Betas, Options, and Portfolios of Hedge Funds

John H. Cochrane

University of Chicago GSB

Objectives• Summarize academic hedge fund research.• Use it: how should one invest in hedge funds?• Think about future and challenges posed by HF• Three themes:

1. Betas: are HF returns “market neutral,” “alternative asset class,” “diversification”?

2. Options: Option-like nature of HF returns. Options and incentives in HF fee structure.

3. Portfolios: HF is not a standalone investment. How do you put HF in a portfolio?

Spectacular growth in HF

Strategy composition

•HF do lots of different things. •Strategy gobbledygook. Who knows what any of this means?•Obscure strategies seems an important part of HF marketing

What are hedge funds?

“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

Not astronomical, but if beta really = 0, these aren’t bad returns! Is beta 0?

Return issues• Questions for all return statistics:

1. Survivors / backfill / self-reported.a. Everyone seems to have beat the average. All alive have! 20% death rate.

b. Best guess: average HF returns are overstated by 2-5% per year

2. Uncertainty about mean returns = σ/√T. If σ = 15% then uncertainty about 5 year mean returns is 2 x 15/ √5 = ± 13%. (And 5 years is a lot!)

3. Dynamic strategies, options. With small probabilities of large disasters, historical averages are especially poor measures (more coming).

4. Very little persistence. The strategy of buying HF that did well in the past does not do well going forward.

→ Evaluating average returns, alphas from return history (track record) is nearly hopeless.

– Historical data are still useful for measuring risks, 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

• No point to paying fees for beta x rm that you can get in an index fund. Hence, beta x rm is the right benchmark; only pay fees for alpha.

• With beta, you can short beta x rm to remove market risk (or the fund could do it and really be market-neutral).

• Risk management: To form a portfolio, controlling market (and other) risks, controlling correlation between HF, you need to know the betas.

• Example: Invest in index futures as an “alternative asset” to get diversification? Beta tells you no!

• 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

Hedge fund alphas and betas – lags and stale prices

Style ER (%/mo) a b a3 b3

Index 0.64 0.46 0.28 0.36 0.44

Std. errors 0.20 0.17 0.04

Short -0.53 0.10 -0.94 0.13 -0.99

Emerg mkts 0.39 0.00 0.58 -0.07 0.69

Event 0.61 0.46 0.22 0.38 0.37

Global Macro 0.93 0.82 0.17 0.74 0.31

Long/Short Eqty 0.73 0.42 0.47 0.32 0.65

& 500i s p it t tr a br 1 2 1 3 2 4 3

1 2 3 4

3

3

i sp sp sp sp it t t t t tr a b r b r b r b r

b b b b b

Source: my regressions using CFSB/Tremeont indices at hedgeindex.com, idea from Asness et al JPM

Not zero!

Bigger with lags

Smaller with lags

Really not zero.

“Alternative asset?”

Long-short doesn’t mean zero beta!

•Lags are important – stale prices or lookback option•Betas are big!

•Correlation with the market is obvious. •Getting out in 2000-2003 was smart! (Mostly due to Global/Macro group)

•“Global macro” yet you see the correlation with US market•Lagged market effect is clear in 1998. Is Nov/Dec 1998 unrelated to Oct?•Dramatic stabilization / change of strategy in mid 2000

Monthly returns on Global Macro HF and US market

•“Emerging markets diversify away from US investments, give us access to a new asset class?”•Names: yes. Betas: no. Names don’t mean much!

Monthly returns on Emerging Market HF and US market

Alphas and betas• Betas are larger than you might have thought, larger than

“market neutral” “absolute return” claim, and interest rate fee benchmark.

• Alphas are correspondingly smaller than average returns. You’re paying performance fees for index-fund components.

• Betas are hard to measure, especially for illiquid securities. At least look longer than 1 month.

• Even if some alpha remains, are HF really about a few percent alpha (plus big risks?)

• Q: “Sure, average alpha is low, but my alpha is big.”

• A: How to separate luck from skill? Only answer: form a portfolio of good-looking funds based on ex-ante information, track them later. So far, little alpha here.

Option reminder. For a fee (option price), you can get the “upside” but not the “downside.” The option value (fee) is higher if the stock is more volatile.

Stock price

Call payoff

If we add risk the option is worth more

If the stock is riskless, the option is worth 0

Option-like HF returns

Stock price

You collect a fee, only pay off if the market goes down a lot. Providing “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 reminder.

Today’s price

Option-like return example: Merger “arbitrage”.

•Cash offer. Borrow, buy target. •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

Merger arb returns

Source: Mark Mitchell and Todd Pulvino, Journal of Finance•Line: like the payoff of writing index puts!

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

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

Merger arb morals• Even though it’s an all-equity strategy (no option

positions) dynamic trading gives an option-like payoff.

• Not necessarily a bad thing! Writing index puts earns a premium. It provides “disaster insurance” to the market.

• But no need to pay 2+20 to write index puts!

• “Alpha”, “beta”, benchmark, performance evaluation should be relative to the strategy of writing index puts!

• (Mitchell and Pulvino are now running a merger-arb hedge fund, so at least they think such alpha is there.)

Hedge fund up/down betas

Style b3 b up b down

Index 0.44 0.08 0.77

Short -0.99 -0.22 -1.82

Emerg mkts 0.69 0.08 1.16

Event 0.37 0.18 0.47

Global Macro 0.31 -0.08 0.66

Long/Short Eqty 0.65 0.19 1.18

( 0) ( 0)i sp sp it up t down t tr a b r b r 1 2 1 3 2 4 3

1 2 3 4

3

3

i sp sp sp sp it t t t t tr a b r b r b r b r

b b b b b

Example: if the market goes up 10%, the HF index goes up 0.8%. But if the market goes down 10%, the HF index goes down 7.7%!

•Source: my regressions using hegefundindex.com data; following Asness et al JPM

•Many near, or above 1. These are big betas!•Many HF styles are much more sensitive to down markets = write puts = “short volatility.”

(Includes 3 lags)

Implications of option-like payoffs

• Need option-return benchmarks for risk management (investing in HF) and compensation benchmarks.

... ...i sp sp put index put it i i t i t tr r r

Option 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

Additional benchmarks matter too!

Style Rm+ Rm- Term+ Term- Corp+ Corp-

Index 0.07 0.72 0.27 0.55 1.01 0.94

Conv arb 0.25 0.20 0.10 0.35 -0.22 1.03

Short -0.32 -1.75 -0.05 0.19 0.62 -0.66

Emerg mkts 0.13 1.03 -0.44 0.20 0.73 2.48

Event 0.21 0.39 0.15 0.32 0.30 1.43

BondArb 0.08 0.12 -0.02 0.35 0.44 1.40

Global Macro -0.09 0.66 0.66 1.17 2.29 1.53

Long/Short Eqty 0.16 1.05 0.09 0.22 0.38 0.84

•Source: my regressions using hegefundindex.com data

•Term = long term gov’t bond return – t bill rate

•Corp = corporate bond return – long term gov’t

•Big betas, especially on corp (default spread)

•Often much more for bad news than for good news

•Market up/down has moderated since 1998, but term, corp up/down still strong

•Most HF strategies amount to “providing liquidity”, “disaster insurance” in some market

Option-like returns mean: beware averages (even more)

• Example. If the return is (1, 1, 1, 1, 1, -10, 1, 1, 1, -10, 1, 1, 1, 1,…) you are very likely to see many years with only +1, “we consistently outperform the market.’’

• 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 in LA.• Distribution of profits from writing puts is very far from normal:

Implications• 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 that change all exposures.)

4. (Next 2: + mechanical rules that update the coefficients.)

• 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. “Small cap growth’’ vs. “Global macro.”

4. Beta is still the right question but we need better ways of getting the answer.

Implications II

• Whole standard style/selection concept is outdated.

1. Does “style” (beta x E(f), passive, no fee) vs. “selection” (alpha, active, fee) make any sense in the post-CAPM 27 factor, dynamic world?

2. “You could get HF return with xyz mechanical strategy.” (e.g. write put.) -- But most investors don’t. So what?

3. How many investors have thought through their exposures to value, size, momentum, put options, etc.?

4. The only beta, alpha that matter are those on the investor’s portfolio. If the investor has not optimized on the extra factors, it’s alpha!

5. Maybe “style” is “selection,” worth a fee!

6. “Program a computer” vs. “Need to hire a human” distinction doesn’t make sense anymore.

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

Fees, incentives, and options

• (0), 2%, 20% = a call option.

• Investor view: Incentive for needless volatility.

• Examples. You are given $1000:

– Do nothing : Fee = $20

– Bet $500 50/50: Expected Fee = $70

• ½ x 0.02 x 500 + ½ x (0.02 x $1500+ 0.20 x $500) = $70

– Bet 99% + $1K,1% -$100K: Expected Fee = $238

• Mean : 0.99 x $2000 + 0.01 x (-$99000) = $990 → lose $10!

• Fee: 0.99×(0.02×$2000 +0.20×$1000)+0.01×0 = $237.60

• Negative mean bet gets manager $238 with 99% prob.

Real strategies to game 2+20

• Write put options.

• Synthesize options with dynamic trades.

– Example: Double or nothing.

• Secret betas.

– Claim “beta zero” yet invest in index.

– Lots of other betas. Example: Value-growth, is “market neutral” yet a mechanical strategy that gives a good average return.

Solutions to the incentive problem

• General partners invest large fractions of their own wealth.

– Huge loss of diversification to GP. Really?

– Cannot apply to HF run by banks, institutions.

• “GP want to preserve their reputations”

– Effective?

• Clearly understood strategy, clear and honest risk management and reporting.

– Not yet, but I can’t see any other way!

Contracts II. Risk and Reward or Magic Alpha?

• Example: Spring 2005: GM downgraded. HF (short treasury, long corporate) have big losses.

• Big losses lead to withdrawals. Funds have to sell illiquid securities at the worst possible time.

• Why should losses lead to withdrawals? If investors understood the risk and strategy they would double up!

• Answer 1: If investors understood it they wouldn’t pay 2+20! – Catch-22. Honest: investors won’t pay 2+20. Sell alpha magic: investors pull

out at the worst time.

• Answer 2: High-water marks, losses mean the fund will will lose managers. Also, slow marking to market means early withdrawers get more. It’s rational to pull out, like a bank run– High water marks can be bad for investors, lock-in can be good for investors!

• General point. The fee and contract structure is important.

• (Future: is there “bounceback” in HF returns, so long term investors should ignore price drops? Nobody has checked yet. If so, it changes everything.)

•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 portfolio, not a standalone investmentStandard: “passive” index plus “active” including multiple HF

Hedge funds as part of a portfolio

• Problem 1: Risk management. Must know betas!– How much are you overall short volatility?– What is the chance that all HF investments go down together?

• Problem 2: Cost and fee explosion. 1. Is HF shorting something you already own?

a. Portfolio is (10 A, 10 B). HF is long A short B.

b. Is (11A, 9 B) really worth short cost, 2+20 fee?

2. Are HF offsetting each other? a. Is 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 investments

• “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) to the mix does not make you more diversified – it makes you less 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. Why pay fund 1 to long A

short B and fund 2 to long B short A? – HF are not taking idiosyncratic risk. (If so, 2+20 is a disaster!) – Hedge style betas with passive, not multiple active

investments!

Bottom line• Many large betas on a bewildering variety of new styles;

Option-like returns with big tails. • Betas, risks are hard to measure with historical data: style drift,

short samples, too many styles. • Standard view of investor-manager relation.

– Both sides understand betas– Clear “style” (no fee) vs. “selection” (fee) separation. – Investor has already optimized “style” choice in passive investments.

• Our world– HF sketchy on betas, investors have no clue.– Most investors have not thought about multiple betas, passive “styles.”– “style” vs. “selection”, “alpha” vs. “beta” is no longer relevant in the post-

CAPM, dynamic, 20-factor world. HF exist largely to collect large premia for holding risks of unusual styles.

– Alpha based on track record, statistical analysis is close to hopeless.

• Yes, I have asked more questions than I have answered. Large rewards for figuring out how to answer these questions!

• HF communication:

1. HF must figure out and disclose betas and tail probabilities, based on holdings not regressions. (Compensation for accuracy?)

2. Intriguing alternative: HF or intermediary figures out beta (alpha?) to you.

3. Passive portfolios to hedge HF investments?

4. Alpha claims need clear stories, clear risks.

• Investor education:

1. It’s OK to “shop for bargains” (earn high risk premia), and accept risk; not just alpha, arbitrage, magic.

2. Strategy honesty might also stop panicked withdrawals.

3. Lockins are good for investors!

4. HF Investor needs to understand huge variety of styles, risks.

5. Test: complain if your manager exceeds the benchmark by 6 x tracking error?

• Fees, costs

1. Fees need to reflect at least the easy betas! (Or HF need actually to hedge!)

2. How to control fees and trading costs in a portfolio of HF?

A new communication model?

Another view

• Understanding HF: A brilliant marketing success in a marketing business.– “Absolute Returns,’’ ”Market-Neutral,” “Alternative asset,”

“Near-Arbitrage”… “Alternative beta,” “Entrepreneur” – Whatever they mean, they separate rich people, money.– 2% + 20% “We only charge if we win.” – Makes sense for a single investment. Makes much less

sense in the light of day, thinking about forming a portfolio that is part passive, part active and spread over many funds.

I don’t mean to sound negative

• 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.

• Once all the problems are overcome.

The end

• Questions?