a joint work with … Devraj Basu EDHEC Business School Alexander Stremme Warwick Business School

1. Sail with Hedge Funds in the Storm? A New Approach Daniel Chi-Hsiou Hung Durham Business School Durham University http://www.dur.ac.uk/d.c.hung a joint work with …Devraj Basu EDHEC Business School Alexander StremmeWarwick Business School INQUIRE Hedge Fund Replication Project

2. Introduction overview literature theory results extensions investigating asset pricing anomalies … • hedge funds … • have seen assets under management grow … • … from $170 billion in 1995 to over $1.5 trillion in 2007 • adopt dynamic strategies that have option-like features • high returns but apparently no systematic risk • … relative to the CAPM • thus hedge fund managers seem to be ‘alpha’ generators INQUIRE Hedge Fund Replication Project

3. Introduction overview literature theory results extensions investigating asset pricing anomalies … • hedge funds … • thus high fees might be justified • however the traditional CAPM is not a suitable benchmark: • unable to capture both the dynamic and nonlinear natures • … of hedge fund payoffs / returns • a benchmark suitable for hedge fund performance … • … should incorporate both of these features INQUIRE Hedge Fund Replication Project

4. Introduction overview literature theory results extensions investigating asset pricing anomalies … • hedge fund benchmarks: • option payoffs have been used to capture the nonlinearity • e.g. Agarwal and Naik (2004). • however one could also use higher moments of the market return • e.g. Hasanhodzic and Lo (2007). • dynamic nature of payoffs may lead to return predictability • e.g. Amenc et. al (2003). INQUIRE Hedge Fund Replication Project

5. Introduction overview literature theory results extensions investigating asset pricing anomalies … • Why does this matter: • There is increasing evidence that hedge funds deliver “alpha” in the form of “alternative beta”, that is using possibly dynamic exposures to other systematic factors • This approach is the basis for hedge fund replication. • Fung, Hseih and Naik use the Fung and Hseih (2001) and Agarwal and Naik (2004) model, • Kat and Palaro (2006) have pioneered a technique based on managed futures. • Hasanhodzic and Lo (2006) use a factor based approach. INQUIRE Hedge Fund Replication Project

6. Introduction overview literature theory results extensions investigating asset pricing anomalies … • Hedge Fund Replication: • These approaches all seek to capture hedge fund returns using liquid traded factors at low cost. • This idea has caught the attention by the industry with Goldman Sachs and State Street among others launching replicators. • However the recent performance of hedge fund indices, particularly in 2008, should give one pause to consider whether hedge funds returns are worth replicating at all. INQUIRE Hedge Fund Replication Project

7. Introduction overview literature theory results extensions investigating asset pricing anomalies … • Hedge Fund Replication: • The following report from the blog AllAboutAlpha summarizes the situation for September 2008 INQUIRE Hedge Fund Replication Project

8. Introduction overview literature theory results extensions investigating asset pricing anomalies … • Hedge Fund Replication: • Our idea is to try to capture the essence of what hedge funds do-nonlinear exposures to the market and dynamic factor exposures. • We first analyze whether higher moments of the market return can capture these non-linearities. • We then examine the evidence for time-variation in the factor exposures. • We combine these to construct our “optimal benchmark” using traded versions of our factors. Our “optimal benchmark” may be regarded as a hedge fund strategy of the global macro type as well. INQUIRE Hedge Fund Replication Project

9. Introduction overview literature theory results extensions investigating asset pricing anomalies … • Hedge Fund Replication: • Global macro strategies were the “least bad” category in September 2008-again from AllAbout Alpha INQUIRE Hedge Fund Replication Project

10. Introduction overview literature theory results extensions investigating asset pricing anomalies … • Hedge Fund Replication: • Our approach is the first to try to systematically capture the non-linearities as well as time-variation in hedge fund returns. • The construction of an optimal benchmark is a new, more absolute return type approach to replication - in contrast to the traditional factor based approaches • It is a relatively low cost portfolio as it is based on liquid traded assets. • Benchmarking hedge funds against this new benchmark gives us an idea of the extent to which their returns are “alternative beta”. INQUIRE Hedge Fund Replication Project

11. Introduction overview literature theory results extensions • our “Optimal Benchmark”: • is optimal in the sense that it optimally utilizes the conditioning information… • incorporates second and third moment of the market return • … as extra factors (Skewness and Kurtosis factors) • incorporates time-varying factor risk premiums that are • … functions of yield curve variables • thus attempts to capture both the nonlinear and dynamic nature • … of hedge fund payoffs INQUIRE Hedge Fund Replication Project

12. Introduction overview literature theory results extensions • methodology: • our “Optimal Benchmark” is unconditionally efficient • … with respect to the conditioning information (predictive variables) • these were introduced in Hansen and Richard (1987) • and then Ferson and Siegel (2001) • and in Abhyankar, Basu and Stremme (2008) INQUIRE Hedge Fund Replication Project

13. Introduction overview literature theory results extensions • related literature: • Fung and Hsieh (2001) • Agarwal and Naik (2004) • Favre and Ranaldo (2005) • focus on hedge fund pricing • Amenc, Bied and Martellini (2003) • study return predictability in hedge fund indices • and findbenefits of tactical asset allocation are potentially large • Ferson and Siegel (2001) • extend the traditional asset allocation framework • to incorporate return predictability • builds on the fundamental paper by Hansen and Richard (1987) 13 INQUIRE Hedge Fund Replication Project

14. Introduction overview literature methodology results extensions • methodology: • we identify the priced risk factors that different types of hedge funds have a significant exposure using “in-sample” data … • the excess return on the market portfolio • the skewness and kurtosis factors (to capture hedge funds’ tendency to “bet” on asymmetric or “extreme” market movements) • the change in the VIX (to capture hedge funds taking positions on the basis of anticipated changes in volatility) • bond returns: the Lehman U.S. Corporate AA Intermediate Bond Index (to capture hedge funds’ exposure to non-equity markets) • credit spreads: the return difference b.t. … • the Lehman U.S. Corporate BAA Intermediate Bond Index • the Lehman U.S. Treasury index • the Goldman Sachs Commodity index INQUIRE Hedge Fund Replication Project

15. Introduction literature methodology results extensions • constructing the skewness and kurtosis factors: • the factor-mimicking portfolios of coskewness and cokurtosis: • compute conditional coskewness (it) and cokurtosis (it) of of all CRSP individual stocks of NYSE, AMEX and NASDAQ • the monthly return differences between the equally weighted portfolios of top 30% and bottom 30% coskewness and cokurtosis INQUIRE Hedge Fund Replication Project

16. Introduction literature methodology results extensions • methodology: • The predictive instruments … • The 1 month Treasury Bill rate (TBIM) • the term spread: the return difference between the 10 year Treasury bond and the 1 year Treasury bill • the credit spread: the return difference between 1 year AAA corporate bonds and Treasury bonds • the level of the VIX INQUIRE Hedge Fund Replication Project

17. Introduction literature methodology results extensions • methodology: • The factors are all liquidly traded factors with relatively low transaction costs • The predictive variables represent readily available public information INQUIRE Hedge Fund Replication Project

18. predicted component Introduction literature methodology results extensions • establish the relationship between the factors and instruments: • estimate, for each style, a VAR predictive regression simultaneously across all assets and instruments: • at the same time taking into account the possible autocorrelation in the instruments INQUIRE Hedge Fund Replication Project

19. Introduction literature methodology results extensions • instruments & conditional variance-covariance matrix • choose the instruments that have significant predictive power for the chosen factors • using the “difference in squared Sharpe ratio” test • which allows us to ascertain if any given predictive instrument provides significant economic gain • obtain the conditional mean t-1 and the variance-covariance matrix t-1 of the factor returns, as functions of the realized values of the instruments, zt-1 INQUIRE Hedge Fund Replication Project

20. Introduction literature methodology results extensions • measuring the value of return predictability without use of predictability … where R0 is the set of returns … on fixed-weight portfolios: vector of portfolio weights … unconditionally constant over time Devraj Basu, Daniel Hung and Alexander Stremme 20 INQUIRE Hedge Fund Replication Project

21. Introduction literature methodology results extensions • measuring the value of return predictability without use of predictability … where R0 is the set of returns … on fixed-weight portfolios: optimally using predictability … where R* is the set of returns … on managed portfolios: vector of portfolio weights … unconditionally constant over time vector of managed weights … functions of instruments t-1 = f(zt-1) Devraj Basu, Daniel Hung and Alexander Stremme 21 INQUIRE Hedge Fund Replication Project

22. Introduction overview literature theory results extensions measuring the value of return predictability managed portfolios: without use of predictability … where R0 is the set of returns … on fixed-weight portfolios optimally using predictability … where R* is the set of returns … on managed portfolios lemma: the fixed-weight Sharpe ratio can be written as … unconditional expected returns unconditional covariance matrix

23. Introduction overview literature theory results extensions measuring the value of return predictability managed portfolios: without use of predictability … where R0 is the set of returns … on fixed-weight portfolios optimally using predictability … where R* is the set of returns … on managed portfolios theorem: the optimally managed Sharpe ratio can be written as … conditional Sharpe ratio conditional covariance matrix

24. Introduction overview literature theory results extensions measuring the value of return predictability managed portfolios: without use of predictability … where R0 is the set of returns … on fixed-weight portfolios optimally using predictability … where R* is the set of returns … on managed portfolios implication (see also Cochrane 1999) … the higher the variability … … of the conditional Sharpe ratio the higher the economic gains … … from return predictability!

25. Introduction overview literature theory results extensions measuring the value of return predictability managed portfolios: without use of predictability … where R0 is the set of returns … on fixed-weight portfolios optimally using predictability … where R* is the set of returns … on managed portfolios definition: to measure the extent to which predictability expands the frontier … define: always  0 because R0  R*

26. Introduction overview literature theory results extensions measuring the value of return predictability managed portfolios: without use of predictability … where R0 is the set of returns … on fixed-weight portfolios optimally using predictability … where R* is the set of returns … on managed portfolios proposition: the test has a known distribution … in finite samples: define: asymptotically:

27. Introduction literature methodology results extensions • our “Optimal Benchmark”: • We then construct, for each fund style, a dynamically managed portfolio of a set of tradable factors • We form the efficient portfolios of the factors “out-of-sample” • the weight of the unconditionally efficient portfolio is a deterministic function of the instruments: • where is the conditional maximum squared Sharpe ratio, • w is a constant depending on the target mean or volatility of the portfolio INQUIRE Hedge Fund Replication Project

28. Introduction overview literature theory results extensions results: efficient portfolio weights weights as functions of conditional Sharpe ratio and mean instruments: TB1M, TSPR, CONV, CSPR

29. Introduction overview literature theory results extensions data: 12 hedge fund “style” indices: Distressed Securities (DS) Emerging Markets (EMT) Equity Market Neutral (EMN) Event Driven (ED) Fixed Income (FI) Global Macro (GM) Market Timing (MT) Merger Arbitrage (MAI) Relative Value Arbitrage (RV) Short Selling Index (SS) Commodity Trading Advisors (CTA) Sector Funds (SC) INQUIRE Hedge Fund Replication Project

30. Introduction overview literature theory results extensions • results: INQUIRE Hedge Fund Replication Project

31. Introduction overview literature theory results extensions • results: • The next table shows the performance of the benchmarks for each category • It also shows the performance of the equally weighted portfolio of individual funds both in an absolute sense and relative to the benchmark. • The performance of the benchmark in terms of the individual funds measured by what percentile it matches is also given. INQUIRE Hedge Fund Replication Project

32. Introduction overview literature theory results extensions • results: INQUIRE Hedge Fund Replication Project

33. Introduction overview literature theory results extensions • results: INQUIRE Hedge Fund Replication Project

34. Introduction overview literature theory results extensions • results: INQUIRE Hedge Fund Replication Project

35. Introduction overview literature theory results extensions • results: • For 8 of the 12 categories theses achieve Sharpe ratios of around 0.65 while for the other four (EMN, GM, MA and SS), they are lower at around 0.38. • Hence there are 8 categories that may be regarded as worth replicating form our perspective. • Our benchmark portfolios typically match the median return of the fund sample, and in most cases beat the Sharpe ratio of at least 35% of the funds, before fees. INQUIRE Hedge Fund Replication Project

36. Introduction overview literature theory results extensions • results: • The equally weighted portfolios have high alphas with respect to our benchmarks, which might be regarded as a drawback of our approach. • Nonetheless the results illustrate that our methodology does not just capture what is “already there”, a practitioner criticism of hedge fund replication. • Our benchmarks capture quite generic aspects of each hedge fund strategy, namely non-linear dynamic exposures and is able to replicate these at a relatively lower cost. • In this sense our approach resembles Kat and Palaro (2006) who use dynamic trading strategies to match the risk profiles of hedge funds. INQUIRE Hedge Fund Replication Project

37. Introduction overview literature theory results extensions • results: Over the Credit Crunch-Performance of Style Indices INQUIRE Hedge Fund Replication Project

38. Introduction overview literature theory results extensions • results: Credit Crunch-Performance of Dynamic Benchmarks INQUIRE Hedge Fund Replication Project

39. Introduction overview literature theory results extensions • results:Relative Performance of Dynamic Benchmarks INQUIRE Hedge Fund Replication Project

40. Introduction overview literature theory results extensions • results: Credit Crunch • Some hedge fund categories such as CTA, GM, SS, ELS did well over the credit crunch period. • However, over this period, each dynamic benchmark achieves a higher Sharpe ratio than the style index. • The benchmarks are constructedusing only publicly available information and “dumb” in the sense of being mechanically constructed • Their performance calls into question the assumption of “skill” of hedge fund managers across an entire style. INQUIRE Hedge Fund Replication Project