NO.PZ2018120301000037
问题如下：
Schuylkill and Chaopraya now discuss Option 2. Chaopraya estimates the present value of the four future cash flows as $230,372, with a money duration of $2,609,700 and convexity of 135.142. She considers three possible portfolios to immunize the future payments, as presented in Exhibit 2.
Determine
the most appropriate immunization portfolio in Exhibit 2. Justify your
decision.
选项：
解释：
Answer:
Justification:
Portfolio
2 is the most appropriate immunization portfolio because it is the only one
that satisfies the following two criteria for immunizing a portfolio of
multiple future outflows:
- Money Duration: Money durations of all three possible immunizing portfolios match or closely match the money duration of the outflow portfolio. Matching money durations is useful because the market values and cash flow yields of the immunizing portfolio and the outflow portfolio are not necessarily equal.
- Convexity: Given that the money duration requirement is met by all three possible immunizing portfolios, the portfolio with the lowest convexity that is above the outflow portfolio’s convexity of 135.142 should be selected. The dispersion, as measured by convexity, of the immunizing portfolio should be as low as possible subject to being greater than or equal to the dispersion of the outflow portfolio. This will minimize the effect of non-parallel shifts in the yield curve. Portfolio 3’s convexity of 132.865 is less than the outflow portfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 and Portfolio 2 have convexities that exceed the convexity of the outflow portfolio, but Portfolio 2’s convexity of 139.851 is lower than Portfolio 1’s convexity of 147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.
The
immunizing portfolio needs to be greater than the convexity (and dispersion) of
the outflow portfolio. But, the convexity of the immunizing portfolio should be
minimized in order to minimize dispersion and reduce structural risk
提示：在Match multiple liabilities时，虽然要求是Asset money duration (BPV) = Liability money duration (BPV)，但是在做题目时，并不会出现严格相等的情况。一般的情形是，给的待选3个Portfolio的BPV是近似地等于负债的Money duration，或多或少都无所谓，只要Portfolio资产的BPV不要差负债的BPV太多，我们就认为从BPV这个角度上是满足免疫条件的。
至于BPV的差距多少才能接受？这点是需要对比着看的，如本题3个Portfolio，虽然Portfolio 3的BPV离负债BPV最近，但其Convexity不满足条件，所以Portfolio 3肯定不能选。那剩下的Portfolio 1,2的BPV与负债BPV的差异我们认为就是可以接受的，且Portfolio 1与2的BPV差不多都离负债的BPV差200多，所以从BPV这个角度看，3个组合都满足要求。
在BPV近似的情况下，资产的BPV可以大于负债BPV，也可以小于BPV，只要差异不过大即可。
在BPV满足条件的情况下，接下来我们需要按照Convexity的条件，进一步选出最佳的组合。
我理解是因为convexity太小，现金流太集中，虽然BPV差不多，所以不行，这么理解对吗？
