But guess what? Treasury Inflation-Indexed Securities Less Volatile

278 SECTION THREE

PV = PV (coupons) + PV (final payment)

= (coupon × annuity factor) + (face value × discount factor)

.08 .08(1.08) 4 ]

= $140 × 1 [ 1 – 1 + $1,000 ×

1.08 4

= $463.70 + $735.03 = $1,199

4 The 6 percent coupon bond with maturity 2002 starts with 3 years left until maturity and sells for $1,010.77. At the end of the year, the bond has only 2 years to maturity and in- vestors demand an interest rate of 7 percent. Therefore, the value of the bond becomes

PV at 7% = $60 + $1,060 = $981.92

(1.07) (1.07) 2

You invested $1,010.77. At the end of the year you receive a coupon payment of $60 and have a bond worth $981.92. Your rate of return is therefore

Rate of return = $60 + ($981.92 – $1,010.77) = .0308, or 3.08%

$1,010.77

The yield to maturity at the start of the year was 5.6 percent. However, because interest rates rose during the year, the bond price fell and the rate of return was below the yield to matu- rity.

5 By the end of this year, the bond will have only 1 year left until maturity. It will make only one more payment of coupon plus face value, so its price will be $1,060/1.056 = $1,003.79. The rate of return is therefore

$60 + ($1,003.79 – $1,007.37) = .056, or 5.6%

$1,007.37

6 At an interest rate of 5.6 percent, the 3-year bond sells for $1,010.77. If the interest rate jumps to 10 percent, the bond price falls to $900.53, a decline of 10.9 percent. The 30-year bond sells for $1,057.50 when the interest rate is 5.6 percent, but its price falls to $622.92 at an interest rate of 10 percent, a much larger percentage decline of 41.1 percent.