# 9

# Hedging the Risk of an Energy Futures Portfolio^{§}

Carol Alexander

This chapter considers a hedging problem for a trader in futures on crude oil, heating oil and unleaded gasoline and on the crack spreads based on these energy commodities. We first explain how the trader can map his current position to use constant maturity futures as risk factors. This has many advantages over using spot price or prompt futures prices plus discount rates as risk factors. Then we show how the trader can quantify his key risk factors, assess the risk of his portfolio and determine the most cost-effective hedging strategies.

The outline of this chapter is as follows. Section 9.1 explains the risk factor mapping process, and the advantages of using constant maturity futures as risk factors; Section 9.2 describes the portfolio to be hedged and Section 9.3 explains how principal component analysis is applied to reduce the dimension of the risk factor space and to isolate the key sources of risk; Section 9.4 assesses the risk of the portfolio and describes how best to hedge this risk; and Section 9.5 concludes.

## 9.1 MAPPING PORTFOLIOS TO CONSTANT MATURITY FUTURES

Constant maturity futures are not traded instruments. However, a time series of constant maturity commodity futures can be obtained by *concatenation* of adjacent futures prices. For instance, a time series for a constant maturity 1-month futures price can be obtained by taking the prompt futures with expiry less than or equal to 1 month and the ...