The asset and liability portfolios of financial institutions generate patterns of future cash flows that must conform to many restrictions in order to assure solvency and profitability. Many institutions, including insurance companies and pension funds, have definite and certain future commitments of funds. These institutions may wish to invest funds now so that their cash inflows (investment with accumulated earnings) will match their future commitments. In principle, the simplest way to meet future commitments exactly is to purchase single payment notes (or zero coupon bonds) which mature on the commitment dates. For long-term commitments, such instruments are not readily obtainable, at least in the United States. Most available bonds promise coupon payments over time so that these payments would have to be reinvested at unknown future interest rates in order to realize an accumulated sum at any future date when a commitment must be discharged. Since future interest rates are unknown at the initial moment of investment, it is not certain what accumulated earnings will be at future dates. In the absence of default, the risk of not meeting future commitments may be minimized by adopting investment strategies based on the concept of duration. Duration is a measure of the average maturity of an income stream; it is a weighted average of the dates at which the income payments are received, where the weights add to unity and are related to the present value of the income stream. Dating from the initial work of Macaulay [9] and Hicks [6], duration has been shown to be important in constructing portfolios that are hedged or ‘immunized’ from the possible ravages of interest rate uncertainty.