61
CHAPTER 12
FIXEDINCOME PORTFOLIO
MANAGEMENTPART II
PROBLEMS
1. Your client has asked you to construct a £2 million bond portfolio. Some of the bonds that
you are considering for this portfolio have embedded options. Your client has specified that he
may withdraw £25,000 from the portfolio in six months to fund some expected expenses. He
would like to be able to make this withdrawal without reducing the initial capital of £2 million.
A. Would shortfall risk be an appropriate measure of risk while evaluating the portfolios
for your client?
B. What are some of the shortcomings of the use of shortfall risk?
2. e market value of the bond portfolio of a French investment fund is €75 million. e
duration of the portfolio is 8.17. Based on the analysis provided by the in-house economists,
the portfolio manager believes that the interest rates are likely to have an unexpected decrease
over the next month. Based on this belief, the manager has decided to increase the duration
of its entire bond portfolio to 10. e futures contract it would use is priced at €130,000 and
has a duration of 9.35. Assume that the conversion factor for the futures contract is 1.06.
A. Would the fund need to buy futures contracts or sell?
B. Approximately, how many futures contracts would be needed to change the duration
of the bond portfolio?
3. e trustees of a pension fund would like to examine the issue of protecting the bonds in
the fund’s portfolio against an increase in interest rates using options and futures. Before
discussing this with their external bond fund manager, they decide to ask four consultants
about their recommendations as to what should be done at this time. It turns out that
each of them has a different recommendation. Consultant A suggests selling covered calls,
62 Part I: Learning Objectives, Summary Overview, and Problems
Consultant B suggests doing nothing at all, Consultant C suggests selling interest rate
futures, and Consultant D suggests buying puts. e reason for their different recom-
mendations is that although all consultants understand the pension fund’s objective of
minimizing risk, they differ with one another in regards to their outlook on future interest
rates. One of the consultants believes interest rates are headed downward, one has no
opinion, one believes that the interest rates would not change much in either direction,
and one believes that the interest rates are headed upward. Based on the consultants’ rec-
ommendations, could you identify the outlook of each consultant?
4. e current credit spread on bonds issued by Great Foods Inc. is 300 bps. e manager of
More Money Funds believes that Great Foods’ credit situation will improve over the next
few months, resulting in a smaller credit spread on its bonds. She decides to enter into a
six-month credit spread forward contract taking the position that the credit spread will
decrease. e forward contract has the current spread as the contracted spread, a notional
amount of $10 million, and a risk factor of 5.
A. On the settlement date six months later, the credit spread on Great Foods bonds is
250 bps. How much is the payoff to More Money Funds?
B. How much would the payoff to More Money Funds be if the credit spread on the
settlement date is 350 bps?
C. How much is the maximum possible gain for More Money Funds?
5. Consider a collateralized debt obligation (CDO) that has a $250 million structure. e
collateral consists of bonds that mature in seven years, and the coupon rate for these bonds
is the seven-year Treasury rate plus 500 bps. e senior tranche comprises 70 percent of
the structure and has a floating coupon of Libor plus 50 bps. ere is only one junior
tranche that comprises 20 percent of the structure and has a fixed coupon of seven-year
Treasury rate plus 300 bps. Compute the rate of return earned by the equity tranche in
this CDO if the seven-year Treasury rate is 6 percent and the Libor is 7.5 percent. ere
are no defaults in the underlying collateral pool. Ignore the collateral manager’s fees and
any other expenses.
6. Assume that the rates shown in the table below accurately reflect current conditions in the
financial markets.
Dollar/Euro Spot Rate 1.21
Dollar/Euro 1-Year Forward Rate 1.18
1-Year Deposit Rate:
Euro 3%
US 2%
In the table, the one-year forward dollar/euro exchange rate is mispriced, because it doesn’t
reflect the interest rate differentials between the United States and Europe.
A. Calculate the amount of the current forward exchange discount or premium.
B. Calculate the value that the forward rate would need to be in order to keep riskless
arbitrage from occurring.
7. Assume that a US bond investor has invested in Canadian government bonds. e dura–
tion of a 12-year Canadian government bond is 8.40, and the Canadian country beta is
0.63. Interest rates in the United States are expected to change by approximately 80 bps.
How much can the US investor expect the Canadian bond to change in value if US rates
change by 80 bps?
Chapter 12 Fixed-Income Portfolio Management—Part II 63
8. Assume that the spread between US and German bonds is 300 bps, providing German
investors who purchase a US bond with an additional yield income of 75 bps per quarter.
e duration of the German bond is 8.3. If German interest rates should decline, how
much of a decline is required to completely wipe out the quarterly yield advantage for the
German investor?
9. A portfolio manager of a Canadian fund that invests in the yen-denominated Japanese
bonds is considering whether or not to hedge the portfolio’s exposure to the Japanese
yen using a forward contract. Assume that the short-term interest rates are 1.6 percent in
Japan and 2.7 percent in Canada.
A. Based on the in-house analysis provided by the fund’s currency specialists, the portfolio
manager expects the Japanese yen to appreciate against the Canadian dollar by 1.5 per–
cent. Should the portfolio manager hedge the currency risk using a forward contract?
B. What would be your answer if the portfolio manager expects the Japanese yen to ap-
preciate against the Canadian dollar by only 0.5 percent?
10. A British fixed-income fund has substantial holdings in US dollar-denominated bonds.
e fund’s portfolio manager is considering whether to leave the fund’s exposure to the US
dollar unhedged or to hedge it using a UK pound–US dollar forward contract. Assume that
the short-term interest rates are 4.7 percent in the United Kingdom and 4 percent in the
United States. e fund manager expects the US dollar to appreciate against the pound by
0.4 percent. Assume IRP holds. Explain which alternative has the higher expected return
based on the short-term interest rates and the manager’s expectations about exchange rates.
e following information relates to Questions 11–16
Sheila Ibahn, a portfolio manager with TBW Incorporated, is reviewing the performance of L.P.
Industries’ $100 million fixed-income portfolio with Stewart Palme from L.P. Industries. TBW
Incorporated employs an active management strategy for fixed-income portfolios. Ibahn explains
to Palme that the portfolio return was greater than the benchmark return last year and states:
“We outperformed our benchmark by using inter-sector allocation and individual
security selection strategies rather than a duration management strategy. Howev-
er, at this point in the interest rate cycle, we believe we can add relative return by
taking on additional interest rate risk across the portfolio.”
Ibahn recommends purchasing additional bonds to adjust the average duration of the portfo-
lio. After reviewing the portfolio recommendations, Palme asks Ibahn:
“How can we adjust the portfolio’s duration without contributing significant funds
to purchase additional bonds in the portfolio?”
Ibahn responds:
Ibahn 1 We could employ futures contracts to adjust the duration of the portfolio,
thus eliminating the need to purchase more bonds.
Ibahn 2 We could lever the portfolio by entering into either an overnight or 2-year
term repurchase agreement [repo] and use the repo funds to purchase addi–
tional bonds that have the same duration as the current portfolio. For exam–
ple, if we use funds from a $25 million overnight repo agreement to purchase
bonds in addition to the current $100 million portfolio, the levered portfolio’s
64 Part I: Learning Objectives, Summary Overview, and Problems
change in value for a 1% change in interest rates would equal $5,125,000
while giving you the portfolio duration you require. Unfortunately the cur–
rent cost of the repo is high because the repo collateral is “special collateral”
but the margin requirement is low because the collateral is illiquid.
After listening to Ibahn, Palme agrees to use a repo to lever the portfolio but leaves the repo
term decision to Ibahn’s discretion. Because the yield curve is inverted, the cost of both the
overnight and the 2-year term repo is higher than the yield on the levered portfolio. As Ibahn
and Palme discuss the repo term, Palme asks two final questions:
Palme 1 “What is the effect of leverage on a portfolio’s range of returns if interest rates
are expected to change?”
Palme 2 “If interest rates are unchanged over a six-month period, what is the effect on
the levered portfolio return compared to the unlevered portfolio return?”
11. Given Ibahn’s recommendation, which of the following interest rate forecasts is TBW
Incorporated most likely using?
A. A flattening of the yield curve.
B. An upward parallel shift in the yield curve.
C. A downward parallel shift in the yield curve.
12. Referring to Ibahn’s first response to Palme, which of the following best describes TBW’s
most likely course of action?
A. Sell interest rate futures contracts to increase portfolio duration.
B. Buy interest rate futures contracts to increase portfolio duration.
C. Buy interest rate futures contracts to decrease portfolio duration.
13. Referring to Ibahn’s second response to Palme, the levered portfolio would have:
A. the same duration if either the overnight repo or the 2-year term repo is used.
B. a longer duration if the overnight repo is used instead of the 2-year term repo.
C. a shorter duration if the overnight repo is used instead of the 2-year term repo.
14. In Ibahn’s second response to Palme, the duration of the sample leveraged portfolio is closest to:
A. 4.10.
B. 5.13.
C. 6.83.
15. Is Ibahn’s second response to Palme regarding the cost and margin requirements for the
repo most likely correct?
High Repo Cost Low Margin Requirement
A. No No
B. Yes Yes
C. Yes No
16. In response to Palme’s two final questions, the levered portfolio’s range of returns and six-
month return when compared to the unlevered portfolio most likely would be:
Levered Portfolio Range of Returns Levered Portfolio Six-month Return
A. narrower lower
B. narrower higher
C. wider lower
Chapter 12 Fixed-Income Portfolio Management—Part II 65
e following information relates to Questions 17–22 and is based on “Fixed-Income
Portfolio Management—Part I” and this chapter
e investment committee of the US-based Autónoma Foundation has been dissatisfied with
the performance of the fixed-income portion of their endowment and has recently fired the
fixed-income manager.
e investment committee has hired a consultant, Julia Santillana, to oversee the portfolio
on an interim basis until the search for a new manager is completed. She is also expected to
assess the portfolio’s risks and propose investment ideas to the committee.
Total Return Analysis and Scenario Analysis
During a meeting between Santillana and members of the committee, a member asks her to
discuss the use of total return analysis and scenario analysis before executing bond trades. In
her response, Santillana states:
• “To compute total return, the manager needs a set of assumptions about the investment
horizon, the expected reinvestment rate, and the expected change in interest rates.”
• “If the manager wants to evaluate how the individual assumptions affect the total return
computation, she can use scenario analysis.”
• “Scenario analysis can lead to rejection of a strategy that is acceptable from a total return
perspective.”
Use of Repurchase Agreements
During the meeting, Santillana reviews with the investment committee a hypothetical trans–
action in which leverage is used. A manager with $2 million of funds to invest purchases
corporate bonds with a market value of $7 million. To partially finance the purchase, the
manager enters into a 30-day repurchase agreement with the bond dealer for $5 million.
e 30-day term repo rate is assumed to be 4.20 percent per year. At the end of the 30 days,
when the transaction expires, the corporate bonds are assumed to have increased in value
by 0.30 percent. Santillana uses this information to demonstrate the effects of leverage on
portfolio returns.
Responding to a question asked by a committee member, Santillana explains: “e quality
of collateral as well as short sellers’ positions affect the repo rate.”
International Bond Investing and Hedging
Santillana also mentions to the investment committee that the Foundation’s current portfolio
does not include international bonds. She describes the benefits of investing in international
bonds and answers the committee’s questions. Exhibit 1 displays information she uses dur–
ing the meeting to clarify her answers. e 1-year interest rate is used as a proxy for the
risk-free rate.
66 Part I: Learning Objectives, Summary Overview, and Problems
EXHIBIT 1 Summary Information Relevant to International Bond Investing
UK Japan Germany Singapore US
1-year interest rate (percent) 6.24 0.97 4.69 2.09 5.30
Yield on 10-year government bond/note (percent) 5.04 1.67 4.36 2.74 4.62
Expected one-year currency appreciation in
percent (USD per local currency)
0.10 0.50 0.95 1.60 N/A
10-year bond duration 7.34 9.12 7.72 8.19 7.79
e committee is persuaded by Santillana’s presentation and decides to invest in inter-
national bonds. As a result, Santillana considers whether she should recommend currency
hedging using forward contracts, assuming that interest rate parity holds.
During the discussion on international bond investing, a member comments that inves-
tors in Japan and Singapore in particular should be investing in the United States because of
the difference in bond yields. Santillana agrees but explains that investors should also perform
a breakeven spread analysis when investing internationally.
17. Is Santillana correct in her statements about total return analysis and scenario analysis?
A. Yes.
B. No, because scenario analysis cannot evaluate how individual assumptions affect the
total return computation.
C. No, because scenario analysis cannot lead to a rejection of a strategy with an accept-
able expected total return.
18. e 30-day rate of return on the hypothetical leveraged portfolio of corporate bonds is
closest to:
A. –0.05 percent.
B. 0.05 percent.
C. 0.18 percent.
19. Is Santillana correct in her explanation of factors affecting the repo rate?
A. Yes.
B. No, only the quality of collateral is correct.
C. No, only the short sellers’ position is correct.
20. Based on Exhibit 1 and assuming interest rates remain unchanged, which bond will have
the highest hedged return?
A. UK 10-year.
B. Japan 10-year.
C. Germany 10-year.
21. Based on Exhibit 1 and assuming interest rates remain unchanged, which bond will have
the highest expected unhedged return?
A. UK 10-year.
B. Germany 10-year.
C. Singapore 10-year.
22. Based on Exhibit 1, for investors that purchased 10-year US notes, the spread widening in
basis points that will wipe out the additional yield gained for a quarter is closest to:
A. 6.03 in Singapore.
B. 8.09 in Japan.
C. 13.48 in the United Kingdom.
Chapter 12 Fixed-Income Portfolio Management—Part II 67
e following information relates to Questions 23–28 and is based on “Fixed-Income
Portfolio Management—Part I” and this chapter
Salvatore Choo, the Chief Investment Ocer at European Pension Fund (EPF), wishes to
maintain the fixed-income portfolio’s active management but recognizes that the portfolio
must remain fully funded. e portfolio is run by World Asset Management, where Jimmy
Ferragamo, a risk manager, is analyzing the portfolio (shown in Exhibit 1), whose benchmark
has a duration of 5.6. None of the bonds in the portfolio have embedded options. However,
EPF’s liability has a duration of 10.2, creating an asset liability mismatch for the pension fund.
EXHIBIT 1 EPF Portfolio
Maturity Market Value (000) Duration
2-year bond €421,000 1.8
5-year bond €1,101,000 4.8
10-year bond €1,540,000 8.4
Total €3,062,000 6.2
Choo is utilizing a contingent immunization (CI) approach to achieve better returns for the
fund, so by his understanding of CI, he can use the entire fixed-income portfolio for active
management until the portfolio drops below the safety net level or the terminal value.
Ferragamo runs the following risk statistics on the EPF portfolio to ensure that they are
not outside the EPF trustee guidelines. He has the following comment:
“e portfolio value at risk, as opposed to shortfall risk and standard deviation,
determines the most the portfolio can lose in any month.”
Ferragamo has collected the following data on the bund (German Bond) future, which has
a conversion factor of 1.1, and the cheapest to deliver bond is priced at €100,000 and has a
duration of 8.2.
In addition to his CIO responsibilities, Choo is also responsible for managing the fund-
ing liabilities for a new wing at the local hospital, which is currently fully funded utilizing a
standard immunization approach with noncallable bonds. However, he is concerned about the
various risks associated with the liabilities including interest rate risk, contingent claim risk,
and cap risk.
Choo is interested in using cash flow matching rather than immunization to fund a
liability for the new wing. e liability is denominated in euros and will be a lump sum
payment in five years. e term structure of interest rates is currently a steep upward-sloping
yield curve.
23. Given the term structure of interest rates and the duration mismatch between EPF’s
benchmark and its pension liability, the plan should be most concerned about a:
A. flattening of the yield curve.
B. steepening of the yield curve.
C. large parallel shift up in the yield curve.
24. Choo’s understanding of contingent immunization (CI) is:
A. correct.
B. incorrect, because CI does not use a terminal value.
C. incorrect, because CI does not allow for active management.
68 Part I: Learning Objectives, Summary Overview, and Problems
25. Is Ferragamo’s comment correct?
A. Yes.
B. No, because shortfall risk would provide this information.
C. No, because value at risk does not indicate the magnitude of the very worst possible
outcomes.
26. Based on the data Ferragamo collected on the bund and Exhibit 1, Choo can adjust the
EPF portfolio duration to match the benchmark duration by selling:
A. 2,240 contracts.
B. 2,406 contracts.
C. 2,465 contracts.
27. Are Choo’s concerns regarding various risks of funding the hospital liability correct?
A. Yes.
B. No, because interest rate risk is not a factor.
C. No, because contingent claim risk is not a factor.
28. Which of the following would best immunize the hospital liability?
A. A five-year euro coupon bond.
B. A five-year euro zero-coupon bond.
C. Equal investment in three- and seven-year euro zero-coupon bonds.
e following problem is based on “Fixed-Income Portfolio Management—Part I” and
this chapter
29. A portfolio manager decided to purchase corporate bonds with a market value of €5 mil-
lion. To finance 60 percent of the purchase, the portfolio manager entered into a 30-day
repurchase agreement with the bond dealer. e 30-day term repo rate was 4.6 percent
per year. At the end of the 30 days, the bonds purchased by the portfolio manager have
increased in value by 0.5 percent and the portfolio manager decided to sell the bonds. No
coupons were received during the 30-day period.
A. Compute the 30-day rate of return on the equity and borrowed components of the
portfolio.
B. Compute the 30-day portfolio rate of return.
C. Compute the 30-day portfolio rate of return if the increase in value of the bonds was
0.3 percent instead of 0.5 percent.
D. Use your answers to parts B and C above to comment on the effect of the use of lever-
age on the portfolio rate of return.
E. Discuss why the bond dealer in the above example faces a credit risk even if the bond
dealer holds the collateral.