Bond duration

Duration answers a practical question: if interest rates move, how much will this bond's price move? It is calculated as the weighted average time an investor waits to receive the bond's cash flows, with each payment weighted by its present value. Because a bond's price is just the present value of its future payments, cash flows that arrive further in the future are discounted more heavily and therefore react more sharply to a change in rates.

Two features drive duration. Maturity works in the obvious direction — a 30-year bond has a longer duration than a 5-year bond of the same coupon. Coupon works in the opposite direction: a high coupon returns more of the investor's money early, shortening the average wait, while a low coupon leaves more of the return locked in the final principal payment. That is why low-coupon bonds are more price-volatile than high-coupon bonds of the same maturity, and why a zero-coupon bond has a duration exactly equal to its maturity — its single cash flow arrives at the end.

Modified duration turns the measure into an estimate. A bond with a modified duration of 7 will lose roughly 7% of its value if yields rise by one percentage point, and gain roughly 7% if yields fall by one point. The estimate is approximate because the price-yield relationship is curved rather than straight, but it is close enough for comparing risk across bonds. Investors who expect rates to fall buy long-duration bonds to maximize price gains; those who fear rising rates shorten duration to limit losses.

Duration is a staple of fixed-income questions on the Series 7 and Series 65 exams. You should be able to rank bonds by volatility from their coupons and maturities, explain why a zero-coupon Treasury (such as a STRIP) is the most interest-rate-sensitive bond of a given maturity, and recognize that duration measures interest rate risk rather than default risk.