Exercise Show that if the yield to maturity increases, then holding-period return is less than that initial yield. For example, suppose in Example 10.10 that by the end of the first year, the bond's yield to maturity is 8.5%. Find the one-year holding-period return and compare it to the bond's initial 8% yield to maturity. Example: Fair HPR To illustrate built-in capital gains or losses, suppose a bond was issued several years ago when the interest rate was 7%. The bond's annual coupon rate was thus set at 7%. (We will suppose for sim- plicity that the bond pays its coupon annually.) Now, with three years left in the bond's life, the interest rate is 8% per year. The bond's fair market price is the present value of the remaining annual coupons plus payment of par value. That present value is $70 x Annuity factor(8%, 3) + $1,000 x PV factor(8%, 3) = $974.23 which is less than par value. In another year, after the next coupon is paid and remaining maturity falls to two years, the bond would sell at $70 x Annuity factor(8%, 2) + $1,000 > PV factor(8%, 2) = $982.17 thereby yielding a capital gain over the year of $7.94. If an investor had purchased the bond at $974.23, the total return over the year would equal the coupon payment plus capital gain, or $70 + $7.94 = $77.94. This represents a rate of return of $77.94/$974.23, or 8%, exactly the current rate of return available elsewhere in the market. 226