Capital Asset Pricing Model (CAPM) - Definitions, Formulas & Examples

Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between the expected return and risk of investing in a security. It shows that the expected return on a security is equal to the risk-free return plus a risk premium, which is based on the beta of that security. As an analyst, you could use CAPM to decide what price you should pay for a particular stock. If Stock A is riskier than Stock B, the price of Stock A should be lower to compensate investors for taking on the increased risk.

Formula:    k_e = R_f + (R_m – R_f )β_j

Note: “Risk Premium” = (Rm – Rrf)

Equation requires the following three parameters to estimate a firm’s cost of

equity:

1. The risk-free rate (Rf):

2. The market risk premium (Rm – Rf):

3. The beta of the firm’s share (β_j):

Let's Know about "Dividend-Growth Approach".

The dividend-growth approach has limited application in practice because of its two assumptions. First, it assumes that the dividend per share will grow at a constant rate, g, forever. Second, the expected dividend growth rate, g, should be less than the cost of equity, ke, to arrive at the simple growth formula. These assumptions imply that the dividend-growth approach cannot be applied to those companies, which are not paying any dividends, or whose dividend per share is growing at a rate higher than ke, or whose dividend policies are highly volatile. The dividend–growth approach also fails to deal with risk directly. In contrast, the CAPM has a wider application although it is based on restrictive assumptions. The only condition for its use is that the company’s share is quoted on the stock exchange. Also, all variables in the CAPM are market determined and except the company specific share price data, they are common to all companies. The value of beta is determined in an objective manner by using sound statistical methods. One practical problem with the use of beta, however, is that it does not probably remain stable over time.

How is Beta determined ?

A beta of any portfolio of securities is the weighted average of the betas of the securities, where the weights are the proportions of investments in each security. Adding a high beta (beta greater than 1.0) security to a diversified portfolio increase the portfolio’s risk, and adding a low beta (beta less than zero) security to a diversified security reduces the portfolio’s risk. The beta co-efficient for a security (or asset) can be found by examining security’s historical returns rela tive to the return of the market. As it is, not feasible to take all securities, a sample of securities is used. The Capital Asset Pricing Model (CAPM) uses these beta co-efficients to estimate the required rate of return on the securities. The current rate on government securities can be used as a riskless rate. The difference between the long-run average rate of returns between shares and government securities may represent the risk premium.

Examples:

Cost of Equity = Risk-Free Rate of Return + Beta * (Market Rate of Return - Risk-Free Rate of Return).

Assume the following for Asset XYZ:

Risk-Free Rate of Return = 3%

Market Rate of Return  = 10%

Beta = 0.75

Market Rate of Return = 10%

Return on Equity = 0.03 + [0.75 * (0.10 - 0.03)]

                                                      = 0.0825 = 8.25%