72 Part One Value
bre44380_ch03_046-075.indd 72 09/30/15 12:47 PM
- Spot interest rates and yields Look again at Table 3.5. Suppose that spot interest rates all
change to 4%—a “flat” term structure of interest rates.
a. What is the new yield to maturity for each bond in the table?
b. Recalculate the price of bond A. - Spot interest rates and yields Assume annual coupons.
a. What is the formula for the value of a two-year, 5% bond in terms of spot rates?
b. What is the formula for its value in terms of yield to maturity?
c. If the two-year spot rate is higher than the one-year rate, is the yield to maturity greater or
less than the two-year spot rate? - Measuring term structure The following table shows the prices of a sample of U.S. Trea-
sury strips in February 2012. Each strip makes a single payment of $1,000 at maturity.
a. Calculate the annually compounded, spot interest rate for each year.
b. Is the term structure upward- or downward-sloping or flat?
c. Would you expect the yield on a coupon bond maturing in February 2017 to be higher or
lower than the yield on the 2014 strip? - Bond returns and yields
a. An 8%, five-year bond yields 6%. If this yield to maturity remains unchanged, what will
be its price one year hence? Assume annual coupon payments and a face value of $100.
b. What is the total return to an investor who held the bond over this year?
c. What can you deduce about the relationship between the bond return over a particular
period and the yields to maturity at the start and end of that period? - Duration True or false? Explain.
a. Longer-maturity bonds necessarily have longer durations.
b. The longer a bond’s duration, the lower its volatility.
c. Other things equal, the lower the bond coupon, the higher its volatility.
d. If interest rates rise, bond durations rise also. - Duration Calculate the durations and volatilities of securities A, B, and C. Their cash
flows are shown below. The interest rate is 8%. - Term-structure theories The one-year spot interest rate is r 1 = 5% and the two-year rate
is r 2 = 6%. If the expectations theory is correct, what is the expected one-year interest rate in
one year’s time?
Maturity Price (%)February 2014 99.523%
February 2015 98.937
February 2016 97.904
February 2017 96.034Period 1 Period 2 Period 3A 40 40 40
B 20 20 120
C 10 10 110