问题如下：
The second project for Soto is to help Hudgens immunize a $20 million portfolio of liabilities. The liabilities range from 3.00 years to 8.50 years with a Macaulay duration of 5.34 years, cash flow yield of 3.25%, portfolio convexity of 33.05, and basis point value (BPV) of $10,505. Soto suggested employing a duration-matching strategy using one of the three AAA rated bond portfolios presented in Exhibit 2.
Which portfolio in Exhibit 2 fails to meet the requirements to achieve immunization for multiple liabilities?
选项：
A.Portfolio A
Portfolio B
Portfolio C
解释：
A is correct.
The two requirements to achieve immunization for multiple liabilities are for the money duration (or BPV) of the asset and liability to match and for the asset convexity to exceed the convexity of the liability. Although all three portfolios have similar BPVs, Portfolio A is the only portfolio to have a lower convexity than that of the liability portfolio (31.98, versus 33.05 for the $20 million liability portfolio), and thus, it fails to meet one of the two requirements needed for immunization.
老師好，想問一個跟這題無關的問題。
關於Swaption，一直不懂的就是 Payer swaption是在利率上升的時候執行，因為當初如果long payer swaption，目的其實是因為我要降低duration，因為BPV asset > BPV liability，所以應該是在利率上升時，其實我也不想執行，因為我想付越多越高的duration出去才對？ 真的想很久還是沒想懂，麻煩老師了謝謝！
