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Emmmmmmmua · 2022年03月05日

为什么不需要 减 均值的平方

NO.PZ2020011303000083

问题如下:

Suppose that the observations on a stock price (in USD) at the close of trading on 15 consecutive days are 40.2, 40.0, 41.1, 41.0, 40.2, 42.3, 43.1, 43.4, 42.9, 41.8, 43.7, 44.3, 44.4, 44.8, and 45.1. Estimate the daily volatility.

选项:

解释:

The 14 daily returns are 0.498%, 2.75%, –0.243%, . The average of the squared returns is 0.000534, and the volatility estimate is the square root of this or 2.31%.

volatility^2 不是应该等于 average of the squared returns - 均值的平方 吗?


这道题的答案 只算到 average of the squared returns = 0.000534 然后直接开方了。


均值 = 0.00848 ,为什么不用 0.000534 - 0.00848^2

1 个答案

李坏_品职助教 · 2022年03月05日

嗨,从没放弃的小努力你好:


这道题首先是默认daily return的均值为0,因为return的变化幅度确实太小。


这样的话14个daily returns序列的方差就等于各个return自平方的平均数,所以volatility就是方差再开根号。

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