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 © 2010 Hedge Fund Research, Inc. www.hedgefundresearch.com

HFR Strategy C lass ific a tion

Equity Hedge Event-Driven Macro Relative Value Fund of Funds

Equity Market Neutral

Fundamental

Growth

Fundamental Value

Quantitative Directional

Sector

Activist

Credit Arbitrage

Distressed / Restructuring

Merger Arbitrage

Private Issue / Regulation D

A gric u ltu re

E ne rg y

M eta ls

M ulti

Active Trading

Commodity

Fixed Income – Asset Backed

Fixed Income –

Convertible Arbitrage

Fixed Income – Corporate

Fixed Income –

Sovereign

Volatility

Conservative

Diversified

Market Defensive

Strategic

Energy / B as ic

M ate r ia ls

Technology /

H ea lthca re

Special Situations

Currency

Energy

Yield Alternatives

Multi-Strategy Discretionary Infrastructure

Short Bias Systematic

Real Estate

Multi-Strategy Discretionary Thematic

Multi-Strategy

Systematic Diversified

Multi-Strategy

2

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

-Source: Malkiel and Saha Financial Analysts Journal

Backfill Not Backfilled

14.65% 7.34%

Live Defunct Both

Hedge 13.74% 5.39% 9.32%

Mutual 9.73% 5.20% 8.49%

•Fraction of Top half that repeat: 51.56%

•Backfill bias:

•Survivor bias:

•Good funds?

Return Biases and Statistics

•Moral: Don’t trust average returns, alphas! Can still use date for risk, betas

Risk??

Return smoothing or illiquidity

•True

•Reported

•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

i m it i i t t

i mi i

r r

E r E r

• 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?

i m it i i t t

i mi i

r r

E r E r

• 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!

( ) ( ) ...i i i

i m m v b it i t t t tr r value bonds

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)

E(Rx) alpha t(a) rmrf R2 a-Sharpe s(e)

HFIndex 0.55 0.33 ( 2.86) 0.41 0.46 0.21 1.61

ConvArb 0.39 0.23 ( 1.78) 0.32 0.25 0.13 1.78

ShortBias -0.52 -0.10 (-0.49) -0.77 0.66 -0.04 2.87

EmergMkt 0.47 0.14 ( 0.56) 0.62 0.37 0.04 3.47

EquitMktNeut 0.21 0.01 ( 0.07) 0.39 0.17 0.00 2.79

EventDriven 0.57 0.37 ( 4.39) 0.39 0.56 0.32 1.17

Distress 0.63 0.42 ( 4.44) 0.42 0.52 0.32 1.31

Multi-Strat 0.54 0.34 ( 3.50) 0.39 0.48 0.25 1.36

RiskArb 0.30 0.23 ( 3.21) 0.14 0.33 0.23 0.98

BondArb 0.19 0.04 ( 0.33) 0.30 0.25 0.02 1.48

GlobalMacro 0.81 0.70 ( 3.60) 0.23 0.10 0.26 2.69

LongShtEqty 0.62 0.34 ( 2.51) 0.53 0.57 0.18 1.87

1993 – 2010, monthly betas include three lags

Alphas and market betas

•…and we also need betas on value, growth, momentum, carry, etc. etc. •And option writing

Option betas?

Stock price

•You collect a fee, only pay off if the market goes down a lot. •Provide “disaster insurance”

Writing put profit

Fee (put price)

Most of the time, stock ends up here. You make a small profitindependent of stock price. Looks like “alpha”, “arbitrage”.

Rarely, the stock ends up here. You lose a huge amount

Writing put options

Today’s price

Put writing returns

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:

Stock price

Writing put profit

Dynamic Trading = Options!

“Contrarian” – more stocks at lower price

Put value

•“We don’t trade those dangerous derivatives” •Maybe you do!

Option-like return example: Merger “arbitrage”.

• 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!

Price

•Source: Mitchell and Pulvino, using CFSB/Tremont merger-arb index

•News: 1) “occasional catastrophes’’ 2) catastrophes more likely in market declines

Return benchmarks

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 putsSource: 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.

i sp sp SPPo it i i t i t i t i t tr r SPPo s SMB h HML

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)

E(Rx) alpha t(a) rmrf hml smb umd term def R2 a-Sharpe s(e)

HFIndex 0.53 0.16 ( 1.42) 0.36 0.02 0.10 0.16 0.05 0.30 0.61 0.12 1.36

ConvArb 0.38 0.06 ( 0.53) 0.03 0.00 0.15 0.07 -0.12 1.09 0.59 0.04 1.32

ShortBias -0.47 -0.16 (-0.84) -0.67 0.29 -0.53 0.19 -0.50 0.61 0.79 -0.07 2.27

EmergMkt 0.46 0.13 ( 0.47) 0.46 -0.07 0.32 0.11 -0.26 0.41 0.45 0.04 3.26

EquitMktNeut 0.21 0.04 ( 0.23) 0.11 0.23 -0.17 0.19 -0.46 0.80 0.47 0.02 2.23

EventDriven 0.55 0.29 ( 3.38) 0.30 0.08 0.13 0.03 -0.02 0.23 0.64 0.28 1.04

Distress 0.62 0.35 ( 3.58) 0.30 0.14 0.08 0.02 -0.05 0.35 0.62 0.30 1.17

Multi-Strat 0.51 0.26 ( 2.61) 0.31 0.03 0.20 0.05 -0.01 0.14 0.58 0.22 1.22

RiskArb 0.31 0.18 ( 2.45) 0.11 0.00 0.13 -0.02 0.07 0.10 0.45 0.20 0.88

BondArb 0.18 -0.06 (-0.76) 0.04 0.08 0.03 0.12 -0.29 0.99 0.64 -0.06 1.03

GlobalMacro 0.81 0.33 ( 1.62) 0.31 0.21 0.08 0.17 0.29 0.17 0.25 0.13 2.48

LongShtEqty 0.60 0.21 ( 1.99) 0.51 -0.17 0.16 0.19 0.11 0.10 0.81 0.16 1.25

More factors

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. More right hand variables than data points.

2. HF styles shift – betas not constant over time.

3. HF style groups mean little.

4. 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

2%

2% + 20%

Portfolio value

Management fee

•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!

•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….

HF as part of a portfolioA large institutional investor’s portfolio

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”– 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.

• “We need to add ‘alternative investments,’ ‘new asset classes’ to ‘make our rate of return targets.’”

– 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.