How to Calculate Expected Return With Beta & Market Risk Premiums

You can use the capital asset pricing model, or CAPM, to estimate the return on an asset -- such as a stock, bond, mutual fund or portfolio of investments -- by examining the asset's relationship to price movements in the market.

For example, you might want to know the three-month expected return on the shares of XYZ Mutual Fund, a hypothetical fund of American stocks, using the S&P 500 index to represent the overall stock market. CAPM can provide the estimate using a few variables and simple arithmetic.

The variables used in the CAPM equation are:

• Expected return on an asset (r_a), the value to be calculated
• Risk-free rate (r_f), the interest rate available from a risk-free security, such as the 13-week U.S. Treasury bill. No instrument is completely without some risk, including the T-bill, which is subject to inflation risk. However, the T-bill is generally accepted as the best representative of a risk-free security, because its return is guaranteed by the Federal Reserve, which is empowered to print money to pay it. Current T-bill rates are available at the Treasury Direct website.
  
• Beta of the asset (β_a), a measure of the asset's price volatility relative to that of the whole market
  
• Expected market return (r_m), a forecast of the market's return over a specified time. Because this is a forecast, the accuracy of the CAPM results are only as good as the ability to predict this variable for the specified period.
  

The market risk premium is the expected return of the market minus the risk-free rate: r_m - r_f. The market risk premium represents the return above the risk-free rate that investors require to put money into a risky asset, such as a mutual fund. Investors require compensation for taking on risk, because they might lose their money. If the risk-free rate is 0.4 percent annualized, and the expected market return as represented by the S&P 500 index over the next quarter year is 5 percent, the market risk premium is (5 percent - (0.4 percent annual/4 quarters per year)), or 4.9 percent.

Beta is a measure of how an asset's price moves in conjunction with price changes in the market. A β with a value of +1 indicates perfect positive correlation: The market and asset move in lockstep on a percentage basis. A β of -1 indicates perfect negative correlation -- that is, if the market goes up 10 percent, the asset would be expected to fall 10 percent. The betas of individual assets, such as mutual funds, are published on the issuer's website.

To find the expected return, plug the variables into the CAPM equation:

r_a = r_f + β_a(r_m - r_f)

For example, suppose you estimate that the S&P 500 index will rise 5 percent over the next three months, the risk-free rate for the quarter is 0.1 percent and the beta of the XYZ Mutual Fund is 0.7. The expected three-month return on the mutual fund is (0.1 + 0.7(5 - 0.1)), or 3.53 percent.