Correlation Risk, Cross-Market Derivative Products, and Portfolio Performance

Abstract

We consider portfolios whose returns depend on at least three variables and show the effect of the correlation structure on the probabilities of the extreme outcomes of the portfolio return, using a multivariate binomial approximation. The portfolio risk is then managed by using derivatives. We illustrate this risk management both with simple options, whose payoff depends upon only one of the underlying variables, and with more complex instruments whose payoffs (and values) depend upon the correlation structure.

The question of benchmarking portfolio performance is complicated by the use of derivatives, especially complex derivatives, since these instruments fundamentally alter the distribution of returns. We use the multivariate binomial model to set performance benchmarks for multicurrency, international, portfolios. Our model is illustrated using a simple example where a German institution invests a proportion of its funds in German equities, and the remainder in UK equities. Portfolio performance is measured in Deutsche Marks and depends upon (1) the Dax index, (2) the FTSE index, and (3) the Deutsche Mark-Sterling exchange rate.

The output of the model is a simulation of possible outcomes from the portfolio hedging strategy. The difference in our methodology is that we are able to retain the simplicity of the binomial distribution, used extensively in the analysis of options, in a multivariate context. This is achieved by building three (or more) binomial trees for the individual variables and capturing the correlation structure with the use of varying conditional probabilities.