Roncalli, Thierry and Weisang, Guillaume (2008): Tracking problems, hedge fund replication and alternative beta.
Download (1552Kb) | Preview
As hedge fund replication based on factor models has encountered growing interest among professionals and academics, and despite the launch of numerous products (indexes and mutual funds) in the past year, it faced many critics. In this paper, we consider three of the main critiques, namely the lack of reactivity of hedge fund replication and its deficiency in capturing tactical allocations; its failure to apprehend non-linear positions of the underlying hedge fund industry and higher moments of hedge fund returns; and, finally, the lack of access to the alpha of hedge funds. To address these problems, we consider hedge fund replication as a general tracking problem which may be solved by means of Bayesian filters. Using the linear Gaussian model as a basis for discussion, we provide the reader with an intuition for the inner tenets of the Kalman filter and illustrate the results' sensitivity to the algorithm specification choices. This part of the paper includes considerations on the type of strategies which can be replicated, as well as the problem of selecting factors. We then apply more advanced Bayesian filters' algorithms, known as particle filters, to capture the non-normality and non-linearities documented on hedge fund returns. Finally, we address the problem of accessing the pure alpha by proposing a core/satellite approach of alternative investments between high-liquid alternative beta and less liquid investments.
|Item Type:||MPRA Paper|
|Original Title:||Tracking problems, hedge fund replication and alternative beta|
|Keywords:||tracking problem; hedge fund replication; alternative beta; global tactical asset allocation; Bayes filter; Kalman filter; particle filter; numerical algorithms (SIS, GPP, SIR and RPF); skewness; kurtosis; non-linear exposure; alpha|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C60 - General
|Depositing User:||Thierry Roncalli|
|Date Deposited:||14. Mar 2012 23:07|
|Last Modified:||11. Feb 2013 16:35|
Vikas Agarwal and Narayan Y. Naik. Performance evaluation of hedge funds with optionbased and buy-and-hold strategies. London Business School, Working Paper, August 2000.
Vikas Agarwal and Narayan Y. Naik. Risks and portfolio decisions involving hedge funds. Review of Financial Studies, 17(1):63-98, 2004.
Noël Amenc, Sina El Bied, and Lionel Martellini. Evidence of predictability in hedge fund returns. Financial Analysts Journal, 59:32-46, September 2003.
Noël Amenc, Walter Géhin, Lionel Martellini, and Jean-Christophe Meyfredi. The myths and limits of passive hedge fund replication. EDHEC Risk and Asset Management Research Centre, Working Paper, June 2007.
Noël Amenc, Lionel Martellini, Jean-Christophe Meyfredi, and Volker Ziemann. Passive hedge fund replication: Beyond the linear case. EDHEC Risk and Asset Management Research Centre, Working Paper, 2008.
Gaurav S. Amin and Harry M. Kat. Hedge fund performance 1990-2000: Do the "money machines" really add value? Journal of Financial and Quantitative Analysis, 38(2):251-274, June 2003.
Sanjeev Arulampalam, Simon Maskell, Neil J. Gordon, and Tim Clapp. A tutorial on particle lters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transaction on Signal Processing, 50(2):174-188, February 2002.
Adelchi Azzalini and Antonnella Capitanio. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. JRSS Ser. B, 65:367-389, 2003.
Olivier Cappé and Eric Moulines. On the use of particle ltering for maximum likelihood parameter estimation. In European Signal Processing Conference, Antalya, Turkey, September 2005.
Thomas Della Casa, Mark Rechsteiner, and Ayako Lehmann. Attack of the 'hedge fund' clones. Man Investments Research, Working Paper, 2008.
Antonio Diez de los Rios and Rene Garcia. Assessing and valuing the non-linear structure of hedge fund returns. Bank of Canada Working Paper, October 2008.
Arnaud Doucet and Vladislav B. Tadic. Parameter estimation in general state-space models using particle methods. Annals of the Institute of Statistical Mathematics, 55(2):409-422, 2003.
William Fung and David A. Hsieh. Empirical characteristics of dynamic trading strategies: The case of hedge funds. Review of Financial Studies, 10(2):275-302, 1997.
William Fung and David A. Hsieh. A primer on hedge funds. Journal of Empirical Finance, 6:309-331, September 1999.
William Fung and David A. Hsieh. The risk in hedge fund strategies: Theory and evidence from trend followers. Review of Financial Studies, 14(2):313-341, 2001.
William Fung and David A. Hsieh. The risk in hedge fund strategies: Theory and evidence from long/short equity hedge funds. Working Paper, 2004.
William Fung and David A. Hsieh. Hedge fund replication strategies: Implications for investors and regulators. Financial Stability Review, 10:55-66, April 2007.
Jasmina Hasanhodzic and Andrew Lo. Can hedge-fund returns be replicated?: The linear case. Journal of Investment Management, 5(2):5-45, 2007.
Lars Jaeger. Alternative Beta Strategies and Hedge Fund Replication. John Wiley & Sons, New York, 1st edition, 2009.
Michael S. Johannes and Nick Polson. Particle ltering and parameter learning. University of Chicago, Working Paper, March 2007.
Harry M. Kat. Alternative routes to hedge fund return replication. Journal of Wealth Management, 10(3):25-39, 2007.
Harry M. Kat and Helder P. Palaro. Replication and evaluation of funds of hedge funds returns. In Fund of Hedge Funds: Performance, Assessment, Diversication and Statistical Properties (eds: Greg Gregoriou), Chapter 3, Elsevier Press, 2006.
Robert C. Merton. On market timing and investment performance. I. an equilibrium theory of value for market forecasts. Journal of Business, 54(3):363-406, July 1981.
Jimmy Olsson, Olivier Cappé, Randal Douc, and Eric Moulines. Sequential monte carlo smoothing with application to parameter estimation in nonlinear state space models. Bernoulli, 14(1):155-179, 2008.
Michael K. Pitt and Neil Shephard. Filtering via simulation: Auxiliary particle lters. Journal of the American Statistical Association, 94(446):590-599, June 1999.
George Poyiadjis, Arnaud Doucet, and Sumeetpal S. Singh. Maximum likelihood parameter estimation in general state-space models using particle methods. In Proceedings of the American Statistical Association, JSM 05, August 2005.
George Poyiadjis, Arnaud Doucet, and Sumeetpal S. Singh. Particle methods for optimal filter derivative: application to parameter estimation. In Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing, March 2005.
Branko Ristic, Sanjeev Arulampalam, and Neil J. Gordon. Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House, Boston, 1st edition, 2004.
Thierry Roncalli. TSM: Time Series and Wavelets for Finance. Global Design, Paris, 1996.
Thierry Roncalli and Jerome Teiletche. An alternative approach to alternative beta. Journal of Financial Transformation, Cass-Capco Institute Paper Series on Risk, 2008.
Thierry Roncalli and Guillaume Weisang. PF: A Gauss Library for Particle Filters. 2008. http://www.thierry-roncalli.com/#gauss_l17.
Thomas B. Schön, Adrian G. Wills, and Brett Ninness. Maximum likelihood nonlinear system estimation. In Proceedings of the 14th IFAC Symposium on System Identication, Newcastle, Australia, pages 1003-1008, March 2006.
William F. Sharpe. Asset allocation: management style and performance measurement. Journal of Portfolio Management, 18(2):7-19, 1992.
Adrian G. Wills, Thomas B. Schön, and Brett Ninness. Parameter estimation for discrete-time nonlinear systems using EM. In Proceedings of the 17th IFAC World Congress on Automatic Control, Seoul, Korea, July 2008.