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Explanation:
To hedge the portfolio's interest rate risk, we need to set up a system of equations that will eliminate the portfolio's Key Rate 01 (KR01) exposures to both the 2-year and 5-year spot rates.
We need to find positions A and B such that:
For 2-year rate exposure:
1,600 + 48A + 4B = 0
1,600 + 48A + 4B = 0
For 5-year rate exposure:
-3,450 + 5A + 65B = 0
-3,450 + 5A + 65B = 0
From the first equation:
48A + 4B = -1,600
12A + B = -400 (dividing by 4)
B = -400 - 12A
48A + 4B = -1,600
12A + B = -400 (dividing by 4)
B = -400 - 12A
Substitute into the second equation:
-3,450 + 5A + 65(-400 - 12A) = 0
-3,450 + 5A - 26,000 - 780A = 0
-29,450 - 775A = 0
775A = -29,450
A = -38
-3,450 + 5A + 65(-400 - 12A) = 0
-3,450 + 5A - 26,000 - 780A = 0
-29,450 - 775A = 0
775A = -29,450
A = -38
Now solve for B:
B = -400 - 12(-38)
B = -400 + 456
B = 56
B = -400 - 12(-38)
B = -400 + 456
B = 56
Therefore, the correct hedging strategy is to short 38 of Bond A and buy 56 of Bond B, which corresponds to option C.
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A risk manager at a fixed-income hedge fund wants to hedge the interest rate risk exposure of a portfolio. The manager has determined that a 1-bp increase in the 2-year spot rate would decrease the value of the portfolio by INR 1,600, however a 1-bp increase in the 5-year spot rate would increase the value of the portfolio by INR 3,450. The manager plans to hedge the portfolio's exposure using the following two bonds whose key rate 01s (KR01s) are shown below:
| Bond | 2-year KR01 (INR) | 5-year KR01 (INR) |
|---|---|---|
| A | 48 | 5 |
| B | 4 | 65 |
Which of the following transactions would most effectively hedge against the portfolio's interest rate risk?
A
Buy 38 of Bond A and short 56 of Bond B
B
Buy 75 of Bond A and short 29 of Bond B
C
Short 38 of Bond A and buy 56 of Bond B
D
Short 75 of Bond A and buy 29 of Bond B