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What is Duration?

by Elizabeth Moran | Jun 02, 2010

A bond's maturity gives little indication of how much of its return is paid out during its life or the timing and size of its cash flows. For example, a zero coupon bond has no coupon payments during the life of the bond and returns face value at maturity. In contrast, a typical fixed rate bond pays a coupon twice a year as well as returning face value at maturity. Maturity alone is thus inadequate as an indicator of the bond's sensitivity to moves in market interest rates.

Consider two bonds with the same term to maturity but different coupons: the higher coupon bond generates a larger proportion of its return in the form of coupon payments than a lower coupon payment and so it pays out its return at a faster rate. Due to this, the higher coupon bond's price is theoretically less sensitive to interest rate fluctuations. Duration is the weighted average period of a bond's cash flow. Graphically it can be thought of as the point where a bond's cash flows are in balance (see graph below).

An effective way to analyse payment characteristics and interest rate sensitivities is the average maturity of a bond's cash flow stream, calculated by weighting the average time to receipt of cash flow payments by the present value of cash flow payments (see example in table below).

To calculate the duration multiply the first column (the term to cash flow in years), which is 0.5, by the present value of $3,365.38, to get $1.682.69 and continue down the table, the second row, multiplying 1 by $3,235.95, the third row 1.5 by $3,111.49 and so on. Adding the present values multiply by the term gives you $268,154.02, then dividing by the $97,378.93 price equates to a duration of 2.75 years.

If the coupon were higher, the investment would actually have a shorter duration due to the larger cash flows with higher present values occurring sooner which pulls the duration shorter. Likewise if the bond was a zero coupon bond, there would only be one cash flow - it would be $100,000 in three years, its present value being $78,000, however, as there is only the one cash flow the duration would also be three years.