投資學英文版課件：Chap010 Arbitrage Pricing Theory and Multifactor Models of Risk and Return

1、CHAPTER 10Arbitrage Pricing Theory and Multifactor Models of Risk and Return10-1Single Factor ModelReturns on a security come from two sources:Common macro-economic factorFirm specific eventsPossible common macro-economic factorsGross Domestic Product GrowthInterest Rates 10-2Single Factor Model Equ

2、ationri = Return on security i= Factor sensitivity or factor loading or factor betaF = Surprise in macro-economic factor(F could be positive or negative but has expected value of zero)ei = Firm specific events (zero expected value)10-3Multifactor ModelsUse more than one factor in addition to market

3、returnExamples include gross domestic product, expected inflation, interest rates, etc.Estimate a beta or factor loading for each factor using multiple regression.10-4Multifactor Model Equationri = Return for security iGDP = Factor sensitivity for GDP IR = Factor sensitivity for Interest Rate ei = F

4、irm specific events10-5Multifactor SML Models GDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP IR = Factor sensitivity for Interest RateRPIR = Risk premium for Interest Rate10-6InterpretationThe expected return on a security is the sum of:The risk-free rateThe sensitivity to GDP times t

5、he risk premium for bearing GDP riskThe sensitivity to interest rate risk times the risk premium for bearing interest rate risk10-7Arbitrage Pricing TheoryArbitrage occurs if there is a zero investment portfolio with a sure profit.Since no investment is required, investors can create large positions

6、 to obtain large profits.10-8Arbitrage Pricing TheoryRegardless of wealth or risk aversion, investors will want an infinite position in the risk-free arbitrage portfolio.In efficient markets, profitable arbitrage opportunities will quickly disappear.10-9APT & Well-Diversified PortfoliosrP = E (rP) +

7、 bPF + ePF = some factorFor a well-diversified portfolio, eP approaches zero as the number of securities in the portfolio increases and their associated weights decrease10-10Figure 10.1 Returns as a Function of the Systematic Factor10-11Figure 10.2 Returns as a Function of the Systematic Factor: An

8、Arbitrage Opportunity10-12Figure 10.3 An Arbitrage Opportunity10-13Figure 10.4 The Security Market Line10-14APT ModelAPT 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 can be

9、extended to multifactor models.10-15APT and CAPMAPTEquilibrium means no arbitrage opportunities.APT equilibrium is quickly restored even if only a few investors recognize an arbitrage opportunity.The expected returnbeta relationship can be derived without using the true market portfolio.CAPMModel is

10、 based on an inherently unobservable “market” portfolio.Rests on mean-variance efficiency. The actions of many small investors restore CAPM equilibrium.CAPM describes equilibrium for all assets.10-16Multifactor APTUse of more than a single systematic factorRequires formation of factor portfoliosWhat

11、 factors?Factors that are important to performance of the general economyWhat about firm characteristics?10-17Two-Factor ModelThe multifactor APT is similar to the one-factor case.10-18Two-Factor ModelTrack with diversified factor portfolios:beta=1 for one of the factors and 0 for all other factors.

12、The factor portfolios track a particular source of macroeconomic risk, but are uncorrelated with other sources of risk.10-19Where Should We Look for Factors?Need important systematic risk factorsChen, Roll, and Ross used industrial production, expected inflation, unanticipated inflation, excess retu

13、rn on corporate bonds, and excess return on government bonds.Fama and French used firm characteristics that proxy for systematic risk factors.10-20Fama-French Three-Factor ModelSMB = Small Minus Big (firm size)HML = High Minus Low (book-to-market ratio)Are these firm characteristics correlated with actual (but currently unknown) systematic risk factors?10-21The Multifactor CAPM and the