Tài chính doanh nghiệp - Chapter 11: Arbitrage pricing theory and multifactor models of risk and return

Chapter 11Arbitrage Pricing Theory and Multifactor Models of Risk and ReturnSingle Factor ModelReturns on a security come from two sourcesCommon macro-economic factorFirm specific eventsPossible common macro-economic factorsGross Domestic Product GrowthInterest Rates Single Factor Model EquationRi = E(ri) + Betai (F) + eiRi = Return for security iBetai = Factor sensitivity or factor loading or factor betaF = Surprise in macro-economic factor(F could be positive, negative or zero)ei = Firm specific eventsMultifactor ModelsUse more than one factor in addition to market returnExamples include gross domestic product, expected inflation, interest rates etc.Estimate a beta or factor loading for each factor using multiple regression.Multifactor Model EquationRi = E(ri) + BetaGDP (GDP) + BetaIR (IR) + eiWhereRi = Return for security iBetaGDP= Factor sensitivity for GDP BetaIR = Factor sensitivity for Interest Rateei = Firm specific eventsMultifactor SML ModelsE(r) = rf + BGDPRPGDP + BIRRPIR Where BGDP = Factor sensitivity for GDPRPGDP = Risk premium for GDPBIR = Factor sensitivity for Interest RateRPIR = Risk premium for GDPArbitrage Pricing TheoryArbitrage - arises if an investor can construct a zero investment portfolio with a sure profit.Since no investment is required, an investor can create large positions to secure large levels of profit.In efficient markets, profitable arbitrage opportunities will quickly disappear.APT & Well-Diversified PortfoliosrP = E (rP) + bPF + ePWhere:F = some factorFor a well-diversified portfolio: eP approaches zero Similar to CAPMPortfolios and Individual SecurityFE(r)%PortfolioFE(r)%Individual SecurityDisequilibrium ExampleE(r)%Beta for F1076Risk Free 4ADC.51.0Disequilibrium ExampleShort Portfolio CUse funds to construct an equivalent risk higher return Portfolio D.D is comprised of A & Risk-Free AssetArbitrage profit of 1%APT with Market Index PortfolioE(r)%Beta (Market Index)Risk Free M1.0[E(rM) - rf]Market Risk PremiumAPT applies to well diversified portfolios and not necessarily to individual stocks.With APT it is possible for some individual stocks to be mispriced - not lie on the SML.APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio.APT can be extended to multifactor models.APT and CAPM Compared