# How to Calculate the Beta Coefficient for a Single Stock

by Cynthia Gaffney ; Updated April 19, 2017The beta coefficient is a metric used to measure the difference between the average market return and the return on an individual stock or portfolio of stocks. The beta of the market equals one, so portfolio or stock betas close to one will emulate the market's average return. Beta serves as a measure of risk, and higher betas imply higher returns with higher risk profiles. The capital asset pricing model (CAPM) provides a simple way to solve for an individual stock's beta.

Familiarize yourself with the CAPM formula and the required formula inputs. The formula starts with a required return, which is the return on your individual stock. Use the formula as follows: required return = risk - free rate + beta(return on market - risk-free rate). For your required return, use the month-end closing price for the stock being analyzed.

Locate the risk-free rate. Use the current rate of return for 10-year U.S. Treasury securities as a proxy for the risk-free rate. Find this rate on the Daily Treasury Yield Curve Rates chart, which can be found on the U.S. Department of the Treasury's website. The 10-year treasury yield at the time of this writing is 1.88 percent, or .0188. For ease of calculation in the following example, round up to .02.

Estimate the return premium based on the expected market return. Analysts commonly use the S&P 500's average return over a 10-year period to approximate the expected market return. For this example, assume a return premium (market return - risk-free rate) of 5 percent, or.05. This average premium is based on studies performed on decades' worth of market premium data.

Plug the numbers into the equation. For example, if the stock's return was 12 percent, then the equation would be 0.12 = .02 + B(.05), with B = beta.

Solve the equation for beta. This requires some simple algebra. First, subtract the risk-free rate, .02, from both sides of the equation. This results in 0.10 = B(.05). Then divide both sides of the equation by the market premium of .05. The result of two is the beta coefficient for the individual stock.

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