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Chapter 8

Chapter 8. Risk and Return. Topics Covered. Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives. Markowitz Portfolio Theory.

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Chapter 8

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  1. Chapter 8 Risk and Return

  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 1990-2001 Proportion of Days Daily % Change

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

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

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

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

  9. Markowitz Portfolio Theory • Expected Returns and Standard Deviations vary given different weighted combinations of the stocks Expected Return (%) Reebok 35% in Reebok Coca Cola Standard Deviation

  10. 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

  11. 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

  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%

  13. 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

  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%

  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? DIVERSIFICATION

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

  17. Efficient Frontier Return B AB A Risk

  18. Efficient Frontier Return B N AB A Risk

  19. Efficient Frontier Return B N ABN AB A Risk

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

  21. Efficient Frontier Return Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return Risk

  22. Efficient Frontier Return Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return Risk

  23. Efficient Frontier Return B N ABN AB A Risk

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

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

  26. Security Market Line Return . Risk Free Return = Security Market Line (SML) rf BETA

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

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

  29. 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

  30. 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

  31. Testing the CAPM Return vs. Book-to-Market Dollars High-minus low book-to-market Low minus big http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

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

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

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

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