indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that

you are managing a pension fund with obligations to make perpetual payments of

$2 million per year to beneficiaries. The yield to maturity on all bonds is 16%.

a. If the duration of five-year maturity bonds with coupon rates of 12% (paid annually)

is 4 years and the duration of 20-year maturity bonds with coupon rates of 6% (paid

annually) is 11 years, how much of each of these coupon bonds (in market value)

will you want to hold to both fully fund and immunize your obligation?

b. What will be the par value of your holdings in the 20-year coupon bond?

11. You are managing a portfolio of $1 million. Your target duration is 10 years, and you

can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity,

each currently yielding 5%.

a. How much of each bond will you hold in your portfolio?

b. How will these fractions change next year if target duration is now nine years?

12. You manage a pension fund that will provide retired workers with lifetime annuities.

You determine that the payouts of the fund are essentially going to resemble level

perpetuities of $1 million per year. The interest rate is 10%. You plan to fully fund the

obligation using 5-year and 20-year maturity zero-coupon bonds.

a. How much market value of each of the zeros will be necessary to fund the plan if

you desire an immunized position?

b. What must be the face value of the two zeros to fund the plan?

13. Your client is concerned about the apparent inconsistency between the following two

statements.

• Short-term interest rates are more volatile than long-term rates.

• The rates of return of long-term bonds are more volatile than returns on short-term

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securities.

Discuss why these two statements are not necessarily inconsistent.

14. As part of your analysis of debt issued by Monticello Corporation, you are asked to

evaluate two specific bond issues, shown in the table on the next page.

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10 Managing Bond Portfolios

Monticello Corporation

Bond Information

Bond A Bond B

(callable) (noncallable)

Maturity 2013 2013

Coupon 11.50% 7.25%

Current price 125.75 100.00

Yield to maturity 7.70% 7.25%

Modified duration to maturity 6.20 6.80

Call date 2007 ”

Call price 105 ”

Yield to call 5.10% ”

Modified duration to call 3.10 ”

a. Using the duration and yield information in the table, compare the price and yield

behavior of the two bonds under each of the following two scenarios:

i. Strong economic recovery with rising inflation expectations.

ii. Economic recession with reduced inflation expectations.

b. Using the information in the table, calculate the projected price change for bond B if

the yield-to-maturity for this bond falls by 75 basis points.

c. Describe the shortcoming of analyzing bond A strictly to call or to maturity.

15. A 30-year maturity bond making annual coupon payments with a coupon rate of 12%

has duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield

to maturity of 8%. Use a financial calculator to find the price of the bond if its yield to

maturity falls to 7% or rises to 9%. What prices for the bond at these new yields would

be predicted by the duration rule and the duration-with-convexity rule? What is the

percent error for each rule? What do you conclude about the accuracy of the two rules?

16. A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective

annual yield) has convexity of 150.3 and modified duration of 11.81 years. A 30-year

maturity 6% coupon bond making annual coupon payments also selling at a yield to

maturity of 8% has nearly identical duration”11.79 years”but considerably higher

convexity of 231.2.

a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual

percentage capital loss on each bond? What percentage capital loss would be

predicted by the duration-with-convexity rule?

b. Repeat part (a), but this time assume the yield to maturity decreases to 7%.

c. Compare the performance of the two bonds in the two scenarios, one involving an

increase in rates, the other a decrease. Based on their comparative investment

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performance, explain the attraction of convexity.

d. In view of your answer to (c), do you think it would be possible for two bonds with

equal duration, but different convexity, to be priced initially at the same yield to

maturity if the yields on both bonds always increased or decreased by equal

amounts, as in this example? Would anyone be willing to buy the bond with lower

convexity under these circumstances?

17. One common goal among fixed-income portfolio managers is to earn high incremental

returns on corporate bonds versus government bonds of comparable durations. The

approach of some corporate-bond portfolio managers is to find and purchase those

corporate bonds having the largest initial spreads over comparable-duration government

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Essentials of Investments, Portfolios Companies, 2003

Fifth Edition

372 Part THREE Debt Securities

bonds. John Ames, HFS™s fixed-income manager, believes that a more rigorous

approach is required if incremental returns are to be maximized.

The following table presents data relating to one set of corporate/government spread

relationships (in basis points, b.p.) present in the market at a given date:

CURRENT AND EXPECTED SPREADS AND DURATIONS

OF HIGH-GRADE CORPORATE BONDS (ONE-YEAR HORIZON)

Initial Spread Expected Expected Duration

Bond over Horizon Initial One Year

Rating Governments Spread Duration from Now

Aaa 31 b.p. 31 b.p. 4 years 3.1 years

Aa 40 b.p. 50 b.p. 4 years 3.1 years

a. Recommend purchase of either Aaa or Aa bonds for a one-year investment horizon

given a goal of maximizing incremental returns.

Ames chooses not to rely solely on initial spread relationships. His analytical

framework considers a full range of other key variables likely to impact realized

incremental returns including: call provisions, and potential changes in interest rates.

b. Describe variables, in addition to those identified above, that Ames should include in

his analysis and explain how each of these could cause realized incremental returns

to differ from those indicated by initial spread relationships.

18. The following questions appeared in past CFA examinations.

a. Which set of conditions will result in a bond with the greatest price volatility?

(1) A high coupon and a short maturity.

(2) A high coupon and a long maturity.

(3) A low coupon and a short maturity.

(4) A low coupon and a long maturity.

b. An investor who expects declining interest rates would be likely to purchase a bond

that has a coupon and a term to maturity.

(1) Low, long

(2) High, short

(3) High, long

(4) Zero, long

c. With a zero-coupon bond:

(1) Duration equals the weighted average term to maturity.

(2) Term to maturity equals duration.

(3) Weighted average term to maturity equals the term to maturity.

(4) All of the above.

d. As compared with bonds selling at par, deep discount bonds will have:

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(1) Greater reinvestment risk.

(2) Greater price volatility.

(3) Less call protection.

(4) None of the above.

19. The ability to immunize a bond portfolio is very desirable for bond portfolio managers

in some instances.

a. Discuss the components of interest rate risk”that is, assuming a change in interest

rates over time, explain the two risks faced by the holder of a bond.

b. Define immunization and discuss why a bond manager would immunize his or her

portfolio.

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Essentials of Investments, Portfolios Companies, 2003

Fifth Edition

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10 Managing Bond Portfolios

c. Explain why a duration-matching strategy is a superior technique to a maturity-

matching strategy for the minimization of interest rate risk.

d. Explain how contingent immunization, another bond portfolio management

technique, differs from conventional immunization. Discuss why a bond portfolio

manager would engage in contingent immunization.

20. You are the manager for the bond portfolio of a pension fund. The policies of the fund

allow for the use of active strategies in managing the bond portfolio.

It appears that the economic cycle is beginning to mature, inflation is expected to

accelerate, and, in an effort to contain the economic expansion, central bank policy is

moving toward constraint. For each of the situations below, state which one of the two

bonds you would prefer. Briefly justify your answer in each case.

a. Government of Canada (Canadian pay), 10% due in 2005, and priced at 98.75 to

yield 10.50% to maturity;

or

Government of Canada (Canadian pay), 10% due in 2015, and priced at 91.75 to

yield 11.19% to maturity.

b. Texas Power and Light Co., 71„2% due in 2010, rated AAA, and priced at 85 to yield

10.1% to maturity;

or

Arizona Public Service Co., 7.45% due in 2010, rated A , and priced at 75 to yield

12.1% to maturity.

c. Commonwealth Edison, 23„4% due in 2010, rated Baa, and priced at 61 to yield

12.2% to maturity;

or

Commonwealth Edison, 153„8% due in 2010, rated Baa, and priced at 114 to yield

12.2% to maturity.

d. Shell Oil Co., 83„4% sinking fund debentures due in 2020, rated AAA (sinking fund

begins in 2010 at par), and priced at 69 to yield 11.91% to maturity;

or

Warner-Lambert, 87„8% sinking fund debentures due in 2020, rated AAA (sinking

fund begins in 2014 at par), and priced at 75 to yield 11.31% to maturity.

e. Bank of Montreal (Canadian pay), 12% certificates of deposit due in 2004, rated

AAA, and priced at 100 to yield 12% to maturity;

or

Bank of Montreal (Canadian pay), floating-rate notes due in 2010, rated AAA.

Coupon currently set at 10.65% and priced at 100 (coupon adjusted semiannually to

0.5% above the three-month Government of Canada Treasury bill rate).

21. The following bond swaps could have been made in recent years as investors attempted

to increase the total return on their portfolio.

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From the information presented below, identify the reason(s) investors may have

made each swap.

Bodie’Kane’Marcus: III. Debt Securities 10. Managing Bond © The McGraw’Hill

Essentials of Investments, Portfolios Companies, 2003

Fifth Edition

374 Part THREE Debt Securities

Action Call Price YTM (%)

a. Sell Baa1 Electric Pwr. 1st mtg. 105„8% due 2009 108.24 95 11.71

Buy Baa1 Electric Pwr. 1st mtg. 63„8% due 2010 105.20 79 11.39

b. Sell Aaa Phone Co. notes 81„2% due 2010 101.50 90 10.02

Buy U.S. Treasury notes 91„2% due 2010 NC 97.15 9.78

c. Sell Aa1 Apex Bank zero coupon due 2011 NC 35 10.51

Buy Aa1 Apex Bank float rate notes due 2028 103.90 90 ”

d. Sell A1 Commonwealth Oil & Gas 1st mtg. 71„2%

due 2018 105.75 72 11.09

Buy U.S. Treasury bond 71„2% due 2024 NC 80.60 9.40

e. Sell A1 Z mart convertible deb. 3% due 2018 103.90 62 6.92

Buy A2 Lucky Ducks deb. 73„4% due 2024 109.86 65 12.43

22. A member of a firm™s investment committee is very interested in learning about the

management of fixed-income portfolios. He would like to know how fixed-income

managers position portfolios to capitalize on their expectations concerning three factors

which influence interest rates:

a. Changes in the level of interest rates.

b. Changes in yield spreads across/between sectors.

c. Changes in yield spreads as to a particular instrument.

Assuming that no investment policy limitations apply, formulate and describe a fixed-

income portfolio management strategy for each of these factors that could be used to

exploit a portfolio manager™s expectations about that factor. (Note: Three strategies are

required, one for each of the listed factors.)

23. Long-term Treasury bonds currently are selling at yields to maturity of nearly 8%.

You expect interest rates to fall. The rest of the market thinks that they will remain

unchanged over the coming year. In each question, choose the bond that will provide

the higher capital gain if you are correct. Briefly explain your answer.

a. (1) A Baa-rated bond with coupon rate 8% and time to maturity 20 years.

(2) An Aaa-rated bond with coupon rate 8% and time to maturity 20 years.

b. (1) An A-rated bond with coupon rate 4% and maturity 20 years, callable at 105.

(2) An A-rated bond with coupon rate 8% and maturity 20 years, callable at 105.

c. (1) A 6% coupon noncallable T-bond with maturity 20 years and YTM 8%.

(2) A 9% coupon noncallable T-bond with maturity 20 years and YTM 8%.

24. Currently, the term structure is as follows: one-year bonds yield 7%, two-year bonds

yield 8%, three-year bonds and greater maturity bonds all yield 9%. You are choosing

between one-, two-, and three-year maturity bonds all paying annual coupons of 8%,

once a year. Which bond should you buy if you strongly believe that at year-end the

yield curve will be flat at 9%?

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