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Bus350 Review sheet
Lecture 5 APT Three major assumptions:
* Capital markets are perfectly competitive
* Investors always prefer more wealth to less wealth with certainty
* The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
* In contrast to CAPM, APT does not assume:
* A mean-variance efficient market portfolio
* Normally distributed security returns
* Quadratic utility function
In APT multiple factors expected to have an impact on all assets, contrast with CAPM insistence that only beta is relevant
The APT model:
E(Ri)=λ0+ λ1bi1+ λ2bi2+…+ λkbik
where:
λ0=the expected return on an asset with zero systematic risk
λj=the risk premium related to the j th common risk factor
bij=the pricing relationship between the risk premium and the asset; that is, how responsive asset i is to the j th common factor, called factor betas or factor loadings
In APT multiple factors expected to have an impact on all assets, contrast with CAPM insistence that only beta is relevant
E(RA)=(0.8) λ1 + (0.9) λ2 If λ1=4% and λ2=5%, then it is easy to compute the expected returns for the stocks: E(RA)=7.7%
Expected Prices One Year Later: Assume that all three stocks are currently priced at $35 and do not pay a dividend
Estimate the price: E(PA)=$35(1+7.7%)=$37.70
Assume the actual price of stock A will be $37.20 one year later, then arbitrage trading will lead to new current price: E(PA)=$37.20 / (1+7.7%)=$34.54
The Equation Rit = ai + [bi1F1t + bi2 F2t + . . . + biK FKt] + eit
Where: Fit=Period t return to the jth designated risk factor Rit =Security i’s return that can be measured a either a nominal or excess return to
Fama and French multifactor model: SMB (i.e. small minus big) is the return to a portfolio of small capitalization stocks less the return to a portfolio of large capitalization stocks. HML (i.e. high minus low) is the return to a portfolio of stocks with high...