How to calculate stock volatility in %?

Question

How can I calculate the stock volatility in percentage? Do i have to use sd() function without any other calculation ?

Thanks

Answer 1

BNaul's answer is probably not the one you're looking for. If you want to calculate Black-Scholes style volatility, you need to calculate an annualized volatility of log-returns. That means, calculate the log return series $\ln(s_t/s_{t-1})$ for each $t$, take the standard deviation, and then adjust it by the square root of time to obtain the annualized figure. This volatility can be used in pricing models that require Black Scholes vol.

Answer 2

You're looking for the standard deviation of log returns, appropriately annualized and converted to percentage (i.e. multiplied by 100).

Here is an example of computing annual vol from daily prices:

library(tseries)
data <- get.hist.quote('VOD.L')
price <- data$Close
ret <- log(lag(price)) - log(price)
vol <- sd(ret) * sqrt(250) * 100

Notes:

1. The above code should really be using prices adjusted for corporate actions (dividends, splits etc).
2. 250 is the (approximate) number of trading days in a year.

Answer 3

When volatility is described as a percentage, that means it's being given as a fraction of the mean. So if the standard deviation of the price is 10 and the mean is 100, then the price could be described as 10% volatile.

In R terms, this would mean:

vol_percent = sd(price) / mean(price)

EDIT: This could also have been easily found on the Wikipedia article for volatility.