# Capital Asset Pricing Model (CAPM)

A method for calculating the required rate of return, discount rate or cost of capital

A method for calculating the required rate of return, discount rate or cost of capital

The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between expected return and risk of a security. It shows that the return on a security is equal to the risk-free return plus a risk premium, which is based on the beta of that security. Below is an illustration of the CAPM concept.

CAPM is calculated according to the following formula:

Where:

Ra = Expected return on a security

Rrf = Risk-free rate

Ba = Beta of the security

Rm = Expected return on market

Note: Risk Premium = (Rm – Rrf)

The CAPM formula is used to calculate the expected return on investable asset. It is based on the premise that investors have assumptions of systematic risk (also known as market risk or non-diversifiable risk) and need to be compensated for it in the form of a risk premium – an amount of market return greater than the risk-free rate. By investing in a risky security, investors want a higher return for taking on additional risk.

The “Ra” notation above represents the expected return of a capital asset over time, given all of the other variables in the equation. The expected return is a long-term assumption about how an investment will play out over its entire life.

The “Rff” notation is for the risk-free rate, which represents the time value of money is typically equal to the yield on a 10-year US government bond. The risk-free rate should correspond to the country where the investment is being made, and the maturity of the bond should match the time horizon of the investment. Professional convention, however, is to typically use the 10-year rate not matter what because it’s the most heavily quote and liquid bond.

To learn more, check out our free fixed-income fundamentals course.

The beta (denoted as “Ba” in the CAPM formula) is a measure of a stock’s risk (volatility of returns), which is the fluctuation of its price changes relative to the market. In other words, it is the stock’s sensitivity to market risk. For instance, if a company’s beta is equal to 1.5 the security has 150% of the volatility of returns of the market. However, if the beta is equal to 1, the expected return on a security is equal to the return on the market. A beta of -1 means security has a perfect negative correlation with the market.

To learn more: read about asset beta vs equity beta.

From the above components of CAPM we can simplify the formula to reduce (expected return of the market – risk free rate) to be the “market risk premium”. The market risk premium is the excess return expected to compensate an investor for the additional volatility of returns they will experience over and above the risk-free rate.

The CAPM formula is widely used in the finance industry by various professions such as investment bankers, financial analysts, and accountants. It is an integral part of the weight average cost of capital (WACC) as CAPM calculates the cost of equity.

WACC is used extensively in financial modeling. It can be used to find the net present value (NPV) of the future cash flows of an investment and to further calculate its enterprise value and finally its equity value.

Suppose the following information about a stock is known:

- It trades on the NYSE and its operations are based in the United States
- The current yield on a U.S. 10-year treasury is 2.5%
- The average historical annual return for U.S. stocks is 10.0%
- The beta of the stock is 1.25 (meaning it’s average weekly return is 1.25x as volatile as the S&P500 over the last 2 years)

What is the expected return of the security using the CAPM formula?

- Expected return = Risk Free Rate + [Beta x (Market Return – Risk Free Rate)]
- Expected return = 2.5% + [1.25 x (10.0% – 2.5%)]
- Expected return = 11.9%

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