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Chapter 8 Risk and Return

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

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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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Markowitz Portfolio Theory Price changes vs. Normal distribution Microsoft - Daily % change 1990-2001 Proportion of Days Daily % Change

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

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

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

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

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

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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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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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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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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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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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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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Efficient Frontier A B Return Risk (measured as )

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Efficient Frontier A B Return Risk AB

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Efficient Frontier A B N Return Risk AB

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Efficient Frontier A B N Return Risk AB ABN

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

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Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return

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Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return

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Efficient Frontier Return Risk A B N AB ABN

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Security Market Line Return Risk. rfrf Risk Free Return = Efficient Portfolio Market Return = r m

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Security Market Line Return. rfrf Risk Free Return = Efficient Portfolio Market Return = r m BETA1.0

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

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

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Capital Asset Pricing Model R = r f + B ( r m - r f ) CAPM

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

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

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