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海胆君 · 2021年02月28日

为什么dayn协方差的均值用X和Y的乘积？

  1. FRM I
  2. Quantitative

NO.PZ2019040801000027

问题如下：

The price percent changes of stock X and Y were 5.0% and 1.0%, respectively. The correlation estimate based on the historical data of the two on day n-1 is 0.6, the estimated standard deviations of price of X and Y on day n-1 were 2.3% and 1.7%, respectively. Suppose the analyst uses the EWMA model with λ = 0.97 to update the correlation and covariance. What is the new estimate of the correlation between X and Y on day n?

选项：

A.

0.34.

B.

0.42.

C.

0.60.

D.

0.68.

解释：

C is correct.

考点：EWMA模型

解析：先计算day n-1时候的协方差：

cov(X, Y) = ΡX,Y x σXσY = 0.6 * 2.3% * 1.7% = 0.000235

然后通过EWMA模型

估计day n的协方差：covn = 0.97 * 0.000235 + 0.03 * 5% * 1% = 0.00024295

估计X的方差：σ2X,n = 0.97 x 0.023^2 + 0.03 x 0.05^2 = 0.00058813

X的标准差就是0.00058813^0.5=0.02425

估计Y的方差：σ2Y,n = 0.97 x 0.0172 + 0.03 x0.012 = 0.0003078 + 0.000003 = 0.0002833

Y的标准差就是0.0002833^0.5=0.01683

最后新的相关系数就是协方差除以X标准差再除以Y的标准差：

0.00024295/（0.02425*0.01683）=0.5952

【估计day n的协方差：covn = 0.97 * 0.000235 + 0.03 * 5% * 1% = 0.00024295】里面相当于【Un-1^2=5% * 1%】，这是为啥呢我也不知道X和Y什么关系啊，直接乘？

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品职答疑小助手雍 · 2021年02月28日

嗨，爱思考的PZer你好：


不要把后面那项想成是协方差的均值，根据EWMA模型的公式，先看方差的那个后面那项就是直接乘的收益率，而协方差的后面那项乘的是两者的收益率。

公式的话，强化串讲第52页有的~

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努力的时光都是限量版，加油！

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