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NO.PZ2023100703000064

问题如下：

Risk analyst uses data from the HS300 index over the past 260 weeks to estimate the long-term average correlation of the common stocks and mean reverting rate. And find the average long-term stock correlation of the HS 300 Index is 22%, and the regression output estimates the following regression relationship: Y = 0.34-0.55X. Assume that in first week of March 2020, the average weekly correlation of all HS300 stocks was 65%. Based on the mean reverting rate in regression analysis, what is the estimated one-week autocorrelation?

选项：

A.0.219

B.0.23

C.0.35

D.0.45

解释：

To find the estimated one-week autocorrelation based on the mean reverting process, we can use the following formula:

单期自相关率+均值回归率=1，所以自相关率只要拿1减去均值回归率，即1-0.55=0.45

公式只考虑 t时刻correlation系数且用的不是-（1-a）=-0.55

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pzqa39 · 2024年08月01日

嗨，爱思考的PZer你好：

股票价格的波动是受到两部分影响的，第一部分就是autocorrelation还有另一个名字叫trending，也就是趋势影响；第二部分是长期均值，也就是mean reverting的影响，这俩部分与股票价格做回归，系数相加是等于1的。

另外关于0.55的正负号的问题，原版书里面是这样写的

所以按照FRM的写法，均值复归系数等于这个beta的相反数，本题中就是（-0.55）的相反数，即55%。

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