Bài giảng Investment - chapter 10: Arbitrage Pricing Theory and Multifactor Models of Risk and Return

CHAPTER 10Arbitrage 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 = Return for security I = 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) + GDP GDP + IR IR + ei ri = Return for security i GDP= Factor sensitivity for GDP IR = Factor sensitivity for Interest Rate ei = Firm specific eventsMultifactor SML ModelsE(r) = rf + GDPRPGDP + IRRPIR GDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP IR = Factor sensitivity for Interest RateRPIR = Risk premium for Interest RateArbitrage Pricing TheoryArbitrage - arises if an investor can construct a zero investment portfolio with a sure profitSince no investment is required, an investor can create large positions to secure large levels of profitIn efficient markets, profitable arbitrage opportunities will quickly disappearAPT & Well-Diversified PortfoliosrP = E (rP) + bPF + ePF = some factorFor a well-diversified portfolio: eP approaches zero Similar to CAPM,Figure 10.1 Returns as a Function of the Systematic FactorFigure 10.2 Returns as a Function of the Systematic Factor: An Arbitrage OpportunityFigure 10.3 An Arbitrage OpportunityFigure 10.4 The Security Market LineAPT applies to well diversified portfolios and not necessarily to individual stocksWith APT it is possible for some individual stocks to be mispriced - not lie on the SMLAPT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolioAPT can be extended to multifactor modelsAPT and CAPM ComparedMultifactor APTUse of more than a single factorRequires formation of factor portfoliosWhat factors?Factors that are important to performance of the general economyFama-French Three Factor ModelTwo-Factor ModelThe multifactor APR is similar to the one-factor case But need to think in terms of a factor portfolioWell-diversifiedBeta of 1 for one factorBeta of 0 for any otherExample of the Multifactor ApproachWork of Chen, Roll, and RossChose a set of factors based on the ability of the factors to paint a broad picture of the macro-economyAnother Example:Fama-French Three-Factor ModelThe factors chosen are variables that on past evidence seem to predict average returns well and may capture the risk premiumsWhere:SMB = Small Minus Big, i.e., the return of a portfolio of small stocks in excess of the return on a portfolio of large stocksHML = High Minus Low, i.e., the return of a portfolio of stocks with a high book to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratioThe Multifactor CAPM and the APMA multi-index CAPM will inherit its risk factors from sources of risk that a broad group of investors deem important enough to hedgeThe APT is largely silent on where to look for priced sources of risk