Duration is a measure of interest-rate RISK (bond price volatility) that includes both the coupon rate and the time to maturity of the bond. Most BONDS, both government and corporate debt instruments, are issued with a fixed interest rate (the coupon rate) for a set period of time (maturity). Duration incorporates both these features. A weighted average of each of the coupon payments plus final payment (return of principal) at the maturity date, duration is calculated by the formula



where:
D = duration of the bond
PB = price of the bond = · CFt /(1 + i)t
CF = coupon or principal payment at time t
i = interest rate
t = time period in which the principal or coupon
payment is made

In the formula, duration is the present value of all cash flows discounted according to the length of time until they are received and divided by the price of the bond, which is the present value of all cash flows. Duration is directly related to maturity and inversely related to the coupon rate. The longer the time until maturity, the higher the duration, and the higher the coupon rate, the lower the duration. Since duration measures interest rate risk, financial managers can match the duration of their ASSETS and liabilities. Thus if INTEREST RATES rise (causing a decline in bond prices), decline values of financial assets will be offset by declining costs of liabilities. During the 1980s, many SAVINGS AND LOAN ASSOCIATION managers, faced with increased competition for deposits from nonbank financial institutions (particularly stock brokerage firms), used short-term deposits to finance long-term LOANS. When interest rates continued to rise, the value of their assets (loans) declined while their liabilities did not decrease, contributing to the S&L; crisis.