# Models of CAPM Calculation

by Michael Alpert ; Updated July 27, 2017The Capital Asset Pricing Model (CAPM) suggests that an investor can expect the returns on her security investment, like stocks, to be positively related to the security’s beta, which measures an element of a security’s risk. The actual CAPM formula states that a security’s expected return (ER) is equal to the risk-free rate (RF) plus the beta of the security (B) multiplied by the difference between the expected return on the market (ERM) and the RF. Put another way: ER = RF + B(ERM – RF). It may seem complex, but the CAPM model is really a combination of several smaller models and formulas, including beta, the risk free rate and expected return of the market. Breaking the model into smaller chunks helps simplify the process.

## Risk Free Rate

To work through the CAPM model, it is necessary first to find the risk-free rate (RF). Treasury bills with a maturity of one year or less are often used as an RF, as they have virtually no risk of default. For the current calculated example, an RF of two percent is assumed.

## Beta

Search for a company’s beta (B) using an online finance site, such as Yahoo Finance. While it is possible to calculate B, several online resources provide educated estimates that can save time. For example, assume that Fake, Inc has a B of 1.7 for this calculation.

## Market Return

Find the expected return on the market (ERM), which has a formula of its own. The ERM is equal to the risk-free rate (RF) plus the return on portfolio (RP). To find the risk premium, many economists will look at the difference between historical risk free rates and returns on securities over a period of time. For example, assume a historical risk free rate of 2.5 percent. For this same time period, assume an 11 percent return on all common stocks. The difference between these two numbers (11 percent - 2.5 percent = 8.5 percent) represents the RP of the return an investor can expect for his risk. Assuming this figure is indicative of the future risk premium, it can be added to the assumed RF rate of 2 percent. So, the expected return equals 10.5 percent (8.5 percent + 2 percent).

## Put it All Together

Put the models together to represent the final CAPM model. Start by subtracting the expected ERM at 10.5 percent from the RF estimate of 2 percent for a difference of 8.5 percent. Revisit our original formula: ER = RF + B(ERM – RF). By completing with the inputs previously identified, it is evident that the expected return on a security is equal to an RF of 2 percent plus a B of 1.7 multiplied by the difference between the ERM of 10.5 percent and the RF of 2 percent. Put another way: 16.45 percent = 2 percent + 1.7(10.5 percent – 2 percent).

#### References

- Corporate Finance: Core Principles and Applications; Ross, Westerfield, Jaffe and Jordan; 2007 McGraw Hill
- Investopedia: Risk-Free Rate Definition

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