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55
CHAPTER 11
FIXED-INCOME PORTFOLIO
MANAGEMENT—PART I
PROBLEMS
1. e table below shows the active return for six periods for a bond portfolio. Calculate the
portfolio’s tracking risk for the six-period time frame.
Period
Portfolio
Return
Benchmark
Return
Active
Return
1 14.10% 13.70% 0.400%
2 8.20 8.00 0.200
3 7.80 8.00 −0.200
4 3.20 3.50 −0.300
5 2.60 2.40 0.200
6 3.30 3.00 0.300
2. e table below shows the spread duration for a 70-bond portfolio and a benchmark in-
dex based on sectors. Determine whether the portfolio or the benchmark is more sensitive
to changes in the sector spread by determining the spread duration for each. Given your
answer, what is the effect on the portfolio’s tracking risk?
Portfolio Benchmark
Sector
% of
Portfolio
Spread
Duration
% of
Portfolio
Spread
Duration
Treasury 22.70 0.00 23.10 0.00
Agencies 12.20 4.56 6.54 4.41
56 Part I: Learning Objectives, Summary Overview, and Problems
Portfolio Benchmark
Sector
% of
Portfolio
Spread
Duration
% of
Portfolio
Spread
Duration
Financial institutions 6.23 3.23 5.89 3.35
Industrials 14.12 11.04 14.33 10.63
Utilities 6.49 2.10 6.28 2.58
Non-US credit 6.56 2.05 6.80 1.98
Mortgage 31.70 1.78 33.20 1.11
Asset backed — 2.40 1.57 3.34
CMBS — 5.60 2.29 4.67
Total 100.00 100.00
3. You are the manager of a portfolio consisting of three bonds in equal par amounts of
$1,000,000 each. e first table below shows the market value of the bonds and their du-
rations. (e price includes accrued interest.) e second table contains the market value
of the bonds and their durations one year later.
Initial Values
Security Price Market Value Duration Dollar Duration
Bond #1 $106.110 $1,060,531 5.909 ?
Bond #2 98.200 981,686 3.691 ?
Bond #3 109.140 1,090,797 5.843 ?
Portfolio dollar duration =?
After 1 Year
Security Price Market Value Duration Dollar Duration
Bond #1 $104.240 $1,042,043 5.177 ?
Bond #2 98.084 980,461 2.817 ?
Bond #3 106.931 1,068,319 5.125 ?
Portfolio dollar duration = ?
As manager, you would like to maintain the portfolio’s dollar duration at the initial level by
rebalancing the portfolio. You choose to rebalance using the existing security proportions of
one-third each. Calculate:
A. the dollar durations of each of the bonds.
B. the rebalancing ratio necessary for the rebalancing.
C. the cash required for the rebalancing.
e following information relates to Questions 4–9
e investment committee of Rojas University is unhappy with the recent performance of the
fixed-income portion of their endowment and has fired the current fixed-income manager. e
current portfolio, benchmarked against the Barclays Capital US Aggregate Index, is shown in
Exhibit 1. e investment committee hires Alfredo Alonso, a consultant from MHC Consult-
ing, to assess the portfolio’s risks, submit ideas to the committee, and manage the portfolio on
an interim basis.
Chapter 11 Fixed-Income Portfolio Management—Part I 57
EXHIBIT 1 Rojas University Endowment Fixed-Income Portfolio Information
Portfolio Index
Sector % Duration* % Duration*
Treasuries 47.74 5.50 49.67 5.96
Agencies 14.79 5.80 14.79 5.10
Corporates 12.35 4.50 16.54 5.61
Mortgage-backed securities 25.12 4.65 19.10 4.65
*Spread durations are the same as effective durations for all sectors with spread risk.
Alonso notices that the fired manager’s portfolio did not own securities outside of the
index universe. e committee asks Alonso to consider an indexing strategy, including related
benefits and logistical problems. Alonso identifies three factors that limit a manager’s ability to
replicate a bond index:
Factor #1 a lack of availability of certain bond issues
Factor #2 the limited market capitalization of the bond universe
Factor #3 differences between the bond prices used by the manager and the index
provider
Alonso has done further analysis of the current US Treasury portion of the portfolio and
has discovered a significant overweight in a 5-year Treasury bond ($10 million par value). He
expects the yield curve to atten and forecasts a six-month horizon price of the 5-year Treasury
bond to be $99.50. erefore, Alonso’s strategy will be to sell all the 5-year Treasury bonds, and
invest the proceeds in 10-year Treasury bonds and cash while maintaining the dollar duration
of the portfolio. US Treasury bond information is shown in Exhibit 2.
EXHIBIT 2 US Treasury Bond Information
Issue Description (Term to Maturity,
Ticker, Coupon, Maturity Date) Duration Price* ($) Yield (%)
5-year: T 4.125% 15 May 2011 4.53 100.40625 4.03
10-year: T 5.25% 15 May 2016 8.22 109.09375 4.14
*Prices are shown per $100 par value.
4. e duration of the Rojas University fixed-income portfolio in Exhibit 1 is closest to:
A. 5.11.
B. 5.21.
C. 5.33.
5. e spread duration of the Rojas University fixed-income portfolio in Exhibit 1 is closest
to:
A. 2.58.
B. 4.93.
C. 5.21.
58 Part I: Learning Objectives, Summary Overview, and Problems
6. Based on the data in Exhibit 1, the bond portfolio strategy used by the fired manager can
best be described as:
A. pure bond index matching.
B. enhanced indexing/matching risk factors.
C. active management/larger risk factor mismatches.
7. Regarding the three factors identified by Alonso, the factor least likely to actually limit a
manager’s ability to replicate a bond index is:
A. #1.
B. #2.
C. #3.
8. Using Alonso’s forecasted price and the bond information in Exhibit 2, the expected
6-month total return of the Treasury 4.125% 15 May 2011 is closest to (assume zero ac-
crued interest at purchase):
A. −0.90%.
B. 1.15%.
C. 1.56%.
9. Using Exhibit 2, the par value of 10-year bonds to be purchased to execute Alonso’s strat-
egy is closest to:
A. $5,072,000.
B. $5,489,000.
C. $5,511,000.
e following information relates to Questions 10–15
e State Retirement Board (SRB) provides a defined benefit pension plan to state employees.
e governors of the SRB are concerned that their current fixed-income investments may not
be appropriate because the average age of the state employee workforce has been increasing. In
addition, a surge in retirements is projected to occur over the next 10 years.
Chow Wei Mei, the head of the SRB’s investment committee, has suggested that some of
the future pension payments can be covered by buying annuities from an insurance company.
She proposes that the SRB invest a fixed sum to purchase annuities in seven years time, when
the number of retirements is expected to peak. Chow argues that the SRB should fund the
future purchase of the annuities by creating a dedicated fixed-income portfolio consisting of
corporate bonds, mortgage-backed securities, and risk-free government bonds. Chow states:
Statement #1 “To use a portfolio of bonds to immunize a single liability, and remove all
risks, it is necessary only that 1) the market value of the assets be equal to
the present value of the liability and 2) the duration of the portfolio be
equal to the duration of the liability.”
Chow lists three alternative portfolios that she believes will immunize a single, seven-year
liability. All bonds in Exhibit 1 are option-free government bonds.
Chapter 11 Fixed-Income Portfolio Management—Part I 59
EXHIBIT 1 Alternative Portfolios for F.unding an Annuity Purchase in Seven Years
Portfolio Description
Portfolio Yield
to Maturity (%)
A Zero-coupon bond with a maturity of 7 years 4.20
B Bond with a maturity of 6 years
Bond with a maturity of 8 years
4.10
C Bond with a maturity of 5 years
Bond with a maturity of 9 years
4.15
Chow then states:
Statement #2 “Because each of these alternative portfolios immunizes this single,
seven-year liability, each has the same level of reinvestment risk.”
e SRB governors would like to examine different investment horizons and alternative
strategies to immunize the single liability. e governors ask Chow to evaluate a contingent
immunization strategy using the following assumptions:
• e SRB will commit a $100 million investment to this strategy.
• e horizon of the investment is 10 years.
• e SRB will accept a 4.50 percent return (semiannual compounding).
• An immunized rate of return of 5.25 percent (semiannual compounding) is possible.
Marshall Haley, an external consultant for the SRB, has been asked by the governors to
advise them on the appropriateness of its investment strategies. Haley notes that, although state
employee retirements are expected to surge over the next 10 years, the SRB will experience a
continual stream of retirements over the next several decades. Hence, the SRB faces a schedule
of liabilities, not a single liability. In explaining how the SRB can manage the risks of multiple
liabilities, Haley makes the following statements:
Statement #1 “When managing the risks of a schedule of liabilities, multiple liability im-
munization and cash ow matching approaches do not have the same risks
and costs. Whereas cash ow matching generally has less risk of not satisfy-
ing future liabilities, multiple liability immunization generally costs less.”
Statement #2 “Assuming that there is a parallel shift in the yield curve, to immunize
multiple liabilities, there are three necessary conditions: i) the present value
of the assets be equal to the present value of the liabilities; ii) the composite
portfolio duration be equal to the composite liabilities duration; and iii) I
cannot remember the third condition.”
Statement #3 “Horizon matching can be used to immunize a schedule of liabilities.”
10. Is Chow’s Statement #1 correct?
A. Yes.
B. No, because credit risk must also be considered.
C. No, because the risk of parallel shifts in the yield curve must also be considered.
60 Part I: Learning Objectives, Summary Overview, and Problems
11. Is Chow’s Statement #2 correct?
A. No, Portfolio B is exposed to less reinvestment risk than Portfolio A.
B. No, Portfolio B is exposed to more reinvestment risk than Portfolio C.
C. No, Portfolio C is exposed to more reinvestment risk than Portfolio B.
12. Which of the following is closest to the required terminal value for the contingent immu-
nization strategy?
A. $100 million.
B. $156 million.
C. $168 million.
13. Is Haley’s Statement #1 correct?
A. Yes.
B. No, because multiple liability immunization is generally less risky than cash ow
matching.
C. No, because cash ow matching is generally less costly than multiple liability immu-
nization.
14. e condition that Haley cannot remember in his Statement #2 is that the:
A. cash ows in the portfolio must be dispersed around the horizon date.
B. cash ows in the portfolio must be concentrated around the horizon date.
C. distribution of durations of individual assets in the portfolio must have a wider range
than the distribution of the liabilities.
15. e most appropriate description of the strategy that Haley suggests in his Statement #3 is
to create a portfolio that:
A. has cash ows concentrated around the horizon date.
B. is duration matched but uses cash ow matching in the later years of the liability
schedule.
C. is duration matched but uses cash ow matching in the initial years of the liability
schedule.
