# Interpreting stock price standard deviation

Admittedly a basic question, but here it goes… I’m working on some analysis, the outcome of which depends, in part, on a company’s stock price say in six-months time and/or a year’s time. I would like to take the current stock price (e.g, \$5) and annualized standard deviation (e.g., 50%) to arrive at the stock’s likely price range over the six-month and one-year interval. Can anyone help with the math behind this?

Standard deviation measures volatility of returns - not prices. So the first thing you’d do is compute the mean annual return of the stock over, say, five years. Then use the daily returns (over the same five years) to compute standard deviation then annualize it (square root of trading days in a year times the daily standard deviation). If the stock has an ave annual return of 10% and a standard deviation of 20%, this means there’s a 68% chance of the stock returning anywhere from -10% to 30% in a year. Use the return numbers to apply to the current stock price to get a range. Two standard deviations out is 95% and three is 99.7%. If you already have the annualized standard deviation then it’s pretty simple. Just get the ave annual return of the stock and you’re off.

Sweep the Leg Wrote: ------------------------------------------------------- > Standard deviation measures volatility of returns > - not prices. So the first thing you’d do is > compute the mean annual return of the stock over, > say, five years. Then use the daily returns (over > the same five years) to compute standard deviation > then annualize it (square root of trading days in > a year times the daily standard deviation). > > If the stock has an ave annual return of 10% and a > standard deviation of 20%, this means there’s a > 68% chance of the stock returning anywhere from > -10% to 30% in a year. Use the return numbers to > apply to the current stock price to get a range. > Two standard deviations out is 95% and three is > 99.7%. > > If you already have the annualized standard > deviation then it’s pretty simple. Just get the > ave annual return of the stock and you’re off. Assuming a normal distribution, right? Which the OP may not be but I think it’s a safe assumption he is.

Look at the pricing of forwards.

Sweep the Leg Wrote: ------------------------------------------------------- > Standard deviation measures volatility of returns > - not prices. So the first thing you’d do is > compute the mean annual return of the stock over, > say, five years. Then use the daily returns (over > the same five years) to compute standard deviation > then annualize it (square root of trading days in > a year times the daily standard deviation). > > If the stock has an ave annual return of 10% and a > standard deviation of 20%, this means there’s a > 68% chance of the stock returning anywhere from > -10% to 30% in a year. Use the return numbers to > apply to the current stock price to get a range. > Two standard deviations out is 95% and three is > 99.7%. > > If you already have the annualized standard > deviation then it’s pretty simple. Just get the > ave annual return of the stock and you’re off. i agree, although i would recommend calculating the expected return for the stock via CAPM rather than calculating the mean annual return over 5 years, then use the standard deviation of returns to establish a confidence interval around the CAPM-calculated expected return

Really? That’s kind of odd actually. Considering you’re using past information to calculate the std dev you may as well use the same info to get your mean returns. Why guess at a return then use historical numbers for volatility? I have problems with the CAPM anyway. It’s right up there with dividend discount models and communism; great in theory but never works in practice.

well if you are in the CAPM-naysayers camp then i guess you’d have problems with that methodology. i was just suggesting it as an alternative since the normal distibution of returns assumption is consistent with CAPM. plus, to estimate the CAPM-expected return you’d still be looking at the historical data for your beta and market risk premium