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Slides by Matthew Will

Principles of Corporate Finance Brealey and Myers Sixth Edition. Risk and Return. Slides by Matthew Will. Chapter 8. Irwin/McGraw Hill. The McGraw-Hill Companies, Inc., 2000. Topics Covered. Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM

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Slides by Matthew Will

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  1. Principles of Corporate Finance Brealey and Myers Sixth Edition • Risk and Return Slides by Matthew Will Chapter 8 Irwin/McGraw Hill • The McGraw-Hill Companies, Inc., 2000

  2. Topics Covered • Markowitz Portfolio Theory • Risk and Return Relationship • Testing the CAPM • CAPM Alternatives

  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. • The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.

  4. Markowitz Portfolio Theory Price changes vs. Normal distribution Microsoft - Daily % change 1986-1997 # of Days (frequency) Daily % Change

  5. Markowitz Portfolio Theory Price changes vs. Normal distribution Microsoft - Daily % change 1986-1997 # of Days (frequency) Daily % Change

  6. Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment C % probability % return

  7. Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment D % probability % return

  8. Markowitz Portfolio Theory • Expected Returns and Standard Deviations vary given different weighted combinations of the stocks. Expected Return (%) McDonald’s 45% McDonald’s Bristol-Myers Squibb Standard Deviation

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

  10. Efficient Frontier • Lending or Borrowing at the risk free rate (rf) allows us to exist outside the efficient frontier. Expected Return (%) T Lending Borrowing rf S Standard Deviation

  11. Efficient Frontier Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp 28 60% 15% Big Corp 42 40% 21% Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Return = weighted avg = Portfolio = 17.4%

  12. Efficient Frontier Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp 28 60% 15% Big Corp 42 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

  13. Efficient Frontier Example Correlation Coefficient = .3 Stocks s % of Portfolio Avg Return Portfolio 28.1 50% 17.4% New Corp 30 50% 19% NEW Standard Deviation = weighted avg = 31.80 NEW Standard Deviation = Portfolio = 23.43 NEW Return = weighted avg = Portfolio = 18.20%

  14. Efficient Frontier Example Correlation Coefficient = .3 Stocks s % of Portfolio Avg Return Portfolio 28.1 50% 17.4% New Corp 30 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

  15. Efficient Frontier Example Correlation Coefficient = .3 Stocks s % of Portfolio Avg Return Portfolio 28.1 50% 17.4% New Corp 30 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?

  16. Efficient Frontier Example Correlation Coefficient = .3 Stocks s % of Portfolio Avg Return Portfolio 28.1 50% 17.4% New Corp 30 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

  17. Efficient Frontier Return B A Risk (measured as s)

  18. Efficient Frontier Return B AB A Risk

  19. Efficient Frontier Return B N AB A Risk

  20. Efficient Frontier Return B N ABN AB A Risk

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

  22. Efficient Frontier Return Low Risk High Return Risk

  23. Efficient Frontier Return Low Risk High Return High Risk High Return Risk

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

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

  26. Efficient Frontier Return Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return Risk

  27. Efficient Frontier Return B N ABN AB A Risk

  28. Security Market Line Return . Efficient Portfolio Risk Free Return = rf Risk

  29. Security Market Line Return . Market Return = rm Efficient Portfolio Risk Free Return = rf Risk

  30. Security Market Line Return . Market Return = rm Efficient Portfolio Risk Free Return = rf Risk

  31. Security Market Line Return . Market Return = rm Efficient Portfolio Risk Free Return = rf BETA 1.0

  32. Security Market Line Return Market Return = rm Security Market Line (SML) Risk Free Return = rf BETA 1.0

  33. Security Market Line Return SML rf BETA 1.0 SML Equation = rf + B ( rm - rf )

  34. Capital Asset Pricing Model R = rf + B ( rm - rf ) CAPM

  35. Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-65 SML 30 20 10 0 Investors Market Portfolio Portfolio Beta 1.0

  36. Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1966-91 30 20 10 0 SML Investors Market Portfolio Portfolio Beta 1.0

  37. Testing the CAPM Company Size vs. Average Return Average Return (%) Company size Smallest Largest

  38. Testing the CAPM Book-Market vs. Average Return Average Return (%) Book-Market Ratio Highest Lowest

  39. Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio

  40. Consumption Betas vs Market Betas Stocks (and other risky assets) Market risk makes wealth uncertain. Wealth = market portfolio

  41. Consumption Betas vs Market Betas Stocks (and other risky assets) Market risk makes wealth uncertain. Standard CAPM Wealth = market portfolio

  42. Consumption Betas vs Market Betas Stocks (and other risky assets) Stocks (and other risky assets) Market risk makes wealth uncertain. Standard CAPM Wealth = market portfolio Consumption

  43. Consumption Betas vs Market Betas Stocks (and other risky assets) Stocks (and other risky assets) Wealth is uncertain Market risk makes wealth uncertain. Standard CAPM Wealth Consumption is uncertain Wealth = market portfolio Consumption

  44. Consumption Betas vs Market Betas Stocks (and other risky assets) Stocks (and other risky assets) Wealth is uncertain Market risk makes wealth uncertain. Consumption CAPM Standard CAPM Wealth Consumption is uncertain Wealth = market portfolio Consumption

  45. Arbitrage Pricing Theory Alternative to CAPM Expected Risk Premium = r - rf = Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …

  46. Arbitrage Pricing Theory Alternative to CAPM Expected Risk Premium = r - rf = Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + … Return = a + bfactor1(rfactor1) + bf2(rf2) + …

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

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