Chapter 11  Managing Bond Portfolios
CHAPTER 11
MANAGING BOND PORTFOLIOS
1.
Duration can be thought of as a weighted average of the ‘maturities’ of the cash flows
paid to holders of the perpetuity, where the weight for each cash flow is equal to the
present value of that cash flow divided by the total present value of all cash flows.
For
cash flows in the distant future, present value approaches zero (i.e., the weight becomes
very small) so that these distant cash flows have little impact, and eventually, virtually
no impact on the weighted average.
2.
A low coupon, long maturity bond will have the highest duration and will, therefore,
produce the largest price change when interest rates change.
3.
A rate anticipation swap should work. The trade would be to long the corporate bonds
and short the treasuries. A relative gain will be realized when rate spreads return to
normal.
4.
25 = (D/1.06)x.0025x1050…solving for D = 10.09
5.
d.
6.
The increase will be larger than the decrease in price.
7.
While it is true that shortterm rates are more volatile than longterm rates, the longer
duration of the longerterm bonds makes their rates of return more volatile.
The higher
duration magnifies the sensitivity to interestrate savings.
Thus, it can be true that
rates
of shortterm bonds are more volatile, but the
prices
of longterm bonds are more
volatile.
8.
Computation of duration:
a.
YTM = 6%
(1)
(2)
(3)
(4)
(5)
Time until
Payment
(Years)
Payment
Payment
Discounted at
6%
Weight
Column (1)
×
Column (4)
1
60
56.60
0.0566
0.0566
2
60
53.40
0.0534
0.1068
3
1060
890
.00
0
.8900
2
.6700
Column Sum:
1000.00
1.0000
2.8334
Duration = 2.833 years
111
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b.
YTM = 10%
(1)
(2)
(3)
(4)
(5)
Time until
Payment
(Years)
Payment
Payment
Discounted at
10%
Weight
Column (1)
×
Column (4)
1
60
54.55
0.0606
0.0606
2
60
49.59
0.0551
0.1101
3
1060
796.39
0
.8844
2
.6531
Column Sum:
900.53
1.0000
2.8238
Duration = 2.824 years, which is less than the duration at the YTM of 6%
9.
The percentage bond price change is:
– Duration
×
0327
.
0
10
.
1
0050
.
0
194
.
7
y
1
y

=
×

=
+
∆
or a 3.27% decline
10. Computation of duration, interest rate = 10%:
(1)
(2)
(3)
(4)
(5)
Time until
Payment
(Years)
Payment
(in millions
of dollars)
Payment
Discounted
At 10%
Weight
Column (1)
×
Column (4)
1
1
0.9091
0.2744
0.2744
2
2
1.6529
0.4989
0.9977
3
1
0
.7513
0.2267
0.6803
Column Sum:
3.3133
1.0000
1.9524
Duration = 1.9524 years
11. The duration of the perpetuity is: (1 + y)/y = 1.10/0.10 = 11 years
Let w be the weight of the zerocoupon bond.
Then we find w by solving:
(w
×
1) + [(1 – w)
×
11] = 1.9523
⇒
w = 9.048/10 = 0.9048
Therefore, your portfolio should be 90.48% invested in the zero and 9.52% in the
perpetuity.
12. The percentage bond price change will be:
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 Spring '10
 SukwonThomasKim
 Management, Interest Rates, Perpetuity

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