Hedge Funds
John H. Cochrane
University of Chicago
Booth School of Business
Outline
• What are hedge funds / strategies
• Returns, alphas and betas
– Selection biases, illiquidity
– Alphas and betas
– Multiple (too many) betas; option-like returns
• Fees, incentives, options, contracts
• Hedge funds as part of a portfolio
• Hedge funds as marketing
What are hedge funds?
• Legal / Fee. Partnership; 2+20.
• Strategies: “Abolute returns,” “Alternative asset class,”
“market-neutral,” “alpha,” “providing liquidity,” “arbitrage,”
“leverage,” “long-short”
• Strategies:
HFR Strategy Classification
Equity Hedge
Event-Driven
Macro
Relative Value
Fund of Funds
Equity Market
Neutral
Activist
Active Trading
Fixed Income –
Asset Backed
Conservative
Fundamental
Growth
Credit Arbitrage
Commodity
Fixed Income –
Convertible Arbitrage
Diversified
Fundamental
Value
Distressed /
Restructuring
Fixed Income –
Corporate
Market Defensive
Quantitative
Directional
Merger Arbitrage
Fixed Income –
Sovereign
Strategic
Sector
Private Issue /
Regulation D
Agriculture
Energy
Metals
Volatility
Multi
Energy / Basic
Materials
Special Situations
Currency
Technology /
Healthcare
Multi-Strategy
Short Bias
Multi-Strategy
Yield Alternatives
Discretionary
Energy
Infrastructure
Systematic
Real Estate
Discretionary
Thematic
Multi-Strategy
Systematic
Diversified
Multi-Strategy
2
HFR © 2010 Hedge Fund Research, Inc. www.hedgefundresearch.com
What are hedge funds?
• Legal / Fee
• Strategies
– HF do lots of different things.
– Strategy gobbledygook.
– Obscure strategies seem an important part of HF marketing
• An insider view:
“Hedge funds are investment pools that are relatively unconstrained in what they
do. They are relatively unregulated (for now), charge very high fees, will not
necessarily give you your money back when you want it, and will generally not
tell you what they do. They are supposed to make money all the time, and when
they fail at this, their investors redeem and go to someone else who has recently
been making money. Every three or four years they deliver a one-in-a-hundred
year flood. They are generally run for rich people in Geneva, Switzerland, by rich
people in Greenwich, Connecticut.” -Cliff Asness, Journal of Portfolio Management 2004.
Returns
Returns?
•
•
•
Skill vs. Luck? Survivors / backfill / self-reported?
Nearly impossible to tell “Is this fund good?”
Portfolios of funds to study styles
Returns—survivor bias
Return Biases and Statistics
•Backfill bias:
Backfill
Not Backfilled
14.65%
7.34%
•Survivor bias:
Live
Defunct
Both
Hedge
13.74%
5.39%
9.32%
Mutual
9.73%
5.20%
8.49%
•Good funds?
•Fraction of Top half that repeat: 51.56%
•Moral:
Don’t trust average returns, alphas! Can still use date for risk, betas
-Source: Malkiel and Saha Financial Analysts Journal
Risk??
Return smoothing or illiquidity
•Reported
•True
•Reported returns: Mean is not far off.
•Variance and sensitivity to market (beta) are understated
•Sharpe ratio mean/std. dev is overstated
Return smoothing or illiquidity
return
rho
t
R2
v(12)/12v(1)
------------------------------------------------------------------------rmrf
0.14
1.96
0.019
1.401
hml
0.11
1.61
0.013
1.393
smb
-0.07
-1.02
0.005
0.732
umd
0.08
1.07
0.006
1.177
term
-0.01
-0.08
0.000
0.517
-----------------------------------------------------------------------HFIndex
0.20
2.89
0.040
1.554
ConvArb
0.56
9.63
0.315
2.820
ShortBias
0.09
1.27
0.008
0.787
EmergMkt
0.31
4.77
0.101
1.899
EquitMktNeut
0.06
0.83
0.003
1.184
EventDriven
0.36
5.48
0.129
2.122
Distress
0.39
6.06
0.154
2.401
Multi-Strat
0.30
4.49
0.091
1.918
RiskArb
0.27
3.97
0.072
1.179
BondArb
0.53
8.85
0.279
2.453
GlobalMacro
0.08
1.11
0.006
1.316
LongShtEqty
0.20
2.89
0.040
1.346
MgdFuture
0.05
0.74
0.003
0.621
1993-2010
Returns and betas
Alphas and betas – a reminder
• We often characterize returns for fund i by
rt   i   i rt  
i
E r
m
i

i
t
 i  iE r
m

• Beta: tendency of return to rise if the market rises
• Beta times rm: How much of the return can you get in
an index fund. (“Style”)
• Alpha: average return earned in excess of this.
(“Selection”)
• Epsilon: extra risk beyond index fund.
Why do we care about beta so much?
rt   i   i rt   t
i
m
E r
•
•
•
•
•
•
•
i

i
i
 iE r
m

Beta: how much adding a bit of i raises the portfolio variance
No point to paying fees for beta x rm that you can get in an index fund.
With beta, you or fund can short beta x rm to remove market risk
Beta: two managers doing the same thing?
Index futures as an “alternative asset” to get diversification?
Names don’t matter! Only betas matter!
In fact, you want to know betas corresponding to all passive strategies!
rt   i   i rt   i ( value t )   i ( bonds t )  ...   t
i
m
m
v
b
i
Monthly returns
E(rx) s(rx) Sharpe Annual ( tstat)
HFIndex
0.49
2.22
0.22
0.76 ( 3.11)
ConvArb
0.37
2.05
0.18
0.62 ( 2.55)
ShortBias -0.43
4.92 -0.09 -0.30 ( -1.23)
EmergMkt
0.47
4.43
0.11
0.37 ( 1.51)
EquitMktNeut
0.20
3.06
0.07
0.23 ( 0.95)
EventDriven
0.55
1.76
0.31
1.08 ( 4.41)
Distress
0.62
1.91
0.32
1.11 ( 4.56)
Multi-Strat
0.52
1.87
0.28
0.96 ( 3.91)
RiskArb
0.31
1.19
0.26
0.91 ( 3.74)
BondArb
0.16
1.73
0.09
0.32 ( 1.30)
GlobalMacro
0.74
2.90
0.26
0.89 ( 3.64)
LongShtEqty
0.56
2.88
0.19
0.68 ( 2.76)
-----------------------------------------------------------------rmrf
0.46
4.72
0.10
0.34 ( 1.39)
hml
0.28
3.51
0.08
0.27 ( 1.12)
smb
0.22
3.70
0.06
0.21 ( 0.85)
umd
0.48
5.68
0.08
0.29 ( 1.19)
term
0.41
2.93
0.14
0.49 ( 1.99)
def
0.26
2.27
0.11
0.39 ( 1.60)
Alphas and market betas
HFIndex
ConvArb
ShortBias
EmergMkt
EquitMktNeut
EventDriven
Distress
Multi-Strat
RiskArb
BondArb
GlobalMacro
LongShtEqty
E(Rx)
0.55
0.39
-0.52
0.47
0.21
0.57
0.63
0.54
0.30
0.19
0.81
0.62
alpha
0.33
0.23
-0.10
0.14
0.01
0.37
0.42
0.34
0.23
0.04
0.70
0.34
t(a) rmrf
( 2.86) 0.41
( 1.78) 0.32
(-0.49) -0.77
( 0.56) 0.62
( 0.07) 0.39
( 4.39) 0.39
( 4.44) 0.42
( 3.50) 0.39
( 3.21) 0.14
( 0.33) 0.30
( 3.60) 0.23
( 2.51) 0.53
R2 a-Sharpe
0.46
0.21
0.25
0.13
0.66 -0.04
0.37
0.04
0.17
0.00
0.56
0.32
0.52
0.32
0.48
0.25
0.33
0.23
0.25
0.02
0.10
0.26
0.57
0.18
s(e)
1.61
1.78
2.87
3.47
2.79
1.17
1.31
1.36
0.98
1.48
2.69
1.87
1993 – 2010, monthly betas include three lags
•…and we also need betas on value, growth, momentum, carry, etc. etc.
•And option writing
Option betas?
Writing put options
•You collect a fee, only pay off if the market goes down a lot.
•Provide “disaster insurance”
Most of the time, stock ends up here. You make a small profit
independent of stock price. Looks like “alpha”, “arbitrage”.
Fee (put price)
Stock price
Today’s price
Rarely, the stock ends up here. You lose a huge amount
Writing put profit
Put writing returns
Return
Write OTM put returns
Time
Option betas?
Option-like returns: beware averages (even more)
• If the return is (1, 1, 1, 1, 1, -10, 1, 1, 1, -10, 1, 1, 1, 1,…) you are
likely to see only +1, “we consistently outperform the market.’’
• The actual mean return depends on how likely the disaster -10 is.
You need a long history to figure that out based on statistics.
• Like writing earthquake insurance.
• The distribution of profits from writing puts is very far from normal:
P ro b a b ility
P u t e xp ire s o u t o f m o n e y; p o c k e t p u t p ric e
S to c k fa lls m o re th a n , s a y, 2 0 % . L o s e b ig !
0
P ro fit
Dynamic Trading = Options!
Writing put profit
Stock price
“Contrarian” – more stocks at lower price
Put value
•“We don’t trade those dangerous derivatives”
•Maybe you do!
Option-like return example:
Merger “arbitrage”.
Price
M e rg e r a n n o u n c e d
M e rg e r c o m p le te d
O ffe r p ric e
Buy
M e rg e r fa ils
T im e
• Large chance of a small return if successful. (Leverage: a large return)
•Small chance of a large loss if unsuccessful.
•The strategy seems unrelated to the overall market, “beta zero”
•But…offer is more likely to be unsuccessful if the market falls!
•Payoff is like an index put!
•Source: Mitchell and Pulvino, using CFSB/Tremont merger-arb index
•News: 1) “occasional catastrophes’’ 2) catastrophes more likely in market declines
Return benchmarks
rt   i   i rt
i
sp
sp
 i
SP P o
SP P o t  s i SM B t  hi H M Lt   t
i
ER
(%/mo)
alpha
SPPo
(puts)
SMB
(size)
HML
(value)
Event Arb
1.03
0.04
-0.92
0.15
0.08
Restructure
1.29
0.43
-0.63
0.24
0.12
Event driven
1.33
0.20
-0.94
0.31
0.12
Rel. value arb
1.15
0.38
-0.64
0.17
0.08
SPPo = return from rolling over out-of-the-money puts
Source: Agarwal and Naik RFS, using HFR data
• Morals:
1. Including option benchmarks can reveal big betas.
2. And hence alphas a lot less than average returns.
Hedge fund index and market return
Multi-Strategy index and market return
Long-Short equity index and market return
Global-macro index and market return
Event-driven index and market return
Equity-market-neutral index and market return
Emerging-market hedge fund index and market return
Distressed investing index and market return
Convertible-Arbitrage index and market return
Bond-Arbitrage index and market return
Next: compare to alternative passive strategies
Momentum
Value-Growth
BAA – AAA
(see bond, convertible)
Term premium (borrow short, lend long)
More factors
HFIndex
ConvArb
ShortBias
EmergMkt
EquitMktNeut
EventDriven
Distress
Multi-Strat
RiskArb
BondArb
GlobalMacro
LongShtEqty
E(Rx)
0.53
0.38
-0.47
0.46
0.21
0.55
0.62
0.51
0.31
0.18
0.81
0.60
alpha
0.16
0.06
-0.16
0.13
0.04
0.29
0.35
0.26
0.18
-0.06
0.33
0.21
t(a) rmrf
( 1.42) 0.36
( 0.53) 0.03
(-0.84) -0.67
( 0.47) 0.46
( 0.23) 0.11
( 3.38) 0.30
( 3.58) 0.30
( 2.61) 0.31
( 2.45) 0.11
(-0.76) 0.04
( 1.62) 0.31
( 1.99) 0.51
hml
0.02
0.00
0.29
-0.07
0.23
0.08
0.14
0.03
0.00
0.08
0.21
-0.17
smb
0.10
0.15
-0.53
0.32
-0.17
0.13
0.08
0.20
0.13
0.03
0.08
0.16
umd
0.16
0.07
0.19
0.11
0.19
0.03
0.02
0.05
-0.02
0.12
0.17
0.19
term
0.05
-0.12
-0.50
-0.26
-0.46
-0.02
-0.05
-0.01
0.07
-0.29
0.29
0.11
def
0.30
1.09
0.61
0.41
0.80
0.23
0.35
0.14
0.10
0.99
0.17
0.10
R2 a-Sharpe
0.61
0.12
0.59
0.04
0.79 -0.07
0.45
0.04
0.47
0.02
0.64
0.28
0.62
0.30
0.58
0.22
0.45
0.20
0.64 -0.06
0.25
0.13
0.81
0.16
s(e)
1.36
1.32
2.27
3.26
2.23
1.04
1.17
1.22
0.88
1.03
2.48
1.25
Implications and challenges
•
Need lots of factors = benchmarks.
1. Market, value, size, momentum, term, default, currency…
2. Plus options on all of these.
3. (Next: + mechanical timing strategies.)
•
Standard regression method is strained to the limit.
1.
2.
3.
4.
More right hand variables than data points.
HF styles shift – betas not constant over time.
HF style groups mean little.
Beta is still the right question but we need better ways of
getting the answer. Portfolio analysis!
Implications II
• Whole style/selection concept is outdated.
1. “Style” (beta x E(f), passive, beta known and hedged, no
fee) vs. “selection” (alpha, active, fee)
2. “You could get HF return with xyz mechanical strategy.” (e.g.
write put.) -- But most investors don’t.
3. How many investors know their exposures to value, size,
momentum, put options, etc.; understand the premiums, and
can program the computer?
4. Maybe “style” is “selection,” worth a fee! “This is my skill”
5. There is no alpha vs. beta. There is only beta you
understand and beta you don’t understand.
6. Challenge = opportunity!
Fees
•
Management + performance.
– Often 2% + 20% of gains.
•
Funds of funds charge 2% + 20% too!
•
•
→ Massive number of new funds!
→ How do they attract money, and
maintain such high fees?
Fees, incentives, and options
Management fee
2% + 20%
2%
Portfolio value
•Quiz: Name this payoff
Fees, incentives, and options
• (0), 2%, 20% = a call option.
• Incentive for needless volatility/option writing.
(Financial crisis more generally)
– Responses? Coinvest, “Reputation,” High water
marks . Do they work?
• Hot money and magic alpha: Liquidity,
withdrawals, Catch 22, lockups.
– A stop loss order is not a put option.
– Maybe you want to keep the others from leaving!
• The contract structure matters!
• Challenge = opportunity!
HF as part of a portfolio
A large institutional investor’s portfolio
•The Absolute Return portion of the portfolio is primarily invested in non-directional hedge funds. That is, returns should be
independent of the direction of global equity, fixed income or currency markets. Strategies include Global Convertible Arbitrage,
Global Merger Arbitrage, Long/Short Equity and Blended Strategies….
Hedge funds as part of a portfolio
•
Problem 1: Risk management.
–
–
–
•
Will all HF go down together?
Will HF lose when everything else loses?
Betas!
Problem 2: Cost and fee explosion.
1.
Is HF short something you own?
a. Portfolio is (10 A, 10 B). HF is long A short B.
b. Is (11A, 9 B) worth short cost, 2+20 fee?
2. Are HF offsetting?
a. HF #1 long A, short B. HF #2 short A, long B.
b. You pay ½ ( 2 + 20 ) for sure, plus short costs for nothing.
3. Cost explosion – portfolio of options ≠ option on portfolio.
a. 100 mean zero stocks in one fund: 2% for sure.
b. 100 stocks in 100 funds: 2% + ½ (20%) for sure!
Silliness in HF portfolios/investing
•
“Hedge funds give us diversification”
–
•
“We need to add ‘alternative investments,’ ‘new asset
classes’ to ‘make our rate of return targets.’”
–
•
•
You can’t be more diversified than the market portfolio. If you have A
and B, adding (long A, short B) does not make you more diversified.
Most HF are not a new asset class. They trade in exactly the same
stuff you already own. And you can’t wish returns.
“We hold a lot of funds to diversify across managers”
–
And get back to the market portfolio.
–
If so, 2+20 is a disaster!
–
Hedge style betas with passive, not multiple active investments!
“If things get bad we’ll sell on the way down, limit tail risk”
–
Fallacy 101. A stop order is not a put option. Sell to who?
Bottom line so far
• Return statistics: Short, selected, managed.
• Betas on many new styles; Option-like returns with big tails.
• Standard view of investor-manager relation.
– Both sides understand betas
– Clear “style” (no fee) vs. “selection” (fee, information,skill) separation.
– Investor has already optimized “style” choice in passive investments.
• Our world
–
–
–
–
HF sketchy on betas, premiums, investors have no clue.
Investors have not thought about multiple betas, passive “styles.”
There is no alpha, there is only beta you know and beta you don’t know.
Alpha based on track record, statistical analysis is close to hopeless.
• Large rewards for figuring out how to answer these questions!
HF: A brilliant marketing success in
a marketing business.
• “Absolute Returns,’’ ”Market-Neutral,” “Alternative
asset,” “Near-Arbitrage”… “Alternative beta,”
• They separate rich people, money!
• 2% + 20% “We only charge if we win.”
• Names, fees: Good “framing” to ignore portfolio,
evaluate as standalone investments.
• “Business model” is the biggest key to success!
Many opportunities
• Complex products, trading strategies need expert
investors (HF).
• There are rewards to new “style” risks.
• HF organizational form can be a useful way to access
these investments.
• Lots of opportunities to run better funds, help form
portfolios, manage risks, write better contracts, better
marketing/business model, just avoid silliness.