Durations for Portfolio of Bonds Priced on Different Term Structures

Duration is commonly used as a first approximation measure of the interest rate risk of both individual bonds and portfolios of bonds. A study develops the duration of a portfolio of bonds that trade on different term structures because of, for example, differences in credit quality. In contrast to the duration of a portfolio of bonds priced on the same term structure, the duration of a portfolio of bonds priced on different term structures is shown to be a function of the future values of the composite securities at the portfolio duration date rather than their present values. Portfolio duration expressions for such portfolios are derived for alternate assumptions about the stochastic process driving moments in interest rates across securities. It is also shown that portfolio durations based on present-value weights are a special case of those based on future-value weights.