The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk, or the general perils of investing, and expected return for assets, particularly stocks.1 CAPM evolved as a way to measure this systematic risk. It is widely used throughout finance for pricing risky securities and generating expected returns for assets, given the risk of those assets and cost of capital.

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The formula for calculating the expected return of an asset given its risk is as follows:1

\begin{aligned} &ER_i = R_f + \beta_i ( ER_m - R_f ) \\ &\textbf{where:} \\ &ER_i = \text{expected return of investment} \\ &R_f = \text{risk-free rate} \\ &\beta_i = \text{beta of the investment} \\ &(ER_m - R_f) = \text{market risk premium} \\ \end{aligned}​ERi​=Rf​+βi​(ERm​−Rf​)where:ERi​=expected return of investmentRf​=risk-free rateβi​=beta of the investment(ERm​−Rf​)=market risk premium​

Investors expect to be compensated for risk and the time value of money. The risk-free rate in the CAPM formula accounts for the time value of money. The other components of the CAPM formula account for the investor taking on additional risk.

The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.

A stock’s beta is then multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required return or discount rate they can use to find the value of an asset.

The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared with its expected return. In other words, it is possible, by knowing the individual parts of the CAPM, to gauge whether the current price of a stock is consistent with its likely return.

For example, imagine an investor is contemplating a stock valued at $100 per share today that pays a 3% annual dividend. The stock has a beta compared with the market of 1.3, which means it is riskier than a market portfolio. Also, assume that the risk-free rate is 3% and this investor expects the market to rise in value by 8% per year.

The expected return of the stock based on the CAPM formula is 9.5%:

\begin{aligned} &9.5\% = 3\% + 1.3 \times ( 8\% - 3\% ) \\ \end{aligned}​9.5%=3%+1.3×(8%−3%)​

The expected return of the CAPM formula is used to discount the expected dividends and capital appreciation of the stock over the expected holding period. If the discounted value of those future cash flows is equal to $100, then the CAPM formula indicates the stock is fairly valued relative to risk.

There are several assumptions behind the CAPM formula that have been shown not to hold up in reality. Modern financial theory rests on two assumptions: One, securities markets are very competitive and efficient (that is, relevant information about the companies is quickly and universally distributed and absorbed) and two, these markets are dominated by rational, risk-averse investors, who seek to maximize satisfaction from returns on their investments.

As a result, it's not entirely clear whether CAPM works. The big sticking point is beta. When professors Eugene Fama and Kenneth French looked at share returns on the New York Stock Exchange, the American Stock Exchange, and Nasdaq, they found that differences in betas over a lengthy period did not explain the performance of different stocks. The linear relationship between beta and individual stock returns also breaks down over shorter periods of time. These findings seem to suggest that CAPM may be wrong.2

Despite these issues, the CAPM formula is still widely used because it is simple and allows for easy comparisons of investment alternatives.

Including beta in the formula assumes that risk can be measured by a stock’s price volatility. However, price movements in both directions are not equally risky. The look-back period to determine a stock’s volatility is not standard because stock returns (and risk) are not normally distributed.

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk, or the general perils of investing, and expected return for assets, particularly stocks.1 CAPM evolved as a way to measure this systematic risk. It is widely used throughout finance for pricing risky securities and generating expected returns for assets, given the risk of those assets and cost of capital.

0 seconds of 2 minutes, 39 secondsVolume 75%

2:39

The formula for calculating the expected return of an asset given its risk is as follows:1

\begin{aligned} &ER_i = R_f + \beta_i ( ER_m - R_f ) \\ &\textbf{where:} \\ &ER_i = \text{expected return of investment} \\ &R_f = \text{risk-free rate} \\ &\beta_i = \text{beta of the investment} \\ &(ER_m - R_f) = \text{market risk premium} \\ \end{aligned}​ERi​=Rf​+βi​(ERm​−Rf​)where:ERi​=expected return of investmentRf​=risk-free rateβi​=beta of the investment(ERm​−Rf​)=market risk premium​

Investors expect to be compensated for risk and the time value of money. The risk-free rate in the CAPM formula accounts for the time value of money. The other components of the CAPM formula account for the investor taking on additional risk.

The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.

A stock’s beta is then multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required return or discount rate they can use to find the value of an asset.

The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared with its expected return. In other words, it is possible, by knowing the individual parts of the CAPM, to gauge whether the current price of a stock is consistent with its likely return.

For example, imagine an investor is contemplating a stock valued at $100 per share today that pays a 3% annual dividend. The stock has a beta compared with the market of 1.3, which means it is riskier than a market portfolio. Also, assume that the risk-free rate is 3% and this investor expects the market to rise in value by 8% per year.

The expected return of the stock based on the CAPM formula is 9.5%:

\begin{aligned} &9.5\% = 3\% + 1.3 \times ( 8\% - 3\% ) \\ \end{aligned}​9.5%=3%+1.3×(8%−3%)​

The expected return of the CAPM formula is used to discount the expected dividends and capital appreciation of the stock over the expected holding period. If the discounted value of those future cash flows is equal to $100, then the CAPM formula indicates the stock is fairly valued relative to risk.

There are several assumptions behind the CAPM formula that have been shown not to hold up in reality. Modern financial theory rests on two assumptions: One, securities markets are very competitive and efficient (that is, relevant information about the companies is quickly and universally distributed and absorbed) and two, these markets are dominated by rational, risk-averse investors, who seek to maximize satisfaction from returns on their investments.

As a result, it's not entirely clear whether CAPM works. The big sticking point is beta. When professors Eugene Fama and Kenneth French looked at share returns on the New York Stock Exchange, the American Stock Exchange, and Nasdaq, they found that differences in betas over a lengthy period did not explain the performance of different stocks. The linear relationship between beta and individual stock returns also breaks down over shorter periods of time. These findings seem to suggest that CAPM may be wrong.2

Despite these issues, the CAPM formula is still widely used because it is simple and allows for easy comparisons of investment alternatives.

Including beta in the formula assumes that risk can be measured by a stock’s price volatility. However, price movements in both directions are not equally risky. The look-back period to determine a stock’s volatility is not standard because stock returns (and risk) are not normally distributed.