How to Calculate Beta From Volatility & Correlation

Beta value measures a stock's correlated volatility compared to the market as a whole. The entire market offers a beta value of 1.0 -- if a stock has a beta greater than that, it is considered more volatile than the market, and should therefore offer a higher return to be worth incurring the added risk. If a stock is lower than 1.0, then it is more stable than the market. The traditional definition of beta is the covariance between the market and an individual stock, divided by the stock's variance.

Find out the volatility of the individual stock, the volatility of the market, and the correlation between the individual stock and the market. The volatility is measured by the standard deviation of historical prices, which essentially represents how much they fluctuate relative to the price average. Correlation predicts how closely the movement of the individual stock matches that of the market. Correlation may be values between -1 and 1, with 1 representing a perfect match, such as a 10 percent increase in the stock coinciding with a 10 percent increase in the market. A correlation of -1 means an inverse movement, such as a 10 percent increase in the stock coinciding with a 10 percent decrease in the market.

Divide the individual stock's volatility by the market's volatility to calculate relative volatility. For example, if the market typically fluctuates by 20 percent, and the stock fluctuates by 30 percent, then dividing 30 by 20 gives a relative volatility of 1.5.

Multiply the value from Step 2 by the correlation to calculate beta. If the example stock had a 0.8 correlation with the market, then you multiply 0.8 times 1.5 to get a beta value of 1.2. This means that with respect to correlation, the individual stock is 20 percent more volatile than the market, so it comes with more risk. It should also be noted that a correlation of 0.4 would produce a beta of 0.6, which indicates a less volatile stock. However, this is not necessarily true. Because beta is a measurement of correlated volatility, this value may also mean there's insufficient correlation to produce accurate conclusions. Therefore, knowledge of the correlation is important in determining the usefulness of the beta value.