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Colin · 2021年08月27日

用COV算可以吗？

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2016070202000020

问题如下：

You are given the following information about the returns of stock P and stock Q: variance of return of stock P=100； variance of return of stock Q=225; covariance between the return of stock P and the return of stock Q=53.2. At the end of 1999, you are holding USD 4 million in stock P. You are considering a strategy of shifting USD 1 million into stock Q and keeping USD 3 million in stock P. What percentage of risk, as measured by standard deviation of return, can be reduced by this strategy?

选项：

A.

0.5%

B.

5.0%

C.

7.4%

D.

9.7%

解释：

The variance of the original portfolio is 1,600, implying a volatility of 40. The new portfolio has variance of ;32×100+12×225+2×53.2×3×1=1,444;3^2\times100+1^2\times225+2\times53.2\times3\times1=1,444. This gives a volatility of 38, which is a reduction of 5%.

您好，  ϕi2 wi2 +  ϕj2 wj2 +2Covij 这个公式可以用吗？要是不能得话，为啥只能2wiwj  ϕj ϕi ρ的？

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1 个答案

李坏_品职助教 · 2021年08月27日

嗨，爱思考的PZer你好：


这道题考察的是投资组合方差的计算公式。


你说的两个公式是完全等价的，因为协方差cov = ρ * σ1 * σ2。 题目的参考答案用的其实就是cov，题干中给出的53.2是stock P 和stock Q之间的cov。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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