# Thread: average of standard deviations

1. ## average of standard deviations

Hello,

I am computing "daily volatility" as the standard deviation of periodic intraday returns. To compute "monthly volatility", can I just compute a simple average of daily volatilities over the 30 day period? Do you see any problem with it? How different will this be over computing the standard deviation of returns over the entire month?

thanks for any suggestions.
Sam

2. Hello,

Originally Posted by saminny
Hello,

I am computing "daily volatility" as the standard deviation of periodic intraday returns. To compute "monthly volatility", can I just compute a simple average of daily volatilities over the 30 day period? Do you see any problem with it? How different will this be over computing the standard deviation of returns over the entire month?

thanks for any suggestions.
Sam
Assuming that it's the same characteristics (law essentially - average/standard deviation) over the days, you can do it this way.

$\displaystyle \mathbb{E}(30X)=30 \mathbb{E}(X)$

$\displaystyle var(30X)=30^2 var(X)$

$\displaystyle \sigma(30X)=\sqrt{var(30X)}=30 \sqrt{var(X)}=30 \sigma(X)$