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Kathy苏苏 · 2022年08月14日

为什么不选组合1?

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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.


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

为什么不选组合1?组合2的MD小于负债的MD呀。组合3的C小于负债的C。应该选组合1呀。谢谢老师。组合2的MD怎么判断是近似等于负债的MD呢。差多少算是近似等?

1 个答案

pzqa015 · 2022年08月14日

嗨,从没放弃的小努力你好:


三个组合的money duration都是百万级别的数字,与负债的money duration相差几百,也就是相差万分之一,这样的误差,是可以接受的,况且实务中很难做到资产与负债的money duration完全相等,只要近似相等即可。但是这个标准到底是多少,书上并没有一个定量的指标,这类题,要揣测出题者的意图。

负债的convexity是135.142,三个portfolio中,有两个portfolio的convexity大于负债的convexity,只有一个小于它,所以,这道题出题人想考察的是根据convexity来选择最优portfolio。所以,不能选择portfolio1。


如果出题人想考察根据money duration来判断,会把不同portfolio的money duration做的差距很大,一目了然就可以根据money duration做出排除。

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

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