Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks.

CAPM 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.

 Understanding the Capital Asset Pricing Model (CAPM)

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

ERi​=Rf​+βi​(ERm​−Rf​)

where: ERi​=expected return of investment

Rf​=risk-free rate

βi​=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 to its expected return.

EXAMPLE

For example, imagine an investor is contemplating a stock worth $100 per share today that pays a 3% annual dividend. The stock has a beta compared to 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%:

​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.

Problems With the CAPM

There are several assumptions behind the CAPM formula that have been shown not to hold 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.

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