Chapter 13

Managing Linear Risk*

Risk that has been measured can be managed. This chapter turns to the active management of market risks. An important aspect of managing risk is hedging, which consists of taking positions that lower the risk profile of the portfolio.

Techniques for hedging have been developed in the futures markets, where farmers, for instance, use financial instruments to hedge the price risk of their products. In this case, the objective is to find the optimal position in a futures contract that minimizes the volatility of the total portfolio. This portfolio consists of two positions, a fixed inventory exposed to a risk factor and a hedging instrument.

In this chapter, we examine hedging in cases where the value of the hedging instrument is linearly related to the underlying risk factor. This involves futures, forwards, and swaps. The next chapter examines risk management using nonlinear instruments (i.e., options).

In general, hedging can create hedge slippage, or basis risk. Basis risk arises when changes in payoffs on the hedging instrument do not perfectly offset changes in the value of the inventory position. Hedging is effective when basis risk is much less than outright price risk.

This chapter discusses the management of risk with linear instruments. Section 13.1 presents unitary hedging, where the quantity hedged is the same as the quantity protected. Section 13.2 then turns to a general method for finding the optimal hedge ratio. This method is applied ...