The Impact of Basis Risk on Optimal Hedging and Hedge Efficiency

Abstract

We analyze the dependency of the optimal hedge and its efficiency on the correlation between the asset to be hedged, and the hedge instrument. The optimal portion of the hedge instrument depends on this correlation, and on the ratio of the volatilities. Efficiency is defined as the percental decrease in volatility caused by the hedge. The connection between the efficiency E of the optimal hedge, and the correlation rho is given by E = 1 - sqrt(1 - rho^2)

This means that basis risk is really substantial whenever the absolute value of the correlation is smaller than 1. The result is independent of any assumptions on distributions.

The mathematics of our result are not new. Arguments like this are used in the theory of Monte Carlo simulation.

Keywords: hedge, optimal hedge, correlation, efficiency, basis risk

JEL Classification: C00, D81, G11