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Q3. If the entire yield curve undergoes a parallel shift such that the rate at all key maturities increases by 50 basis points, what will the value of the portfolio be? ffice ffice" />
A) $980,537.50.
B) $1,019,462.50.
C) $961,075.00.
Correct answer is A)
|
Key Rate Durations |
|
Issue |
Value ($1,000's) |
weight |
3 mo |
2 yr |
5 yr |
10 yr |
15 yr |
20 yr |
25 yr |
30 yr |
Effective Duration |
|
Bond 1 |
100 |
0.10 |
0.03 |
0.14 |
0.49 |
1.35 |
1.71 |
1.59 |
1.47 |
4.62 |
11.4 |
|
Bond 2 |
200 |
0.20 |
0.02 |
0.13 |
1.47 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
1.62 |
|
Bond 3 |
150 |
0.15 |
0.03 |
0.14 |
0.51 |
1.40 |
1.78 |
1.64 |
2.34 |
2.83 |
10.67 |
|
Bond 4 |
250 |
0.25 |
0.06 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.06 |
|
Bond 5 |
300 |
0.30 |
0.00 |
0.88 |
0.00 |
0.00 |
1.83 |
0.00 |
0.00 |
0.00 |
2.71 |
|
Total Portfolio |
|
1.00 |
0.0265 |
0.325 |
0.4195 |
0.345 |
0.987 |
0.405 |
0.498 |
0.8865 |
3.8925 |
Since the yield curve underwent a parallel shift, the impact on portfolio value can be computed directly using the portfolio's effective duration. There are two methods that can be used to calculate effective duration in this situation. Both methods use the market weight of the individual bonds in the portfolio. As shown in the third column of the table above, the market weight of each bond equals: Bond value/Portfolio value, where the portfolio value is $1,000,000.
Method 1) Effective duration of the portfolio is the sum of the weighted averages of the key rate durations for each issue.
The 3-month key rate durations for the portfolio can be calculated as follows:
(0.10)(0.03) + (0.20)(0.02) + (0.15)(0.03) + (0.25)(0.06) + (0.30)(0) = 0.0265
This method can be used to generate the rest of the key rate duration shown in the bottom row of the table above and summed to yield an effective duration = 3.8925.
Method 2) Effective duration of the portfolio is the weighted average of the effective durations for each issue. The effective duration of each issue is the sum of the individual rate durations for that issue. These values are shown in the right-hand column of the table above. Using this approach, the effective duration of the portfolio can be computed as:
(0.10)(11.4) + (0.20)(1.62) + (0.15)(10.67) + (0.25)(0.06) + (0.30)(2.71) = 3.8925
Using an effective duration of 3.8925, the value of the portfolio following a parallel 50 basis point shift in the yield curve is computed as follows:
Percentage change = (50 basis points)(3.8925) = 1.9463% decrease
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发表于 2009-3-16 17:57
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