NO.PZ201812020100001202
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
老师，麻烦帮忙看下这个答案能拿全分嘛？谢谢！
Portfolio 2 is the most appropriate immunization portfolio.
To immunize the future payments of Option 2. The portfolio should:
- The market value should be no less than the present value of future cash flow of $230,372. All these three portfolios could meet this requirement.
- The money duration should match that close to $2,609,700. Again, all these three portfolios could match.
- To best mitigate the structural risk, the convexity of the portfolio should exceed the convexity of future cash outflow of 135.142, and the difference should be minimized. Portfolio 3 has a convexity of 132.865, which is less than 135.142 and should be excluded. Portfolio 2 has a convexity of 139.851, which exceeds 135.142 and is smaller than the convexity of Portfolio 1. Therefore, Portfolio 2 is the most appropriate.