Replicating the Properties of Hedge Fund Returns

In this article, the authors implement a multivariate extension of the Dybvig [1988] Payoff Distribution Model that can be used to replicate not only the marginal distribution of most hedge fund returns but also their dependence on other asset classes. In addition to proposing ways to overcome the hedging and compatibility inconsistencies in Kat and Palaro [2005], the authors extend the results of Schweizer [1995] and adapt American option pricing techniques to evaluate the model and also derive an optimal dynamic trading (hedging) strategy. The proposed methodology can be used as a benchmark for evaluating fund performance, as well as to replicate hedge funds or generate synthetic funds.

[1]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[2]  Kathryn Dixon Jost.  Do Market Timing Hedge Funds Time the Market , 2008 .

[3]  Jasmina Hasanhodzic,et al.  Can Hedge-Fund Returns Be Replicated?: The Linear Case , 2006 .

[4]  Bruno Rémillard,et al.  Goodness-of-fit Procedures for Copula Models Based on the Integral Probability Transformation , 2003 .

[5]  W. Fung,et al.  The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers , 2001 .

[6]  James Durbin,et al.  Weak convergence of the sample distribution function when parameters are estimated , 1973 .

[7]  W. Stute,et al.  Bootstrap based goodness-of-fit-tests , 1993 .

[8]  P. Glasserman,et al.  Estimating security price derivatives using simulation , 1996 .

[9]  Martin Schweizer,et al.  Variance-Optimal Hedging in Discrete Time , 1995, Math. Oper. Res..

[10]  V. Agarwal,et al.  Risks and Portfolio Decisions Involving Hedge Funds , 2004 .

[11]  M. Mitchell,et al.  Characteristics of Risk and Return in Risk Arbitrage , 2000 .

[12]  B. Rémillard,et al.  Goodness-of-fit tests for copulas: A review and a power study , 2006 .

[13]  Gary M. Lee,et al.  Nonlinear interpolation , 1971, IEEE Trans. Inf. Theory.

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[15]  Bruno Rémillard,et al.  Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation , 2006 .

[16]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[17]  Pierre Del Moral,et al.  Monte Carlo Approximations of American Options that Preserve Monotonicity and Convexity , 2010 .

[18]  R. Nelsen.  An Introduction to Copulas , 1998 .

[19]  Harry M. Kat,et al.  Hedge Fund Performance 1990–2000: Do the “Money Machines” Really Add Value? , 2003, Journal of Financial and Quantitative Analysis.

[20]  Helder P. Palaro,et al.  Who Needs Hedge Funds? A Copula-Based Approach to Hedge Fund Return Replication , 2005 .

[21]  Paul Wilmott,et al.  Paul Wilmott on Quantitative Finance , 2010 .

[22]  Paul Wilmott.  Paul Wilmott on Quantitative Finance Volume 2 , 2001 .

[23]  Philip H. Dybvig.  Distributional Analysis of Portfolio Choice , 1988 .