Generating a target payoff distribution with the cheapest dynamic portfolio: an application to hedge fund replication

Abstract

This paper provides a new method for constructing a dynamic optimal portfolio for asset management. This method generates a target payoff distribution using the cheapest dynamic trading strategy. As a practical example, the method is applied to hedge fund replication. This dynamic portfolio strategy is regarded as an extension of a hedge fund replication methodology that was developed by Kat and Palaro and Papageorgiou et al. to address multiple trading assets with both long and short positions. Empirical analyses show that such an extension significantly improves the performance of replication in practice.

Keywords:

• Alternative investments
• Investment strategy
• Portfolio optimization
• Hedge funds

Classification:

• G1
• G2
• G11
• G20

Acknowledgments

This research is supported by CARF (Center for Advanced Research in Finance) and the global COE program ‘The research and training center for new development in mathematics’. We are very grateful to two anonymous referees for their precious comments, which have improved the previous version of this paper substantially. Also, we thank Hideki Yamauchi and Takahiko Suenaga at GCI Asset Management Inc. and Tetsuya Aoki at GCI Investment Management Singapore Pte. Ltd. for their constant support. All the contents expressed in this research are solely those of the authors and do not represent any views or opinions of any institution. The authors are not responsible or liable in any manner for any losses and/or damages caused by the use of any contents of this research. Takahashi and Yamamoto (2010b) is the summary of this research. It is based on the presentation entitled ‘A new hedge fund replication method with the dynamic optimal portfolio’ presented at the Global Conference on Business and Finance Kailua-Kona, Hawaii, 2010.

Notes

The results of in-sample studies will be provided upon request.

The martingale method with Malliavin calculus readily gives us the dynamic portfolio that generates the payoffs. See, for example, Karatzas and Shreve (1998) for the basics of the martingale method and Nualart (2006) for the introduction to Malliavin calculus. For the application of Malliavin calculus to the dynamic optimal portfolio and its closed-form evaluation, see, for example, Ocone and Karatzas (1991) and Takahashi and Yoshida (2004).