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

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 2 Topics Covered Markowitz Portfolio Theory Risk and Return Relationship Testing the CAPM CAPM Alternatives

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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.

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 4 Markowitz Portfolio Theory Price changes vs. Normal distribution Microsoft - Daily % change 1986-1997 # of Days (frequency) Daily % Change

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 5 Markowitz Portfolio Theory Price changes vs. Normal distribution Microsoft - Daily % change 1986-1997 # of Days (frequency) Daily % Change

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 6 Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment C % probability % return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 7 Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment D % probability % return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 8 Markowitz Portfolio Theory Bristol-Myers Squibb McDonald’s Standard Deviation Expected Return (%) 45% McDonald’s Expected Returns and Standard Deviations vary given different weighted combinations of the stocks.

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 9 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.

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 10 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 T S

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 11 Efficient Frontier 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%

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 12 Efficient Frontier 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

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 13 Efficient Frontier 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%

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 14 Efficient Frontier 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

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 15 Efficient Frontier 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?

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 16 Efficient Frontier 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

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 17 Efficient Frontier A B Return Risk (measured as )

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 18 Efficient Frontier A B Return Risk AB

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 19 Efficient Frontier A B N Return Risk AB

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 20 Efficient Frontier A B N Return Risk AB ABN

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 21 Efficient Frontier A B N Return Risk AB Goal is to move up and left. WHY? ABN

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 22 Efficient Frontier Return Risk Low Risk High Return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 23 Efficient Frontier Return Risk Low Risk High Return High Risk High Return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 24 Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 25 Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 26 Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 27 Efficient Frontier Return Risk A B N AB ABN

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 28 Security Market Line Return Risk. rfrf Efficient Portfolio Risk Free Return =

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 29 Security Market Line Return Risk. rfrf Risk Free Return = Market Return = r m Efficient Portfolio

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 30 Security Market Line Return Risk. rfrf Risk Free Return = Market Return = r m Efficient Portfolio

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 31 Security Market Line Return BETA. rfrf Risk Free Return = Market Return = r m Efficient Portfolio 1.0

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 32 Security Market Line Return BETA rfrf Risk Free Return = Market Return = r m 1.0 Security Market Line (SML)

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 33 Security Market Line Return BETA rfrf 1.0 SML SML Equation = r f + B ( r m - r f )

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 34 Capital Asset Pricing Model R = r f + B ( r m - r f ) CAPM

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 35 Testing the CAPM Avg Risk Premium 1931-65 Portfolio Beta 1.0 SML 30 20 10 0 Investors Market Portfolio Beta vs. Average Risk Premium

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 36 Testing the CAPM Avg Risk Premium 1966-91 Portfolio Beta 1.0 SML 30 20 10 0 Investors Market Portfolio Beta vs. Average Risk Premium

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 37 Testing the CAPM Average Return (%) Company size SmallestLargest Company Size vs. Average Return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 38 Testing the CAPM Average Return (%) Book-Market Ratio HighestLowest Book-Market vs. Average Return

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 39 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 40 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain.

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 41 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Standard CAPM

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 42 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Stocks (and other risky assets) Consumption Standard CAPM

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 43 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Stocks (and other risky assets) Consumption Wealth Wealth is uncertain Consumption is uncertain Standard CAPM

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 44 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Stocks (and other risky assets) Consumption Wealth Wealth is uncertain Consumption is uncertain Standard CAPM Consumption CAPM

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 45 Arbitrage Pricing Theory Alternative to CAPM Expected Risk Premium = r - r f = B factor1 (r factor1 - r f ) + B f2 (r f2 - r f ) + …

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 46 Arbitrage Pricing Theory Alternative to CAPM Expected Risk Premium = r - r f = B factor1 (r factor1 - r f ) + B f2 (r f2 - r f ) + … Return= a + b factor1 (r factor1 ) + b f2 (r f2 ) + …

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© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 8- 47 Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978-1990)

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