U.S. Treasury bonds pay coupon

U.S. Treasury bonds pay coupon interest semiannually. Suppose a Treasury bond matures in two years, the annual coupon rate is 8 percent, the face value is $1,000, and the annual yield to maturity ( R) is 12 percent. See Table 9–3for the calculation of the duration of this bond. As the calculation indicates, the duration, or weighted-average time to maturity, on this bond is 1.883 years. Table 9–4shows that if the annual coupon rate is lowered to 6 percent, duration rises to 1.909 years. Since 6 percent coupon payments are lower than 8 percent, it takes longer to recover the initial investment in the bond. In Table 9–5duration is calculated for the original 8 percent bond, assuming that the yield to maturity increases to 16 percent. Now duration falls from 1.883 years (in Table 9–3 ) to 1.878 years. The higher the yield to maturity on the bond, the more the investor earns on reinvested coupons and the shorter the time to recover the initial investment. Finally, when the maturity on a bond decreases to 1 year (see Table 9–6 ), its duration falls to 0.980 year. Thus, the shorter the maturity on the bond, the more quickly the initial investment is recovered.

Table 9–3




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