1. 5-1 “Modern” Finance? u “Modern Finance Theory” has many components: u Sharpe’s “Capital Asset Pricing Model” (CAPM) u Modigliani-Miller’s “Dividend Irrelevance Theorem” u Markowitz’s risk-averse portfolio optimization model u Arbitrage Pricing Theory (APT) u “Modern” as compared to pre-1950 theories that emphasized behavior of investors as explanation of stock prices, value investing, etc. u Initially appeared to explain what “old finance” could not u But 50 years on… u Foundation is Sharpe’s CAPM:

2. 5-2 Defining Return Income received change in market price beginning market price Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. D t P t - P t-1 D t + (P t - P t-1 ) P t-1 R =

3. 5-3 Return Example $10 $9.50 $1 dividend The stock price for Coke Co. was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year? $1.00 $9.50$10.00 $1.00 + ($9.50 - $10.00 ) $10.00 R R = 5% = 5%

4. 5-4 Defining Risk What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? The variability of returns from those that are expected.

5. 5-5 Determining Expected Return (Discrete Dist.) R =  ( R i )( P i ) R is the expected return for the asset, R i is the return for the i th possibility, P i is the probability of that return occurring, n is the total number of possibilities. R =  ( R i )( P i ) R is the expected return for the asset, R i is the return for the i th possibility, P i is the probability of that return occurring, n is the total number of possibilities. n i=1

6. 5-6 How to Determine the Expected Return and Standard Deviation Coke Share R i P i (R i )(P i ) -.15.10 -.015 -.03.20 -.006.09.40.036.21.20.042.33.10.033.090 Sum 1.00.090 Coke Share R i P i (R i )(P i ) -.15.10 -.015 -.03.20 -.006.09.40.036.21.20.042.33.10.033.090 Sum 1.00.090 The expected return, R, for Stock is.09 or 9%

7. 5-7 Determining Standard Deviation (Risk Measure)   =  ( R i - R ) 2 ( P i ) Standard Deviation  Standard Deviation, , is a statistical measure of the variability of a distribution around its mean. It is the square root of variance.   =  ( R i - R ) 2 ( P i ) Standard Deviation  Standard Deviation, , is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. n i=1

8. 5-8 How to Determine the Expected Return and Standard Deviation Stock BW R i P i (R i )(P i ) (R i - R ) 2 (P i ) -.15.10 -.015.00576 -.03.20 -.006.00288.09.40.036.00000.21.20.042.00288.33.10.033.00576.090.01728 Sum 1.00.090.01728 Stock BW R i P i (R i )(P i ) (R i - R ) 2 (P i ) -.15.10 -.015.00576 -.03.20 -.006.00288.09.40.036.00000.21.20.042.00288.33.10.033.00576.090.01728 Sum 1.00.090.01728

9. 5-9 Determining Standard Deviation (Risk Measure)   =  ( R i - R ) 2 ( P i )   =.01728 .131513.15%  =.1315 or 13.15%   =  ( R i - R ) 2 ( P i )   =.01728 .131513.15%  =.1315 or 13.15% n i=1

10. 5-10 Certainty Equivalent CE Certainty Equivalent (CE) is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Risk Attitudes

11. 5-11 Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Risk Averse Most individuals are Risk Averse. Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Risk Averse Most individuals are Risk Averse. Risk Attitudes

12. 5-12 Provides a convenient measure of systematic risk of the volatility of an asset relative to the markets volatility. Gauges the tendency of a security’s return to move in tandem with the overall market’s return Average systematic risk High systematic risk, more volatile than the market Low systematic risk, less volatile than the market CAPM CAPM

13. 5-13 The Concept of Beta (cont.) Return on Individual Stock Return on the market 30 -- 20 -- 10 -- 0 -10 -- -20 -- -20-10 | 10 20 30 |||||| Stock L, Low Risk: β = 0.5 Stock A, Average Risk: β = 1.0 Stock H, High Risk: β = 1.5

14. 5-14 Company NameBeta Tucson Electric Power0.65 California Power & Lighting0.70 Litton Industries0.75 Tootsie Roll0.85 Quaker Oats0.95 Standard & Poor’s 500 Stock Index1.00 Procter & Gamble1.05 General Motors1.15 Southwest Airlines1.35 Merrill Lynch1.65 Roberts Pharmaceutical1.90 Betas:

15. 5-15 The SML and WACC The SML and WACC Expected return 16% -- 14% -- 7% -- 15% -- A B Incorrect rejection = 8% SML WACC = 15% Beta Incorrect acceptance If a firm uses its WACC to make accept/reject decisions for all types of projects, it will have a tendency toward incorrectly accepting risky projects and incorrectly rejecting less risky projects.

16. 5-16 The SML and the Subjective Approach The SML and the Subjective Approach Expected return 14% -- 10% -- 7% -- Low risk (-4%) SML Beta WACC = Moderate risk (+0%) High risk (+6%) 20% -- With the subjective approach, the firm places projects into one of several risk classes. The discount rate used to value the project is then determined by adding (for high risk) or subtracting (for low risk) an adjustment factor to or from the firm’s WACC.

17. 5-17 Arbitrage Pricing Theory u We focus on betas and ignore unsystematic issues—residual variances and total variances u Because unsystematic risk can be easily diversified u Assets with identical betas should have identical rates of return, because they are equally risky u Otherwise, arbitrage would be possible u These assets should also have identical intercepts

18. 5-18 Arbitrage Pricing Theory Line E(r i ) = Expected Return Slope = = risk premium Risk class of assets O and U Overpriced asset O U Underpriced asset 0 RFR Factor beta U and O violate the law of one price—they are in the same risk class but have different expected rates of return.

19. 5-19 Over- and Underpriced Assets u Investors will sell asset O (because it is overpriced) u Excess supply for O will drive down the market price u Expected return for O will rise u This process will continue until O’s expected rate of return is competitive u Investors will buy asset U (because its expected rate of return is unusually high) u Excess demand for U will drive up the market price u Expected return for U will fall

20. 5-20 An Arbitrage Portfolio u To maximize profits investors will u Sell asset O short and simultaneously go long in asset U (equal dollar value as in O) u Will not have any of their own cash invested in their arbitrage portfolio u Use the cash proceeds from the short sale of O to buy the long position in U u This portfolio would be riskless and will earn a profit > 0

21. 5-21 Formal Definition of Arbitrage Opportunity u Arbitrage opportunity u A perfectly hedged portfolio u With a zero initial cost u No cash flows prior to the termination of the position u A certain, positive value at the end of the investment period

22. 5-22 The Bottom Line u CML and SML are based on Markowitz efficient portfolios u SML can be used to find over- and under- valued assets u A characteristic line is used to determine a company’s beta u While the CML and SML cannot be derived under unrealistic assumptions, the models still rationalize complex behavior u Recent studies support equilibrium portfolio theory

23. 5-23 The Bottom Line u APT supports multiple risk factors u Requires fewer assumptions u Mathematically equivalent to SML when the market portfolio is the only risk factor u Four risk factors have been isolated

24. 5-24 CONCLUSION CONCLUSION Research has shown the CAPM to stand up well to criticism, although attacks against it have been increasing in recent years. Until something better presents itself, however, the CAPM remains a very useful item in the financial management tool kit.

25. 5-25 CAPM Example CAPM Example u Suppose that the required return on the market is 12% and the risk free rate is 5%. k j = k RF +  j ( k M – k RF ) Security Market Line

26. 5-26 Beta 1.51.0.50 15% 10% 5% Risk Free Rate CAPM Example u Suppose that the required return on the market is 12% and the risk free rate is 5%. k j = 5% +  j (12% – 5% )

27. 5-27 Beta 1.51.0.50 15% 10% 5% Risk & Return on market CAPM Example u Suppose that the required return on the market is 12% and the risk free rate is 5%. k j = 5% +  j (12% – 5% ) Risk Free Rate

28. 5-28 Beta 1.51.0.50 15% 10% 5% CAPM Example u Suppose that the required return on the market is 12% and the risk free rate is 5%. SML Connect Points for Security Market Line Market

29. 5-29 Beta 1.5.50 15% 10% 5% SML 13.4% 1.0 1.2 If beta = 1.2 k j = 13.4 k j = 13.4 CAPM Example Suppose that the required return on the market is 12% and the risk free rate is 5%. k j = 5% +  j (12% – 5% ) Market