Chapter 6

1. Chapter6 Market Equilibrium

2. The seminal work of Sharpe (1964) and Lintner (1965) present the Capital Asset Pricing Model • http://bus.cba.utulsa.edu/byersj/7003/Documents/

3. Illustrating diversification effects of a stock portfolio Company-Specific Risk, Unique, nonsystematic, diversifiable sp (%) 35 Stand-Alone Risk, sp 20 0 Market Risk, systematic risk, nondiversifiable 10 20 30 40 2,000+ # Stocks in Portfolio

4. 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. 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. The minimum-variance frontier of risky assets E(r) Efficient frontier Individual assets Global minimum variance portfolio Minimum variance frontier St. Dev.

7. 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. ALTERNATIVE CALS CAL (P) CAL (A) E(r) M M P P CAL (Global minimum variance) A A G F s P P&F A&F M

9. 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) / s [ E(RP) - Rf) / s P] > [E(RA) - Rf) / sA] Regardless of risk preferences combinations of P & F dominate

10. Single Factor Model ri = E(Ri) + ßiF + e ßi = 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. Single Index Model ( ) ( ) b a e r r r r - = + - + i f m f i i i Risk Prem Market Risk Prem or Index Risk Prem a = the stock’s expected return if the market’s excess return is zero i (rm - rf)= 0 ßi(rm - rf)= the component of return due to movements in the market index ei = firm specific component, not due to market movements

12. Let: Ri = (ri - rf) Risk premium format Rm = (rm - rf) Ri = ai + ßi(Rm)+ ei Risk Premium Format

13. 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. Estimating the Index Model Excess Returns (i) . . . . . . Security Characteristic Line . . . . . . . . . . . . . . . . . . . . Excess returns on market index . . . . . . . . . . . . . . . . . . . . . . . . Ri = ai + ßiRm + ei

15. 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. Measuring Components of Risk si2 = bi2sm2 + s2(ei) where; si2 = total variance bi2sm2 = systematic variance s2(ei) = unsystematic variance

17. Examining Percentage of Variance Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = r2 ßi2 sm2 / s2 = r2 bi2sm2 / bi2sm2 + s2(ei) = r2

18. Advantages of the Single Index Model • Reduces the number of inputs for diversification • Easier for security analysts to specialize

19. 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. 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. 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. 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. 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. Final Comments • Skip section I. L.2 • Problems: 6.2,6.4,6.5,6.6,6.9