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.

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