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- 1. Dr. Muath Asmar Investment& Portfolio Management AN-NAJAH NATIONAL UNIVERSITY Faculty of Graduate Studies
- 2. INVESTMENTS | BODIE,KANE, MARCUS ©2021 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education. Chapter Ten Arbitrage Pricing Theory and Multifactor Models of Risk and Return
- 3. INVESTMENTS | BODIE,KANE, MARCUS • Arbitrage is the exploitation of security mispricing in such a way that risk-free profits can be earned • Most basic principle of capital market theory is that well-functioning security markets rule out arbitrage opportunities • Generalization of the security market line of the CAPM to gain richer insight into the risk- return relationship • Arbitrage pricing theory (APT) Overview ©2021 McGraw-Hill Education
- 4. INVESTMENTS | BODIE,KANE, MARCUS • Recall stock variability may be decomposed into the following sources: • Market (i.e., systemic) risk • Largely due to macroeconomic events • Firm-specific (i.e., idiosyncratic) effects • Risk premiums may depend on correlations with extra-market risk factors • E.g., inflation, interest rates, volatility, etc. Multifactor Models: A Preview ©2021 McGraw-Hill Education 10-4
- 5. INVESTMENTS | BODIE,KANE, MARCUS • Single-factor model of excess returns 𝑅𝑖 = 𝐸 𝑅𝑖 + 𝐵𝑖 𝐹 + 𝑒𝑖 𝐸(𝑅𝑖) = expected excess return on stock 𝑖 𝐵𝑖 = sensitivity of firm 𝑖 𝐹 = deviation of the common factor from its expected value 𝑒𝑖 = nonsystematic components of returns Factor Models of Security Returns (1 of 3) ©2021 McGraw-Hill Education 10-5
- 6. INVESTMENTS | BODIE,KANE, MARCUS • Extra market sources of risk may arise from several sources • E.g., uncertainty about interest rates or inflation. • Multifactor models posit that returns respond to several systematic risk factors, as well as firm-specific influences • Useful in risk management applications Factor Models of Security Returns (2 of 3) ©2021 McGraw-Hill Education 10-6
- 7. INVESTMENTS | BODIE,KANE, MARCUS 𝑅𝑖 = excess return on security i 𝐵 𝐺𝐷𝑃 = sensitivity of returns to GDP 𝐵𝐼𝑅 = sensitivity of returns to interest rates 𝑒𝑖 = nonsystematic components of returns Factor Models of Security Returns (3 of 3) ©2021 McGraw-Hill Education 10-7 iiIRiGDPii eIRGDPRER
- 8. INVESTMENTS | BODIE,KANE, MARCUS • Arbitrage pricing theory (APT) was developed by Stephen Ross • Predicts a SML linking expected returns to risk, but the path is takes to the SML is quite different • APT relies on three key propositions: 1. Security returns can be described by a factor model 2. There are sufficient securities to diversify away idiosyncratic risk 3. Well-functioning security markets do not allow for the persistence of arbitrage opportunities Arbitrage Pricing Theory ©2021 McGraw-Hill Education 10-8
- 9. INVESTMENTS | BODIE,KANE, MARCUS • Arbitrage opportunity exists when an investor can earn riskless profits without making a net investment • E.g., shares of a stock sell for different prices on two different exchanges • Law of One Price • Enforced by arbitrageurs; If they observe a violation, they will engage in arbitrage activity • This bids up (down) the price where it is low (high) until the arbitrage opportunity is eliminated Arbitrage, Risk Arbitrage, and Equilibrium ©2021 McGraw-Hill Education 10-9
- 10. INVESTMENTS | BODIE,KANE, MARCUS • In a well-diversified portfolio, firm-specific risk becomes negligible, so that only factor risk remains • One effect of diversification is that, when n is large, nonsystematic variance approaches zero • A well-diversified portfolio is on with each weight small enough that for practices purposes the nonsystematic variance is negligible Well-Diversified Portfolios ©2021 McGraw-Hill Education 10-10
- 11. INVESTMENTS | BODIE,KANE, MARCUS Excess Returns as a Function of the Systematic Factor ©2021 McGraw-Hill Education 10-11
- 12. INVESTMENTS | BODIE,KANE, MARCUS Returns as a Function of the Systematic Factor: An Arbitrage Opportunity ©2021 McGraw-Hill Education 10-12
- 13. INVESTMENTS | BODIE,KANE, MARCUS • All well-diversified portfolio with the same beta must have the same expected return • Generally, for any well-diversified P, the expected excess return must be: • Risk premium on portfolio P is the product of its beta and the risk premium of the market index • SML of the CAPM must also apply to well-diversified portfolios The SML of the APT ©2021 McGraw-Hill Education 10-13 ( ) ( )P P ME R E R
- 14. INVESTMENTS | BODIE,KANE, MARCUS An Arbitrage Opportunity ©2021 McGraw-Hill Education 10-14
- 15. INVESTMENTS | BODIE,KANE, MARCUS APT • Built on the foundation of well-diversified portfolios – Cannot rule out a violation of the expected return-beta relationship for any particular asset • Does not assume investors are mean- variance optimizers • Uses an observable market index CAPM • Model is based on an inherently unobservable “market” portfolio • Provides unequivocal statement on the expected return-beta relationship for all securities APT and CAPM ©2021 McGraw-Hill Education 10-15
- 16. INVESTMENTS | BODIE,KANE, MARCUS • To this point, we have examined the APT in a one-factor world • However, there are several sources of systematic risk and exposure to these factors will affect a stock’s appropriate expected return • APT can be generalized to accommodate these multiple sources of risk • Assume a two-factor model: A Multifactor APT (1 of 2) ©2021 McGraw-Hill Education 10-16 1 1 2 2( )i i i i iR E R F F e
- 17. INVESTMENTS | BODIE,KANE, MARCUS • Benchmark portfolios in the APT are factor portfolios • β=1 for one of the factors and β= 0 for any other factors • Factor portfolios track a particular source of macroeconomic risk, but are uncorrelated with other sources of risk • Referred to as a “tracking portfolio” A Multifactor APT (2 of 2) ©2021 McGraw-Hill Education 10-17
- 18. INVESTMENTS | BODIE,KANE, MARCUS • SMB = Small minus big (i.e., the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks) • HML = 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 ratio) Fama-French (FF) Three-Factor Model ©2021 McGraw-Hill Education 10-18 ittiHMLtiSMBMtiMiit eHMLSMBRR
- 19. INVESTMENTS | BODIE,KANE, MARCUS • Begin by estimating Amazon’s beta on each of the FF factors • See Equation 10.10 • Amazon’s expected return in the multifactor model is lower due to the considerable hedging value it offers against the size and value risk factors • This is ignored by the single-factor model Estimating and Implementing a Three-Factor SML ©2021 McGraw-Hill Education 10-19
Editor's Notes
- #7 Recall the single-factor model (introduced in Ch. 8) decomposes returns into systematic and firm-specific components. But, it confines systematic risk to a single factor.
- #8 Note the coefficients on each macro factor measures the sensitivity of share returns to that factor (and are therefore referred to as factor loadings or factor betas).
- #10 The Law of One Price: states that if two assets are equivalent in all economically relevant respects, then they should have the same market price.
- #11 Proofs are located on p314.
- #16 Note that while each model takes a different path to get there, they both arrive at the same security market line. More importantly, they both highlight the distinction between firm-specific and systematic risk.
- #17 The generalization of the APT to accommodate these multiple sources of risk is done in a manner similar to the multifactor CAPM.
- #19 Note: FF is an approach to identify the most likely sources of systematic risk, in which case it uses firm characteristics that seem on empirical grounds to proxy for exposure to systematic risk.