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，有两个问题想请教一下：
1.这题我觉得答案中还少写了一个点，就是PV（asset)≥ PV（liability)原则，所以我在答案的基础上又多加了一条，不知道是否可以，我加粗标为绿色了，请老师帮忙看一下：
portfolio 2 is the most approriate immunization portfolio. Reasons are as the follows:
①market value. Market value of all three possible immunizing portfolios are larger than present value of the four future cash flows ($230,372).
②Money Duration. Money duration of all three possible immunizing portfolios match or closely match the money duration of the outflow portfolio.
③Convexity. The dispersion of the immunizing portfolio should be as low as possible, subject to being greater than or equal to the dispersion of the outflow portfolio. portfolio 3's convexity of 132.865 is less than the outflow portfolio's convexity, so portfolio 3 is inapproriate. Both portfolio 1 and portfolio 2 have convexity that exceeds the convexity of the outflow portfolio, but portfolio 2's convexity is lower than portfolio 1.
Therefore, portfolio 2 is the most approriate immunizing portfolio.
2.还有一个问题就是上文中标黄的那句话，我对dispersion（离散）和diversification（分散）做了一个区分，老师请看下我的理解是否正确：
dispersion越大越离散，意味着现金流发生的时间点隔的比较远，convexity会比较大，比如说barbell就是dispersion大， convexity高，structrural risk会比较大。
diversification高指的是现金流比较分散，就是很多时间点上都有发生现金流，不一定convexity最高，比如说laddered portfolio就是diversification高，可以更好的用来管理流动性。
