Full-Scale Optimization: A Flexible Framework for Hedge Design

Abstract

In this work we consider the application of expected utility optimization to the construction of an optimal hedge. Utility theory provides a rich framework for decision-making under uncertainty and features preferences specified via a range of simple to possibly complex functions of future portfolio returns. Optimal hedge construction examples are discussed in the context of downside protection for domestic equity, and the reduction of currency exposure risk inherent in a foreign equity position. We also quantify the impact of currency derivatives on the risk and return properties of a foreign equity holding. This is done by considering two types of preference specification featuring loss aversion, namely kinked utility and S-shaped utility. Both of these functions have particular relevance for fund managers concerned with the value of a portfolio falling below that of a benchmark, or a pension fund becoming underfunded at a certain point.