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.
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
只记得min convexity降低structural risk，要比目标的convexity大吗？
