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which one the forward rates?

Year: 1 2 3
Spot rates or Forward rates? 10% 12% 14%
Spot rates or Forward rates? 10% 14.0364% 18.1078%
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

334 Part THREE Debt Securities

35. The current yield curve for default-free zero-coupon bonds is as follows:

Maturity (Years) YTM
1 10%
2 11
3 12

a. What are the implied one-year forward rates?
b. Assume that the pure expectations hypothesis of the term structure is correct. If
market expectations are accurate, what will the pure yield curve (that is, the yields to
maturity on one- and two-year zero coupon bonds) be next year?
c. If you purchase a two-year zero-coupon bond now, what is the expected total rate of
return over the next year? What if you purchase a three-year zero-coupon bond?
(Hint: Compute the current and expected future prices.) Ignore taxes.
36. The term structure for zero-coupon bonds is currently:

Maturity (Years) YTM
1 4%
2 5
3 6

Next year at this time, you expect it to be:

Maturity (Years) YTM
1 5%
2 6
3 7

a. What do you expect the rate of return to be over the coming year on a three-year
zero-coupon bond?
b. Under the expectations theory, what yields to maturity does the market expect to
observe on one- and two-year zeros next year? Is the market™s expectation of the
return on the three-year bond greater or less than yours?
37. The following multiple-choice problems are based on questions that appeared in past
CFA examinations.
a. Which bond probably has the highest credit quality?
(1) Sumter, South Carolina, Water and Sewer Revenue Bond.

(2) Riley County, Kansas, General Obligation Bond.
(3) University of Kansas Medical Center Refunding Revenue Bonds (insured by
American Municipal Bond Assurance Corporation).
(4) Euless, Texas, General Obligation Bond (refunded and secured by U.S.
government securities held in escrow).
b. The market risk of an AAA-rated preferred stock relative to an AAA-rated bond is:
(1) Lower
(2) Higher
(3) Equal
(4) Unknown
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

9 Bond Prices and Yields

c. A bond with a call feature:
(1) Is attractive because the immediate receipt of principal plus premium produces a
high return.
(2) Is more apt to be called when interest rates are high because the interest saving
will be greater.
(3) Will usually have a higher yield than a similar noncallable bond.
(4) None of the above.
d. The yield to maturity on a bond is:
(1) Below the coupon rate when the bond sells at a discount, and above the coupon
rate when the bond sells at a premium.
(2) The discount rate that will set the present value of the payments equal to the
bond price.
(3) The current yield plus the average annual capital gains rate.
(4) Based on the assumption that any payments received are reinvested at the
coupon rate.
e. In which one of the following cases is the bond selling at a discount?
(1) Coupon rate is greater than current yield, which is greater than yield to maturity.
(2) Coupon rate, current yield, and yield to maturity are all the same.
(3) Coupon rate is less than current yield, which is less than yield to maturity.
(4) Coupon rate is less than current yield, which is greater than yield to maturity.
f. Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%.
If interest rates remain constant, one year from now the price of this bond will be:
(1) Higher
(2) Lower
(3) The same
(4) Par
g. Which of the following statements is true?
(1) The expectations hypothesis indicates a flat yield curve if anticipated future
short-term rates exceed current short-term rates.
(2) The basic conclusion of the expectations hypothesis is that the long-term rate is
equal to the anticipated short-term rate.
(3) The liquidity hypothesis indicates that, all other things being equal, longer
maturities will have higher yields.
(4) The liquidity preference theory states that a rising yield curve implies that the
market anticipates increases in interest rates.

1. Use the Financial Highlights section of Market Insight (www.mhhe.com/

edumarketinsight) to obtain Standard & Poor™s bond rating of at least 10 firms in
the database. Try to choose a sample with a wide range of bond ratings. Next use
Market Insight™s Annual Ratio Report to obtain for each firm the financial ratios
tabulated in Table 9.3. What is the relationship between bond rating and these
ratios? Can you tell from your sample which of these ratios are the more
important determinants of bond rating?
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

336 Part THREE Debt Securities

Bond Ratings and Yields
Go to bondresources.com and locate the weekly charts for corporate bonds. (Look
under the Corporate tab.) The charts at this site allow you to compare rates and
spreads between corporate bonds of various grades. Locate the charts for seven-year
AAA/A and BBB/B bonds.
Compare the spreads between the AAA/AA/A categories and the BBB/BB/B
categories. Then, answer the following questions:
1. What do these spreads tell you about the relative risk in bonds with various
A ratings compared to bonds with various B ratings?
2. Do the spreads in the graphs indicate any changes in the market™s perception
of credit risk?
Go to standardandpoors.com and click on Resource Center to get basic information
on and definitions of ratings.
3. What is the difference between an issuer and an issue rating? For issue ratings,
compare the C and D rating categories.

1. The callable bond will sell at the lower price. Investors will not be willing to pay as much if
they know that the firm retains a valuable option to reclaim the bond for the call price if

Concept interest rates fall.
CHECKS 2. At a semiannual interest rate of 3%, the bond is worth $40 Annuity factor (3%, 60) $1,000
PV factor (3%, 60) $1,276.76, which results in a capital gain of $276.76. This exceeds the capital
loss of $189.29 ($1,000 $810.71) when the interest rate increased to 5%.
3. Yield to maturity exceeds current yield, which exceeds coupon rate. Take as an example the 8%
coupon bond with a yield to maturity of 10% per year (5% per half year). Its price is $810.71, and
therefore its current yield is 80/810.77 0.0987, or 9.87%, which is higher than the coupon rate
but lower than the yield to maturity.
4. The current price of the bond can be derived from the yield to maturity. Using your calculator, set:
n 40 (semiannual periods); PMT $45 per period; FV $1,000; i 4% per semiannual period.
Calculate present value as $1,098.96. Now we can calculate yield to call. The time to call is five
years, or 10 semiannual periods. The price at which the bond will be called is $1,050. To find
yield to call, we set: n 10 (semiannual periods); PMT $45 per period; FV $1,050;
PV $1,098.96. Calculate the semiannual yield to call as 3.72%.
5. Price $70 Annuity factor (8%, 1) $1,000 PV factor (8%, 1) $990.74
$70 ($990.74 $982.17)
Rate of return to investor 0.080 8%

6. By year-end, remaining maturity is 29 years. If the yield to maturity were still 8%, the bond would
still sell at par and the holding-period return would be 8%. At a higher yield, price and return will
be lower. The yield to maturity is 8.5%. With annual payments of $80 and a face value of $1,000,
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

9 Bond Prices and Yields

the price of the bond is $946.70 (n 29; i 8.5%; PMT $80; FV $1000). The bond initially
sold at $1,000 when issued at the start of the year. The holding-period return is
80 (946.70 1,000)
HPR .0267 2.67%
which is less than the initial yield to maturity of 8%.
7. At the lower yield, the bond price will be $631.67 [n 29, i 7%, FV $1,000, PMT $40].
Therefore, total after-tax income is
Coupon $40 (1 0.36) $25.60
Imputed interest ($553.66 $549.69) (1 0.36) 2.54
Capital gains ($631.67 $553.66) (1 0.28) 56.17
Total income after taxes: $84.31
Rate of return 84.31/549.69 .153 15.3%

8. The coupon payment is $45. There are 20 semiannual periods. The final payment is assumed
to be $600. The present value of expected cash flows is $750. The yield to maturity is 5.42%
semiannually, or 10.8% as an annualized bond equivalent yield.
9. The yield to maturity on two-year bonds is 8.5%. The forward rate for the third year is
f3 8% 1% 9%. We obtain the yield to maturity on three-year zeros from:
y3)3 y2)2 (1 1.0852
(1 (1 f3) 1.09 1.2832

Therefore, y3 .0866 8.67%. We note that the yield on one-year bonds is 8%, on two-year bonds
is 8.5%, and on three-year bonds is 8.67%. The yield curve is upward sloping due solely to the
liquidity premium.

Bodie’Kane’Marcus: III. Debt Securities 10. Managing Bond © The McGraw’Hill
Essentials of Investments, Portfolios Companies, 2003
Fifth Edition



> Analyze the features of a bond that affect the sensitivity of
its price to interest rates.

> Compute the duration of bonds.

> Formulate fixed-income immunization strategies for various
investment horizons.

> Analyze the choices to be made in an actively managed
bond portfolio.

> Determine how swaps can be used to mitigate interest
rate risk.


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