Duration is one measure of the average life of a series of cash payments. For bonds,...

Duration is one measure of the average life of a series of cash payments. For bonds, is duration usually shorter or longer than maturity? Why? When are they equal? Why is duration a better guide to the riskiness of a bond than maturity? Which would entail greater interest rate risk, a 30-year 5% coupon bond or a 30-year zero coupon bond or a Treasury bill? Why?

Expert Solution

Duration is an approximate measure of the the price sensitivity of a bond with respect to changes in interest rates. It is calculated as the sum of the weighted times when cash flows occur, weights being calculated as the present value of cash flow divided by the total present value of the bond. For bonds, duration is usually shorter than maturity as all cash flows are to be paid by maturity and the highest cash flow occurs at maturity.

Bond duration is equal to maturity for zero coupon bonds as they have a single cash flow which occurs at maturity.

Maturity only measures the time till the bond pays back the principal amount. However, duration takes into account, not only the principal payment but also the coupon payments so it is a better measure of interest rate risk than maturity.

Higher duration implies higher interest rate risk so a 30-year zero coupon bond will have the highest risk among all three as the 30-year coupon bond will have shorter duration than 30 years and treasury bills have a duration of one year or less.

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