投资学10版习题答案16
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CHAPTER 16: MANAGING BOND PORTFOLIOS
PROBLEM SETS
1. While it is true that short-term rates are more volatile than
long-term rates, the longer duration of the longer-term bonds makes their prices and their rates of return more volatile. The higher duration magnifies the sensitivity to interest-rate changes.
2. 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.
3. The percentage change in the bond’s price is:
7.1940.0050.0327 3.27%,1 1.10
D y y -
⨯∆=-⨯=-=-+ or a 3.27% decline
4. a.YTM = 6%
(1)
(2)
(3)
(4) (5) Time until Payment (Years) Cash Flow PV of CF (Discount Rate = 6%)
Weight
Column (1) Column (4) 1 $60.00 $56.60 0.0566 0.0566 2
60.00 53.40 0.0534 0.1068 3
1,060.00 890.00 0.8900 2.6700 Column sums $1,000.00
1.0000
2.8334
Duration = 2.833 years
b.YTM = 10%
(1) (2) (3) (4) (5)
Time until
Payment
(Years) Cash Flow
PV of CF
(Discount
Rate =
10%)
Weight
Column (1)
Column
(4)
1 $60.00 $54.55 0.0606 0.0606
2 60.00 49.59 0.0551 0.1102
3 1,060.00 796.39 0.884
4 2.6532
Column sums $900.53 1.0000 2.8240
Duration = 2.824 years, which is less than the duration at
the YTM of 6%.
5. For a semiannual 6% coupon bond selling at par, we use the following
parameters: coupon = 3% per half-year period, y = 3%, T = 6
semiannual periods.
(1) (2) (3) (4) (5)
Time until
Payment
(Years) Cash Flow
PV of CF
(Discount
Rate = 3%) Weight
Column (1)
Column
(4)
1 $3.00 $2.913 0.02913 0.02913
2 3.00 2.828 0.02828 0.05656
3 3.00 2.745 0.02745 0.08236
4 3.00 2.66
5 0.02665 0.10662
5 3.00 2.588 0.02588 0.12939
6 103.00 86.261 0.86261 5.17565
Column sums $100.000 1.00000 5.57971
D = 5.5797 half-year periods = 2.7899 years
If the bond’s yield is 10%, use a semiannual yield of 5% and semiannual coupon of 3%:
(1) (2) (3) (4) (5)
Time until
Payment
(Years) Cash Flow
PV of CF
(Discount
Rate = 5%) Weight
Column (1)
Column