How to Calculate Stock Variance Given the Beta

by Edriaan Koening

Stock investors consider various factors to determine whether a stock provides sufficient returns for the amount of risk it has. Beta measures the extent to which a stock's value moves with the market. A positive beta indicates that a stock moves in the same direction as the market, and a negative beta means that it moves in the opposite direction. Variance indicates the risk level of a certain stock. You can calculate variance if you know the stock's beta and some other factors.

Determine the market standard deviation. If you were to do this manually, you have to perform a long series of complex calculations. You need to first find market variance by calculating the average return of the market during the period of time you are analyzing, deduct the average from every single return figure, find the square root of every difference, add them all up and divide the resulting figure by the number of observations minus 1. You then have to take the root of the variance to get the market standard deviation. You may be able to get this information from your broker.

Find the correlation between the market returns and the stock returns. Correlation measures the relationship between two variables. Manual calculation of correlation requires long, complex calculations. For an accurate figure, you need to take into account the returns of both the market and the stock over a long period, such as five or 10 years. You may have to use thousands of variables in your calculation. Your broker may be able to provide you with this correlation figure.

Multiply the stock beta by the market standard deviation, which you calculated in Step 1.

Divide the result of the calculation in Step 3 by the correlation between the stock and the market. This gives you the stock standard deviation.

Find the square root of the stock standard deviation to get the variance. For example, if the standard deviation of the stock is 0.01, then the variance is 0.0001 (from 0.01 X 0.01).

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