R Programming for Actuarial Science

11 Hedging: Protecting Against a Fall in Equity Markets

Peter McQuire

11.1 Introduction

Like diversification and matching, hedging is a key risk management strategy adopted by many institutions. Its aim is to minimise the net change in the future value of a position, by buying or selling an asset which behaves in the opposite direction to the existing position.

The concept of hedging is mathematically very similar to the concept of matching (see Chapter 10). In this chapter we focus on a specific example, that of how to hedge against a fall in the value of a portfolio of shares by taking a short position in equity index futures. In particular we will look at how we can minimise the uncertainty in our net position when exact hedging is not possible, which will usually be the case in practice, by making use of the “optimum hedge ratio”.

A detailed understanding of futures pricing is not required to understand what follows – the key point is that the value of the “hedging” asset (in this case the futures contract) will tend to move in the opposite direction to that of the original asset or portfolio. For the reader who has not studied futures prior to reading this chapter, included below is a brief introduction. (Please see Hull (2012) chapter 3 for a more detailed explanation of financial futures contracts; the example below aims to explain the essence of futures contracts.)

11.2 Our Example

11.2.1 Futures Contracts – A Brief Explanation

In the fictitious country of Capland ...