NO.PZ202208100100000601
问题如下：
The notional value (in US dollar millions) of the interest rate swap necessary to match the duration profile of the liabilities is closest to:
选项：
A.
33
B.
42
C.
56
解释：
Solution
C is correct. By properly choosing the notional value and the tenor of the swap, Stuyvesant can achieve a combination of the existing portfolio and the interest rate swap that sets the overall portfolio duration to the target duration: (MVP)(MDURP) + (NS)(MDURS) = (MVP)(MDURT). To find the swap notional principal, NS, we need to solve for the following formula:
Note that, in this case, the portfolio is the liabilities, because the swap needs to make up the duration difference to meet the target of 12. The fixed-income portfolio is only 60% of the liabilities; therefore, 7 × 0.60 = 4.2.
A is incorrect. This approach uses US$60 million as MVP instead of the liabilities. Therefore, (12 – 4.2)/14 × 60 = 33.43.
B is incorrect. This approach uses US$100 million as MVP but a denominator or swap duration of 12. Therefore, (12 – 7)/12 × 100 = 41.62.
中文解析：
本题考察的是用利率互换来管理利率风险。
本题注意我们要将资产匹配负债，所以目标的duration是负债的duration为12.因为现在的100million的资产中只有60million的是固定收益类产品，因此资产的久期应该是0.6乘以7等于4.2.
然后直接根据公式Ns=(MDURT-MDURP) (MVP)
/MDURS带入数字计算即可。
1是，asset应该代入60，还是100？
2是，答案的解释还是不能理解。题目都说了Asset the total portfolio是7，如果给定Fixincome 和duration，以及它在组合的weight，那么portfolio的duration应该=W1*D1+W2*D2 不是么
