## Sunday, December 11, 2011

### The Capital Asset Pricing Model (CAPM)

CFA Level 1 - Portfolio Management

The capital asset pricing model (CAPM) is a model that calculates expected return based on expected rate of return on the market, the risk-free rate and the beta coefficient of the stock.

 Formula 17.11 E(R) = Rf + ß( Rmarket - Rf )

Example: CAPM model
Determine the expected return on Newco's stock using the capital asset pricing model. Newco's beta is 1.2. Assume the expected return on the market is 12% and the risk-free rate is 4%.
E(R) = 4% + 1.2(12% - 4%) = 13.6%.

Using the capital asset pricing model, the expected return on Newco's stock is 13.6%.

The Security Market Line (SML)
Similar to the CML, the SML is derived from the CAPM, solving for expected return. However, the level of risk used is the Beta, the slope of the SML.

The SML is illustrated below:

Beta
Beta is the measure of a stock's sensitivity of returns to changes in the market. It is a measure of systematic risk.

 Formula 17.12 Beta = B = Covariance of stock to the market              Variance of the market

Example: Beta
Assume the covariance between Newco's stock and the market is 0.001 and the variance of the market is 0.0008. What is the beta of Newco's stock?

BNewco = 0.001/0.0008 = 1.25

Newco's beta is 1.25.

Determing Whether a Security is Under-, Over- or Properly Valued
As discussed, the SML line can be derived using CAPM, solving for the expected return using beta as the measure of risk. Given that interpretation and a beta value for a specific security, we can then determine the expected return of the security with the CAPM. Then, using the expected return for a security derived from the CAPM, an investor can determine whether a security is undervalued, overvalued or properly valued.

Example:Calculate the expected return on a security and evaluate whether the security is undervalued, overvalued or properly valued.
An investor anticipates Newco's security will reach \$30 by the end of one year. Newco's beta is 1.3. Assume the return on the market is expected to be 16% and the risk-free rate is 4%. Calculate the expected return of Newco's stock in one year and determine whether the stock is undervalued, overvalued or properly valued with a current value of \$25.

E(R)Newco = 4% + 1.3(16% - 4%) = 20%

Given the expected return of Newco's stock using CAPM is 20% and the investor anticipates a 20% return, the security would be properly valued.
• If the expected return using the CAPM is higher than the investor's required return, the security is undervalued and the investor should buy it.
• If the expected return using the CAPM is lower than the investor's required return, the security is overvalued and should be sold.

The Characteristic Line
The characteristic line is line that occurs when an individual asset or portfolio is regressed to the market. The beta is the slope coefficient for the characteristic line and is thus the measure of systematic risk for the asset or portfolio. Recall, a beta is the measure of a stock's sensitivity of returns to changes in the market. It is a measure of systematic risk.

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