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Real Returns

Now suppose that the bond in the previous problem is a TIPS (inflation-indexed) bond with a coupon rate of 4 percent. What will the cash flow provided by the bond be for each of the four inflation rates? What will be the real and nominal rates of return on the bond in each scenario?

27. Real Returns. Now suppose the TIPS bond in the previous problem is a 2-year maturity bond. What will be the bondholder s cash flows in each year in each of the inflation scenarios?

28. Interest Rate Risk. Suppose interest rates increase from 8 percent to 9 percent. Which bond will suffer the greater percentage decline in price: a 30-year bond paying annual coupons of 8 percent, or a 30-year zero coupon bond? Can you explain intuitively why the zero exhibits greater interest rate risk even though it has the same maturity as the coupon bond?

1 a. The ask price is 101 23/32 = 101.71875 percent of face value, or $1,017.1875.

b. The bid price is 101 21/32 = 101.65625 percent of face value, or $1,016.5625.

c. The price increased by 1/32 = .03125 percent of face value, or $.3125.

d. The annual coupon is 6 1/4 percent of face value, or $62.50, paid in two semiannual installments.

e. The yield to maturity, based on the ask price, is given as 5.64 percent.

2 The coupon is 9 percent of $1,000, or $90 a year. First value the 6-year annuity of coupons:

Then value the final payment and add up:

3 The yield to maturity is about 8 percent, because the present value of the bond s cash returns is $1,199 when discounted at 8 percent:

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 investors demand an interest rate of 7 percent. Therefore, the value of the bond becomes

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 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 maturity. 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

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.