Investment Theory and Risk Management, + Website

Duration Redux

In the previous chapter, we worked exclusively with a flat term structure, in which interest centered on the sensitivity of bond prices to a change in yield, . The assumption of a flat term structure is very restrictive. What happens when we relax this constraint? In a world in which spot rates differ across maturities, interest rate risk and duration are no longer tied to a single yield but to the entire term structure; more specifically, to movements in the term structure. That is, we now wish to evaluate , where the are the spot rates that vary across maturities and Δ is a constant that shifts the term structure up or down in a parallel fashion. Parallel shifts are also restrictive but a necessary simplification—since we cannot control for spot rates varying independently by random amounts we instead study parallel shifts .

With continuous compounding, the bond price formula from the previous chapter becomes:

If the cash flows are constant across time, then . As before, ...