Hedge Funds
John H. Cochrane
University of Chicago
Booth School of Business
What are hedge funds?
• Legal/Fee:
“A compensation structure disguised as an asset class”
• Strategies/Marketing:
“Absolute returns,” “Alternative asset class," "market-neutral," "alpha,"
"providing liquidity," "arbitrage," "leverage," “exploit inefficiency.”
• 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
Returns
(1990-2009) Mean Std Dev
HF Index
5.74
7.76
Market Index 5.35 16.12
Sharpe
0.74
0.33
Returns – Skill vs. luck?
• It is nearly impossible to measure skill
from past hedge fund returns.
• Many hedge fund investors chase funds
with good past returns, and are perpetually
disappointed.
• Why is it so hard? …
The Tyranny of σ/√T
5 year performance averages, =0,  =15%
30
20
10
0
-10
-20
-30
0
10
20
30
40
50
60
70
80
90
100
•Uncertainty about average return = volatility(σ) / √ horizon
•Hedge fund: 15%/√5=6.7%! Mutual fund: 1%/ /√5= 0.4%
Return example
• Test: Find the good funds? 1 = make money 0 = lose money
2007
2008
2009
2010
2011
A
1
1
0
1
1
B
0
0
1
1
1
C
1
0
0
0
0
D
0
0
1
1
1
E
1
0
1
1
1
F
0
0
0
1
0
G
0
0
1
1
1
H
1
0
1
1
1
I
0
1
0
1
1
J
0
1
1
1
0
K
0
0
1
1
0
L
0
1
1
1
0
M
1
0
1
0
1
N
0
1
1
1
1
O
0
0
0
0
1
P
1
0
0
0
0
Q
0
0
1
0
1
R
1
1
0
0
1
S
0
1
0
1
1
T
1
1
1
1
1
Return example
• Test: Find the good funds? 1 = make money 0 = lose money
2007
2008
2009
2010
2011
A
1
1
0
1
1
B
0
0
1
1
1
C
1
0
0
0
0
D
0
0
1
1
1
E
1
0
1
1
1
F
0
0
0
1
0
G
0
0
1
1
1
H
1
0
1
1
1
I
0
1
0
1
1
J
0
1
1
1
0
K
0
0
1
1
0
L
0
1
1
1
0
M
1
0
1
0
1
N
0
1
1
1
1
O
0
0
0
0
1
P
1
0
0
0
0
Q
0
0
1
0
1
R
1
1
0
0
1
S
0
1
0
1
1
T
1
1
1
1
1
R S
1 0
1 1
0 0
0 1
1
T
1
1
1
1
1
• Survivor bias. A) in databases B) in your office (4-5!)
A B C D E F G H
2007 1 0 1 0 1 0 0 1
2008 1 0 0 0 0 0 0 0
2009 0
0
1
1
2010 1
1
1
2011 1
1
1
wins 4
4
I J K L M N O
0 0 0 0 1 0 0
1 1 0 1 0 1 0
0 1
1 1 1
1 1
1 0 1
1 1
0 1 1
4 3 4
3
3 4
P Q
1 0
0 0
0
3 5
Return Biases and Statistics
•Backfill bias in mean returns :
Backfill
Not Backfilled
14.65%
7.34%
•Survivor bias in mean returns :
Live
Defunct
Both
Hedge
13.74%
5.39%
9.32%
Mutual
9.73%
5.20%
8.49%
•Fraction of Top half hedge funds that repeat: 51.56%
→Chasing recent performance is a terrible strategy!
•These are databases! “In your office” bias is much worse.
T statistic is useless.
•→ You can’t “Evaluate this fund’s skill.” At best you can
“evaluate this strategy for picking funds.” No known rule
works.
-Source: Malkiel and Saha Financial Analysts Journal
Risk?
Hedge Fund Index Annual Returns
40
30
20
10
0
-10
-20
-30
HF
-40
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Return smoothing or illiquidity
value
•Reported
•True
•Variance and sensitivity to market (beta) are understated
•Sharpe ratio mean/std. dev is overstated
•Reported returns are serially correlated
time
Return smoothing or illiquidity
return
autocorr.
v(12)/12xv(1)
--------------------------------------------------------------------HFIndex
0.20
1.554
ConvArb
0.56
2.820
ShortBias
0.09
0.787
EmergMkt
0.31
1.899
EquitMktNeut
0.06
1.184
EventDriven
0.36
2.122
Distress
0.39
2.401
Multi-Strat
0.30
1.918
RiskArb
0.27
1.179
BondArb
0.53
2.453
GlobalMacro
0.08
1.316
LongShtEqty
0.20
1.346
MgdFuture
0.05
0.621
1993-2010
Alphas and betas
• We break returns in to two components
rti  i  i rtm   ti
• β : tendency of return to rise if the market rises
• β x rm:
1. Return you can get in an index fund. (“Style”)
2. Return = Skill vs. luck, now index exposure.
3. No need to pay fees.
4. Risk management.
• α + ε : Return earned in excess of style. (“Selection”)
• Mutual fund: α = +/-1%; β=1; ε = 1-2%
• Hedge fund: α = big?; β=0?; ε = 10-15%
• “Market neutral,” “Alternative investment,” “Absolute return?”…
Hedge fund index and market return
HFIndex
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Long/short equity: zero portfolio weight doesn’t mean 0 exposure
LongShtEqty
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Emerging markets. Names are not betas!
EmergMkt
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
EventDriven
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
ShortBias
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Alpha or “exotic beta”?
• Many semi-passive styles earn premiums for
bearing new dimensions of risk
1. Equities: Value, small cap, momentum,…;
2. Fixed income: term spread, credit spread,
currency carry…;
3. Dynamic trading, “liquidity provision”: writing put
options or straddles
• Just as important for fee, skill, risk management…
rti  i  i rtm  hi hmlt  si smbt  .....  ti
Value-growth factor: Mechanical using book/market ratios
Good return, uncorrelated with market.
60
50
40
30
20
10
0
-10
-20
-30
hml
Rm
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Momentum—buy winners, short losers
60
50
40
30
20
10
0
-10
-20
-30
umd
Rm
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Credit spread factor (BAA-AAA returns)
HFIndex
40
30
20
10
0
-10
-20
HF
Rm
Def
-30
-40
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Term: Borrow short, lend long
60
50
40
30
20
10
0
-10
-20
-30
term
Rm
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
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
Probability
•“Pennies in front of a steamroller”
•“Writing catastrophe insurance”
•“Providing liquidity to markets”
•“Short volatility”
•Large chance of not seeing loss in
track records
•Standard volatility risk metrics fail
miserably
Put expires out of money; pocket put price
Stock falls more than, say, 20%. Lose big!
0
Profit
“Equity market neutral” hedge fund returns
EquitMktNeut
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Bond “Arbitrage”. (Really a credit spread put)
BondArb
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
Distress
60
50
40
30
20
10
0
-10
-20
-30
Hedge Fund
Market
-40
-50
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
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 and you don’t know it!
Option-like return example:
Merger “arbitrage”.
Price
Merger announced
Merger completed
Offer price
Buy
Merger fails
Time
• 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!
•Quiz: Is this a good fund? (Real data)
4
3.5
3
percent return
2.5
2
1.5
1
0.5
0
-0.5
-1
0
20
40
60
80
months
100
120
140
•Quiz: Is this a good fund? (Real data)
180
Fund x
Stock Market
160
140
120
100
80
60
40
20
0
-20
0
20
40
60
80
100
120
140
•Quiz answer: Fairfield Sentry (Madoff Feeder)
Implications and challenges
rti  i  i rtm  hi hmlt  si smbt  pi put t .....  ti
Summary:
•Need to know “alternative betas” for risk management if not benchmarking, “skill.”
•Regressions won’t work. Need portfolio analysis/disclosure
Alpha vs. “exotic beta”:
•The whole style/selection alpha/beta inefficiency/risk concept is outdated.
•Manager: “that’s not passive/style, that’s my alpha!”
•Alpha/inefficiency is a zero-sum game, and should be diversifiable.
•Alternative beta: Bets all move together. OK to share risks.
“Beta is earned from people who think they are earning Beta, Alpha is earned from people
who think they are earning Alpha. With Beta, it's possible for both sides to be correct and
happy, …. With Alpha, one side is wrong.” (Aaron Brown)
•There is no alpha vs. beta. There is only beta you understand and beta you don’t.
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!
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?
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, form
portfolios, manage risks, write better contracts, better
marketing/business model, just avoid silliness.
Summary
I Returns
• Skill vs. luck? Hard to tell. Survivor bias – in your office bias
• Smoothing: more risk than you think
• Betas: More beta than you think
• Many alternative betas. Option-writing and hundred-year floods
• Alpha/beta is outdated. Many exotic betas.
II Fees, incentives, options, and contracts
• Incentives for risk, managing losses, liquidity.
III Hedge funds in a portfolio.
• Is one short what the other is long?
IV Silliness in HF investing. Marketing. Opportunities/challenges if you
get it right.
Extra slides
Returns?
•
•
•
•
Skill vs. Luck?
Survivors / backfill / self-reported?
“Is this fund good?”
Portfolios of funds to study styles
Returns—survivor bias
•Source: Mitchell and Pulvino, using CFSB/Tremont merger-arb index
•News: 1) “occasional catastrophes’’ 2) catastrophes more likely in market declines
Return benchmarks
rti  i  isp rt sp  iSPPo SPPot  si SMBt  hi HMLt  ti
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.
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!