CAPM & the SML

• The Capital Asset Pricing Model (CAPM) assumes only one efficient portfolio, the market portfolio.

• CAPM and the CML are more strict than simple Mean-Variance and the CAL.

• CAPM and CAL similarities:

• Risk averse investors.

• Shared investor assumptions for expected returns, variances and standard deviations, and covariances of returns.

• The above variables are the only inputs required to calculate the efficient frontier.

• No taxes and no transaction costs.

• CAPM additional assumptions:

• All investors have the same CAL.

• No restrictions for borrowing and lending at the risk free rate.

• No restrictions on short-selling.

• Trading volume does not change prices.

• The CML is the efficient market portfolio, but the CAPM can describe the expected returns for all assets and portfolios.

CAPM: E(Ri) = RF + βi[E(RM) - RF]

• E(Ri) = Return for asset "i"

• RF = Risk-free rate of return

• E(RM) = Expected return of the market portfolio

• βi = The asset's beta

• Beta is the asset's sensitivity to the return on the market portfolio

• Beta is a measure of an asset's risk relative to market portfolio, as asset's with a beta above 1 are considered riskier than the market and beta's below 1 are considered less risky than the market.

• β = Cov(Ri,RM)/σM2

• Security Market Line (SML): Line produced by the CAPM equation for asset "i"

• SMLs & Efficient Markets: In an efficient market securities are correctly priced when the expected risk and expected return equal the SML price of risk.