# How to Calculate the Expected Return of a Portfolio Using CAPM

by Cynthia Hartman ; Updated April 19, 2017Stock market investing brings the potential of financial rewards with a corresponding trade-off of risk. Especially in a difficult market, investments with a positive return and low risk would make investors smile. Portfolio diversification is an effective way to lower risk and generate a positive return. Using the capital asset pricing model (CAPM) to calculate the expected return on your portfolio allows you to assess current results, plan profit expectations and rebalance your investments.

Review and understand the components of the capital asset pricing model, or CAPM. The CAPM formula is RF + beta multiplied by RM minus RF. RF stands for risk-free rate, RM is market return, and beta is the portfolio beta. CAPM theory explains that every investment carries with it two types of risk. The first, systematic risk, known also as beta, is the risk inherent in holding a position in the market. This risk does not go away with diversification. The second risk is unsystematic, representing the performance of individual companies. Since unsystematic risk is diversifiable with appropriate portfolio management, a portfolio's relationship to the market, or beta, is the only remaining determinant of risk and its correlated return.

Locate the risk-free rate. Treasury securities serve as a proxy for the risk-free rate because the U.S. government backs treasuries. This essentially removes all of the risk associated with the securities' return. Check the Federal Reserve Bank's website for ongoing updates to the current rate on 10-year Treasuries. The 10-year treasury rate at August 8, 2011 sits at 2.62 percent.

Determine the risk premium. The risk premium is the remainder after you subtract the risk-free rate from the average market return. Investors expect this additional compensation for investing in individual companies. The market return is defined using S&P compounded returns from 1926 to 2008, which average 10.3 percent. Use this to calculate the risk premium as return on market minus risk-free rate - or 10.3 percent - 2.62 percent = 7.68 percent.

Calculate your portfolio beta, and locate the beta for each asset in the portfolio. The Value Line publication, found in public libraries, provides beta statistics by company. Standard & Poor's Stock Reports and Yahoo! Finance also provide betas by company. Multiply each beta by the percent its asset makes up in the overall portfolio. For example, a stock has a beta of 1.2, and makes up 10 percent of your portfolio. The weighted beta is 1.2 multiplied by 10 percent, or .12. Add up all of the weighted betas to arrive at the portfolio beta.

Assemble and solve the CAPM equation. Take the risk premium result from Step 3, multiply it by the portfolio beta from Step 4, and add this result to the risk-free return from Step 2. For example, the risk premium is the market return minus the risk-free rate, or 10.3 percent minus 2.62 percent = 7.68 percent. Assume a portfolio beta of 1.2; multiply this with the risk premium to get 9.22. Finally, add this result to the risk-free rate: 2.62 percent + 9.22 percent = 11.84 percent expected portfolio return.

#### References

- Stanford University; Revisiting the Capital Asset Pricing Model; Jonathan Burton; May/June, 1998
- Western Washington University; Evaluation of Portfolio Performance
- CNN Money; Don't Expect Another Bull Market; Allen Sloan; March 2008
- Dartmouth College; Finding Betas for Companies and Industries
- Federal Reserve Bank; H.15 Selected Interest Rates; August 8, 2011

#### Photo Credits

- Thinkstock/Comstock/Getty Images