Download What kinds of firms diversify?

SKILL, LUCK AND THE MULTIPRODUCT FIRM:
EVIDENCE FROM HEDGE FUNDS
Rui de Figueiredo
Haas School of Business, University of California
and
Evan Rawley
Wharton School, University of Pennsylvania
Summer Econometric Society Meeting
June 6, 2009
0
Specific Question: What happens to performance when a
hedge fund chooses to launch additional funds?
General Question: What kinds of firms diversify?
Why do some firms diversify? Why don’t all firms diversify?
Use information embedded in ex ante and ex post returns to understand what
kinds of hedge funds diversify
Skill influences performance systematically
Luck influences performance idiosyncratically
Reputation is a noisy measure of skill based on past performance
1
A step toward integrating agency costs with capabilities
Why do firms diversify?
• Agency effects
‒ managers make strategic decisions based on private
incentives and private information
• Ability ≈ skill ≈ capability ≈ quality
‒ long-run average returns ≈ firm fixed effect
2
The diversification literature traditionally focuses on whether
agency costs or skill effects dominate
Firms diversify because managers use private information opportunistically
for private gain (Jensen 1986)
Firms diversify to create value (Panzar and Willig 1977; Teece 1980;
Levinthal and Wu 2006)
Agency costs > value creation (Lang and Stulz 1994)
•Requires persistent mistakes by investors
•Endogeneity of diversification (Campa and Kedia 2002)
•Micro data and relatedness (Villalonga 2004)
In a world with no mistakes (on average) net value creation > 0, even though
there are plenty of “coordination costs” associated with diversification
•Inefficiencies in internal capital markets (Lamont 1997)
•Influence costs (Holmstrom 1979; Rajan, Servaes and Zingales 2000)
•Managerial distraction (Penrose 1959; Schoar 2002)
•Envy costs (Fehr and Schmidt 1999; Nickerson and Zenger 2008)
3
Taking both agency and skill effects seriously
Unpack agency costs: focus on timing decisions – how managers exploit a
temporary performance shock (“luck”) to launch new funds
Allow agency costs to operate in a mistake-free equilibrium where firms have
heterogeneous abilities (“skill”)
• Value creation > costs of diversification due to selection based on skill
– Including agency costs
Measure luck and skill in an event study of hedge fund diversification
• Relationship between diversification and performance patterns tells us
about what kinds of firms choose to diversify
4
The hedge fund industry
The hedge fund industry
• Large: $1.9 trillion in assets under management (AUM) at end 2007
• Roughly 10,000 managers
• up from $100 billion and <1,000 managers in 1990
What are hedge funds?
• Private investment vehicles for “sophisticated” (e.g., wealthy) investors
• Similar to mutual funds in that they invest in a portfolio of securities
• Differ from mutual funds:
 often take extensive short positions
 typically highly leveraged
 non-linear compensation schemes
 Fixed fee (typically 2% of assets under management)
 incentive fee (typically 20% of returns above a benchmark)
Individual hedge funds are part of families of funds (“firms”) and are characterized by
type of strategy {long/short; event driven; fund of funds etc.}
• Some regulatory constraints on replication (observable in the data)
Each fund is a business unit, when firms launch a new fund they diversify
5
Our argument
Assumptions
• Diversification requires investment and returns are observable
• Managers have an incentive to diversify as it increases their
potential earnings
• Investors formulate beliefs about skill based in (large) part on
performance
• Diversification provides additional information about true quality
• Diversification carries some cost
Implications
• Firms are more likely to diversify when they are lucky
• Returns are high just before diversification
• Returns revert to the mean following diversification
• Firms that are skillful are more likely to diversify
• Conditional on mean reversion, better firms diversify
• Reputation disciplines low-skill but lucky firms
6
Evaluating who diversifies
returns
A
Firms that diversify,
perform worse after
diversification
Firms that will
diversify (1)
outperform firms that
won’t (2) and (B)
1
2
B
Firm that don’t diversify, with the
same ex ante characteristics, do
even worse ex post
time
A
Lucky + high ability type (1) diversifies, while lucky type but low
ability type (2) remains focused
B
Low performers don’t diversify
7
Data
Self-reported returns for 156,070 fund-months in 2,045 firms/funds from HFR
and TASS 1977-2006
•Exclude diversified entrants (defined as a firm that diversifies within the
first 12 months of entering HFR or TASS)
•Focus on the first fund launched by a firm
•Returns for diversified firms include only the firm’s first two funds
•Exclude funds with less than 12 months of returns
Data includes monthly raw self-reported returns, assets under management,
age, firm affiliation, strategy and location
8
Standard approach to measuring excess returns
For fund i at time t (month):
(1) Rit = ai + Rft + B1i(Rmt - Rft) + B2i(HMLt - Rft) + B3i(SMBt - Rft) +
B3i(MOMt - Rft) + eit,
R = gross return (adjusted for serial correlation)
HML and SMB are the Fama-French factors (1996), MOM is
momentum as in Carhart (1997)
m indexes market
f indexes the “risk free” return
Excess return ≡ ai + eit
The information ratio ≡ ai + eit / stdvi(eit)
•Controls for non-systematic risk exposure
9
Some key summary statistics
Unit of analysis is the fund-month*
N=156,070 fund months
Monthly excess returns (%)
Total funds in firm (count)
Fund assets under management ($M)
Firm assets under management ($M)
Fraction missing AUM
Fraction diversified
Age (in months)
Strategy 1: Fund of funds
Strategy 2: Long/short fund
Strategy 3: Equity hedge
Strategy 4: Managed futures
Strategy 5: Equity market neutral
Strategy 6: Event driven
Strategy 7: Emerging markets
Strategy 8: Global macro
Strategy 9: Convertible arbitrage
Strategy 10: Fixed income arbitrage
Mean
0.32
2.18
111
258
0.14
0.37
61
0.18
0.23
0.08
0.12
0.05
0.08
0.04
0.03
0.02
0.02
Std dev
4.11
3.66
277
337
0.35
0.48
52
0.38
0.42
0.27
0.32
0.21
0.27
0.21
0.18
0.14
0.15
Min
-11.69
1
0.3
0.3
0
0
2
0
0
0
0
0
0
0
0
0
0
Max
12.75
114
1,920
1,920
1
1
356
1
1
1
1
1
1
1
1
1
1
* 90% of the observations are from 1993-2006; first reported return is dropped for all
funds; excess returns and AUMs are winsorized at the 1st and 99th percentile
Source: HFR and TASS (1977-2006)
10
Excess returns for a firm’s first fund before and after
diversification
N=861 firms, 52,611 fund-months
11
Propensity score matching to establish a counterfactual
(as in Rosenbaum and Rubin 1983)
One to one, asynchronous, nearest neighbor matching without replacement
Matched sample based on:
• Performance: average of 24 months of pre-diversification excess
returns (CAR)
• Time: calendar year
• Size: assets under management
• Age: months since inception
Alternative matching regimes include:
•Performance interacted with calendar time, size and age
•Interactions and polynomials of other variables
12
Distribution of propensity scores
Before trimming and matching
n=97,713 fund-months from 2,045 firms
After trimming and matching
n =797 fund-months in diversified firms
plus 797 matched fund-months
13
Matched returns
14
Alternative (“kitchen sink”) matching
15
Empirical specification
For fund or firm i at time t (month):
Yit = α + λi + Tt + DIVERSIFIEDit + Xcβc + εit,
Y = excess return
λ = fund (or firm) fixed effect
T = calendar time, or event-time fixed effects
DIVERSIFIED = 1 when the firm is diversified and zero otherwise
Xc = controls (as in matching)
ε is the residual
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Legacy fund performance declines following diversification but
increases relative to similar ex ante non-diversifiers
Panel A: Main sample
Dep. Variable
First fund
N
Unmatched
Matched
(1)
(2)
(3)
(4)
Returns
Inf. ratio
Returns
Inf. ratio
-0.13 ***
-0.02
**
0.13
**
0.04
(0.04)
(0.01)
(0.06)
(0.01)
156,070
156,070
87,659
87,659
***
Regressions include firm/fund fixed effects, period fixed effects; and controls for size,
age, and market size
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Robustness checks
Observations weighed by the inverse probability of diversifying in the matched
sample specification (Imbens 2004)
Alternative measures of excess returns (e.g., 5-factor model)
Firm returns (equal and value weighted)
Alternative matching
•Kitchen sink approach, and lagged returns by month approach
Entire sample free of survivor bias
Different CAR lengths
Different matching windows/different event study windows
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Discussion of empirical results
Evidence shows
1. Firms tend to diversify when they do well
2. Legacy fund performance falls following diversification
3. Legacy funds outperform focused firms who look identical ex ante
4. Diversified firms outperform focused firms who look identical ex ante
Firms exploit lucky streaks to diversify
Skill influences diversification decisions
• Better firms diversify
• Firm fixed effects imply skill is “dynamic” here
• Identifying new opportunities within the legacy fund (and via the
new fund)
• Creating synergies where others could not
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So what is going on? A simple theory
A tighter theory would be helpful to understand the mechansims of selection by
investors and managers
Model predictions:
Let
if
a sec ond
1
d 
0 otherwise
fund
launched in
st
r1  pre-diversification returns
r2  post-diversification returns
Then
1
E (r1 | d  1)  E (r1 | d  0)
2
E (r2 | d  1)  E (r1 | d  1)
3
E (r2 | d  1, r1  k )  E (r2 | d  0, r1  k )
20
So what is going on? A theory sketch
Theory needs to explain:
-
If firms can raise more capital with two funds rather than one,
why not diversify?
If diversifiers are better than non-diversifiers, why do investors
update on history (track record) at all?
If investors believe firms that diversify are better than those that
don’t, why don’t all firms diversify?
Our explanation (informally):
- Investors formulate beliefs about skill based in part on history of
returns and decisions of managers
. Beliefs are not degenerate because there are multiple
reasons one may not diversify
- Investment managers considering diversification face tradeoff
. Increase scope increases revenue potential
. But increased scope leads to
- cannibalization…
- …and more information about true quality
- …and is costly
21
Model setup
Players
N invetsment managers
Investor (single) I
Returns
Idiosyncratic shock
returns to the investor in period t from manager j are: r jt   j   jt
excess return
 jt ~ i.i.d.N (0, 2 )
manager characteristic
Note: when a manager has multiple funds, type is same, i.i.d. shock
Manager Types: { j , c j }
1 with probabilit y
otherwise
0
j  
“skillful”
p
c j  [0, ) ~ h(c)
“unskillful”
Corr (c j ,  j )  0
22
Model setup
Sequence of play
Period 1:
1-1: Nature draws a type for each investment manager j
1-2: Investor I chooses weights to the managers
1-3: Returns are realized and period payoffs are obtained
Period 2:
2-1: Each investment manager chooses whether to launch a second fund (d)
2-2: Investor I chooses weights to the managers
2-3: Returns are realized and period payoffs are obtained
Period 3:
3-1: Investor I chooses weights to the managers
3-2: Returns are realized and period payoffs are obtained
23
Model setup
Manager Action Set: to diversify or not
if
a sec ond
1
d jt  
0 otherwise
fund launched in s  t
Manager Payoffs
Stage:
w1 jt  d jt ( w2 jt  c j ) if
u jt  
 w1 jt  d jt w2 jt
launch
in
t
otherwise
T
Multiperiod: v j    t 1u jt
t 1
24
Model setup
Investor solves (Markowitz 1956)…
risk aversion
weights
u It  w Tt μ t 

2
w T't  t w t
expected returns
“ex ante” variance-covariance matrix of returns
in each period myopically
Note: Samuelson (1969) and Merton (1969, 1971) provide
microfoundations under which (with rebalancing) this assumption
about investor behavior would hold, e.g.
(W   1)
- returns are i.i.d. and power utility over multi-period wealth U (W )  1  
- returns are not i.i.d. and log-normal utility over wealth U (WT )  log(WT )
(see also Campbell and Viceira 2001)
1
T
T
Equilibrium Concept: Perfect Bayesian Equilibrium
25
Results: Investor Choices of Weights
Investor solution given their beliefs about investment skill and
uncertainty about returns are…
w 
*
t
Ω t1μ t

Key point is posterior beliefs about a manager’s type, say
q jt
Given setup, this means that:
Et ( j | q jt )  q jt
and let the standard error of the above be denoted  jtˆˆ then
Ω t1
11
r \ c
 11  2   2
ˆ


1tˆ
0
  21

0
 22

0
 31
21
22
0
0
 2 ˆˆ   2
 2 ˆˆ
2 t

2
ˆ
2 tˆ
0

2 t
2
ˆ
2 tˆ
  2
0


0


0

0

 2 ˆˆ   2 
3 t

31
26
Results: Investor Choices of Weights
Lemma 1. The investor’s optimal weight to fund manager i has the following properties:
(i)
(ii)
is independent of the weight to fund manager j i  j ;
is decreasing in  i , and therefore is decreasing in qi
(iii)
is decreasing in the variance (diagonal element of Ω t )
(iv)
is decreasing in Ri2 where Ri2 is from the regression of the returns of
manager i on the returns of the other managers
Key points: (1) because no full investment constraint, we can ignore
dependence between investment managers in investor’s problem;
and (2) weights are decreasing in correlation to other investments
in opportunity set
27
Posterior Distribution
Setup here (unconditional on play of the game) is similar to Morgan
and Vardy (AER 2009))
Let q be the posterior probability that a manager is a high type given a return r and prior
probability p. By Bayes’ rule, then q is simply given by:
 r 1
p


 

q(r ) 
.
 r 1
 r 
 p   
(1  p)
 


  
  
 
(4)
Where  () represents the pdf of a standard Normal random variable. Further, since q is
the mean, it is also useful to define the distribution of q(r) has associated density function
g(q):
  r 1
 r   
  (1  p ) 
 
g (q )   p 
.

 q(1  q)


  
   
(5)
Finally it is useful to note, that by Lemma 1 in Morgan and Vardy, the density g(q) and
associated cumulative density G(q) exhibits first order stochastic dominance in the sense
that for all q>q’, G(.;q) first-order stochastically dominates G(.;q’).
28
Equilibria: Pooling and Separating (on )
Result. There exists a “pooling” equilibrium in which no firm ever
diversifies.
Intuition: Off-path beliefs (if a firm diversifies) are unconstrained. Set q =
0 in this case and done.
Result. There does not exist an equilibrium in which all high types
diversify and all low types do not.
Intuition: Based on the EQM strategies, investors will believe that
diversifiers are high types. But then at least some (low cost) low types will
have an incentive to diversify in expectation. This in turn means it cannot
be an equilibrium.
29
Equilibria: Semi Separating (on )
Result In any non-pooling equilibrium, there will always be a cut-off level
in c such that no manager, regardless of type, will launch a fund.
Intuition: As the costs get very high (e.g. costs are ∞), there are no
incentives to diversify, no matter what the incremental benefits.
Consider first the incentives to diversify given some arbitrary beliefs about
skill given first period returns and diversification
A manager will diversify iff
w12 (r1 ,0)  E ( w13 (r1 ,0))  w12 (r1 ,1)  w13E (( r1 ,1))  w22 (r ,1)  E ( w23 (r ,1))  c
Non-diversification payoff
Diversification payoff
which defines a cutoff given posterior beliefs and expectations of future
performance
c  w12 (r1 ,1)  w13E (( r1 ,1))  w22 (r ,1)  E ( w23 (r ,1))  w12 (r1 ,0)  E ( w13 (r1 ,0))
30
Equilibria: Semi Separating
Result In any non-pooling equilibrium, cutoff levels for high types will be
higher than that for low types
Intuition: Rewriting previous expression gives:
c  ( w12 (r1 ,0)  w12 (r1 ,1))  E ( w13 (r1 ,0)  w13 (r1 ,1))  w22 (r ,1)  E ( w23 (r ,1))
Cannibalization effect
Track record dilution effect
(+ cannibalization)
Scope expansion effect
Return dilution effect:
r’1
=0
=1
Based on the return dilution and scope effects, the cutoff level will be
higher for high types than low types
r1
This implies that for any return level in the first period, the probability a
high type will diversify is higher than a low type
Note: this means that much less “lucky” high types will diversify at higher
rates than more “lucky” low types
31
Equilibria: Semi Separating (on )
Posit the following additional characteristics of equilibria we look for:
(1) That the cutoffs are “sufficiently low”
- not all costs can sustain diversification (eg even when Pr( H  1) )
(2) Cutoffs satisfy earlier condition (ie that c H* (r )  c L* (r ) )
*
(3) That equilibrium cutoff levels for each type are increasing in r (ie ck (r1 )  0 ).
r1
Rationale for (3):
(1) We are only looking for existence of an equilibrium
(2) Rules out some “weird” equilibria
After the first round, each r1 “slice” can have a separate equilibrium leading
to potentially pathological cases
32
Equilibria: Semi Separating (on )
c k* (r1 )
Don’t Diversify
ck* (r1 )
0
r1
Diversify
r1
33
Equilibria: Semi Separating
Result. Given above assumptions, an equilibrium exists, and has the
features:
E (r1 | d  1)  E (r1 | d  0)
E (r2 | d  1)  E (r1 | d  1)
From cutoffs increasing in r1
and Pr(r>k|H)>Pr(r>k|L)
E (r2 | d  1, r1  k )  E (r2 | d  0, r1  k )
From earlier result that high type
is more “willing” to diversify
Intuition: Proof “sketch” is that existence is driven by the fact that the
cutoffs are chosen to satisfy the condition that the ratios of the cutoffs
and the probability of the data for each r maintain the beliefs of the
investor, that the solution is interior and that the conditions on high and
law types are satisfied. There are a multiplicity of such EQA.
34
Equilibria: Semi Separating
Final point: Distinguishing between “synergy” (causal (positive)
effect of diversification) and “selection” (diversification purely
based on ex ante on investment skill)
If synergy is independent of investment skill (eg any manager can
ain benefit of diversification), then you will get only 2 of the 3
hypotheses (i.e. diversification will be completely driven by costs
and so will not be increasing in first period returns)
If synergy is a function of type, then you will have same type of
signaling problems explored here, although a different
substantive interpretation.
35
Conclusion
Firms time fund raising around strong performance because investors infer firm
quality based on historical returns
•Firms consider diversification when they get lucky
However, because investors also infer firm quality based on new business
performance low-skill, but lucky firms will not always diversify
Therefore, firms will diversify when they are both lucky and good
Market discipline (e.g., reputation) moderates agency effects
•Agency effects are still important, even though skill effects > agency costs
36