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M.X996 · 2023年12月17日

在market value 满足的前提下，应该选择最精确的money duration匹配吧？

  1. CFA III
  2. Fixed Income

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.

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

在market value 满足的前提下，应该选择最精确的money duration匹配吧？

这里三个portfolio 都满足了market value 大于 PV of liability ;然后Portfolio 3 的money duration is 2609 707 ，the money duration of the liability is 2609700；在money duration 匹配的基础上，再最后考虑凸度的匹配吧？凸度只是二阶导的影响，所以影响力没有money duration来的重要；为什么放着money duration能精确匹配的不选，要选择近似匹配的其他选项；

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1 个答案

pzqa015 · 2023年12月17日

嗨，努力学习的PZer你好：


不是的

money duration实务中很难做到完全相等，近似相等即可，但对于多大程度算近似相等，原版书并没有说明

这道题三个portfolio的money duration与负债的money duration相差最大的是200多，最小的是7，对于百万级别的数字来说，这就相当于是万分之一的差别，已经很小了，所以，我们认为三个portfolio的money duration都满足条件，要根据convexity来选。

事实上，这类题目一般也都考察convexity这个条件，很少考察money duration的条件。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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