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# Capital Asset Pricing Model (CAPM)

Because investors are risk averse, they will choose to hold a portfolio of securities to take advantage of the benefits of Diversification. Therefore, when they are deciding whether or not to invest in a particular stock, they want to know how the stock will contribute to the risk and expected return of their portfolios.

The standard deviation of an individual stock does not indicate how that stock will contribute to the risk and return of a diversified portfolio. Thus, another measure of risk is needed; a measure of a security's sytematic risk. This measure is provided by the Capital Asset Pricing Model (CAPM).

 Systematic and Unsystematic Risk An asset's total risk consists of both systematic and unsystematic risk. Systematic risk, which is also called market risk or undiversifiable risk, is the portion of an asset's risk that cannot be eliminated via diversification. The systematic risk indicates how including a particular asset in a diversified portfolio wil contribute to the riskiness of the portfolio Unsystematic risk, which is also called firm-specific or diversifiable risk, is the portion of an asset's total risk that can be eliminated by including the security as part of a diversifiable portfolio.

The Capital Asset Pricing Model (CAPM) provides an expression which relates the expected return on an asset to its systematic risk. The relationship is known as the Security Market Line (SML) equation and the measure of systematic risk in the CAPM is called Beta.

### The Security Market Line (SML)

The SML equation is expressed as follows:

where

• E[Ri] = the expected return on asset i,
• Rf = the risk-free rate,
• E[Rm] = the expected return on the market portfolio,
• bi = the Beta on asset i, and
• E[Rm] - Rf = the market risk premium.

The graph below depicts the SML. Note that the slope of the SML is equal to (E[Rm] - Rf) which is the market risk premium and that the SML intercepts the y-axis at the risk-free rate.

In capital market equilibrium, the required return on an asset must equal its expected return. Thus, the SML equation can also be used to determine an asset's required return given its Beta.

### The Beta (Bi)

The beta for a stock is defined as follows:

where

• sim = the Covariance between the returns on asset i and the market portfolio and
• s2m = the Variance of the market portfolio.

Note that, by definition, the beta of the market portfolio equals 1 and the beta of the risk-free asset equals 0.

An asset's systematic risk, therefore, depends upon its covariance with the market portfolio. The market portfolio is the most diversified portfolio possible as it consists of every asset in the economy held according to its market portfolio weight.

 Example Problems 1. Find the expected return on a stock given that the risk-free rate is 6%, the expected return on the market portfolio is 12%, and the beta of the stock is 2. 2. Find the beta on a stock given that its expected return is 16%, the risk-free rate is 4%, and the expected return on the market portfolio is 12%.

The CAPM Exercise provides interactive example problems based upon the SML equation.

© 2002 - 2010 by Mark A. Lane, Ph.D.