Review

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...