Solutions for Chapter 16: Questions and Problems
CHAPTER 16
BOND PORTFOLIO MANAGEMENT STRATEGIES
Answers to Questions
1.
High-yield bonds have been described as having characteristics of common stocks, such
as higher yields and more risks. The higher yield on high-yield bonds (just like common
stocks) compensate the investor for assuming various risks such as risk of default, price
volatility, liquidity, or uncertainty regarding maturity. Since the characteristics of highyield bonds are similar to those of common stocks, it is not surprising that high-yield
bond returns are more correlated to common stocks returns than to investment-grade
bond returns.
2.
Investment horizon a year later = 3
Duration of portfolio a year later = 3.2
While the term-to-maturity has declined by a year, the bond’s duration will decline by
less than one year since duration declines more slowly than term to maturity (see for
example, the “Duration versus Maturity” exhibit graph in Chapter 12). This means that,
assuming no changes in market rates, the portfolio manager must rebalance the
portfolio to reduce its duration to three years.
3.
Several characteristics of duration make it impossible to set a duration equal to the initial
time horizon of a portfolio and ignore it thereafter. First, because duration declines more
slowly than term-to-maturity, even if one assumes no changes in interest rates, the
portfolio manager must periodically rebalance the portfolio. Second, if there is a change
in market rates, the duration of the portfolio will change. If the deviation becomes large
compared to original duration of the portfolio, the manager will again have to rebalance.
Third, the technique assumes that when market rates change, they will change by the
same amount and in the same direction. Since this is not true of the real world, the
manager must assure that the portfolio is composed of various bonds with durations that
bunch around the desired duration of the portfolio. Finally, developing the portfolio can
be a problem since there can always be a problem of acquiring the desired bonds in the
market.
- 128 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 16: Questions and Problems
CHAPTER 16
Answers to Problems
1.
2.
2(a).
(i) The manager purchased a longer maturity, lower coupon bond; by purchasing a longer
duration bond the manager must expect market interest rates to fall.
(ii) The manager will benefit if the shape of the yield curve either stays flat or becomes
downward sloping since he has replaced a shorter-term bond that makes payments every
6 months to one that has no interim cash flows.
(iii) By selling a corporate and purchasing a Treasury bond the manager evidently
believes the corporate-Treasury spread will widen; if this indeed comes to pass, the
Treasury will outperform as the corporate yields rises relative to Treasuries and as
corporate prices fall relative to Treasuries.
$200 million × (1.06)2 = $224.72 million (assuming semiannual coupon payments in the
bond portfolio).
2(b).
Since modified duration will equal the remaining horizon (5 years), the change in bond
price must be +10% or (-5)x(-2%). The new value of the portfolio would then be
$247.192 million or $224.72 million × (1.10).
3(a).
Computation of Duration (assuming 10% market yield)
(1)
(2)
Year Cash Flow
1
120
2
120
3
120
4
120
5
1120
(3)
(4)
PV@10% PVof Flow
.9091
109.09
.8264
99.17
.7513
90.16
.6830
81.96
.6209
695.41
1075.79
(5)
(6)
PV as % of Price
(1) × (5)
.1014
.1014
.0922
.1844
.0838
.2514
.0762
.3047
.6464
3.2321
1.0000
4.0740
Duration = 4.07 years
3(b).
Computation of Duration (assuming 10% market yield)
(1)
(2)
Year Cash Flow
1
120
2
120
3
120
4
1120
(3)
(4)
PV@10% PVof Flow
.9091
109.09
.8264
99.17
.7513
90.16
.6830
764.96
1063.38
Duration = 3.42 years
(5)
(6)
PV as % of Price (1) × (5)
.1026
.1026
.0933
.1866
.0848
.2544
.7194
2.8776
1.0000
3.4212
- 129 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 16: Questions and Problems
3(c).
The duration of the portfolio should always be equal to the remaining time horizon and
duration declines slower than term-to-maturity assuming no change in market interest
rates as shown in a and b above.
4(a).
Computation of Duration (assuming 8% market yield)
(1)
(2)
(3)
(4)
Year Cash Flow PV@8% PVof Flow
1
100
.9259
92.59
2
100
.8573
85.73
3
100
.7938
79.38
4
1100
.7350
808.50
1066.24
Duration = 3.5 years
4(b).
(5)
(6)
PV as % of Price (1) × (5)
.0868
.0868
.0804
.1608
.0745
.2234
.7583
3.0332
1.0000
3.5042
Computation of Duration (assuming 12% market yield)
(1)
(2)
(3)
(4)
Year Cash Flow PV@12% PV of Flow
1
100
.8929
89.29
2
100
.7972
79.72
3
100
.7118
71.18
4
1100
.6355
699.05
939.24
Duration = 3.47 years
(5)
(6)
PV as % of Price (1) × (5)
.0951
.0951
.0849
.1698
.0758
.2274
.7442
2.9768
1.0000
3.4691
4(c).
A portfolio of bonds is immunized from interest rate risk if the duration of the portfolio is
always equal to the desired investment horizon. In this example, although nothing
changes regarding the bond, there is a change in market rates, which causes a change in
duration which would mean that the portfolio is no longer perfectly immunized.
5.
Assuming semi-annual coupons. Current and year-later prices can easily be found using a
financial calculator:
CURRENT CANDIDATE
BOND
BOND
Dollar Investment
839.54
961.16
Coupon
90.00
110.00
i on One Coupon
2.59
3.16
Principal Value at Year End 841.95
961.71
Total Accrued
934.54
1,074.87
Realized Compound Yield 11.0125
11.4999
RCY = [SQRT (Total Accrued/Dollar Investment)-1] × 2
Value of swap: 48.6 basis points in one year
- 130 Copyright © 2010 by Nelson Education Ltd.
Solutions for Chapter 16: Questions and Problems
6.
Assuming semi-annual coupons. Current and year-later prices can easily be found using a
financial calculator:
CURRENT CANDIDATE
BOND
BOND
Dollar Investment
868.21
849.09
Coupon
90.00
90.00
i on One Coupon
2.36
2.36
Principal Value at Year End 869.40
869.40 (assumes mispricing is corrected)
Total Accrued
961.76
961.76
Realized Compound Yield
10.50
12.86
RCY = [SQRT (Total Accrued/Dollar Investment)-1] × 2
Value of swap: 236 basis points in one year
7.
7(a)
The portfolio’s modified duration will be a weighted average of those of the component
bonds. Since there are 5 equally-weighted bonds, the weight of each is 0.20:
portfolio duration = 0.20(2.727+6.404+3.704+4.868+10.909) = 5.722 years
7(b)
The liability’s duration (6.50 years) is less than the portfolio’s duration. This means the
endowment is subject to net reinvestment rate. Cash is coming into the portfolio (via
interest payments and redemptions)faster than the liabilities it is funding. These funds
will need to be reinvested, thus the portfolio is subject to reinvestment risk.
7(c)
Kritzman has shown that a portfolio’s convexity can be increased by spreading out the
cash flows—this is, use a bond ladder strategy and/or seek higher coupon bonds so cash
flows will occur both earlier and later than the duration time frame.
7(d)
If Treasury yields are expected to decline and corporate credit spreads will decline, a
bond portfolio manager should (i) extend durations to capture more price appreciation as
yields decline; this can be done by purchasing longer maturity bonds and bonds with
lower coupon rates (such as zeros) (ii) purchase corporate bonds since if their yields
follow Treasuries and decline—and the corporate credit spreads decline, too—they will
benefit from price appreciation.
- 131 Copyright © 2010 by Nelson Education Ltd.