Performance of Dynamic Hedging Strategies: The Tale of Two Trading Desks

Abstract

Suppose an investment bank consists of two desks trading in equity and equity options, and it operates in a market where equity returns are leptokurtic. It is well known (Schweizer 1994) that the optimal mean-variance trading strategy for the bank as a whole is path-dependent. This paper examines quasi-optimal strategies that preserve the path-independent nature of Black - Scholes option hedging coefficients without excessively compromising bank's overall efficiency. More generally, I investigate the issue of risk-adjusted performance measurement, attribution and investment-hedging separation between two desks trading in derivative and the underlying asset, respectively.

It is shown that both the optimal and quasi-optimal hedging strategies require close coordination between the equity and option desks, insofar as the optimal volume of option sales depends crucially on the relative performance of the two desks. Closed-form expressions for the Sharpe ratio and Certainty Equivalent Growth Rate as well as numerical results for a model calibrated to historical FTSE 100 equity index returns are given.

Keywords: Incremental Sharpe ratio, risk-adjusted returns, dynamic performance measurement, investment-hedging separation, option pricing, mean-variance hedging, Levy process

JEL Classification: G11, C61