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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 October, 2013 {Do not quote without permission} University of Chicago Booth School of Business; [email protected] The author thanks the Pension Real Estate Association for its funding of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. 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