I am interested in calculating high frequency 5-minute intraday volatility. I am going to use the standard Realized volatility which is the square root of the sum of squared log returns.

Given X is the log price of a stock the log return Y is calculated as $$ log \ returns = Y = \frac{x_i+1}{x_i} $$

Then the realized variance is the sum of the squared log returns:

$$ Realized\ Variance = \sum\limits_{i=1}^{n} (y_{t_{i}})^2 $$

$$ Realized \ Volatility = \sqrt{\sum\limits_{i=1}^{n} (y_{t_{i}})^2 } $$

For 5-minute realized volatility n = 78 (there are 6.5 hours in the NYSE trading day)

Now if Y is the log returns and the mean of Y is assumed to be zero you can also calculate a standard deviation

$$ standard \ deviation = \sqrt{\frac{1}{N}\sum\limits_{i=1}^{N} (y_i)^2}$$

So you can see the only difference between the Realized Volatility of Y and the standard deviation of Y is the $$ \frac{1}{N} $$ termin the standard deviation calcualtion.

Can you explain the significance of this? Why does realized variance not have 1/N and how can the 2 be interpreted. Thank you.

reference https://en.wikipedia.org/wiki/Realized_variance


It is all a matter of frequency. For instance if you want to get annual realized volatility you multiply your last expression by $\sqrt{(N*251)}$ or the second to last expression by $\sqrt{(251)}$.

In other words, your last expression is the 5-min realized volatility whereas the second to last expression is the daily realized volatility.

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.