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Ella · 2024年11月09日

duration不一定一样，convexity没法判断吧

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2023100703000078

问题如下：

Given the following bond portfolios:

Which of the following statements is correct?

选项：

A.Portfolio 1 is a barbell portfolio. B.Portfolio 2 is a bullet portfolio. C.It is impossible for Portfolios 1 and 2 to have the same duration. D.Portfolio 2 will have greater convexity than Portfolio 1.

解释：

Since Portfolio 2 has more long-term bonds than short-term bonds and since convexity is related to the square of maturity, Portfolio 2 will have greater convexity. The other statements are incorrect. Portfolio 1 is a bullet portfolio (concentrated in intermediate maturities), and Portfolio 2 is a barbell. It is possible for a bullet and a barbell to have the same duration. In fact, adding the duration contribution of both portfolios gives a duration value of 8.15.

duration不一定一样，convexity没法判断吧

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1 个答案

李坏_品职助教 · 2024年11月09日

嗨，从没放弃的小努力你好：


计算某个债券的convexity的公式：

convexity = ∑t^2 * weight，而weight指的是该债券各个现金流 / 债券价值。


所以convexity其实就是时间的平方和。现金流在长期债券的比重越高，convexity越大。组合1的现金流大部分是集中在10年期的债券，组合2的现金流大部分集中在5年和20年，所以组合2的现金流从时间的平方和来看更大一些，他的convexity更大。

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努力的时光都是限量版，加油！

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