Betas, Options, and Portfolios of Hedge Funds

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Betas, Options, and Portfolios of Hedge Funds

• John H. Cochrane
• University of Chicago GSB

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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
• Betas are HF returns market neutral,
  alternative asset class, diversification?
• Options Option-like nature of HF returns.
  Options and incentives in HF fee structure.
• Portfolios HF is not a standalone investment.
  How do you put HF in a portfolio?

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Spectacular growth in HF
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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

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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.

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Returns
Not astronomical, but if beta really 0, these
arent bad returns! Is beta 0?
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Return issues

• Questions for all return statistics
• Survivors / backfill / self-reported.
• Everyone seems to have beat the average. All
  alive have! 20 death rate.
• Best guess average HF returns are overstated by
  2-5 per year
• Uncertainty about mean returns s/vT. If s 15
  then uncertainty about 5 year mean returns is 2 x
  15/ v5 13. (And 5 years is a lot!)
• Dynamic strategies, options. With small
  probabilities of large disasters, historical
  averages are especially poor measures (more
  coming).
• 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.

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Alphas and betas a reminder

• We often characterize returns for fund i by

• 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.

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Why do we care about beta so much?

• 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!

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Hedge fund alphas and betas lags and stale
prices
Not zero!
Bigger with lags
Smaller with lags
Really not zero. Alternative asset?
Long-short doesnt mean zero beta!

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

Source my regressions using CFSB/Tremeont
indices at hedgeindex.com, idea from Asness et al
JPM
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• Correlation with the market is obvious.
• Getting out in 2000-2003 was smart! (Mostly due
  to Global/Macro group)

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Monthly returns on Global Macro HF and US market

• 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

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Monthly returns on Emerging Market HF and US
market

• Emerging markets diversify away from US
  investments, give us access to a new asset
  class?
• Names yes. Betas no. Names dont mean much!

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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. Youre 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.

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Option-like HF returns
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.
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Writing put options reminder.
You collect a fee, only pay off if the market
goes down a lot. Providing 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
Todays price
Rarely, the stock ends up here. You lose a huge
amount
Writing put profit
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Option-like return example Merger arbitrage.
Price

• 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
• Butoffer is more likely to be unsuccessful if
  the market falls!
• Payoff is like an index put!

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Merger arb returns

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

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• Source Mitchell and Pulvino, using CFSB/Tremont
  merger-arb index
• News 1) occasional catastrophes 2)
  catastrophes more likely in market declines

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Merger arb morals

• Even though its 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 220 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.)

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Hedge fund up/down betas
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!
(Includes 3 lags)

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

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

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Implications of option-like payoffs

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

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Option return benchmarks
SPPo return from rolling over out-of-the-money
puts Source Agarwal and Naik RFS, using HFR data

• Morals
• Including option benchmarks can reveal big betas.
• And hence alphas a lot less than average returns.

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Additional benchmarks matter too!

• Term long term govt bond return t bill rate
• Corp corporate bond return long term govt

• 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

• Source my regressions using hegefundindex.com
  data

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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

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Implications

• Need lots of factors benchmarks.
• Market, value, size, momentum, term, default,
  currency
• Plus options on all of these.
• (Next mechanical timing strategies that change
  all exposures.)
• (Next 2 mechanical rules that update the
  coefficients.)
• Standard regression method is strained to the
  limit.
• More right hand variables than data points.
• HF styles shift betas not constant over time.
• HF style groups mean little. Small cap growth
  vs. Global macro.
• Beta is still the right question but we need
  better ways of getting the answer.

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Implications II

• Whole standard style/selection concept is
  outdated.
• 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?
• You could get HF return with xyz mechanical
  strategy. (e.g. write put.) -- But most
  investors dont. So what?
• How many investors have thought through their
  exposures to value, size, momentum, put options,
  etc.?
• The only beta, alpha that matter are those on the
  investors portfolio. If the investor has not
  optimized on the extra factors, its alpha!
• Maybe style is selection, worth a fee!
• Program a computer vs. Need to hire a human
  distinction doesnt make sense anymore.

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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?

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Fees, incentives, and options
Management fee
2 20
2
Portfolio value
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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(0.022000 0.201000)0.010
  237.60
• Negative mean bet gets manager 238 with 99
  prob.

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Real strategies to game 220

• 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.

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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 cant see any other way!

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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
  wouldnt pay 220!
• Catch-22. Honest investors wont pay 220. 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. Its
  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.)

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HF as part of a portfolio, not a standalone
investment Standard passive index plus
active including multiple HF

• 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.

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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.
• Is HF shorting something you already own?
• Portfolio is (10 A, 10 B). HF is long A short B.
• Is (11A, 9 B) really worth short cost, 220 fee?
• Are HF offsetting each other?
• Is HF 1 long A, short B, HF 2 short A, long B?
• You pay ½ ( 2 20 ) for sure, plus short costs
  for nothing.
• Cost explosion portfolio of options ? option on
  portfolio.
• 100 mean zero stocks in one fund 2 for sure.
• 100 stocks in 100 funds 2 ½ (20) for sure!

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Silliness in HF investments

• Hedge funds give us diversification
• You cant 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
  cant 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,
  220 is a disaster!)
• Hedge style betas with passive, not multiple
  active investments!

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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!

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A new communication model?

• HF communication
• HF must figure out and disclose betas and tail
  probabilities, based on holdings not regressions.
  (Compensation for accuracy?)
• Intriguing alternative HF or intermediary
  figures out beta (alpha?) to you.
• Passive portfolios to hedge HF investments?
• Alpha claims need clear stories, clear risks.
• Investor education
• Its OK to shop for bargains (earn high risk
  premia), and accept risk not just alpha,
  arbitrage, magic.
• Strategy honesty might also stop panicked
  withdrawals.
• Lockins are good for investors!
• HF Investor needs to understand huge variety of
  styles, risks.
• Test complain if your manager exceeds the
  benchmark by 6 x tracking error?
• Fees, costs
• Fees need to reflect at least the easy betas! (Or
  HF need actually to hedge!)
• How to control fees and trading costs in a
  portfolio of HF?

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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.

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I dont 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.

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The end

• Questions?