1. Chapter 6 Market Equilibrium

2. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. The seminal work of Sharpe (1964) and Lintner (1965) present the Capital Asset Pricing Model http://bus.cba.utulsa.edu/byersj/7003/Do cuments/http://bus.cba.utulsa.edu/byersj/7003/Do cuments/

3. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. # Stocks in Portfolio 10 20 30 40 2,000+ Market Risk, systematic risk, nondiversifiable 20 0 Stand-Alone Risk,  p  p (%) 35 Illustrating diversification effects of a stock portfolio Company-Specific Risk, Unique, nonsystematic, diversifiable

4. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. Firm-specific risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification.

5. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Extending Concepts to All Securities The optimal combinations result in lowest level of risk for a given return The optimal trade-off is described as the efficient frontier These portfolios are dominant

6. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. E(r) The minimum-variance frontier of risky assets Efficientfrontier Globalminimumvarianceportfolio Minimumvariancefrontier Individualassets St. Dev.

7. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Extending to Include Riskless Asset The optimal combination becomes linear A single combination of risky and riskless assets will dominate Other Extensions Zero Beta Continuous Time

8. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. E(r) CAL (Global minimum variance) CAL (A) CAL (P) M P A F PP&FA&F M A G P M  ALTERNATIVE CALS

9. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Dominant CAL with a Risk-Free Investment (F) CAL(P) dominates other lines -- it has the best risk/return or the largest slope Slope = (E(R) - Rf) /   E(R P ) - R f ) /  P   E(R A ) - R f ) /    Regardless of risk preferences combinations of P & F dominate

10. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Single Factor Model r i = E(R i ) + ß i F + e ß i = index of a securities’ particular return to the factor F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns Assumption: a broad market index like the S&P500 is the common factor

11. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Single Index Model Risk Prem Market Risk Prem or Index Risk Prem or Index Risk Prem i = the stock’s expected return if the market’s excess return is zero market’s excess return is zero ß i (r m - r f ) = the component of return due to movements in the market index movements in the market index (r m - r f ) = 0 e i = firm specific component, not due to market movements movements   e rrrr i fm i i fi   

12. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Let: R i = (r i - r f ) R m = (r m - r f ) R m = (r m - r f ) Risk premium format R i =  i + ß i (R m ) + e i Risk Premium Format

13. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Applications to Corporate Policy Cost of Capital is directly determined by the CAPM: E(R) Determines the systematic risk What if projects under consideration have different risks than the firm?

14. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Estimating the Index Model Excess Returns (i) SecurityCharacteristicLine.................................................................................................... Excess returns on market index R i =  i + ß i R m + e i

15. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Components of Risk Market or systematic risk: risk related to the macro economic factor or market index Unsystematic or firm specific risk: risk not related to the macro factor or market index Total risk = Systematic + Unsystematic

16. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Measuring Components of Risk  i 2 =  i 2  m 2 +  2 (e i ) where;  i 2 = total variance  i 2  m 2 = systematic variance  2 (e i ) = unsystematic variance

17. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk =  2 ß i 2  m 2 /  2 =  2  i 2  m 2 /  i 2  m 2 +  2 (e i ) =  2 Examining Percentage of Variance

18. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Advantages of the Single Index Model Reduces the number of inputs for diversification Easier for security analysts to specialize

19. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Empirical Tests of CAPM The intercept is significantly different from zero and the slope is less thatn the market risk premium. Implies low Beta stocks earn more than the CAPM would predict and High Beta less Beta dominates other measures of risk. Simple model fit data best. Other factors Price/Earnings ratios Size of firms Dividend yields Seasonality – January Effect Market Capitalization

20. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Debate Continues Model Misspecification of simple linear model vs multi-factor models Design errors and execution errors Survivorship bias Irrational Exuberance Time varying Betas and risk premiums

21. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Roll Critique Only legitimate test of the CAPM is whether or not the Market Portfolio is mean-variance efficient If performance is measured relative to an index that is ex post efficient, then from the mathematics of the efficient set no security will have abnormal performance when measured as a departure from the SML. If performance is measure relative to an ex post in-efficient index, then any ranking of portfolio performance is possible, depending on which inefficient index has been chosen. Implies Joint hypothesis of Theory and Efficient portfolio. Does not say the CAPM is invalid, only test should be interpreted with care.

22. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Arbitrage Pricing Theory Assumptions Perfectly competitive and frictionless markets Homogeneous beliefs of investors about the random return generating process for assets Number of assets is larger than the number of factors Robustness No assumptions about the empirical distributions of asset returns No strong assumptions about individuals’ utility functions (no more than greed and risk aversion) Allows the equilibrium returns of assets to be dependent on many factors. Yields a statement about the relative pricing of any subset of assets; hence the entire universe need not be measured No special role for the market portfolio. Easily extended to multiperiod framework.

23. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Empirical Test of APT Utilize factor analysis Criticism What are the factors? Chen, Roll, and Ross (1986) 4 macro economic factors Index of Industrial production Changes in default risk premium (AAA-Baa) Twists in yield curve (Long-Short term yields) Unanticipated inflation

24. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Final Comments Skip section I. L.2 Problems: 6.2,6.4,6.5,6.6,6.9