Multi-Factor Risk Metrics and Hedges
Amajor weakness of the approach in Chapter 4, and of several of the models of Part Three, is the assumption that movements in the entire term structure can be described by one interest rate factor. To make the case in the extreme, because the six-month rate is unrealistically assumed to predict perfectly the change in the 30-year rate, a (naive) analysis leads to hedging a 30-year bond with a six-month bill. In reality, of course, it is widely recognized that rates in different regions of the term structure are far from perfectly correlated. Put another way, predicted changes in the 30-year rate relative to changes in the 6-month rate can be wildly off target, whether these predicted changes come from a model, like the one implicitly used in the first part of Chapter 4, or from the implicit assumption when using yield-based that the two rates move by the same amount. The risk that rates along the term structure move by different amounts is known as curve risk.
This chapter discusses how to measure and hedge the risks of a security or portfolio in terms of several other securities, where each hedging security is most sensitive to a different part of the term structure. The more securities used in the hedge, the less important are any ...