1. Chapter 8 Principles of Corporate Finance Tenth Edition Portfolio Theory and the Capital Asset Model Pricing Slides by Matthew Will McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

2. 8-2 Topics Covered  Harry Markowitz And The Birth Of Portfolio Theory  The Relationship Between Risk and Return  Validity and the Role of the CAPM  Some Alternative Theories

3. 8-3 Markowitz Portfolio Theory  Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation.  Correlation coefficients make this possible. efficient portfolios  The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.

4. 8-4 Markowitz Portfolio Theory Price changes vs. Normal distribution IBM - Daily % change 1988-2008 Proportion of Days Daily % Change

5. 8-5 Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment A % probability % return

6. 8-6 Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment B % probability % return

7. 8-7 Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment C % probability % return

8. 8-8 Campbell Soup 40% in Boeing Boeing Standard Deviation Expected Return (%) Markowitz Portfolio Theory Expected Returns and Standard Deviations vary given different weighted combinations of the stocks

9. 8-9 Efficient Frontier TABLE 8.1 Examples of efficient portfolios chosen from 10 stocks. Note: Standard deviations and the correlations between stock returns were estimated from monthly returns January 2004-December 2008. Efficient portfolios are calculated assuming that short sales are prohibited. Efficient Portfolios – Percentages Allocated to Each Stock Stock Expected Return Standard Deviation ABCD Amazon.com22.8%50.9%10019.110.9 Ford19.047.219.911.0 Dell13.430.915.610.3 Starbucks9.030.313.710.73.6 Boeing9.523.79.210.5 Disney7.719.68.811.2 Newmont7.036.19.910.2 ExxonMobil4.719.19.718.4 Johnson & Johnson 3.812.67.433.9 Soup3.115.88.433.9 Expected portfolio return22.814.110.54.2 Portfolio standard deviation50.922.016.08.8

10. 8-10 Efficient Frontier 4 Efficient Portfolios all from the same 10 stocks

11. 8-11 Efficient Frontier Standard Deviation Expected Return (%) Each half egg shell represents the possible weighted combinations for two stocks. The composite of all stock sets constitutes the efficient frontier

12. 8-12 Efficient Frontier Standard Deviation Expected Return (%) Lending or Borrowing at the risk free rate ( r f ) allows us to exist outside the efficient frontier. rfrf Lending Borrowing S T

13. 8-13 Efficient Frontier Book Example Correlation Coefficient =.18 Stocks  % of PortfolioAvg Return Campbell15.860% 3.1% Boeing23.7 40% 9.5% Standard Deviation = weighted avg = 19.0 Standard Deviation = Portfolio = 14.6 Return = weighted avg = Portfolio = 5.7% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION

14. 8-14 Efficient Frontier Another Example Correlation Coefficient =.4 Stocks  % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 40% 21% Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Return = weighted avg = Portfolio = 17.4%

15. 8-15 Efficient Frontier Another Example Correlation Coefficient =.4 Stocks  % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 40% 21% Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Return = weighted avg = Portfolio = 17.4% Let’s Add stock New Corp to the portfolio

16. 8-16 Efficient Frontier Previous Example Correlation Coefficient =.3 Stocks  % of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 19% NEW Standard Deviation = weighted avg = 31.80 NEW Standard Deviation = Portfolio = 23.43 NEW Return = weighted avg = Portfolio = 18.20%

17. 8-17 Efficient Frontier Previous Example Correlation Coefficient =.3 Stocks  % of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 19% NEW Standard Deviation = weighted avg = 31.80 NEW Standard Deviation = Portfolio = 23.43 NEW Return = weighted avg = Portfolio = 18.20% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION

18. 8-18 Efficient Frontier A B Return Risk (measured as  )

19. 8-19 Efficient Frontier A B Return Risk AB

20. 8-20 Efficient Frontier A B N Return Risk AB

21. 8-21 Efficient Frontier A B N Return Risk AB ABN

22. 8-22 Efficient Frontier A B N Return Risk AB Goal is to move up and left. WHY? ABN

23. 8-23 Efficient Frontier Goal is to move up and left. WHY? The ratio of the risk premium to the standard deviation is called the Sharpe ratio:

24. 8-24 Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return

25. 8-25 Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return

26. 8-26 Efficient Frontier Return Risk A B N AB ABN

27. 8-27 Security Market Line Return Risk. rfrf Risk Free Return = (Treasury bills) Market Portfolio Market Return = r m

28. 8-28 Security Market Line Return. rfrf Market Portfolio Market Return = r m BETA1.0 Risk Free Return = (Treasury bills)

29. 8-29 Security Market Line Return. rfrf Risk Free Return = BETA Security Market Line (SML)

30. 8-30 Security Market Line Return BETA rfrf 1.0 SML SML Equation = r f + B ( r m - r f )

31. 8-31 Capital Asset Pricing Model CAPM

32. 8-32 Expected Returns TABLE 8.2 StockBeta (β)Expected Return [r f + β(r m – r f )] Amazon2.1615.4 Ford1.7512.6 Dell1.4110.2 Starbucks1.168.4 Boeing1.148.3 Disney.967.0 Newmont.634.7 ExxonMobil.554.2 Johnson & Johnson.503.8 Soup.302.4 These estimates of the returns expected by investors in February 2009 were based on the capital asset pricing model. We assumed 0.2% for the interest rate r f and 7% for the expected risk premium r m − r f.

33. 8-33 SML Equilibrium  In equilibrium no stock can lie below the security market line. For example, instead of buying stock A, investors would prefer to lend part of their money and put the balance in the market portfolio. And instead of buying stock B, they would prefer to borrow and invest in the market portfolio.

34. 8-34 Testing the CAPM Average Risk Premium 1931-2008 Portfolio Beta 1.0 SML 20 12 0 Investors Market Portfolio Beta vs. Average Risk Premium

35. 8-35 Testing the CAPM Portfolio Beta 1.0 SML 12 8 4 0 Investors Market Portfolio Beta vs. Average Risk Premium Average Risk Premium 1966-2008

36. 8-36 Testing the CAPM High-minus low book-to-market Return vs. Book-to-Market Dollars (log scale) Small minus big http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 2008

37. 8-37 Arbitrage Pricing Theory Alternative to CAPM

38. 8-38 Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978-1990)

39. 8-39 Three Factor Model Steps to Identify Factors 1.Identify a reasonably short list of macroeconomic factors that could affect stock returns 2.Estimate the expected risk premium on each of these factors ( r factor 1 − r f, etc.); 3.Measure the sensitivity of each stock to the factors ( b 1, b 2, etc.).

40. 8-40 Three Factor Model TABLE 8.3 Estimates of expected equity returns for selected industries using the Fama-French three-factor model and the CAPM. Three-Factor Model. Factor Sensitivities.CAPM b market b size b book-to- market Expected return* Expected return** Autos1.51.070.9115.77.9 Banks1.16-.25.711.16.2 Chemicals1.02-.07.6110.25.5 Computers1.43.22-.876.512.8 Construction1.40.46.9816.67.6 Food.53-.15.475.82.7 Oil and gas0.85-.130.548.54.3 Pharmaceuticals0.50-.32-.131.94.3 Telecoms1.05-.29-.165.77.3 Utilities0.61-.01.778.42.4 The expected return equals the risk-free interest rate plus the factor sensitivities multiplied by the factor risk premia, that is, rf + (b market x 7) + (b size x 3.6) + (b book-to-market x 5.2) ** Estimated as r f + β(r m – r f ), that is rf + β x 7.

41. 8-41 Web Resources Click to access web sites Internet connection required http://finance.yahoo.com www.duke.edu/~charvey http://mba.tuck.dartmouth.edu/pages/faculty/ken.french