There are strong parallels and differences between the two envelopes puzzle and Siegel’s paradox in foreign exchange. This presentation will compare and contrast the two and show that a real Siegel effect is possible by taking some currency risk. Partly because of the Siegel effect, international investors generally will want to hedge less than 100 percent of their foreign investments. The presentation ends with a practical approach to currency hedging for international portfolios.
Dr. Hu is the Chief Research Officer and Co-chair of the Investment Committee of Campbell & Company. Since he joined the firm, Dr. Hu has had a major role in the ongoing research and development of Campbell& Company’s trading systems, models, and systematic algorithms. As Chief Research Officer he is responsible for the management of the research and investment process. Dr. Hu holds a Ph.D. in Systems and Information Engineering from the Toyohashi University of Technology in Japan.
In this talk we examine analytical properties of drawdowns as path dependent measures of risk. To this effect we derive analytical formulas of the joint law of drawdowns and the speed with which they are realized. We also examine the problem of valuation of drawdown insurance in the form of digital contracts based on drawdown events. We demonstrate that it is possible to replicate the payoff of such contracts by actual trade instruments. We also consider the problem of valuation of such insurance contracts through a continuously paid risk premium and the optimal termination strategy of such a contract under appropriate conditions.