问一道题：NO.PZ2016070201000038

问题如下：

A risk manager uses the past 480 months of correlation data from the Dow Jones Industrial Average (Dow) to estimate the long-run mean correlation of common stocks and the mean reversion rate. Based on historical data, the long-run mean correlation of Dow stocks was 32%, and the regression output estimates the following regression relationship: Y = 0.24 - 0.75X. Suppose that in April 2014, the average monthly correlation for all Dow stocks was 36%. What is the expected correlation for May 2014 assuming the mean reversion rate estimated in the regression analysis?

选项：

32%.

33%.

35%.

37%

解释：

There is a-4% difference from the long-run mean correlation and April 2014 correlation (32% - 36% = -4%). The inverse of the P coefficient in the regression relationship implies a mean reversion rate of75%. Thus, the expected correlation for May 2014 is 33.0%:

${l}S_t=a{(\mu-S_{t-1})}+S_{t-1}\\S_t=0.75{(32\%-36\%)}+0.36=0.33$