“A Brief Survey of Hedge Fund Research”The London School of Economics’ Financial Markets Group14 February 2006Ms. Hilary Till (LSE, MSc in Statistics, 1987) *Premia Risk Consultancy, Inc.* E-mail: [email protected] *Phone: 312-583-1137 * Chicago * Fax: 312-873-39141

Presentation OutlineI.Return SourcesII. Properties of ReturnsIII. Performance MeasurementIV. Risk ManagementV. Investor Preferences and ChoicesVI. ConclusionCover of “In Search of Alpha: Investing in Hedge Funds” byAlexander Ineichen, UBS Global Equity Research, October 2002.Based on Till and Gunzberg (2005).2

I. Return SourcesA. InefficienciesCapacity of Hedge Fund Industry (With an “Alpha Advantage”)in Billions of DollarsAllowable Inefficiency in Private, MutualFund and Institutional Fund Management-0.5%-0.75%-1.0%Required Excess 10.0%2,7504,1255,500Return for 7.5%3,6675,5007,333Hedge Funds 5.0%5,5008,25011,000Similar Argument also in Ross (2004).3

I. Return SourcesB. Risk Premia Relative-Value Bond Funds Equity Risk Arbitrage Value vs. Growth Strategy Small Capitalization Stocks High-Yield Currency InvestingRembrandt’s Storm on the Sea of Galilee, Isabella Stewart GardnerMuseum, Boston, and Cover of Against the Gods: The RemarkableStory of Risk by Peter Bernstein, John Wiley & Sons, 1996.Examples were drawn from Cochrane (1999a,b),Harvey and Siddique (2000), and Low (2000).4

I. Return SourcesC. Illiquidity Benefits: Tick-by-Tick Evaluation of a Good Investment isPainfulProbability of Making Money at Different ScalesSource: Taleb (2001), Table 3.1.ScaleProbability1 year1 quarter1 month1 day1 hour1 minute1 second93%77%67%54%51.3%50.17%50.02%5

I. Return SourcesC. Illiquidity (Continued) Costs: Default and Liquidation RiskSource: Krishnan and Nelken (2003).6

I. Return SourcesD. Eventful Periods Managed Futures programs are now expected to benefit fromevent risk.The Myth of Hedge Fund Market Neutrality: Good News forManaged FuturesDeclines in the S&P 500 of GreaterThan 6% Since 198012345678910111213141516171819S ep -N o v 1 9 8 7A p r -J u l 2 0 0 2J u n -S e p 2 0 0 1J u l-A u g 1 9 9 8F e b -M a r 2 0 0 1J u n -O ct 1 9 9 0S ep -N o v 2 0 0 0S ep 2 0 0 2D ec 2 0 0 2 to F eb 2 0 0 3A u g -S ep 1 9 8 1F e b -M a r 1 9 8 0D ec 1 9 8 1 -M a r 1 9 8 2S ep 1 9 8 6D ec 1 9 8 0 -J a n 1 9 8 1F e b -M a r 1 9 9 4J a n -F e b 2 0 0 0Jan 1990M a y -J u ly 1 9 8 2J u l-S e p 1 9 9 9A v e ra g eS& P 500-3 0 %-2 0 %-1 7 %-1 5 %-1 5 %-1 5 %-1 3 %-1 1 %-1 0 %-1 0 %-1 0 %-1 0 %-8 %-7 %-7 %-7 %-7 %-7 %-6 %M anagedF u tu re s a8 .5 %1 0 .6 %1 .9 %5 .8 %4 .0 %1 9 .4 %2 .7 %1 .9 %1 2 .1 %0 .1 %1 0 .3 %7 .9 %-4 .2 %9 .5 %0 .3 %0 .9 %3 .2 %1 .4 %-0 .5 %H ed g eFunds b-1 2 %5%-2 %-4 .4 %-3 .8 %-9 .4 %-3 .8 %-1 .9 %-6 .4 %-1 .5 %0 .5 %-2 .1 %6 .8 %-2 .1 %0 .7 %a: CISDM (Center for International Securities and Derivatives Markets) Trading Advisor Qualified Index.b: HFR (Hedge Fund Research) Fund Weighted Composite Index.Based on Horwitz (2002), Slide 8.7

II. Properties of ReturnsA. Short-Options-Like ReturnsHFR Event Driven Returns vs. Traditional Portfolio ReturnsLOESS Fit (degree 3, span 1.0000)HFR Event driven monthly returns0.10LPP Pictet Index:a benchmark index for Swissinstitutional investors, which includes Swissequities, global equities, and global bonds.0.05LOESS Fit (Regression):a type of regression used to fit non-linearrelationships. Here, the researchers fit therelationship between hedge fund returnsand market returns. Market returns, in turn,are represented by the LPP Pictet Index.0.00-0.05-0.10-0.06 -0.04 -0.02 Pictet Index monthly returnsHFR: Hedge Fund Research, Inc.Event Driven (Strategy): Also known as “corporate life cycle investing.”Source: Favre and Galeano (2002), Exhibit 8.8

II. Properties of ReturnsA. Short-Options-Like Returns (Continued)Returns of an Options-Based Index Strategy thatMaximizes the Sharpe Ratio vs. an IndexSource: Goetzmann et al. (2002), Figure 4.9

II. Properties of ReturnsB. Long-Options-Like Returns Call optionPayoff ProfileInvestors expect long-options-like profiles fromCTA’s and global macro hedge fund managers.Histogram of Monthly Returns of the Barclay CTA 0Monthly ReturnsSource: Lungarella (2002), Figure 1.10

II. Properties of ReturnsB. Long-Options-Like Returns (Continued) StraddleGloba l Ma cro Style ve rsus the Dolla rPercent per Month6420-2-412345Quintile s of Dollar Re tur nGlobal MacroSource: Fung and Hsieh (1997), Figure 5.US Dollar11

III. Performance MeasurementA. Sharpe Ratio Required Assumptions1.Historical Results Have Some Predictive Ability;2.The Mean and Standard Deviation Are Sufficient Statistics;3.The Investment’s Return Are Not Serially Correlated; andSource: Sharpe (1994).12

III. Performance MeasurementA. Sharpe Ratio (Continued) Required Assumptions (Continued)4.The Candidate Investments HaveSimilar Correlations with theInvestor’s Other Assets.5.Conclusion: Sharpe himselfstates that the use of historicalSharpe ratios as the basis formaking predictions “is subject to serious question.”Source: Lux, (2002).13

III. Performance MeasurementB. Alternative Metrics Asset-Based Style FactorsHedge Fund Styles That Can be Modeled with Asset-Based Style FactorsMarket Timing or DirectionalStrategiesLong/Short or Relative ValueStrategiesHigh beta to standard asset classesLow beta to standard asset classesEvent-DrivenTrend Following vergence on:Commodities Capitalization SpreadValue/Growth SpreadTrend Following:1 and/or 2 aboveExcerpted from Fung and Hsieh (2003), Exhibit 5.5.Convergence on: Credit SpreadMortgageSpreadTrend Following:Credit Spread14

III. Performance MeasurementB. Alternative Metrics (Continued) Asset-Based Style FactorsEquity Arbitrage StrategiesHFR Event Driven Index8.006.004.00Return2.00EDRPED0.00-2.00EDRP: Event DrivenReplicating PortfolioED: HFR Event Driven IndexJul- Aug- Sep- Oct- Nov- Dec- Jan- Feb- Mar- Apr- M Jun- Jul- Aug- Sep- Oct- Nov- Dec0000 00 00 00 00 01 01 01 01 ay- 01 0101 01 01 01 0101-4.00-6.00MonthSource: Agarwal and Naik (2004).15

IV. Risk ManagementA. Incorporating Extreme EventsSample Portfolio with a Maximum Investment in Hedge Funds of gohne considerationwithoutofvonS S ten0,90%0,80%Efficient frontierEffizienzliniemit BerücksichtigungwithconsiderationvonS S ,00NormaleandNormalundmodifiedmodifizierteVaR VaR(in %)(in %)(S refers to skewness, and K refers to kurtosis).Source: Signer and Favre (2002), Exhibit 6.16

IV. Risk ManagementB. Event Risk: Individual ManagersA Derivatives Portfolio’s Exposure to Severe EventsEventOctober 1987 stock market crashGulf War in 1990Fall 1998 bond market debacleAftermath of 9/11/01 attacksMaximum Loss-4.11%-4.12%-6.42%-3.95%Worst-Case EventFall 1998 bond market debacleMaximum Loss-6.42%Value-at-Risk based on recent volatility and correlations3.67%Source: Risk Report from Premia Capital Management, LLCas cited in Till and Eagleeye (2003).17

IV. Risk ManagementC. Event Risk: Fund-of-FundsSource: Johnson et al. (2002).18

IV. Risk ManagementD. Transparency and the Limitations to QuantitativeTechniques Bismarck’s AdviceFrom experience, it seems that hedge fund investors applyBaron von Bismarck's advice on sausages and legislationto their investments:“Anyone who likes legislation or sausage should watchneither one being made.”19

IV. Risk ManagementD. Transparency and the Limitations to QuantitativeTechniques (Continued) Inferring ExposuresHedge-Fund Style RadarsGlobal Macro0.450.40Convertible Arbitrage0.35Fixed Income ArbitrageConvertible Arbitrage0.30Dedicated Short Bias0.250.20Fixed Income Arbitrage0. Short EquityMarket Neutral0.050.05Market Neutral0.000.00Dedicated Short BiasManaged FuturesEmergingManaged FuturesEvent DrivenGlobal MacroLong Short EquityEvent DrivenEmerging“The figure shows the hedge fund radars obtained for a convertible arbitrage fund (left) and a fund of hedge funds (right). The sensitivities (i.e., style-betacoefficients) are estimated using three years of historical data.”Source: Lhabitant (2001).20

IV. Risk ManagementD. Transparency and the Limitations to QuantitativeTechniques (Continued) Inferring Exposures (Continued)Proportional Marginal Variance DecompositionThis graph illustrates Premia Capital’s rolling exposures in energies, metals, U.S. fixed income, livestock, and agriculture during the first eight months of2004. More technically, the graph shows the conventional benchmarks that were most effective in jointly explaining Premia’s daily return varianceusing an advanced returns-based-analysis technique.The benchmarks are the Goldman Sachs (GS) Commodity sector excess return (ER) indices and a Bloomberg U.S. fixed-income index. The graph’s yaxis is the fraction of R-squared that can be attributed to a benchmark exposure. This is also known as the benchmark’s variance component. The middlechart shows each benchmark’s contribution to R-squared over the whole history.Based on Feldman (2005), Slide 8,PRISM Analytics,

IV. Risk ManagementD. Transparency and the Limitations to QuantitativeTechniques (Continued) Cautionary ExampleSimulated Short Volatility Investment Strategy20000001800000Investment 02000007671666156514641363126211611610Time (months)Short Volatility InvestmentSource: Anson (2002), Exhibit 1. (This chart wascreated by Professor J. Clay Singleton of RollinsCollege using the algorithm in Anson’s article.)Investment at T-bill 6%22

V. Investor Preferences and ChoicesA. Types of Products Risk and Loss Aversion In a Situation of Surplus or NotSources: Chen et al. (2002) and Siegmann and Lucas (2002).23

V. Investor Preferences and ChoicesB. How to Incorporate Hedge Funds in an Investor’s OverallPortfolioSix Possible Conceptual Frameworks for Hedge Funds, Part IHOW HEDGE FUNDS SHOULD BE CHARACTERIZED1. Equity Proxies2. Unconventional Betas/Non-StandardPerformance CharacteristicsPOTENTIALIMPLICATIONS FOR MANAGER SELECTIONIMPLICATIONS FOR INSTITUTIONALASSET ALLOCATIONWant managers who capture thepremium of asset class but also curtail downside riskReplace traditionalequity managers withhedge fund managers.Could decide to only use style-pure managersonce factor exposures are defined;Include unconventional betasin plan's long-term asset allocationmodeling.Use investable style tracker funds instead of managers; and/orBe careful to not pay high "alpha" fees for what isactually a type of "beta."Opens up possibility fortactical style selection.Decide which hedge fund stylesare appropriate, given an institution'slevel of risk and loss aversion.3. Alpha Generators/Exploiting InefficienciesEmphasis on managers whose performance cannot belinked to major risk factorsExpectation is that returnpatterns will be unrelated to assetclasses in the core portfolio.Manager selection is a bottom-up exercise.Cannot use hedge fund style and indexdata in asset allocation modeling.For every investor thatbenefits from exploitingan inefficiency, there mustbe an investor supplying theinefficiency:Strategies are thereforeinherently capacity constrained.Source: Till (2004).24

V. Investor Preferences and ChoicesB. How to Incorporate Hedge Funds in an Investor’s OverallPortfolio (Continued)Six Possible Conceptual Frameworks for Hedge Funds, Part I(Continued)HOW HEDGE FUNDS SHOULD BE CHARACTERIZED4. Traditional Factor Exposures with AdditionalReturns from Market Segmentation and Liquidity Premia5. Total Return ProvisionThrough a Fund-of-FundsPOTENTIALIMPLICATIONS FOR MANAGER SELECTIONIMPLICATIONS FOR INSTITUTIONALASSET ALLOCATIONManager selection would be part of a top-down approach.A holistic framework in which allinvestments are represented interms of a common set of factorsEmphasis on fund-of-funds or multi-strategy managersDiversify idiosyncraticoperational risk of individualhedge funds."Style Drift" is acceptable on the part of both managersand the fund-of-funds.Within a fund-of-funds portfolio, rebalancing is not a viableoption.Additional advantage in modeling is as follows:of the hedge fund data that is available,fund-of-fund data have the least biases.Optimal fund-of-fund construction is aresponsibility of the fund-of-fund manager, notthe plan sponsor.6. Unstable Factor ExposuresSource: Till (2004).Hedge Funds can't be integrated into an institutional framework.Don't use hedge funds25

V. Investor Preferences and ChoicesB. How to Incorporate Hedge Funds in an Investor’s OverallPortfolio (Continued)Six Possible Conceptual Frameworks for Hedge Funds, Part IIHOW HEDGE FUNDS SHOULD BE CHARACTERIZED1. Equity ProxiesBENCHMARKWant correlation withS&P but withtruncated downside.Equity mutual funds2. Unconventional Betas/Non-StandardPerformance Characteristics3. Alpha Generators/Exploiting Inefficiencies4. Traditional Factor Exposures with AdditionalReturns from Market Segmentation and Liquidity Premia5. Total Return ProvisionThrough a Fund-of-Funds6. Unstable Factor ExposuresSource: Till (2004).Benchmark is either a linear functionof basic factor exposures, orasset-based style factors, orhedge fund styles.A total-return benchmarkDerived from the factors assumed todrive each hedge fund strategy's returns.Balanced 60/40 Portfolio:But note that this bogey has beendifficult to outperform.Not applicable26

VI. Conclusion We cannot all be exploiters of inefficiencies, providersof insurance, and suppliers of liquidity. Therefore, one will need to accept that most investors’long-term performance will be due to an appropriatelydesigned and executed asset allocation policy.27

References Agarwal, Vikas and Narayan Naik, “Risks and PortfolioDecisions involving Hedge Funds,”