
Explanation:
DV01 (Dollar Value of 1 basis point) represents the absolute change in the price of a bond for a 1 basis point ($0.01%$) shift in the yield curve. Despite the scenario mentioning a 5 basis points shift, the "value of DV01" by definition is intrinsically standardized to a 1 basis point change.
Let's value the initial price of the bond using semi-annual periods. The annual coupon is $6%30$ on a face value bond.
To find DV01, we shift all spot rates up by 1 basis point ($0.01%0.00`5%$ per period) and recalculate the price:
(Note: The exact analytical derivative formulation yields approximately 0.197. If you multiply 0.197 by 5, you get 0.985, which represents the overall price change, not the DV01 metric itself).
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Q.51 Suppose that an investor buys a two-year bond with a face value of 1,000 and which pays a coupon of 6% per year. Assume the following are the prevailing spot rates in the market:
| Maturity Period (Year) | Spot Rate |
|---|---|
| 0.5 | 2.0 |
| 1.0 | 2.5 |
| 1.5 | 3.0 |
| 2.0 | 3.5 |
If all spot rates change by 5 basis points, what will be the value of DV01 for the bond?
A
0.985
B
0.099
C
0.197
D
1.06
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