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nanaluo · 2021年10月05日

请问这里的x为什么等于-rho呢？

  1. FRM I
  2. Financial Markets And Products

NO.PZ2016082404000017

问题如下：

If two securities have the same volatility and a correlation equal to -0.5 their minimum variance hedge ratio is

选项：

A.

  1:1

B.

  2:1

C.

  4:1

D.

  16:1

解释：

ANSWER: B

Set x as the amount to invest in the second security, relative to that in the first (or the hedge ratio). The variance is then proportional to 1+x2+2xρ1+x^2+2x\rho. Taking the derivative and setting to zero, we have x=−ρ=0.5x=-\rho=0.5. Thus, one security must have twice the amount in the other. Alternatively, the hedge ratio is given by N∗=−ρσSσFN\ast=-\rho\frac{\sigma_S}{\sigma_F} which gives 0.5. Answer B is the only one that is consistent with this number or its inverse.

请问这里的x为什么等于-rho呢？

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1 个答案

李坏_品职助教 · 2021年10月05日

嗨，从没放弃的小努力你好：


这里是先对1+x^2+2xρ求一阶导数，结果是2x + 2ρ，令2x + 2ρ = 0，可以得到x = -ρ。

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