Q. 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.
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
别的学员问的同样的问题解答我看了，我也理解了思路是几百万的money duration相差无几，即便是asset money duration小于liability也是满足条件的，然后按照convexity再去判断。
我的问题是，这也是协会的题目，最后考试也会有这样的题目存在吗？就是考这种相差的并不多的，结果选1就是错的，因为2的money duration也满足条件。