market-clearing capitalization rate for these tenants will fall
to 6% (the same as strong-credit tenants) and, therefore, the leased space will increase in
value to $233 per square foot – thereby substantially improving the manager’s promoted
interest (t’’2); if the economic event is unfavorably resolved, the market-clearing
capitalization rate will jump to 8.4% and, therefore, the leased space will decrease in value to
$167 per square foot – thereby keeping the manager’s promoted interest (t’2) out-of-themoney. These tradeoffs are summarized in Exhibit 59:
93
Exhibit 59: Illustration of Manager's Choice between Stong- and Weak-Credit Tenants
When Manager's Interim Promote is "in the Money"
t1
t2
Tenant
Credit
Type
Lease
Rate/sq. ft.
Capitalization
Rate
Building
Value/sq. ft.
Lease
Rate/sq. ft.
Capitalization
Rate
Building
Value/sq. ft.
Value of
Promoted
Interest
Strong
$12.00
6.0%
$200.00
$12.00
6.0%
$200.00
t1 = t2
0.5
$14.00
6.0%
$233.33
t' ' 2
0.5
$14.00
8.4%
$166.67
t' 2
Weak
$14.00
7.0%
$200.00
In this simple example, the investment manager is best served by selecting the risky action –
as indicated by the shaded region of Exhibit 59 – and thereby giving the manager a 50%
chance of realizing a substantial promoted interest. 113 As noted earlier, this sort of behavior
is not confined to managers with incentive fees in their investment management contract.
Consequently, a (typically, core) investment manager without an incentive fee, which has so
far realized below-average performance, is also more likely to consider the risky action.
However as noted earlier, there are other considerations. Foremost among these is that most
managers view the current fund as one of a series of future offerings. As such, investment
managers wish to avoid undue risk-taking (and other imprudent behavior) because it may
damage the manager’s track record – an important ingredient when raising capital for future
fund offerings. As a result, investment managers are inclined to avoid excessively risky
actions and, instead, focus their efforts elsewhere (e.g., other funds). That is, managers may
“limp” through the current fund – trying to avoid excessive under-performance relative to its
peers, while concentrating resources and efforts elsewhere. Clearly, this result is sub-optimal
for the investor.
Interestingly, Panageas and Westerfield (2009) find, in a study focusing on (non-real estate)
hedge funds with high-water marks, 114 that the indefinite (or, at least, indeterminate) life of
these funds has a disciplining effect on fund managers such that they consistently refrain
from selecting the risky action – as simply described above – as means of improving the
expected value of their option-like promoted interest. In the same regard, Figge, et al. (2012)
find that this disciplining effect fades in private-equity funds with finite lives. This indefinite
(or indeterminate) fund life is a key distinction between many private-equity funds and most
non-core real estate funds, where the latter generally specifies a five- to ten-year investment
horizon.
In the same way that this example does not rely on the manager exhibiting risk aversion, the weakcredit tenant’s chances of a favorable outcome does not have to equal 50%. Indeed, the chances may
be less and the manager may still make the riskier choice (i.e., leasing to the weak-credit tenant). This
is a form of risk-shifting or “asset substitution” – see Jensen and Meckling (1976).
113
That is, the fund manager receives a fraction (generally 20%) of the increase in the fund value in
excess of the last-recorded maximum.
114
94
V.D. Lowering Prefs & Promotes ← Improving Alignment of Interests?
If most non-core real estate funds lack the indefinite (or indeterminate) life of non-real estate
private equity funds, what can real estate investors do to improve alignment of interests with
their fund managers? What is a rational mechanism for invoking more effort (and, therefore,
higher expected returns) from the managers (but without unduly compensating the manager
or without invoking excessive risk-taking)? At least one approach to consider is lowering the
investor’s preferred return and the manager’s promoted interest. 115
As a means of examining this approach, let’s revert to our original example – as found in
Exhibits 10 and 11 – in which the fund’s expected return is 12% per annum, with volatility
of 15%, the investor receives a preferred return (ψ ) of 12% per annum and the manager
receives a promoted interest (ϕ ) of 20% of the residual profits. Under these assumptions,
the investor’s net expected return is 10.8% and the difference of 1.2% (i.e., .12 - .108 = .012)
represents the manager’s expected promote. Let’s consider this original example as the “base
case” – as indicated in the left-most column of numbers in Exhibit 60. Then, let’s consider
decreasing the preferred return in increments of one percentage point (as we move left to
right across Exhibit 60) and solving for the fund manager’s promote percentage (ϕ ) such
that investor’s expected net return remains unchanged (at 10.8%) and, therefore, the
expected value of the fund manager’s promoted interest also remains unchanged (at 1.2%)
over all pref-and-promote combinations.
Exhibit 60: Illustration of the Static Tradeoffs Between the Investor's Preferred Return and the Manager's Promoted Interest
Base
Case
Fund's Return Parameters:
Average Return (E [k ])
Sensitivity of Preference & Promote Structure
Standard Deviation (σk )
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
12.0%
15.0%
Investor's Preference (ψ )
12.0%
11.0%
10.0%
9.0%
8.0%
7.0%
6.0%
5.0%
4.0%
3.0%
2.0%
1.0%
0.0%
Residual Splits:
Investor
80.0%
81.6%
83.0%
84.3%
85.4%
86.4%
87.4%
88.2%
88.9%
89.6%
90.3%
90.8%
91.4%
20.0%
18.4%
17.0%
15.7%
14.6%
13.6%
12.6%
11.8%
11.1%
10.4%
9.7%
9.2%
8.6%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
12.0%
1.2%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
10.8%
15.0%
1.4%
13.6%
15.0%
1.3%
15.0%
1.2%
15.0%
1.1%
15.0%
1.1%
15.0%
1.0%
15.0%
0.9%
15.0%
0.9%
15.0%
0.8%
15.0%
0.8%
15.0%
0.8%
15.0%
0.7%
15.0%
0.7%
13.7%
13.8%
13.9%
13.9%
14.0%
14.1%
14.1%
14.2%
14.2%
14.2%
14.3%
14.3%
Manager (Promote = ϕ )
Allocation of Fund-Level Returns:
Likely Returns:
Fund-Level Returns (E [k ])
Manager's Promoted Interest (E[π])
Investor's Net Return (E [ν ])
Volatility (Standard Deviation): (a)
Fund-Level Returns (σ k )
Manager's Promoted Interest (σE[π])
Investor's Net Return (σ E [ν ])
(a)
(b)
Unless returns are perfectly correlated, standard deviations are not additive.
Because of the promoted interest(s), the distribution is no longer symmetrical; consequently, the standard deviation is an incomplete measure of dispersion.
To help orient the reader: The top highlighted row represents the lowering of the investor’s
preferred return in increments of one percentage point (such that the investor’s preferred
A similar assertion could be made with regard to joint ventures (§III.C.3.c) and the relationship
between the fund and the operating partner(s).
115
95
return begins at 12% and ends at 0%). The next highlighted row represents the investment
manager’s promoted interest (ranging from 20% to 8.6%) such that the investor’s expected
net return (of 10.8%), as shown in the third highlighted row, is unchanged across all prefand-promote combinations. Of course, this also implies the expected value of the
investment manager’s promoted interest also remains constant (at 1.2%). The bottom
highlighted row represents the volatility of the expected value of the manager’s promoted
interest. Finally, the four dashed boxes are meant to highlight some of the equivalent prefand-promote combinations as a means of facilitating the discussion.
From an implementation standpoint, notice that the change in the manager’s promoted
interest (necessary to preserve constant expected net returns) does not move in a ratable
manner with a change in the investor’s preferred return. For example, the manager’s
promoted interest is 20% when the investor’s preferred return is 12%. However, dropping
the preferred return in half to 6% does not imply that the manager’s promoted interest also
drops in half (to 10%); instead, the promoted interest drops only to 12.6% (i.e., drops by
approximately 37% rather than 50%). So, investors and managers must exercise care and
rigor when framing a discussion about the tradeoffs involved when changing the preferred
return and the promoted interest. Their views on expected (fund-level) returns impact the
computations necessary to solve for these equivalencies. Of course, their views may differ
and, consequently, investors and managers may have differing views on what pref-andpromote structures constitute equivalent outcomes. 116
Two important insights can be gleaned from Exhibit 60. These insights can make the
reduction in the preferred return and in the promoted interest a “win/win” for both the
investor and the manager.
First, the uncertainty of the manager realizing its promoted interest fades as the investor
lowers its preferred-return requirement. This is intuitive and statistically observable (see the
bottom highlighted row above). 117 Therefore, the risk-averse investment manager (i.e., cares
about the trade-off between E(π) and σE(π)) should be willing to accept a lower promoted
Interestingly, the European Securities and Markets Authority (EMSA) requires that European
Union members incorporate the Alternative Investment Fund Mangers Directive (AIFMD) into
domestic law by July 2013 and that managers of alternative investment funds (AIF) must be
authorized under AIFMD by their national regulator before July 2014. The basic principle of the
AIFMD is that manager remuneration policies must promote sound and effective risk-management.
See Rodrigues (2013).
116
To be more explicit: The probability that the manager’s promoted interest (π ) is in-the-money is
50% when the investor’s preferred return (ψ) is 12% and increases to approximately 65% when the
investor’s preferred return is lowered to 6% – given our assumptions about the distribution of gross
returns. (More generally, P[π > 0] = 1 – Φ(ψ).) However, the expected value of the manager’s
promoted interest [E(π )] is identical under both scenarios – because we have purposefully lowered
the manager’s share (ϕ )of excess profits as the investor’s preferred return is lowered. Said another
way, the manager’s promoted interest is characterized by lower probabilities and higher amounts in
the first scenario and by higher probabilities and lower amounts in the second scenario – such that,
on average, the expected values are identical under both scenarios.
117
96
interest (ϕ) than that shown above. How much less is a function of the manager’s risk
aversion. Specifying the form of the manager’s risk aversion and solving for the lower
promoted interest is beyond the scope of this paper. 118 Obviously, a reduction in the
manager’s promoted interest beneath that shown in Exhibit 60 improves the investor’s
expected return – as compared to the base case. Therefore, both parties find it in their best
interests to collaborate to lower the preferred return and the promoted interest from the
base case.
Second, Exhibit 60 treats the fund-level returns as static (or exogenous). They are not. As
noted earlier (§V.A), the fund’s expected return is a function of the manager’s effort and, in
turn, the manager’s effort is a function of the likelihood that the manager’s promoted
interest will be “in the money.” That is, fund-level returns are endogenous. Consider Exhibit
61 as an illustration of this endogeneity property:
Nevertheless, it may be important to some readers as how to proceed. So, here is a sketch of the
approach: Identify the form of the manager’s risk aversion (e.g., power, quadratic, logarithmic, etc.)
and parameterize that form. As just one of many possible examples, consider the case of power
118
w1− χ
, where: w = wealth (restate E(π) into $) and χ = the coefficient of relative riskutility: u ( w ) =
1− χ
aversion. Then, solve such that the manager’s expected utility is identical under both combinations of
preferred returns (ψ1 v. ψ2) and promoted interests (ϕ1 v. ϕ2), given the distribution of fund-level
  ∞
  ∞


returns (E[k], σk) : u  ϕ1 ( k −ψ 1 ) f ( k )   dk =
u  ϕ2 ∫ ( k −ψ 2 ) f ( k )   dk .
∫


  ψ1
  ψ 2


97
Exhibit 61: Illustration of Market Opportunity Set
vis-a-vis Fund-Specific Returns as a Function of Manager's Effort
Expected Gross Return (k e)
Market Opportunity Set
(Core Properties with Leverage)
Maximum Effort
Fund-Specific
Performance as
f(Manager's Effort)
Minimum Effort
Volatility of Expected Return (σe )
Exhibit 61 contrasts the market’s opportunity set (shown in blue) with an attempt to
illustrate that fund-specific returns improve and risk declines as the investment manager
applies more effort. As the fund-specific returns cross the market’s opportunity set, the fund
produces positive alpha. Again, this increasing application of effort is a function of lowering
the investor’s preferred return and thereby improving the likelihood that the manager’s
realized promote will be in-the-money.
These two insights suggest that both the investor and the manager can benefit by reducing
the preferred return and the promoted interest. The lowered pref improves the chances of
the manager realizing its promoted interest; so, the manager is willing to accept yet a lower
promote which, in turn, leads to more effort and higher returns on average. In essence, this
reduction can create a “win/win” situation for both the investor and the manager.
Anecdotally, it seems that market transactions often lead, in the other direction, to higher
prefs. While this result may permit the investor some initial euphoria, such an arrangement
may ultimately be to the detriment of both parties.
VI. An Empirical Illustration
This section is intended to tie together the previous sections by examining the realized
performance of private real estate funds by their three major strategies (or classifications):
core, value-added and opportunistic. We want to say something, which is based both in
98
evidence and in rigorous theory, about the realized performance of core and non-core funds.
So, let’s sketch a bit of a roadmap by identifying the big questions to be asked: First, what do
the realized returns by strategy look like? Second, how can we use financial theory to
produce estimates of risk-adjusted returns? Third, how shall we interpret the results?
VI.A. The Performance Data
As a starting point, we will utilize the NCREIF-Townsend Fund Returns 119 data set, which
reports gross and net returns by strategy/classification through 2012. While returns are
available before 1996 (particularly for the core funds), the general consensus seems to be
that 1996 represents the first year in which the sample size is sufficiently robust across all
three strategies, but particularly for the non-core funds. In addition to the well-known
problem of appraisal smoothing – see, for example, Geltner (1993) – there are a number of
other problems relating primarily to the data for non-core funds; these include:
“survivorship” bias, voluntary reporting, inconsistent reporting, 120 mark-to-market staleness,
incomplete capture of non-core funds, etc. We will attempt to correct the data for only the
first of these problems (i.e., survivorship bias). The remainder of the problems represents
potential infirmities in the data and readers, therefore, ought to exercise caution when
reviewing and interpreting the results that follow. (In fact, even the title of this section,
“Empirical Illustration,” is a bit of an oxymoron; it is meant to convey that this section
illustrates how one might proceed to analyze the performance data if one had substantial
confidence in the data.) One last caveat before we begin: The returns that follow represent
average fund performance by strategy. As with any average, some funds (and potentially
families of funds) performed above-average while other performed below-average. The
identity of each fund was masked by the data provider (NCREIF-Townsend); thus, we have
no way to tell which funds outperformed their peers and which underperformed.
Taking the reported gross and net returns at face value, we first compute the value-weighted
(arithmetic) average 121 return and its volatility for funds representing these three strategies
and plot them in risk/return space – as illustrated in Exhibit 62. The blue-colored dots
represent the gross returns from the three strategies, while the red-colored dots represent the
net returns (i.e., the impact of fees, costs and promoted interests) from each of these three
strategies. [For purposes of comparison, the NCREIF Property Index (“NPI”) is shown as
the green-colored diamond. Note that the gross return from the average core fund was less
The core funds represent NFI-ODCE index, while both the value-added and opportunistic fund
represent “all funds” category within each non-core strategy; for more information, please see:
https://www.ncreif.org/townsend-fund-returns.aspx
119
For example, most core funds report in a manner proscribed by the Real Estate Information
Standards (http://www.reisus.org/index.html), whereas most non-core funds do not.
120
The use of the arithmetic average – as compared to the geometric (or compounded) average – as
the metric of comparison is preferable for reasons outlined by McLean (2012). However, recall that
2
the geometric average ( 
k ) is roughly equal to the arithmetic average ( k ) less half the variance σ :
121
( )
σ ; e.g., see Bodie, et al. (1992) for this well-known result. Messmore (1995) refers to the

k ≈k −
2
2
difference between the geometric and arithmetic averages as the “variance drain” while Arnott
(2005), in a slightly different context, refers to this difference as the “cost of risk.”
99
than the NPI; this illustrates the difficulties of managers beating the “passive” benchmark –
see §IV.C.]
Exhibit 62: Reported Performance by Fund Type for the
17-Year Period Ended December 31, 2012
18%
Opportunistic
16%
14%
Average Annual Returns
12%
NPI
Core
10%
Value-Added
8%
6%
Gross Returns
Net Returns
4%
2%
0%
0%
5%
10%
15%
20%
25%
Volatility
Source: NCREIF/Townsend and Author's Calculations
The vertical difference between the gross and net returns (by strategy) represents the sum of
the manager’s base and incentive fees. 122 On average, the difference between gross and net
returns is approximately 105 basis point for core funds, 165 basis points for value-added
funds and 350 basis points for opportunity funds. 123 The key question asked by prudent
investors is: Were the higher fees for non-core funds worthwhile? The balance of this
section attempts to answer this important question. The horizontal difference between the
gross and net returns (by strategy) represents the observed reduction in volatility due to
incentive fees; as noted earlier (see §III.B.2), this reduction is a statistical illusion – as the
investor retains all of the downside risk.
From the vantage point of Exhibit 62, it is apparent that value-added funds have, on
average, underperformed core funds: Not only were the net returns lower for value-added
funds lower than core funds’ returns, the value-added funds experienced more volatility;
122
Third-party fees and costs are deducted before computing gross returns.
Spek (2013) finds quite similar differences between gross and net returns, by strategy, using a
different data (comprising 440 (domestic and foreign) funds) and using a different methodology (he
models the ex ante total (base and incentive) fees assuming differing real estate returns by strategy).
123
100
accordingly, value-added funds significantly underperformed core funds on a risk-adjusted
basis. However, it is difficult to make a similar judgment about the performance of the
opportunistic funds: While the (net) returns were higher for opportunistic funds than for
core funds, the opportunistic funds experienced nearly twice the volatility; accordingly, it is
unclear whether the opportunistic funds over- or under-performed core funds on a riskadjusted basis.
But before moving on to that analysis, let’s also acknowledge that it is difficult to take the
opportunity funds’ returns at face value. The returns during and after the 2007-2008
financial crisis seem particularly implausible for the opportunistic funds. Consider the
comparison shown in Exhibit 63:
Exhibit 63: Reported Performance by Fund Type for the 17-Year Period Ended December 31, 2012
Gross (Value-Weighted) Returns
Year
NPI
Net (Value-Weighted) Returns
Non-Core
Core
Non-Core
Core
NFI-ODCE Value-Added Opportunistic NFI-ODCE
Value-Added Opportunistic
Arithmetic Average
1996-2006
12.56%
12.90%
15.00%
24.19%
11.81%
13.40%
20.27%
1996-2012
9.92%
9.49%
10.02%
17.02%
8.45%
8.38%
13.53%
%Δ
(21.05%)
(26.41%)
(33.21%)
(29.64%)
(28.45%)
(37.46%)
(33.23%)
4.16%
4.74%
6.72%
16.20%
4.67%
6.18%
13.68%
Standard Deviation
1996-2006
1996-2012
9.01%
12.27%
16.45%
21.45%
12.12%
16.05%
19.19%
%Δ
116.86%
158.84%
144.75%
32.42%
159.51%
159.56%
40.30%
As indicated above, the core funds’ returns during and after the financial crisis show more
volatility– relative to their pre-financial crisis returns – than do the opportunistic funds. As
one example, the volatility of ODCE returns increased from 4.74% during the pre-financial
crisis (1996-2006) to 12.27% for the period before, during and after the financial crisis
(1996-2012); this represents a percentage increase in volatility of 158.84%. Similarly, the
value-added funds experienced a percentage increase of 144.75%; however, the opportunity
funds experienced a percentage increase of only 32.42%. This seems an odd result; in most
every financial crisis, there is a “flight to quality” (with riskier assets (e.g., those assets found
in opportunity funds) falling more in value than less-risky assets (e.g., those assets found in
core funds)). Moreover, the presumed fall in asset values of the opportunistic funds would
be exacerbated by the generally higher leverage ratios of these funds. In this vein, serious
questions about the after-fee performance of domestic value-added and opportunistic
commercial real estate funds have been raised in the popular press – see, for example, Fitch
(2008) and Troianovski (2009).
What might explain this muted increase in volatility (over this particularly troubled time) visà-vis opportunity funds? Among the potential reasons, there are these: a) The data represent
a particular subset of investment managers for which returns were largely unaffected during
and after the financial crisis. b) The nature of the investment management contracts for
101
opportunity funds requires less frequent reporting of fair market valuations. If so, these
“stale” valuations fail to capture the true volatility of such investments. c) The underlying
property investments of the opportunity funds are more opaque than the properties of core
funds. Consequently, the appraisal of these opaque assets (as well as the mark-to-market
effects of funds’ indebtedness) is more imprecise. Some opportunistic fund managers may
have utilized this imprecision to their advantage, by constraining the (adverse) mark to
market of their portfolios. d) The data for opportunistic funds are susceptible to
“survivorship” bias (i.e., the tendency for poor-performing funds to stop reporting their
results). If so, the returns of the opportunity funds are overstated and the volatility of those
funds is understated.
We have evidence on only the last of these four possibilities. Specifically, a closer
examination of the opportunity fund data reveals that the NCREIF-Townsend returns only
aggregate funds which reported for all four quarters of a given year; however, the individual
quarters show more funds reporting than appear in the yearly data. 124 The disappearing funds
show no data in the following quarter and, consequently, we are left to ponder what became
of their return(s) in the following quarter(s). 125 Here too, there are several possibilities: the
disappearing funds were merged with reporting funds, the disappearing funds merely
stopped reporting but produced returns comparable to their peers, or the disappearing funds
were dissolved with the liquidated assets failing to completely repay the fund’s indebtedness
(i.e., equity investors lost their entire capital contribution). 126
One approach to estimating the magnitude of this survivorship bias is to assume that all of
the disappearing funds experienced a liquidation event equal to some portion, θ, of the
fund’s assets. In the case of θ equal to one, for example, the assumption is that all of the
investors’ capital was lost (i.e., a return of –100% in the period following the fund’s
disappearance); similarly, the case of θ equal to .5 represents the assumption that half of the
During and after the 2007-2008 financial crisis, the difference between those opportunistic funds
reporting for all four quarters in a given year and those reporting in less than four quarters averaged
21.4 funds (or 8.1% of total funds reporting). These disappearing funds are the focus of this inquiry.
Prior to the financial crisis, the difference averaged 16.3 funds (or 13.0% of total funds reporting).
However, the reasons for the differences may be very different: Prior to the financial crisis, the
difference largely relates to funds entering the data (the exclusion of these entrants may well mitigate
the anomalous results often associated with start-up results) due to the formation of new funds.
During and after the financial crisis, the difference might largely relate to funds leaving the data set
(and potentially contributing to the survivorship bias mentioned above) due to adverse performance.
124
The problems of survivorship bias and other difficulties are not confined to real estate funds. For
example, it is notoriously difficult to come by sound data on private-equity returns. For which, there
are a good number of investment styles (e.g., venture capital, leveraged buyouts, mezzanine financing,
currency overlays, etc.) and there are well-known problems of inconsistencies and selection bias. The
latter can substantially overstate the reported risk/return characteristics; for example, see Asness, et
al. (2001) and Cochrane (2005).
125
In those cases involving promissory notes backed by investor subscription agreements, some
investors were obligated to contribute additional capital – even though such contributions benefitted
only the creditor(s). (See §II.C for some of the complications involving unfunded commitments.)
126
102
investors’ capital was lost (i.e., a return of –50% in the following period). Because we have
no way of knowing the appropriate value of θ, Exhibit 64 illustrates the opportunity funds’
gross and net returns and their respective volatilities as θ ranges from zero to 100%
assuming that the survivorship-bias problem, if it existed, occurred in the period 20072011. 127
Exhibit 64: Reported Performance of the Opportunistic Funds for
the 17-Year Period Ended December 31, 2012
with Survivorship Bias Adjustment (θ )
18%
Gross Returns
θ =0
16%
θ = 0.5
Average Annual Returns
14%
Net Returns
θ =1
θ =0
12%
θ = 0.5
10%
θ =1
8%
6%
4%
2%
0%
15%
17%
19%
21%
Volatility
23%
25%
27%
Source: NCREIF/Townsend and Author's Calculations
Not surprisingly, our attempts to mitigate the potential survivorship bias (by varying θ )
worsen the opportunity funds’ return series – reducing the realized average return and
increasing the volatility of that return. Without any empirical support, we assume that θ
equals 50%. [§VI.C will examine the sensitivity of this assumption (θ = 50%).]
Unfortunately, the proposed (θ = .5) adjustment to the opportunity funds does little to
mollify our earlier-stated concerns about “stale” valuations and/or muted “marks” to market
for opportunity funds during and after the financial crisis. Comparing Exhibits 63 and 65, we
see that opportunity funds still show considerably less volatility as compared to core funds at
By 2012, we assume that the survivorship-bias adjustment (θ ) is no longer needed; instead, the
difference between the number of funds in the annual data as compared to the number of funds in
the quarterly data is more likely attributable to the formation of new funds – as was the case for the
difference in the period prior to the financial crisis.
127
103
the very time (during and after the financial crisis) that the opportunity funds should have
shown a significant increase in volatility.
Exhibit 65: Reported and Adjusted Performance by Fund Type
for the 17-Year Period Ended December 31, 2012
Gross (Value-Weighted) Returns
Year
NPI
Net (Value-Weighted) Returns
Non-Core
Core
Non-Core
Core
NFI-ODCE Value-Added Opportunistic * NFI-ODCE
Value-Added Opportunistic *
Arithmetic Average
1996-2006
12.56%
12.90%
15.00%
24.19%
11.81%
13.40%
20.27%
1996-2012
9.92%
9.49%
10.02%
15.18%
8.45%
8.38%
11.76%
%Δ
(21.05%)
(26.41%)
(33.21%)
(37.27%)
(28.45%)
(37.46%)
(41.98%)
4.16%
4.74%
6.72%
16.20%
4.67%
6.18%
13.68%
Standard Deviation
1996-2006
1996-2012
9.01%
12.27%
16.45%
23.04%
12.12%
16.05%
20.91%
%Δ
116.86%
158.84%
144.75%
42.22%
159.51%
159.56%
52.90%
* Adjustment to opportunistic funds, with θ = 50%.
While we will revisit the potentially overstated performance of the opportunity funds (during
and after the financial crisis) in §VI.C.1, for now we will accept the adjusted (θ =.5)
performance of these funds vis-à-vis other investment strategies as shown in Exhibit 66:
104
Exhibit 66: Reported and Adjusted Performance by Fund
Type for the 17-Year Period Ended December 31, 2012
18%
Opportunisitc
16%
θ = 0.5
14%
θ = 0.5
Average Annual Returns
12%
NPI
Core
10%
Value-Added
8%
6%
Gross Returns
Net Returns
4%
2%
0%
0%
5%
10%
15%
20%
25%
Volatility
Source: NCREIF/Townsend and Author's Calculations
We next turn to how we might assess the risk-adjusted performance non-core funds. As
noted earlier (see §III.A), viewing returns in the absence of their riskiness is a fool’s errand.
VI.B. Assessing Risk-Adjusted Performance
While “mainstream” finance might argue for utilizing some form of a factor model 128 to
disentangle systematic returns (“beta”) from positive (or negative) risk-adjusted performance
(“alpha”), those models typically require data sets which are more robust than that available
here. Moreover, their emphasis on efficient (public) markets generally includes assumptions
often violated in private markets (like commercial real estate). As a result, let’s instead use a
simpler technique: let’s use the “law of one price” and financial leverage to create a
risk/return continuum available to any institutional investor. Against the backdrop of this
continuum, we can then determine whether non-core funds outperformed (on a riskadjusted basis) core funds or vice verse.
Of such models, a popular single-factor model is the capital asset pricing model (CAPM) (e.g., see
Sharpe (1964)) and, among the multi-factor models, there are three-factor models (e.g., see Fama and
French (1992)) as well as models that include a fourth factor: “momentum” (e.g., see Carhart (1997))
or liquidity (e.g., Pástor and Stambaugh (2003)). Moreover, because the evaluation of venture capitallike payoffs is particularly challenging (e.g., infrequent and skewed payoffs covering varying time
horizons), some form of a standard stochastic discount factor may be utilized; for example, see:
Korteweg and Nagel (2013).
128
105
VI.B.1. Assessing Risk-Adjusted Performance – Theoretical Basis
The law of one price asserts that two assets which have the same pattern (i.e., the distribution
of risk and return) of expected cash flows ought to have the same price. If not, an arbitrage
opportunity exits: purchase the under-priced asset and simultaneously sell the over-priced
asset. As investors arbitrage away the pricing difference between the two assets, prices will
be brought to their equilibrium value. We use financial leverage to transform the risk/return
characteristics of the core funds into a higher-return/higher-risk strategy – by utilizing
equations (3) and (4) which are reproduced here for your convenience:
σa
(3)
σe =
1 − LTV
ke =
ka − kd LTV
1 − LTV
(4)
However, one important element of financial leverage on which equation (4) is silent is that
the cost of indebtedness (kd) as a function of the loan-to-value (LTV) ratio; as leverage
increases, lenders require an increasing spread (δ ) over the risk-free rate (rf) and
compensation for additional costs and structural differences (γ ) between the Treasury bond
market and the commercial mortgage loan market, as illustrated in Exhibit 67:
Interest Rate per Annum ( k d )
Exhibit 67: Illustration of the Cost of Indebtedness as a Function of Leverage
Mortgage Interest Rate
Default Risk (δ) Premium
Structural Differences (γ) in Payment Schedules, Servicing Fees, Etc .
Risk-free Rate
0%
15%
30%
45%
Loan-to-Value Ratio
106
60%
75%
Conceptually, the cost of indebtedness can be described as:
k d = rf + γ + δ
LTV
1 − LTV
(7)
The default premium (δ ) can be viewed as reflecting the put option129 available to borrowers
of non-recourse loans. The value of this put option increases as the loan-to-value ratio
increases. (To keep matters simple, it is assumed that the loan-to-value ratio and the debtcoverage ratio are mathematical inverses of one another.) Equation (7) is a much-simplified
version of more rigorous option-pricing models – e.g., see Merton (1974) and Titman and
Torous (1989).
Combining Equations (3), (4) and (7) enables us to transform unlevered core assets (or
funds) into higher-risk/higher-return strategies, as shown in Exhibit 68:
Exhibit 68: Illustration of "Law of One Price"
Lever Core Assets to Create Risk/Return Continuum
75% Leverage
Expected Return (k e)
50% Leverage
25% Leverage
k a : Unlevered Core
Fund Returns
0% Leverage
k e : Levered Core Fund Returns
Expected Volatility (σ e)
In both theoretical and practical terms, these levered core returns convert the lowreturn/low-risk starting point (ka) into higher-risk/higher-return strategies – solely as a
function of leverage (i.e., the underlying assets remain the same). This risk/return continuum
The borrower’s ability to “hand back the keys” without incurring further liability can be viewed as
an option granted to the borrower by the lender in return for a higher interest rate than would
otherwise be the case.
129
107
creates the benchmark by which other strategies can be measured. A more detailed
discussion is provided in Appendix 2. This continuum is an example of the law of one price
in action. The application of this law is critical to our evaluation of the performance of noncore strategies. Simply said, we ask ourselves how the non-core funds performed relative to
the investor’s alternative of merely leveraging core funds. Such a comparison is illustrated in
Exhibit 69:
Exhibit 69: Application of "Law of One Price"
Levered Core Assets v. Non-Core Funds
Out-Performing
Non-Core Fund
75% Leverage
Positive
Alpha
Expected Return (k e)
50% Leverage
Negative
Alpha
25% Leverage
Under-Performing
Non-Core Fund
k a : Unlevered Core
Fund Returns
0% Leverage
k e : Levered Core Fund Returns
Expected Volatility (σ e)
Consider two examples of the non-core fund’s performance. In the first instance
(represented by the green icon), the non-core fund out-performs the core-with-leverage
alternative. The measure of that out-performance is represented by the vertical line
extending upward from levered core returns (as represented by the blue curve) to the noncore fund’s return. This is a measure of the fund’s (positive) alpha and indicates that, for a
level of risk identical to the core-with-leverage alternative, the non-core fund provided
additional risk-adjusted return. In the second instance (represented by the red icon), the noncore fund under-performs the core-with-leverage alternative. The measure of that underperformance is also represented by the vertical line, this time extending downward from
levered core returns (as represented by the blue curve) to the non-core fund’s return. This is
a measure of the fund’s (negative) alpha and indicates that, for a level of risk identical to the
core-with-leverage alternative, the non-core fund failed to provide additional risk-adjusted
return. Note: the second non-core fund produced negative risk-adjusted returns (or alpha)
even though its return was higher than the unlevered core performance. (This is another
example of the earlier-cited (§III.A.4) misuse of the term “alpha.”)
108
Note that this continuum is curvilinear – rather than the classic linear relationship (e.g., see:
Sharpe (1964) and Treynor (1961)) between risk and return (§III.A) – due to the increased
cost of borrowing at higher leverage/volatility levels. The steeper the credit curve (i.e., the
higher the default premium (δ )), the more curvature is found in the law-of-one-price
continuum. If, instead, instead one assumes a constant borrowing (and lending) interest rate
– as in the classical finance models of asset-pricing – then riskier strategies are penalized
more heavily (e.g., the positive alpha illustrated in Exhibit 69 would be smaller and negative
alpha would be larger). The other significant departure from classical asset pricing is risk (the
horizontal axis) as measured by total risk (σι) – rather than systematic risk (βι). As such, this
approach essentially assumes that each index – for a given strategy – is highly correlated with
the market return. 130
This notion of levered (core) returns provides the foundation by which we will compare the
performance of the core funds within the NCREIF-Townsend Fund Returns data set to the
non-core funds. (In the alternative, we could attempt to de-lever non-core fund returns;
however, the data are simply not available to do so.) Moreover, levering the core funds is a
far easier task because few of these funds have incentive fees, whereas the non-core funds
more typically have incentive fees – making problematic the computation of estimated net
returns without knowing each non-core fund’s preference-and-promote structure.
VI.B.2. Assessing Risk-Adjusted Performance – Practicalities
To implement the law of one price, we need to estimate two sets of parameters: a) the initial
leverage ratio, on average, of the core funds in the NFI-ODCE Index, and b) the
components that produce the leverage-appropriate interest rate: the risk-free rate (rf ), the
structural frictions (γ ), the default premium (δ ) and the loan term (N). 131 These parameters
must be estimated annually, such that we can synthetically create core funds’ returns at
successively higher leverage ratios for each year of the analysis.
VI.B.2.a. Estimating Core Funds’ Leverage Ratios
Let’s look at each of these parameters individually, beginning with the initial leverage ratio.
While our return data by fund strategy extend back to 1996, data on the average leverage
130
Recall the classic single-factor asset-pricing model (§III.A.3), in which β i = ρi , Mkt
σi
is a
σ Mkt
measure of correlated volatility. To focus only on the total risk (σι) of an index is tantamount to
assuming that each index is highly correlated with the market’s total risk. Because the market’s
volatility (σΜκτ) is a scalar, its exclusion does not impact the results. Finally, we are examining
aggregate results by strategy. These indices of fund-level performance – in all likelihood – have
diversified much of the idiosyncratic risks involved with fund-level investing. These assumptions are
further examined in Appendix 2.
131 For most of the analysis period, the default premium (δ ) varies little with the term of the
mortgage loan (N). This has changed as a result of the 2007-08 financial crisis; thereafter, spreads
over Treasuries on short-term mortgage loans are generally higher than long-term loans – all else
being equal – due to lenders’ concerns about “rollover” or “maturity” risk (i.e., the borrower’s ability
to refinance the loan upon its maturity).
109
ratios of the NFI-ODCE Index funds only extend as far back as June, 2004. Over the period
for which the data are available, the average leverage ratio is 23.9%. To simplify things, we
assume that the (rounded) observed average (24.0%) is representative of the earlier period as
well. 132 The data and its extrapolation are illustrated in Exhibit 70:
Exhibit 70: Observed & Averaged Leverage Ratios
for NFI-ODCE Funds for the Period January, 1996 through December 2012
35%
30%
25%
Averaged
Leverage
Ratios
Observed
Leverage
Ratios
20%
15%
10%
5%
0%
The spike in observed leverage ratios (2009-10) is largely the result of falling property values
(and not investors’ decision to increase borrowing levels). The effect of this spike is to push
observed leverage ratios above the levels targeted by fund managers. Nevertheless, we will
use a presumed initial leverage ratio of 24.0% in all (1996-2012) periods. This is relatively
small departure from the observed (2004-2012) values and is, of course, correct on average.
132 We could have complicated the matter by extending the (linear) trend of reported data back to
1996. This approach produces an average leverage ratio of 13.3% during the period (1996-2004) for
which the data is missing. As a result, the leverage ratio averages 18.65% over the entire (1996-2012)
time period. However, an examination of the levered ODCE properties (but excluding fund-level
debt) in the NPI indicates that the leverage ratios are quite similar for the two periods (1996-2004 v.
2004-2012). Consequently, it was concluded that the averaged approach provides a more
representative estimate than the trended approach.
110
VI.B.2.b. Estimating Leverage Spreads
In order to estimate the annual interest cost, several steps are required. Using the data
underlying the Giliberto-Levy Commercial Mortgage Performance Index and the American
Council of Life Insurers (ACLI) Commercial Mortgage Commitments, we determine
estimated values for structural frictions (γ ) and the default premium (δ ) for each quarter by
identifying the loan’s interest rate relative to Treasuries (rf ) – using fixed-rate, conventional
mortgage loans on “core” properties – by fitting Equation (7), for each property-type and
each quarter. These quarterly values were then averaged to produce annual values and then
weighted by the proportion of each property type in the NCREIF Property Index during
each period to produce estimates of the annual interest rate for core funds for various
leverage ratios. The results are summarized in Exhibit 71:
Exhibit 71: Estimates of the Annual Interest Rate
at Various Leverage Ratios for the Years 1996 through 2012
12%
Interest Expense at 75% LTV
10%
Estimated Annual Interest Expense (k d )
Interest Expense at 50% LTV
8%
Interest Expense at 25% LTV
6%
4%
Structural Differences (γ)
2%
Risk-free Rate
0%
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
Exhibit 71 also displays the three-year Treasury bond (along with an estimate of the
structural frictions (γ)) as a means of indicating the magnitude of the default premium
(δ LTV (1 − LTV ) ) for various leverage ratios at varying points in time. Not surprisingly,
these premia wane before the 2007-08 financial crisis, spike immediately thereafter, and
partially recede more recently. Capturing the variance in default premia (or “spreads”) is an
important part of utilizing financial leverage to extend the law of one price to a comparison
of core and non-core funds.
111
VI.B.2.c. Estimating the Term to Maturity
In order to fairly compare the performance of core funds to non-core funds, it is important
to match the term of the loans in the various fund types. Said another way, we would like to
strip away the effects of varying maturities – presuming that neither core or non-core funds
intended to “play” interest-rate maturities 133 as part of their real estate strategy. Consider the
long-run view of Treasury rates, as shown in Exhibit 72. As a general rule, levered real estate
investors were better served by locking in fixed rates associated with long-dated maturities
prior to 1980; thereafter, the opposite is true.
18%
Exhibit 72: Historical Path of Treasury Bond Interest Rates
for 1- and 10-year Maturities for the Period 1954 through 2012
16%
14%
12%
10%
8%
6%
4%
2%
0%
1-Year Treasury
10-Year Treasury
Typically, the choice of loan maturity is tied to the expected holding period of the fund’s
assets. As a general rule, core funds have longer expected holding periods than non-core
funds and, consequently, core funds tend to have longer-dated loan maturities than their
non-core counterparts.
In the best of circumstances, we would match the maturities of the non-core funds to the
core funds (or vice versa). Unfortunately, we have very little evidence on the average loan
maturity by fund strategy. For purposes of this exercise, we speculate that the average
Very few real estate funds explicitly make a “directional bet” on the path of future interest rates.
Moreover, if real estate fund managers have significant skills with regard to forecasting future interest
rates, they may be better served by becoming bond fund managers.
133
112
maturity term of the core funds is seven years (i.e., N Core = 7) and that the average maturity
term of the opportunity funds 134 is three years (i.e., N Opportunity = 3). While there are many ways
to consider the appropriateness of this latter assumption, consider the opportunity fund
which has 40% of its indebtedness floating with the prime rate of interest and 60% of its
indebtedness represented by five-year, fixed-rate loans; its weighted-average term to maturity
is approximately three years. In any case, §VI.C will briefly examine the sensitivity of these
assumptions (N Core = 7 and N Opportunity = 3) in light of the risk-adjusted performance of the
non-core funds.
VI.B.2.d. The Term to Maturity & Unlevered Returns
Our assumption that the average maturity of the non-core funds’ indebtedness equals three
years implies that one third of the funds’ indebtedness is originated in the current year, one
third was originated in the prior year and the final third was originated two years earlier. This
pattern of loan originations is then overlaid on to the estimated cost of indebtedness in order
to produce an estimated annual interest cost for core funds, such that we can synthetically
create core funds’ returns at successively higher leverage ratios for each year of the analysis.
(For example, N = 3 implies a rolling three-year average of three-year maturities for a given
leverage ratio.)
As a matter of perspective and as shown in Exhibit 73, the rolling three-year interest expense
(kd) is plotted in comparison to unlevered real estate returns (ka), as indicated by the
NCREIF Property Index (NPI).
Because it is clear from Exhibit 62 that value-added funds have under-performed core funds on a
risk-adjusted basis, we focus here solely on opportunity funds.
134
113
30%
Interest Expense at 75% LTV
25%
Interest Expense at 50% LTV
Interest Expense at 25% LTV
Estimated Annual Interest Expense (k d )
10%
20%
15%
5%
10%
5%
0%
0%
-5%
-5%
-10%
Annual NCREIF Property Index Returns (k a )
15%
Exhibit 73: Estimates of the Annual Interest Expense in Comparison
to (Unlevered) Real Estate Returns for the Years 1996 through 2012
-15%
-10%
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
-20%
At leverage ratios of 25% and 50%, real estate investors experienced positive leverage –
because (unlevered) real estate returns exceed the cost of indebtedness – in all years but 2008
and 2009. At a leverage ratio of 75%, real estate investors experienced positive leverage in all
years but 2001, 2002, 2008 and 2009. (The differences in the ranges of the vertical axes make
this comparison less visually apparent.)
However, NPI returns generally exceed core-fund returns (as proxied by the ODCE Index)
– see Exhibit 62 – and, accordingly, we transform Equation (4) to produce an estimate of the
unlevered core-fund/ODCE returns ( ka ,ODCE ) as follows:
ka ,ODCE= ke,ODCE (1 − LTV ) + kd LTV
(8)
where the cost of indebtedness (kd) is a function of ODCE’s average leverage ratio of 24%
and assumed average maturity of seven years. Finally, the estimated unlevered corefund/ODCE returns ( ka ,ODCE ) is used as the basis for utilizing greater levels of leverage in
order to employ the law of one price. Ultimately, this exercise is imprecise because it is
difficult to capture the mark-to-market effect on the fixed-rate debt used within the ODCE
funds. And, in a falling-rate environment (much of what had been experienced during the
time frame of this study), the fair market value of the liability increases – which reduces the
return on equity. So, fixed-rate debt would initially experience rising costs (after
114
consideration of the “mark” and the loan’s interest rate), while floating-rate debt would
experience falling costs (because of the (generally) lowering interest rates). Unfortunately, the
proportion of fixed- to floating-rate debt within ODCE is not available. Moreover, if debts
are held to maturity, the fair-market and book values ultimately converge.
VI.B.3. Assessing Risk-Adjusted Performance – Implementation
We are now in a position to implement the law of one price and assess the risk-adjusted
performance of core and non-core funds. To do so, we begin with leveraging the net core
(ODCE) returns using the estimated cost of indebtedness described above; we begin with a
leverage ratio of 24%, then 25% and thereafter step the leverage ratio in increments of five
percentage points. This is done for each year of the analysis. When finished, we have a
risk/return continuum of net core returns – as shown in Exhibit 74:
Exhibit 74: Reported and Adjusted Performance by Fund Type
for the 17-Year Period Ended December, 2012
with Levered Core Creating the Law-of-One-Price Continuum
16%
Opportunistic
( θ =.5)
14%
Average Annual Compounded Returns
55% LTV
12%
NPI
Core
10%
Value-Added
60% LTV
45% LTV
8%
24% LTV
35% LTV
6%
4%
Gross Returns
Net Returns
2%
0%
0%
5%
10%
15%
20%
25%
Volatility
For the reader’s convenience, selected leverage ratios (24%, 35%, 45%, 55% and 60%) along
the law-of-one-price continuum have been indicated – to provide a sense of the degree of
leverage when employing a strategy of core-with-leverage. [An aside: The law-of-one-price
continuum does not begin exactly with the ODCE net returns. Why? Deleveraging the
ODCE returns assuming that the average debt maturity is seven years while re-leveraging
assuming that the average debt maturity is three years – in order to match the opportunity
funds – slightly improves the initial levered ODCE return while adding slightly more risk.]
115
As noted earlier, this approach elegantly produces a core-with-leverage alternative to which
most any institutional investor could avail itself. And, it does so without having to make
additional assumptions about the fee and pref-and-promote structures of the non-core funds
(i.e., most core funds charge fees on contributed capital and rarely have a substantive
incentive-fee arrangement135).
One last modification must be made before we make our risk-adjusted comparisons. As
noted earlier (§III.B.2), the reduction in the reported standard deviation of fund returns is
largely a statistical illusion. That is, the reduction in the dispersion (and, therefore, the
calculated volatility measure) is attributable to the investor forsaking some of the “upside”
return due to the incentive fee; meanwhile, the investor’s “downside” risk remains
unchanged. Consequently, we restate the standard deviations of the funds’ net returns such
that they are equal to the standard deviations of the funds’ gross returns. This is indicated by
the red squares in Exhibit 75:
Exhibit 75: Reported & Volatility-Adjusted Performance by Fund Type
for the 17-Year Period Ended December, 2012
with Levered Core Creating the Law-of-One-Price Continuum
16%
Opportunistic
(θ = .5)
Average Annual Compounded Returns
14%
12%
NPI
Core
10%
Value-Added
8%
6%
4%
Gross Returns
Net Returns - Unadjusted
2%
0%
Net Returns - Volatility-Adjusted
0%
5%
10%
15%
20%
25%
Volatility
The empirical support for this assertion about the lack of incentive fees can be observed by
comparing the standard deviation of gross and net returns for core funds. These two figures are
nearly identical; therefore, incentive fees play a small role for core funds.
135
116
The final step is to compare the restated non-core funds’ risk/return performance to the
core-with-leverage alternative, at the same level of volatilities 136 – as illustrated in Exhibit 76:
Exhibit 76: Estimated Alpha for Non-Core Funds
for the 17-Year Period Ended December, 2012
16%
Opportunistic
(θ = .5)
14%
Opportunity Funds'
Estimated Alpha: 6 bps
Average Annual Compounded Returns
12%
NPI
Core
10%
Value-Added Funds'
Estimated Alpha: (180) bps
8%
Value-Added
6%
4%
Gross Returns
Net Returns
2%
0%
0%
5%
15%
10%
20%
25%
Volatility
As shown in Exhibit 76, our estimates suggest that – on balance – the value-added funds
underperformed levered core funds (i.e, levered to produce identical volatility) by 180 basis
points (i.e., negative alpha of 1.80%). Given our earlier observations, these results are not
surprising. However, what can be considered surprising is that investors willingly paid such
large (base and incentive) fees for, on average, such mediocre performance (again, earlier
caveats with regard to data quality ought to be heeded). Instead, investors could have merely
applied more leverage to their core-fund investments and outperformed the (net) returns
produced by the value-added funds. Among other matters, it argues that investors ought to
revisit the preference-and-promote structure of the value-added funds.
These comparisons between the core-with-leverage and the non-core funds are imperfect. As
earlier noted (in §VI.B.1. and § III.B.2, respectively), the use of non-recourse debt effectively
provides a put option to the borrower and, consequently, the investor’s/borrower’s downside risk is
truncated; meanwhile, the inclusion of an incentive fee in the investment management contract
provides a call option to the fund manager and, consequently, the investor’s upside risk is truncated.
While we counteract this latter asymmetry by utilizing the standard deviation of gross returns, it
remains true that the levered borrower has a truncated distribution with regard to negative returns. In
fairness, this is also true of the non-core funds which almost invariably use high degrees of leverage.
Smetters and Zhang (2013) discuss measures to correct for non-normal risks.
136
117
Conversely, Exhibit 76 also shows that – on balance – the opportunity funds outperformed
levered core funds by 6 basis points (i.e., positive alpha of 0.06%). This small difference –
particularly when viewed in the context of an average opportunity fund return of
approximately 11.5% with a standard deviation of approximately 23% – is, statistically
speaking, indistinguishable from zero (here too, earlier caveats with regard to data quality
ought to be heeded). So, on one level, it could be argued that investors ought to be
indifferent between allocations to opportunity funds and to have merely applied more
leverage to their core-fund investments. However, on two other levels, this indifference can
be severely questioned.
First and as noted earlier, the data on opportunity funds’ returns during and after the
financial crisis looks suspicious; in particular, it looks like the volatility of those
returns was artificially dampened. 137 If so, the alpha estimated in Exhibit 76 is
overstated. If the overstatement is sufficient, then investors would have been better
served by having allocated to more highly levered core funds.
Second, the index returns shown here represent aggregate fund-type performance.
As such, these indices greatly dampen the idiosyncratic risks experienced by a single
fund. Yet, because no investor holds the index, all investors are exposed to some
amount of idiosyncratic risk. The more homogenous nature of the assets in core
funds suggests that the idiosyncratic risks may be far less when investing in core
funds as compared to investing in opportunity funds. If so, investors would have
been better served by having allocated to more highly levered core funds (as
compared to opportunity funds), because they would have received essentially the
same average return with much less idiosyncratic risk.
While both issues are addressed more substantively in the following section, the nearly
equivalent (net) risk-adjusted performance of core and opportunistic funds comes as little
surprise to believers in market efficiency (i.e., active investors arbitrage away the surplus that
one approach might temporarily hold over the other). 138 It seems that investors, by and large,
have (explicitly or implicitly) understood that investing in opportunity funds is an alternative
to utilizing higher degrees of leverage in their core portfolios. 139
To be fair, another possibility exists: the opportunity funds have greater global diversification –
such that their mix of developed and developing economies, mix of debt and equity holdings, mix of
currency holdings, etc. – produced less-volatile returns during this period of time. The data do not
permit us to examine this possibility.
137
Other than faulty data, the poor risk-adjusted performance of the value-added funds is more
difficult to explain away in theoretical terms.
138
139 Interestingly, the notion of utilizing higher leverage with portfolios of safer (i.e., core-type) assets
seems to be precisely the strategy successfully employed by Berkshire-Hathaway. According to
Frazzini, Kabiller and Pedersen (2013), “…the secret to Buffett’s success is his preference for cheap,
high-quality stocks combined with his consistent use of leverage…” These authors indicate that
Buffett employs approximately 60% leverage and that this debt is of low-cost (because BerkshireHathaway’s debt is highly rated (AAA from 1989 to 2009) and because of the “float” associated with
its insurance-underwriting business).
118
VI.C. Caveats Regarding Risk-Adjusted Performance
Of course, we should be cautious about applying backward-looking analyses to expectations
about future outcomes. Markets go through cycles and investors learn (sometimes painful)
lessons about what did and did not work in those prior cycles. Moreover, managers adapt to
changing market conditions. As markets re-price themselves and managers’ business models
undergo significant changes, the past can be a poor roadmap for future conditions. Surely,
one can argue that the 2007-08 financial crisis was a once-in-a-generation event which may
have disproportionately harmed the performance of the non-core funds. Similarly, the poor
quality of the data (see §VI.A) may have unfairly hampered our analyses. More broadly, we
should regard our model of fund/strategy performance as an approximation and, therefore,
we ought to concern ourselves with plausible deviations from our approximating model (e.g.,
see Hansen and Sargent (2008)). So, what caveats should we consider? There seems to be
three major considerations: a) results which are time-period specific, b) the dispersion and
(potential) persistence in manager returns and c) the sensitivities of the major assumptions
used in this analysis. Let’s look at each in turn.
VI.C.1. Time-Period Specific Results
Any fair-minded analysis of style-based performance ought to embrace a full market cycle.
The first decade or so of our analysis period witnessed substantial property appreciation,
while the last five or so years witness a horrific collapse in property values followed by a
more-recent recovery. Unfortunately, we have reliable property-level data only on core
properties. The strong cyclical pattern of core properties is summarized in Exhibit 77:
119
Exhibit 77: NCREIF Property Index: Market Values, Rescaled NOI and
Capitalization Rates Based on a $100 Investment for the Period 1978 through 2012
$400
9.5%
$350
8.5%
$300
6.5%
$200
5.5%
$150
4.5%
$100
3.5%
$50
Capitalization Rates (Right Axis)
Market Values
2011
2012
2010
2009
2008
2007
2006
2005
2004
2003
2001
2002
1999
Rescaled NOI
2000
1998
1997
1996
1995
1994
1993
1991
1992
1990
1989
1988
1987
1986
1985
1984
1983
1981
1982
1980
2.5%
1979
$0
Average Capitalization Rate (Right Axis)
To help orient the reader: The blue line indicates the growth in unlevered, core property
values – assuming an initial $100 investment in the NCREIF Property Index in 1978 – over
the period ending in 2012. Similarly, the red line indicates the growth in (restated) net
operating income assuming a $100 of income 140 in 1978 over the same period. (Both
property values and incomes are indexed to the left-hand vertical axis.) Given a time series
of property values and income levels, it is a simple matter to construct a time series of
capitalization rates; these rates are shown by the top line of the shaded region (and are
indexed to the right-hand vertical axis). As earlier noted, it is presumed that the “flight to
quality” occurring during and after the 2007-08 financial crisis worsened the property-level
performance of non-core properties (relative to the core properties).
These spiking property values beg the question: What if certain fund managers and/or
investors 141 were able to time the market? Exhibits 78 and 79 attempt to address this
While a $100 property investment does not produce $100 of income, both indices are set to $100
so as to improve the visual comparison of changes in property values v. income levels. Without
restating the income levels, it would be difficult to visually discern the differences in changing
property values and income levels.
140
It cannot be the case that all fund managers and/or investors exhibit such capabilities; if they
could, then all fund managers and/or investors would have fled the non-core markets as the 2007-08
financial crisis approached.
141
120
Capitalization Rate
$250
1978
Market Value and Rescaled NOI
7.5%
question by indicating the “alpha” (i.e., risk/return performance which lies above the law-ofone-price continuum – generated by levering core properties) investors would have earned in
value-added and opportunistic funds at various entrance and exit dates. Both exhibits
assume that the investor’s minimum holding period is five years. (This timeframe not only
reflects an estimate of the minimum lock-up period that many investors face in these funds,
but also reflects that shorter holding periods are excessively “noisy” from the standpoint of
the summary statistics.) Exhibit 78 identifies the risk-adjusted performance (i.e., “alpha”) for
start dates ranging from 1996 to 2007 and exit dates ranging from 2001 to 2012; any
combination of incoming and exiting dates are visible. Each combination was computed in
the same manner for which it was computed in the earlier section; as a cases in point, an
investor entering the non-core market in 1996 and exiting in 2012 would receive exactly the
value-added alpha (-1.80%) identified in Exhibit 76.
Exhibit 78: Value-Added Funds' Estimated Alpha for Various Holding Periods
2001
2002
2003
2004
2005
Exiting Year
2006
2007
2008
2009
2010
2011
Incoming Year
2007
2012
(3.19%)
2006
(3.05%) (2.92%)
2005
(2.96%) (2.74%) (2.68%)
2004
(1.59%) (2.45%) (2.34%) (2.34%)
2003
(2.82%) (1.35%) (2.13%) (2.07%) (2.10%)
2002
(1.39%) (2.50%) (1.31%) (2.00%) (1.97%) (2.00%)
2001
0.31%
2000
0.04%
1999
1998
0.28%
NA*
0.06%
(1.62%) (0.77%) (1.46%) (1.47%) (1.53%)
(0.08%) (0.24%) (1.83%) (1.00%) (1.58%) (1.58%) (1.63%)
(0.43%) (0.52%) (0.65%) (2.02%) (1.20%) (1.70%) (1.69%) (1.73%)
(0.04%) (1.45%) (1.56%) (1.63%) (2.72%) (1.88%) (2.27%) (2.21%) (2.21%)
1997
(1.10%) (0.79%) (0.95%) (1.39%) (1.48%) (1.59%) (2.41%) (1.47%) (1.87%) (1.86%) (1.88%)
1996
(0.89%) (0.94%) (0.69%) (0.87%) (1.29%) (1.39%) (1.48%) (2.30%) (1.40%) (1.77%) (1.76%) (1.80%)
* Not applicable - The reported volatility of the value-added funds during this period is less than that of the core funds for the same period.
As is readily apparent from Exhibit 78, there are very few instances of in which the valueadded funds have – on average – produced positive alpha. (Additionally, the few positive
instances are essentially zero.) So much for market timing. Moreover, it is particularly
damning that most investment holding periods between 1996 and 2007 – a period when
commercial real estate values were persistently appreciating (see Exhibit 77) – produced
negative alphas for value-added funds. So, it cannot be argued that the poor (risk-adjusted)
performance realized over the entire 17-year period (1996-2012) is attributable to the oncein-a-generation financial crisis. Even in the best of times, value-added funds
underperformed.
Exhibit 79 compares the risk-adjusted performance of opportunity funds to the core-withleverage alternative (in the same manner as described above) for the same ranges of
incoming and exiting years.
121
Exhibit 79: Opportunity Funds' Estimated Alpha for Various Holding Periods
Exiting Year
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
(2.46%)
2007
(2.46%) (2.86%)
2006
2005
2004
Incoming Year
2012
7.22%
3.96%
0.51%
(0.37%)
4.60%
1.52%
0.60%
2003
(0.88%)
6.19%
4.05%
1.39%
0.58%
2002
(3.78%) (0.32%)
5.46%
3.62%
1.26%
0.53%
5.04%
3.42%
1.27%
0.60%
2000
(0.41%) (0.65%) (2.47%) (0.46%)
4.14%
2.78%
0.89%
0.31%
1999
(1.52%) (2.24%) (2.38%) (3.87%) (1.54%)
3.03%
1.90%
0.24%
(0.25%)
2001
0.76%
(1.54%)
0.36%
1998
(0.47%) (2.38%) (3.71%) (3.81%) (4.95%) (2.53%)
2.18%
1.23%
(0.24%) (0.66%)
1997
(1.99%) (1.66%) (2.27%) (3.50%) (3.60%) (4.68%) (2.31%)
2.41%
1.52%
0.11%
(0.31%)
1996
(2.00%) (1.26%) (1.11%) (1.64%) (2.78%) (2.95%) (3.93%) (1.84%)
2.66%
1.82%
0.48%
0.06%
Like the value-added funds, it is particularly damning that opportunity funds produced
negative alphas for almost all investment holding periods between 1996 and 2007 (i.e., a
period when commercial real estate values were persistently appreciating – see Exhibit 77). If
opportunity funds underperformed in the best of times, how can it be they outperformed in
the worst of times (the aftermath of the financial crisis – the positive alphas shown in 2009,
2010 and, for some starting years, 2011 in Exhibit 79)? It would seem that they cannot. As
compared to core funds, opportunity funds often have lesser-quality assets financed with
more leverage. So, it is axiomatic that their returns are more severely hampered during a
market downturn (when there is a “flight to quality”). Therefore and as earlier cited (see
§VI.A), we are left with the two possible explanations: 1) The nature of the investment
management contracts for opportunity funds requires less frequent reporting of fair market
valuations. If so, these “stale” valuations fail to capture the true volatility of such
investments. 2) The underlying property investments of the opportunity funds are more
opaque than the properties of core funds. Consequently, the appraisal of these opaque assets
is more imprecise. 142 Some opportunistic fund managers may have utilized this imprecision
to their advantage, by constraining the (adverse) mark to market of their portfolios. If either
The appraisal process is inherently backward-looking and reflexive (in the sense that much of the
valuation estimate is based upon the recent trades of comparable properties). [See Quan and Quigley
(1991) for a description of the appraiser’s valuation problem in light of incomplete market
information.] The less common (either by number or by characteristics) a property, the more opaque
is the appraisal process and, therefore, the greater is the imprecision of the valuation estimate. The
very nature of value-added and opportunistic strategies is often to invest in properties which are few
in number and/or in competitors. As such, the valuation estimates may be subject to greater error for
the value-added and opportunistic funds. If so and due to appraisal smoothing, the volatility of valueadded and opportunistic may be understated; as a result, these types of funds would unfairly benefit
from a performance comparison based upon appraisal-based return characteristics.
142
122
or both are the case, then the positive alphas shown in 2009, 2010 and, for some starting
years, 2011 in Exhibit 79 may be artifacts of a flawed valuation process. 143
These results seem consistent with the findings of Shilling and Wurtzebach (2012), who used
discriminate functions to examine the risk-adjusted gross return performance of core, valueadded and opportunistic strategies using property-level data (focusing on sold properties in
the NCREIF database). Their results suggest that the higher returns of non-core investments
were largely due to leverage (and often “cheap” leverage) and market conditions
(fluctuations in the business, credit and real estate cycles).
Moreover, concerns about the after-fee (or net) performance of higher-risk/higher-return
strategies are not confined to institutional real estate investing – nor are these concerns
necessarily recent: For example, consider: a) David Swensen (of the Yale Endowment Fund)
has suggested that leveraged buyout funds have substantially underperformed the S&P
500. 144 b) Before the 2007-2008 financial collapse, Warren Buffett (of Berkshire-Hathaway)
wagered that hedge funds would underperform the S&P 500 over the ten-year period ended
in 2017; he has long been skeptical of the after-fee performance of such private funds. 145
VI.C.2. Dispersion and Persistence in Manager-Specific Results
It is important to reiterate that this study deals with average fund performance by strategy; in
other words, the data mask the performance of individual funds. Because the data are
masked, little can be said about manager-specific performance other than the following
broad generalizations:
First, like other areas of finance, it is widely believed that there is widening dispersion of real
estate investment managers’ performance as they engage in riskier strategies. A stylistic
illustration of this concept is presented in Exhibit 80:
Perhaps non-core real estate investing has experienced the same sort of maturity as other forms of
private equity. For example, Sensoy, et al. (2013) argue that the maturation of the (non-real estate)
private equity – predominately leveraged-buyout and venture-capital funds – has led to “an industrywide decline in returns” (p.25).
143
For the period 1987-1998, the (gross) return of buyout funds produced a 48% annual return; such
funds had a debt-to-equity ratio of 5.2:1. Over the same time, the return of the S&P 500 was 17%
with a debt-to-equity ratio of 0.8:1. Had the S&P 500 been levered at the same ratio as the buyout
funds, the levered funds would have produced a return of 86% – outperforming the LBO funds by
36 percentage points. See Swensen (2000). A similar – but less dramatic – finding was found when
looking at the comparative performance of hedge funds over the 1980-2004 period; see Griffin and
Xu (2009).
144
More specifically, Warren Buffett bet – on January 1, 2008 – Protégé Partners LLC that the S&P
500 would outperform (net of fees and costs) five funds of hedge funds, selected by Protégé
Partners, over the ten-year period ended in 2017. See Loomis (2008).
145
123
Exhibit 80: Illustration of Dispersion in Manager-Specific Performance
Gross Returns as a Function of Investment Strategy
Expected Return (k e)
Upper Quartile Performance
Average Fund-Manager Performance
Lower Quartile Performance
Volatility of Expected Return (σ e)
Exhibit 80 takes an equilibrium view that suggests, on average, riskier strategies produce
higher returns and that the dispersion in manager-specific performance of gross returns
widens as the volatility of the strategy increases. The implications of this illustration are
twofold: a) Investors face increasingly asymmetric net returns as the riskiness of the strategy
increases; that is, as riskier strategies produce a widening dispersion between “winning” and
“losing” fund managers, investors are required to pay larger promoted interests to fund
managers on the winning funds while absorbing the entirety of the underperformance of the
losing funds. b) It is an open question as to whether the equilibrium condition holds. This is
clearly not the case with value-added funds’ historical performance vis-à-vis core funds.
Second and as noted above, the performance measures reported herein represent aggregate
(i.e., value-weighted) performance. The nature of index aggregates (or portfolios) is such that,
while the index’s return equals the (value-weighted) average of each of the funds’ returns, the
index’s volatility is lower than the (value-weighted) average of each of the funds’ volatility. 146
Conversely said, averaging across the measured volatility of all the funds produces a statistic
(or measure) which is higher than the reported volatility of the index. Due to the
mathematical complexities of this point, a more detailed discussion is provided in Appendix
This statement is true provided that all funds’ returns are not perfectly correlated with one
another.
146
124
2. Nevertheless, the point is simply that investors which are poorly diversified within one or
both of the non-core strategies are likely to have experienced significantly more volatility
than is represented by the index – even if the selected funds’ risk and return matched the
average of its peers.
Third, we have little evidence on the persistence of fund managers’ performance. 147
Moreover, most managers offer a “family” (or series) of funds. Does outperformance in one
of the manager’s funds suggest that other funds in the manager’s family also outperform?
We cannot say. An earlier paper by Hahn, et al. (2005) suggests substantial persistence in
opportunistic returns by fund manager; however, that paper’s conclusions rest on a time
period ending before the 2007-08 financial crisis. Surely, any robust treatment of persistence
must cover at least one full market cycle. A more recent paper by Fairchild, et al. (2011) finds
substantial persistence in one-year returns by open-end core funds; however, as the authors
point out, one-year returns do not match the investment horizons of either the funds or its
investors. In the arena of (non-real estate) private equity, there is evidence of substantial
persistence in returns by sponsor; for example, see Gompers, et al. (2010) and Kaplan and
Schoar (2005). This issue of persistence is an important one. If investors can plausibly use
past performance to identify likely future performance, then it may well be the case that outperforming fund managers in past investments deserve higher-than-average (base and
incentive) fees in future funds. If, instead, future performance is unrelated to past
performance, then it may well be the case that investors are best served by minimizing (base
and incentive) fees in future funds. 148
VI.C.3. Sensitivity of Major Assumptions
To simplify the following analyses and accompanying discussions, we only examine results
for the opportunistic funds – as the value-added funds generally produced disappointing
(risk-adjusted) performance from varying perspectives. Let’s focus on three important
assumptions we made when estimating the alpha of opportunistic funds: a) the proportion
(θ ) of lost equity for non-reporting opportunistic funds as a result of the 2007-08 financial
crisis, b) the average term to maturity (N Core ) of the core funds’ indebtedness and c) the
average term to maturity (N Opportunity ) of the non-core funds’ indebtedness.
VI.C.3.a Survivorship Bias Among Opportunity Funds
In the first case, we had assumed that the magnitude of the survivorship bias (θ ) for
opportunity funds equals 50%. What is the sensitivity of this assumption? Exhibit 81
illustrates the alpha earned by opportunity funds assuming that the proportion (θ ) might
alternatively equal 0% or 100%:
147 Similarly, our data set does not permit us to answer the questions of: (i) whether manager X
outperformed manager Y, (ii) whether certain sub-strategies (e.g., value-added apartments v. valueadded retail) outperformed or (iii) whether certain investor types (public v. corporate pension plans v.
endowment funds v. banks, etc.) performed better than others.
Also in the context of non-real estate private equity – predominately leveraged-buyout and
venture-capital funds – Robinson and Sensoy (2012) find that compensation is largely unrelated to
net-of-fee cash flow performance.
148
125
Exhibit 81: Opportunity Funds |Sensitivity of Alpha to Assumed Percentage (θ ) of Survivorship Bias
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(2.00%)
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(2.00%)
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(2.00%)
2002
(1.99%)
(1.26%)
2002
(1.99%)
(1.26%)
2002
(1.99%)
(1.26%)
Opportunistic Funds' Estimated Alpha, Given θ = 0%
Exit Year
2003
2004
2005
2006
2007
2008
2009
2010
2011
11.02%
9.52%
8.34%
7.57%
6.50%
5.23%
4.28%
4.42%
4.56%
8.12%
8.30%
7.35%
6.52%
5.99%
5.19%
4.16%
3.40%
3.59%
3.78%
2.33%
4.74%
5.34%
4.84%
4.33%
4.03%
3.48%
2.67%
2.10%
2.36%
2.62%
Opportunistic Funds' Estimated Alpha, Given θ = 50%
Exit Year
2005
2006
2003
2004
2007
2008
2009
2010
2011
7.22%
6.19%
5.46%
5.04%
4.14%
3.03%
2.18%
2.41%
2.66%
3.96%
4.60%
4.05%
3.62%
3.42%
2.78%
1.90%
1.23%
1.52%
1.82%
(2.46%)
0.51%
1.52%
1.39%
1.26%
1.27%
0.89%
0.24%
(0.24%)
0.11%
0.48%
Opportunistic Funds' Estimated Alpha, Given θ = 100%
Exit Year
2003
2004
2005
2006
2007
2008
2009
2010
2011
0.11%
1.12%
0.94%
0.90%
1.03%
0.51%
(0.25%)
(0.88%)
(0.53%)
(0.14%)
(6.83%)
(3.46%)
(2.11%)
(1.90%)
(1.66%)
(1.33%)
(1.57%)
(2.11%)
(2.54%)
(2.11%)
(1.64%)
(0.47%)
(1.66%)
(1.11%)
(0.47%)
(1.66%)
(1.11%)
(0.47%)
(1.66%)
(1.11%)
(1.52%)
(2.38%)
(2.27%)
(1.64%)
(1.52%)
(2.38%)
(2.27%)
(1.64%)
(1.52%)
(2.38%)
(2.27%)
(1.64%)
(0.41%)
(2.24%)
(3.71%)
(3.50%)
(2.78%)
(0.41%)
(2.24%)
(3.71%)
(3.50%)
(2.78%)
(0.41%)
(2.24%)
(3.71%)
(3.50%)
(2.78%)
0.76%
(0.65%)
(2.38%)
(3.81%)
(3.60%)
(2.95%)
0.76%
(0.65%)
(2.38%)
(3.81%)
(3.60%)
(2.95%)
0.76%
(0.65%)
(2.38%)
(3.81%)
(3.60%)
(2.95%)
(1.92%)
(0.18%)
(1.37%)
(2.94%)
(4.18%)
(3.96%)
(3.27%)
(3.78%)
(1.54%)
(2.47%)
(3.87%)
(4.95%)
(4.68%)
(3.93%)
(5.75%)
(2.88%)
(3.66%)
(4.86%)
(5.87%)
(5.58%)
(4.76%)
0.83%
1.13%
1.61%
0.65%
(0.55%)
(1.64%)
(1.50%)
(1.09%)
(0.88%)
(0.32%)
0.36%
(0.46%)
(1.54%)
(2.53%)
(2.31%)
(1.84%)
(2.38%)
(1.56%)
(0.70%)
(1.42%)
(2.40%)
(3.31%)
(3.06%)
(2.53%)
3.66%
3.06%
2.76%
2.71%
1.95%
0.95%
0.14%
0.43%
0.79%
2012
1.37%
1.37%
3.45%
4.11%
3.78%
3.41%
3.21%
2.77%
2.08%
1.58%
1.86%
2.12%
2012
(2.46%)
(2.86%)
(0.37%)
0.60%
0.58%
0.53%
0.60%
0.31%
(0.25%)
(0.66%)
(0.31%)
0.06%
2012
(6.83%)
(6.74%)
(3.96%)
(2.72%)
(2.47%)
(2.20%)
(1.85%)
(2.04%)
(2.50%)
(2.87%)
(2.44%)
(1.99%)
The boxed results in the middle of Exhibit 81 are identical to the results shown in Exhibit
79, because they are based on identical assumptions. 149 The values above (θ = 0) and below
(θ =1) the boxed results represent the sensitivity of changing the base assumptions with
regard only to the survivorship bias of the opportunity funds (during the 2007-2011 period).
Recall that the survivorship-bias problem, if it exists at all, is assumed to apply only to the 20072011 time period.
149
126
When the survivorship bias is ignored (θ = 0), opportunity funds produce positive alphas in
every instance in which the investor holds the investment until to 2009 through 2012 (and
for certain starting points ending with 2008). The average difference in annual alpha as
between all of the θ = 0 and θ = .5 outcomes equals 1.75%. When the survivorship bias is
assumed to be rampant (θ = 1), opportunity funds produce negative alpha in every instance
in which the investor holds the investment through 2011, but excluding 2009 and for certain
starting points ending with 2010. The average difference in alpha as between all of the θ = .5
and θ = 1 outcomes equals 1.67%. 150 This perspective (θ = 0, .5 and 1) reinforces the earlier
conjecture that the opportunity funds’ positive alphas may be artifacts of a flawed valuation
process.
VI.C.3.b Core Funds’ Average Debt Maturity
In the second case, we assumed that the average term to maturity (N Core) of the core funds’
indebtedness was equal to seven years. What is the sensitivity of this assumption? Exhibit 82
illustrates the alpha earned by opportunity funds assuming that the average term to maturity
(NCore) might alternatively equal five or ten years:
Said another way, every 10 percentage point increase in θ reduces the annual alpha for the index
of opportunistic funds by approximately 35 basis points.
150
127
Exhibit 82: Opportunity Funds |Sensitivity of Alpha to Assumed Core Funds' Average Debt Maturity
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(1.85%)
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(2.00%)
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(2.00%)
2002
Opportunistic Funds' Estimated Alpha, Given N Core = 5 Years
Exiting Year
2003
2004
2005
2006
2007
2008
2009
(1.22%)
(2.12%)
(2.00%)
(1.38%)
0.01%
(1.83%)
(3.35%)
(3.17%)
(2.48%)
1.25%
(0.21%)
(1.96%)
(3.41%)
(3.28%)
(2.60%)
(3.23%)
(1.10%)
(2.07%)
(3.49%)
(4.62%)
(4.38%)
(3.64%)
(0.46%)
0.12%
0.79%
(0.08%)
(1.18%)
(2.20%)
(2.00%)
(1.54%)
7.54%
6.51%
5.77%
5.35%
4.42%
3.29%
2.41%
2.63%
2.87%
(1.81%)
(1.08%)
(0.30%)
(1.43%)
(0.90%)
2002
Opportunistic Funds' Estimated Alpha, Given N Core = 7 Years
Exiting Year
2003
2004
2005
2006
2007
2008
2009
(1.99%)
(1.26%)
2002
(1.99%)
(1.28%)
(0.47%)
(1.66%)
(1.11%)
(1.52%)
(2.38%)
(2.27%)
(1.64%)
(0.41%)
(2.24%)
(3.71%)
(3.50%)
(2.78%)
0.76%
(0.65%)
(2.38%)
(3.81%)
(3.60%)
(2.95%)
(3.78%)
(1.54%)
(2.47%)
(3.87%)
(4.95%)
(4.68%)
(3.93%)
(0.88%)
(0.32%)
0.36%
(0.46%)
(1.54%)
(2.53%)
(2.31%)
(1.84%)
7.22%
6.19%
5.46%
5.04%
4.14%
3.03%
2.18%
2.41%
2.66%
Opportunistic Funds' Estimated Alpha, Given N Core = 10 Years
Exiting Year
2003
2008
2004
2005
2006
2007
2009
(0.49%)
(1.68%)
(1.15%)
(1.59%)
(2.43%)
(2.32%)
(1.69%)
(0.54%)
(2.35%)
(3.78%)
(3.56%)
(2.84%)
0.57%
(0.80%)
(2.50%)
(3.91%)
(3.73%)
(3.03%)
(4.02%)
(1.70%)
(2.64%)
(4.02%)
(5.07%)
(4.79%)
(4.03%)
(1.30%)
(0.68%)
0.06%
(0.73%)
(1.79%)
(2.76%)
(2.52%)
(2.04%)
6.89%
5.88%
5.18%
4.80%
3.93%
2.84%
2.00%
2.24%
2.50%
2010
2011
4.24%
4.89%
4.35%
3.92%
3.71%
3.05%
2.15%
1.45%
1.73%
2.02%
(2.22%)
0.81%
1.82%
1.69%
1.56%
1.57%
1.16%
0.49%
(0.01%)
0.34%
0.70%
2010
2011
3.96%
4.60%
4.05%
3.62%
3.42%
2.78%
1.90%
1.23%
1.52%
1.82%
(2.46%)
0.51%
1.52%
1.39%
1.26%
1.27%
0.89%
0.24%
(0.24%)
0.11%
0.48%
2010
2011
3.63%
4.28%
3.76%
3.36%
3.18%
2.57%
1.70%
1.05%
1.34%
1.64%
(2.72%)
0.20%
1.21%
1.10%
0.99%
1.03%
0.68%
0.04%
(0.44%)
(0.06%)
0.30%
2012
(2.22%)
(2.59%)
(0.05%)
0.93%
0.91%
0.86%
0.92%
0.61%
0.03%
(0.41%)
(0.06%)
0.30%
2012
(2.46%)
(2.86%)
(0.37%)
0.60%
0.58%
0.53%
0.60%
0.31%
(0.25%)
(0.66%)
(0.31%)
0.06%
2012
(2.72%)
(3.13%)
(0.68%)
0.29%
0.28%
0.26%
0.36%
0.09%
(0.46%)
(0.86%)
(0.50%)
(0.12%)
Here too, the boxed results in the middle of Exhibit 82 are identical to the results shown in
Exhibit 79, because they are again based on identical assumptions. The values above (N Core =
5) and below (N Core = 10) the boxed results represent the sensitivity of changing the base
assumptions with regard only to the average term to maturity (N Core ) of the core funds’
indebtedness. When the assumption regarding the average term to maturity of the core
funds’ indebtedness is shortened to N Core = 5, the opportunity funds’ alpha improves by
approximately 30 bps on average – relative to our base case (N Core = 7). When the
128
assumption regarding the average term to maturity of the core funds’ indebtedness is
lengthened to N Core = 10, the opportunity funds’ alpha worsens by approximately 20 bps on
average – relative to our base case (N Core = 7). These effects are attributable to what was
generally an upward-sloping yield curve over the analysis period (see Exhibit 72 for a sense
of the time-varying difference between short- and long-term Treasury rates). As the core
funds’ (levered-equity) returns (proxied by the ODCE index) were de-levered (in order to
produce imputed asset-level returns) at assumed debt maturities of 5, 7 and 10 years and
then re-levered at an assumed debt maturity of 3 years (so as to replicate the assumed debt
maturity of the opportunity funds), the reduction in debt maturities worsened the imputed
asset-level returns for core funds (i.e., given known equity-level returns, replacing the higher
interest costs associated with long-dated debt with lower interest costs associated with
intermediate-dated debt produces lower imputed asset-level returns as from N Core = 7 to N Core
= 5 (or, N Core = 10 to N Core = 7)). The worsened core-fund returns improves the positive
alpha earned by opportunity funds (or, depending in the time period analyzed, narrows the
negative alpha earned by opportunity funds). The improvement in core-fund returns is
greatest when the difference in assumed debt maturities is greatest (i.e., N Core = 10 v. N Opportunity
= 3).
However, these effects are fairly small on balance. The difference between any estimated
alpha for opportunity funds when the assumption regarding the average term to maturity of
the core funds’ indebtedness is shortened to N Core = 5 and the corresponding alpha when the
assumption regarding the average term to maturity of the core funds’ indebtedness is
lengthened to N Core = 10 averages approximately 50 basis points per annum. 151
VI.C.3.c Opportunity Funds’ Average Debt Maturity
In the third case, we assumed that the average term to maturity (N Opportunity ) of the opportunity
funds’ indebtedness was equal to three years. What is the sensitivity of this assumption?
Exhibit 83 illustrates the alpha earned by opportunity funds assuming that the average term
to maturity (NOpportunity ) might alternatively equal two or four years:
Said another way, every one-year increase in N Core reduces the annual alpha for the index of
opportunity funds by approximately 10 basis points.
151
129
Exhibit 83: Opportunity Funds |Sensitivity of Alpha to Assumed Opportunity Funds' Average Debt Maturity
Opportunistic Funds' Estimated Alpha, Given N
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(2.36%)
2002
2003
(2.86%)
(2.15%)
(1.03%)
(2.71%)
(2.19%)
2004
(2.96%)
(3.66%)
(3.63%)
(2.96%)
2005
(2.26%)
(3.94%)
(5.36%)
(5.07%)
(4.28%)
(1.26%)
(2.33%)
(3.99%)
(5.37%)
(5.19%)
(4.42%)
Incoming Year
2001
(2.00%)
2002
2003
(1.99%)
(1.26%)
(0.47%)
(1.66%)
(1.11%)
2004
(1.52%)
(2.38%)
(2.27%)
(1.64%)
2005
(0.41%)
(2.24%)
(3.71%)
(3.50%)
(2.78%)
Incoming Year
2001
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
(1.99%)
2002
(1.79%)
(1.05%)
2003
(0.23%)
(1.22%)
(0.68%)
2004
(0.70%)
(1.75%)
(1.62%)
(1.02%)
2005
0.74%
(1.18%)
(2.80%)
(2.65%)
(2.00%)
1.92%
0.36%
(1.45%)
(2.93%)
(2.84%)
(2.19%)
(0.88%)
(0.32%)
0.36%
(0.46%)
(1.54%)
(2.53%)
(2.31%)
(1.84%)
Opportunity
Exiting Year
2006
2007
(2.19%)
(0.59%)
(1.64%)
(3.07%)
(4.22%)
(3.99%)
(3.28%)
2009
2010
2011
7.14%
5.87%
4.94%
4.54%
3.72%
2.61%
1.76%
1.99%
2.25%
3.95%
4.42%
3.69%
3.09%
2.90%
2.34%
1.46%
0.79%
1.09%
1.39%
(2.73%)
0.23%
1.13%
0.87%
0.60%
0.64%
0.35%
(0.30%)
(0.77%)
(0.40%)
(0.02%)
2009
2010
2011
7.22%
6.19%
5.46%
5.04%
4.14%
3.03%
2.18%
2.41%
2.66%
3.96%
4.60%
4.05%
3.62%
3.42%
2.78%
1.90%
1.23%
1.52%
1.82%
(2.46%)
0.51%
1.52%
1.39%
1.26%
1.27%
0.89%
0.24%
(0.24%)
0.11%
0.48%
2009
2010
2011
7.47%
6.63%
5.92%
5.45%
4.51%
3.37%
2.49%
2.70%
2.95%
4.09%
4.88%
4.49%
4.07%
3.82%
3.15%
2.25%
1.55%
1.82%
2.11%
(2.27%)
0.75%
1.86%
1.86%
1.74%
1.70%
1.29%
0.61%
0.10%
0.45%
0.80%
2012
(2.73%)
(3.18%)
(0.72%)
0.17%
0.03%
(0.13%)
(0.04%)
(0.26%)
(0.81%)
(1.21%)
(0.83%)
(0.47%)
= 3 Years
2008
(3.78%)
(1.54%)
(2.47%)
(3.87%)
(4.95%)
(4.68%)
(3.93%)
Opportunistic Funds' Estimated Alpha, Given N
(1.41%)
(1.28%)
(0.53%)
(1.19%)
(2.26%)
(3.24%)
(3.02%)
(2.54%)
Opportunity
Exiting Year
2006
2007
0.76%
(0.65%)
(2.38%)
(3.81%)
(3.60%)
(2.95%)
= 2 Years
2008
(6.55%)
(3.27%)
(4.00%)
(5.31%)
(6.41%)
(6.14%)
(5.34%)
Opportunistic Funds' Estimated Alpha, Given N
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
Opportunity
Exiting Year
2006
2007
2012
(2.46%)
(2.86%)
(0.37%)
0.60%
0.58%
0.53%
0.60%
0.31%
(0.25%)
(0.66%)
(0.31%)
0.06%
= 4 Years
2008
(0.16%)
0.46%
1.01%
0.10%
(1.03%)
(2.06%)
(1.89%)
(1.43%)
2012
(2.27%)
(2.56%)
0.01%
1.08%
1.15%
1.10%
1.12%
0.79%
0.20%
(0.25%)
0.10%
0.45%
Like before, the boxed results in the middle of Exhibit 83 are identical to the results shown
in Exhibit 79, because they are again based on identical assumptions. The values above
(NOpportunity = 2) and below (N Opportunity = 4) the boxed results represent the sensitivity of
changing the base assumptions with regard only to the average term to maturity (N Opportunity )
of the opportunity funds’ indebtedness. When the assumption regarding the average term to
130
maturity of the opportunity funds’ indebtedness is shortened to N Opportunity = 2, the
opportunity funds’ worsens by approximately 85 bps on average – relative to our base case
(N Opportunity = 3). When the assumption regarding the average term to maturity of the
opportunity funds’ indebtedness is lengthened to N Opportunity = 4, the opportunity funds’ alpha
improves by approximately 50 bps on average – relative to our base case (N Opportunity = 3).
These effects are attributable to the time-series variation in mortgage interest rates (see
Exhibit 71 for a sense of time-varying mortgage interest rates). When the assumption
regarding the average term to maturity of the opportunity funds’ indebtedness is shortened
to N Opportunity = 2, the interest expense for a given year represents the two-year moving (equalweighted) average of this year’s rate and the prior year’s rate. When the assumption
regarding the average term to maturity of the opportunity funds’ indebtedness is lengthened
to N Opportunity = 4, the interest expense for a given year represents the four-year moving (equalweighted) average of this year’s rate and the three prior years’ rates. 152 Because interest rates
are generally declining over the analysis period (see Exhibits 71 and 72), the reduction in
debt maturities improved the levered returns for core funds. The improved core-fund
returns narrows the positive alpha earned by opportunity funds (or, depending in the time
period analyzed, worsens the negative alpha earned by opportunity funds).
These effects are, on balance, more impactful than changes in the assumptions about the
average term to maturity of the core funds’ indebtedness (Exhibit 82). Here (Exhibit 83), the
difference between any estimated alpha when the assumption regarding the average term to
maturity of the opportunity funds’ indebtedness is shortened to N Opportunity = 2 and the
corresponding alpha when the assumption regarding the average term to maturity of the
opportunity funds’ indebtedness is lengthened to N Opportunity = 4 averages approximately 135
basis points per annum. 153
VII. Conclusions
The fee structures utilized by real estate funds, and their implications for investors in those
funds, is a complex and important topic. Investors must recognize and deal with this
complexity; there is no single and simple answer to the questions involved. So, when
evaluating fee structures it is important to remember that the future fund returns are
inherently unknowable. Accordingly, investors must evaluate their investments based on the
range of probable returns – not just the most likely (or expected) return. Moreover, investors
must also consider both the static and dynamic effects of fees on returns: Static effects deal
with computing net returns to investors, given the fund’s gross return. Dynamic effects
relate to potential changes in manager incentives (and behavior) due to the fee structure;
consequently, dynamic effects can change the fund’s gross (and, therefore, net) returns.
152
( )
In general, a fund’s average loan maturity N equals half of the typical loan’s maturity at loan
origination (N ) – assuming that the fund has an equal amount of such loans coming due each year
and that the loan originations occur at the midpoint of each year.
Said another way, every one-year increase in N Opportunity increases the annual alpha for the index of
opportunity funds by approximately 65 basis points.
153
131
Base Fees
Base management fees may be calculated on a variety of metrics (e.g., GAV, NAV, invested
capital, etc.). The equivalence between fees under these different metrics is easily shown and
provides a clearer understanding of the circumstances under which fees would be higher or
lower with different outcomes or conditions. In the end, no single fee structure is optimal in
all circumstances. To the extent investors believe they have favorable forecasting capabilities,
they should combine their expectations about possible future returns with how such fee
metrics behave under these economic scenarios.
Along with ongoing base management fees, there are certain types of fees (and fund costs)
typically charged to investors only at acquisition or disposition. The longer an investment is
held, the greater the time over which these one-time fees are amortized. Assuming investors
cannot select those managers who will outperform and merely want to minimize fees, then
lengthening the holding period of the investment (for a particular real estate strategy)
constitutes a form of fee reduction.
Promotes and Preferred Returns
A manager’s promoted interest truncates the possible upside for fund investors. The optionlike nature of a promote reduces the net return that investors should expect. This holds true
even if investors expect the fund’s gross return equals the preferred return. When analyzing
fee structures, investors must weigh the reduction in return that should be expected (the
static effect of the promote) against the possibility of the manager generating alpha (i.e.,
excess risk-adjusted returns) due to the incentives a promote creates for the manager (the
dynamic effect).
The expected value of the promoted interest (and, therefore, the expected cost to an
investor) depends crucially on three concepts: the level of the promote, the spread between
the fund’s expected gross return and the investor’s preferred return, and the volatility of the
fund’s return. The effect of volatility is perhaps the least understood of these. Like other
contingent claims, a promoted interest will have a greater expected value to the manager
(and a greater expected cost to investors) when fund returns are more volatile. Fund
volatility can be effected by the particular types of properties in which the fund invests,
capital-market changes, the manager’s expertise and leverage. Because of its effect on
volatility, increasing the leverage used by a fund increases the expected value of the promote
to the manager (and increases the expected cost to the investor). Investors must weigh the
higher expected fees against the effects of the fund using higher leverage.
Dynamic Effects – Alignment of Interests
Dynamic issues arising from fund fee structures can effect the gross return expected by
investors, because the fee structures effect the incentives managers have to adopt certain
investment strategies and/or to expend effort on the fund.
For instance, a promote that is deeply in-the-money (particularly later in the life of the fund)
incentivizes managers to adopt conservative strategies in order to preserve its promote.
Conversely, a promote that is deeply out-of-the-money incentivizes managers to adopt
higher risk strategies in an attempt to earn a promote and/or to expend less effort
(something difficult for investors to observe) on managing the (out-of-the-money) fund and
redeploy resources to other funds in which a promote is more likely to be earned. The
132
balance between these two outcomes depends on – among other factors – the extent to
which a manager cares about its reputation, (in particular as it relates to future fund-raising
initiatives). When evaluating incentive-fee structures, investors should bear in mind that the
levels of the promote and the preferred return can be balanced against one another. It is
possible to lower both without changing the expected net return (assuming no change in the
manager’s behavior); this may be advantageous if the new combination is believed to better
align the manager’s and investors’ interests (i.e., the manager’s behavior changes to the
investors’ benefit). For example, starting from a given a level of preferred return and
promote, one could lower the preferred return to zero and then lower the promote to a
point where the manager’s expected promote (and, therefore, the expected net return to
investors) is the same as it was under the higher-pref/higher-promote structure. This would
have the potential benefit of giving the manager an increased incentive to expend effort on
the fund because the probability of earning a promote is higher; this, in turn, may increase
the fund’s expected gross return and the investors’ net return.
Variations on the Basic Pref & Promote Structure
Many variations of the basic “pref and promote” structure are possible; common variations
include a tiered system of promotes becoming effective at multiple preferred returns
(producing a multi-tiered “waterfall” structure) and the use of a catch-up provision.
All else equal, a catch-up provision reduces the investors’ expected returns (in a static sense
(i.e., assuming that they have no impact on manager incentives and behavior)). However,
managers and investors can negotiate over the existence of a catch-up provision and the
level of the promote. As is true with various pref-and-promote combinations, it is also
possible to lower the level of the promote to a point where an investor should be indifferent
between the lower promote with a catch-up and a higher promote without a catch-up. This
is possible because at very high gross fund returns a lower promote with a catch-up
produces higher net returns than a higher promote without a catch-up. The levels of the
promote and catch-up required to balance these effects depend, of course, on the probability
of the high gross return scenario occurring. This is another example of investors needing to
consider not just their base-case scenario for fund performance, but the distribution of
possible outcomes that may occur.
Another possible complication in analyzing promote structures are funds that invest in
properties via joint ventures which themselves involve promotes. This results in a doublepromote structure being borne by the investor, accentuating the issues involved. Moreover,
if these investments are accessed via a fund of funds, there can even be a triple promote
structure.
Consideration must also be given to other features of the fee structure, including the
possibility of renegotiation of incentive structures if the fund underperforms expectations,
early payment of incentive fees and claw-back provisions as well as the effects of the
manager’s co-investment; all of which complicate the analysis of optimal fee structures.
Investors must also decide whether it is best to set a fixed preferred return or set it relative
to an index. A fixed pref may unfairly reward (or punish) a manager for market-wide
movements over which the manager has no (or little) control. On the other hand, setting the
preferred return at a spread over an index runs the risk that a promote will be paid when the
fund has not met a minimum absolute return required by the investor.
133
To deal with some of the issues involved in setting fixed versus relative preferred returns,
some investors have adopted the use of “double bogey” benchmarks in which a manager
must beat two hurdles to earn a full incentive fee. This can take the form of an absolute
return hurdle (sometimes in the form of a real (i.e., after-inflation) required rate of return)
combined with a peer-based or real estate index-based hurdle (such as beating a NCREIF
index by as certain amount). This type of system may help mitigate some issues with
traditional, single-benchmark incentive systems. However, it may also introduce its own
issues: for example, a manager under such a system may have an incentive to adopt an
aggressive investment strategy to maximize the probability of beating both benchmarks.
Historical Performance of Core, Value-Add and Opportunistic Fund Indices
As different fee structures and incentive systems are typically used across the core, value-add
and opportunistic spectrum of real estate funds, the report concludes with an empirical
comparison of the risk-adjusted performance of these categories.
Based on the periods examined, it appears the value-add funds underperform the other two
categories on a risk-adjusted basis and it is possible the performance of the average
opportunistic fund is being artificially inflated due to issues with the data quality. However, it
should also be pointed out that this result holds for the average fund in each category, not
for every fund in a specific category. Further, and perhaps most importantly, there are issues
with the data availability, especially for (closed-end) value-add and opportunistic funds.
Research on these types of funds is hampered by incomplete coverage of the universe of
funds, possible biases in fund inclusion in the indices, issues with return measurement and
vintage years and other issues. Perhaps the greatest lesson of this empirical investigation is
that it would be to the benefit of investors and the industry overall to demand greater
transparency in these sectors of the market, allowing more definitive analyses to be
conducted. There is, however, no panacea; investment management will remain an imperfect
art.
134
VIII. Appendix 1: Notation Glossary
This section is intended to provide a handy summary of pertinent notation used herein:
AUM = assets under management
C = “ceiling”
D = final fund & property disposition costs
e = random error
E[*] = expected value of *
E[v] = fund’s expected gross return
E[π ] = manager’s expected promote
F = “floor”
GAV = gross asset value
I = initial fund & property costs
i = loan’s stated interest rate
ka = nominal return on assets
kd = nominal cost of debt
ke = nominal return on equity
LTV = loan-to-value ratio
N = # assets in the portfolio
NAV = net asset value
P = manager’s performance
P[*] = probability of *
Pts = loan origination fees & costs
ra = real return on assets
rd = real cost of debt
re = real return on equity
rf = risk-free rate
s = sample standard deviation
S = sliding-scale incentive fee
T = holding period
u[w ] = utility of wealth
W = manager’s effort (or work)
X = catch-up distribution as % of invested
capital

x = geometric average
x = sample arithmetic average
α = risk-adjusted returns
β = sensitivity to market returns
χ = coefficient of relative risk aversion
ε =effective interest rate
ϕ = manager’s promote
λ = the “catch-up” rate
µ = population average
θ = proportion of survivorship bias
ρ = inflation rate
ρa,d = correlation between asset returns and
debt costs
ρi,j = correlation between any two assets i
and j
σ = population standard deviation
σa = standard deviation of return on assets
σd = standard deviation of cost of debt
σe = standard deviation of return on equity
σP = standard deviation of portfolio returns
ψ = investor’s preferred return
135
IX. Appendix 2: Further Thoughts on Risk
This appendix is intended to examine more closely two previous concepts: a) certain
implications regarding the law of one price, and b) the difference between the volatility of
index returns and the average volatility of all funds’ returns.
IX.A. Implications Regarding the Law of One Price
Let’s begin by recalling the law of one price: Two assets which have the same pattern (i.e.,
the distribution of risk and return) of expected cash flows ought to have the same price. (If
not, an arbitrage opportunity exists: buy the underpriced asset and sell the overpriced asset.)
As it applies in our setting, this law suggests that all investors have the option to lever up
their core real estate holdings, thereby creating an expanded risk/return continuum. If noncore funds offer superior risk-adjusted returns relative to core funds, then investors are
better served by investing in non-core funds; conversely, if non-core funds offer inferior
risk-adjusted returns relative to core funds, then investors are better served by investing in
core funds – with leverage suitable to their risk preference.
For the reader’s convenience, Exhibit 68 is recreated below as Appendix 2-A, with leverage
opportunities of 0%, 40% and 60% highlighted:
Exhibit A.2.1: Illustration of the Law of One Price
Lever Core Assets to Create Risk/Return Continuum
Expected Return (k e)
60% Leverage
40% Leverage
k a : Unlevered Core
k e : Levered Core Fund Returns
Fund Returns
0% Leverage
Expected Volatility (σ e)
136
This graph (and the two that follow) are shown scale-free, so as to permit the reader to focus
on the equilibrium condition (i.e., when the law of one price holds); the particular numeric
values of which are ever-changing. 154
To be clear, the use of leverage increases the expected return (indicated below by the vertical
dashed lines) on equity while also increasing the volatility (indicated below by the dispersion
in the solid bell-shaped curves) of those returns. The graph is not intended to indicate which
of these distributions (or any other distribution representing other leverage levels) is
preferable; that selection can only be made in light of the investor’s risk tolerance.
Exhibit A.2.2: Risk/Return Distributions
for Selected Levered-Equity Opportunities
0% Leverage
Frequency
40% Leverage
60% Leverage
Expected Return (k e )
Combining these first two graphs produces a third, as shown below. Here, the three leveredequity distributions are overlaid on the law of one price (the 10th and 90th percentiles are also
displayed for context): 155
This section utilizes total risk (σ ), as opposed to systematic risk (β ). If investors prefer to think in
terms of systematic risk, the relationship (assuming, for simplicity, a tax rate of zero) between levered
154
(
)
and unlevered betas is well known:
=
β Leveraged βUnleveraged 1 (1 − LTV ) .
A technical note: Exhibit A.2.3 includes the dispersion as well as the mean of the return in its
vertical dimension. Consequently, Exhibit A.2.3 utilizes a taller vertical axis than Exhibit A.2.1 which
includes only the mean in its vertical dimension. The result of the taller vertical axis in Exhibit A.2.3
155
137
Exhibit A.2.3: Illustration of Law of One Price and
Risk/Return Distributions for Selected Levered-Equity Opportunities
60% Leverage
40% Leverage
Frequency
Expected Return (k e )
0% Leverage
Expected Volatility (σe )
There is no “free lunch.” In equilibrium, investors must accept greater volatility as they chase
higher expected returns – whether they pursue levered-core funds or equally volatile noncore funds.
On the other hand, many investors are currently overpaying for that lunch: Because the
volatility of core assets is lower than non-core assets, the cost of debt capital is less when
using core assets as the collateral (as compared to using non-core assets – for an identical
leverage ratio); yet, many investors choose to use lower leverage ratios in their core funds.
IX.B. Volatility Differences: Index v. Average of All Funds
IX.B.1.
Some Thoughts on Index & Fund Characteristics
Let’s begin by noting that a well constructed (“market”) index simply represents a portfolio
of the underlying securities or, in our case, private commercial real estate funds.
Consequently, the index represents the well known characteristics of a portfolio; the index’s
return (kI) is simply a weighted average (wi = weight of the ith fund) of all of the funds’
returns (ki) comprising the index:
is to visually obscure the curvature found in this particular example of the law of one price, as
exemplified in Exhibit A.2.1.
138
k I = ∑ wi ki
(A.2.1)
and the volatility of those index returns (σI) is less than the weighted average of all of the
funds’ volatilities (σi) comprising the index:
=
σI
∑ w σ + ∑∑ w σ w σ
2
i
2
i
i
i
j
j
ρi , j ∀i ≠ j
(A.2.2)
where, as before, ρi,j = the correlation between the returns of any two funds (arbitrarily
designated as funds i and j). 156 As also noted before (§III.C.3.c), let’s simplify the
mathematics of volatility calculation by making three simplifying assumptions: a) all funds
1

are the same size  wi =  , b) all have the same volatility (σ i2 = σ 2 ) and c) all have the
N

same correlation with one another ( ρi , j = ρ ) ; then, the (market or) index volatility
simplifies to: 157
=
σI σ
1 N −1
+
(ρ )
N
N
(A.2.3)
But because the index presumably contains a large number of funds (more true for the
universe of opportunity funds 158 than for core funds), the index volatility further simplifies
(as N → ∞) to:
σI =σ ρ
(A.2.4)
With regard to our discussion (§VI.C.2) about the comparison of a particular investor’s
performance relative to the index, we can think of the typical investor who invests in (N)
funds that each have the same volatility as the average volatility of any fund in the index
(σ ) and that those funds have the same correlation with one another as do the funds in the
index ( ρ ) ; in such cases, this typical investor experiences portfolio volatility (σ P ) equal to:
=
σP σ
1 N −1
+
(ρ )
N
N
(A.2.5)
The notation ∀ i ≠ j means “for all i not equal to j.” In our case, this simply means any two nonidentical funds.
156
157
If the last two assumptions are met, then the first is not needed to derive equation A.2.4.
It is probably also true that there is a greater variety in fund sizes for the universe of opportunity
funds than for core funds; consequently, a handful of large opportunity funds are more likely to
dominate the opportunity-fund index than might be the case for the core-fund index.
158
139
(Equation A.2.5 is identical to A.2.3, because they reflect the same assumptions.) Finally, we
can think of the ratio of typical investor’s volatility to that of the index:
σP
=
σI
σ
1 N −1
+
(ρ )
N
N =
σ ρ
N −1
1
+
Nρ
N
(A.2.6)
Because ρ is less than one, this ratio is greater than one. Not surprisingly, the typical
σP
1
.
=
σI
ρ
To provide the reader with some sense of this magnitude, consider an example in which ρ
equals .25; in this case, the ratio σ P σ I equals 2.0 at N = 1. That is, the investor experiences
twice the volatility of the index – even though the investor’s fund has the same volatility of
each the funds comprising the index. As investors adds more funds to their portfolios, the
volatility of their portfolios naturally approaches the volatility of the index (i.e., as N → ∞,
σ P → σ I .)
investor suffers the lack of diversification most significantly when N = 1; then,
This presentation is a variation of the well known effects of portfolio diversification (e.g., see
Fisher and Lorie (1970) for an early empirical examination), in which portfolio volatility
decreases as more securities are added; ultimately, the investor is left with the undiversifiable
risk of the market (or systematic risk). These effects, which can be also derived from the
concepts explored above, are displayed below:
140
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
→ 1.0
1.0
1.0
→ 1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0
5
10
15
20
25
30
35
40
45
50
Portfolio's Correlation with the Market: ρ P,I
Ratio of Portfolio Volatility to Index Volatility: σ p/σ I
Exhibit A.2.4: Illustration of Fund's Volatility
and Correlation with the Market Index
0.0
Number of Funds in the Investor's Portfolio
Let’s first focus on the red, downward-sloping curve, which represents the ratio of the
investor’s portfolio volatility to that of the index’s volatility. As before, let’s assume ρ
equals .25; in this case, the ratio equals 2.0 when N = 1. (More generally, the ratio equals
1 ρ when N = 1.) As the investor adds more funds to its portfolio, the ratio approaches
one (i.e., as N → ∞, σ P → σ I ). Let’s next focus on the blue, upward-sloping curve, which
represents the correlation of the investor’s returns to that of the index’s returns (ρP,I ). While
we will not sketch the mathematics here, it can be shown that the correlation (ρP,I ) equals
ρ when N = 1.159 Continuing with our earlier assumption that ρ equals .25, this means
that ρP,I equals .50 when N = 1. Also and not surprisingly, the correlation (ρP,I ) approaches
one (i.e., as N → ∞, ρ P , I → 1) as the investor adds more funds to its portfolio. For this
reason, the earlier decision (§III.A.3 and §VI.B) to utilize total risk (σ ), rather than
systematic risk (β ), is of lesser consequence. That is, the correlation of an index with the
market approaches one; consequently, the total risk (σ ) and the systematic risk (β ) of an
159
More generally, the correlation between a portfolio of N funds and the market index can be
defined as: ρ P , I =
N
; when N = 1, ρ P , I equals
N −1+ 1 ρ
141
ρ
; for this purpose,
0 < ρ < 1.
index represent nearly identical measures of the dispersion of returns (for a given strategy):
=
β i ρi , M
IX.B.2.
σ i as N →∞ σ i
and σ M is merely a scalar.

→
σM
σM
Some Thoughts on Fund Dispersion
Via the law of one price, let’s begin by assuming that the real estate market operates in
equilibrium – in particular, let’s assume that non-core strategies can be perfectly replicated by
levering core assets. (Of course, §VI indicates that this ideal is not always realized.) For
purposes of illustration, assume that the index representing core funds can be replicated by
leveraging core assets 25%, the index representing value-added funds can be replicated by
leveraging core assets 40% and the index representing opportunistic funds can be replicated
by leveraging core assets 60%, as indicated below:
Exhibit A.2.5: Illustration of the Law of One Price
Lever Core Assets to Create Risk/Return Continuum
25%
Expected Return (k e)
20%
60% Leverage =
Opportunity Index
40% Leverage =
Value-Add Index
15%
10%
k a : Unlevered Core
k e : Levered Core Fund Returns
Fund Returns
25% Leverage
= Core Index
5%
0%
0%
5%
10%
15%
20%
25%
30%
35%
40%
Expected Volatility (σ e)
It is an instructive question to ask: What might the dispersion of funds look like around each
index? To answer this question, let’s use the hypothetical value-added index (as indicated by
the green dot above) – which, for our purposes, has an average return of 11% and a standard
deviation of 15% – as a starting point to illustrate this dispersion. Recall our earlier three
simplifying assumptions: a) all funds are the same size, b) all have the same volatility and c) all
have the same correlation with one another. Let’s further assume the value-added index is
compromised of 80 equal-weighted funds; each of which has 70% correlation with any other
fund. Then, the average volatility of any value-added fund’s return is approximately 18%:
142
=
σI σ
1 N −1
+
(ρ )
N
N
.15 σ
=
1 79
+ (.7 )
80 80
σ ≈ .179
However, in order to proceed with our examination of dispersion, we must relax at least one
of our three simplifying assumptions; it seems most natural to relax the assumption
regarding all funds having the same volatility. Let’s arbitrarily do so by assuming that the
volatility of volatility equals half its mean (i.e., the volatility distribution can be described as
having an average of ≈18% and volatility of ≈9%). Consequently, one hypothetical sample of
this dispersion looks like:
Exhibit A.2.6: Hypothetical Illustration of the Difference between
the Average Fund's Volatility and Fundi 's Volatility
50%
40%
30%
Realized Returns
20%
Average Fund's Risk &
Return Characteristics
10%
0%
Major Assumptions:
-10%
The average return of any one fund equals ~11%.
The average volatility of any one fund equals ~18%.
-20%
-30%
The average correlation between a given fund's return and its volatility equals 80%.
0%
10%
20%
30%
40%
Standard Deviation of Realized Returns
To help orient the reader, each small grey dot hypothetically represents a given fund’s
risk/return performance, while the large grey dot represents the average fund’s risk/return
performance. It is important to reiterate that, given our assumptions, the volatility of the
index returns is 15% while the average volatility of any one fund’s return is approximately
143
18%. The difference between these two figures represents the average penalty for the most
poorly diversified (N =1) portfolios, as shown below:
Exhibit A.2.7: Hypothetical Illustration of the Difference between
the Average Fund's Volatility and the Index's Volatility
50%
40%
30%
Realized Returns
20%
Average Fund's Risk &
Return Characteristics
10%
Market Index's Risk &
Return Characteristics
0%
-10%
-20%
-30%
0%
10%
20%
30%
40%
Standard Deviation of Realized Returns
In some respects, it is more elegant and more helpful to identify the ellipses that comprise,
on average, a certain proportion of the expected outcomes. This is shown below for
ellipses 160 containing, on average, half and two-thirds of the likely outcomes (given our
underlying assumptions). Each ellipse is centered at the (assumed) average value-added
fund’s return (≈11%) and at the average volatility of any one value-added fund’s return
(≈18%); each ellipse is rotated at the presumed correlation between a fund’s return and its
volatility (ρµ,σ = .8).
The mathematics rely on the properties of the bivariate normal distribution. Former student, Tom
McGuiness, was most helpful in assisting with the modeling of these relationships.
160
144
Exhibit A.2.8: Hypothetical Illustration of the Difference between
the Average Fund's Volatility and the Index's Volatility
50%
40%
30%
Realized Returns
20%
Average Fund's Risk &
Return Characteristics
10%
Market Index's Risk &
Return Characteristics
0%
-10%
-20%
-30%
0%
10%
20%
30%
40%
Standard Deviation of Realized Returns
As before, this exhibit also highlights that the (assumed) volatility of the value-added index
returns is 15% while the (presumed) average volatility of any one value-added fund’s return
is approximately 18%. This (favorable) diversification effect is not found with returns; as
noted earlier, the index’s average return and the average return of any one value-added fund
are identical (≈11%, given our assumptions).
Finally, let’s extend this discussion about the dispersion of value-added fund-level returns to
the other two real estate strategies: core and opportunistic. In so doing, let’s make the
following assumptions:
Major Assumptions Used to Illustrate the Dispersion in Fund-Level Returns
Number of Funds (N)
Expected Return (E[k])
Volatility of Index Returns (σΙ)
Average Volatility of Fund Returns (σ )
Core
Value-Added
Opportunistic
12.6%
6.3%
17.9%
8.9%
29.0%
14.5%
0.90
0.80
0.70
0.80
0.60
0.80
20
9.5%
12.0%
Volatility of Volatility (σσ )
Average Correlation among Funds ( ρ )
Correlation between Risk and Return (ρµ,σ )
145
80
10.9%
15.0%
180
14.0%
22.5%
Essentially, we are assuming that there is less correlation ( ρ ) among any two funds in a
given strategy as investors move into riskier funds. And, let’s merge these dispersion
assumptions with our earlier law-of-one-price continuum:
Exhibit A.2.9: Illustration of the Law of One Price
Lever Core Assets to Create Risk/Return Continuum
25%
60% Leverage =
Opportunity Index
20%
Expected Return (k e)
40% Leverage =
Value-Add Index
15%
10%
k a : Unlevered Core
Fund Returns
k e : Levered Core Fund Returns
5%
25% Leverage
= Core Index
0%
0%
5%
10%
15%
20%
25%
30%
35%
40%
Expected Volatility (σ e)
To help orient the reader, the blue, green and red dots represent (as before) the equilibrium
returns to indices of core, value-added and opportunistic investing, respectively – assuming
the law of one price (as indicated by the black curve) holds. The grey-shaded dots to the
immediate right of each of these indices represent the average risk/return performance of a
fund in a given investment strategy. (Again, the distance from one dot to the other – within a
given strategy – represents the average penalty for the most poorly diversified (N =1)
portfolios.) Finally, the blue, green and red ellipses comprise, on average, a certain
proportion of the expected outcomes for each of the three strategies.
At long last we have come to the point raised in §VI.C.2., the performance measures
reported in §VI represent aggregate (or index) performance. The nature of index aggregates
is such that the index’s volatility is lower than the average of each of the funds’ volatility
(while the index’s return equals the average of each of the funds’ returns). Conversely said,
averaging across the measured volatility of all the funds produces a statistic which is higher
than the reported volatility of the index. The takeaway point is simply that investors which
are poorly diversified within one or both of the non-core strategies are likely to experience
significantly more volatility than is represented by the index – even if the selected funds’
146
returns match the average of its peers. The good news is that much of the difference
between the index’s volatility and the volatility of the investor’s portfolio can be eliminated
by the selection of additional funds. Given our assumptions, that distance – for a given
strategy – can be narrowed to less than 50 basis points if the investor holds 2 or more core
funds, 7 or more value-added funds and 15 or more opportunistic funds. Recall, however,
that our underlying assumptions include that each fund possesses the “average”
characteristics of a given strategy.
147
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