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

Abstract

* 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 institutions. The authors are not responsible or liable in any manner for any losses and/or damages caused by the use of any contents in this research. Takahashi and Yamamoto (2010) is the summary of this research. It is based on the presentation entitled "A New Hedge Fund Replication Method with the dynamic Optimal Portfolio at Global Conference on Business and Finance 2010

Optimal payoffs under state-dependent preferences

“…This finding is consistent with the result obtained byTakahashi and Yamamoto (2013), who apply it to replicate a joint distribution in the hedge fund industry.10 To see this, recall that the joint distribution between the twin f (S t , S T ) and S T is fixed and thus also the joint distribution between the twin and ξ T (as ξ T is a decreasing function of S T due to (2)). All twins f (S t , S T ) with such a property have the same price E[ξ T f (S t , S T )].…”

“…2 The results of Takahashi and Yamamoto (2013) are stated in a general market, but the proof of their basic Theorem 3.1 in Appendix A.1 only holds when the number of states is countable. The proof of their main theorem, Theorem 3.3 (Appendix A.3.…”

“…Using our framework, we can characterize optimal payoffs explicitly (Theorems 3.2 and 3.4) in this setting. Such explicit characterizations are derived independently in Theorems 3.1 and 3.3 of Takahashi and Yamamoto (2013) but proved only for cases in which there is a countable number of states 2 . Furthermore, we show that optimal strategies in this setting become conditionally increasing functions of the terminal value of the underlying risky asset.…”

“…The paper draws its inspiration from the last section inBernard, Boyle and Vanduffel (2014a), in which a constrained cost-efficiency problem is solved when the joint distribution between the wealth and some benchmark is determined in some specific area (local dependence constraint).2 The results ofTakahashi and Yamamoto (2013) are stated in a general market, but the proof of their basic Theorem 3.1 in Appendix A.1 only holds when the number of states is countable. The proof of their main theorem, Theorem 3.3 (Appendix A.3.…”