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尚好的青春 · 2024年06月12日

相差要多少算近似相等

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000037

问题如下：

Schuylkilland Chaopraya now discuss Option 2. Chaopraya estimates the present value ofthe four future cash flows as $230,372, with a money duration of $2,609,700 andconvexity of 135.142. She considers three possible portfolios to immunize thefuture payments, as presented in Exhibit 2.


Determinethe most appropriate immunization portfolio in Exhibit 2. Justify yourdecision.

解释：

Answer:

Justification:

Portfolio2 is the most appropriate immunization portfolio because it is the only onethat satisfies the following two criteria for immunizing a portfolio ofmultiple 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 possibleimmunizing portfolios, the portfolio with the lowest convexity that is abovethe outflow portfolio’s convexity of 135.142 should be selected. Thedispersion, as measured by convexity, of the immunizing portfolio should be aslow as possible subject to being greater than or equal to the dispersion of theoutflow portfolio. This will minimize the effect of non-parallel shifts in theyield curve. Portfolio 3’s convexity of 132.865 is less than the outflowportfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 andPortfolio 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 of147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.

Theimmunizing portfolio needs to be greater than the convexity (and dispersion) ofthe outflow portfolio. But, the convexity of the immunizing portfolio should beminimized in order to minimize dispersion and reduce structural risk

有没有一个门槛比例之类可以界定，我感觉200多又不算相差的少，但是答案有这么写，想怎么解释都是按照答案来倒推，下次遇见类似的还是拿不准

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1 个答案

发亮_品职助教 · 2024年06月12日

嗨，从没放弃的小努力你好：


这块原版书还真没有一个严格的标准。但就回到做题而言，一定是可以选出来的。

因为总有几个Portfolio的几个指标比较离谱，满足不了immunization的要求，所以可以通过排除法选择出来一个最佳的。


因为这里是在几个Portfolio里面选出相对而言最佳的，几个组合之间一比较就有了分析的相对标准benchmark，所以还是比较容易选出来的。后面碰到其他题目，mock题和经典题就会有感觉，其实就是几个Portfolio之间的数据比较着选出最优的，不存在一个严格的标准直接判断出答案。


像这道题分析思路是这样：

负债的Money duration=$2,609,700，三个组合的Money duration分别是

Portfolio 1 = 2609,981，Portfolio 2 = 2609,442，Portfolio 3=2609,770


Portfolio 3的Money duration最接近，其他两个差不多，所以Portfolio 3有潜力是最佳，现在要通过其他条件验证portfolio 3能不能选，观察convexity，负债的convexity = 135.142，Portfolio 3的convexity = 132.865，Portfolio 3的convexity不满足大于的条件，所以直接排除。


剩下Portfolio 1和2的BPV基本和liability的BPV差不多，两个Portfolio和Liability的BPV差异差不多大，无法根据BPV选择出最佳，所以都是备选。观察convexity指标，Portfolio 2的convexity在大于liability convexity的基础上，又相对更小，所以Portfolio 2更好，本题选Portfolio 2.


几个Portfolio之间就是用这种比较着分析的方法找到最佳组合的，并不存在一个严格的标准直接选出最优的。

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努力的时光都是限量版，加油！

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