,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.,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,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.,Markowitz Portfolio Theory,Price changes vs. Normal distribution IBM - Daily % change 1988-2008,Proportion of Days,Daily % Change,Markowitz Portfolio Theory,Standard Deviation VS. Expected Return Investment A,% probability,% return,Markowitz Portfolio Theory,Standard Deviation VS. Expected Return Investment B,% probability,% return,Markowitz Portfolio Theory,Standard Deviation VS. Expected Return Investment C,% probability,% return,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,Efficient Frontier,Efficient Frontier,4 Efficient Portfolios all from the same 10 stocks,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,Efficient Frontier,Standard Deviation,Expected Return (%),Lending or Borrowing at the risk free rate (rf) allows us to exist outside the efficient frontier.,rf,Lending Borrowing,S,T,Efficient Frontier,Book Example Correlation Coefficient = .18 Stocks s % of Portfolio Avg Return Campbell 15.8 60% 3.1% Boeing 23.7 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,Efficient Frontier,Another 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%,Efficient Frontier,Another 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% Lets Add stock New Corp to the portfolio,Efficient Frontier,Previous 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%,Efficient Frontier,Previous 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,Efficient Frontier,A,B,Return,Risk (measured as s),Efficient Frontier,A,B,Return,Risk,AB,Efficient Frontier,A,B,N,Return,Risk,AB,Efficient Frontier,A,B,N,Return,Risk,AB,ABN,Efficient Frontier,A,B,N,Return,Risk,Goal is to move up and left. WHY?,ABN,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:,Efficient Frontier,Return,Risk,Low Risk High Return,High Risk High Return,Low Risk Low Return,High Risk Low Return,Efficient Frontier,Return,Risk,Low Risk High Return,High Risk High Return,Low Risk Low Return,High Risk Low Return,Efficient Frontier,Return,Risk,A,B,N,AB,ABN,Security Market Line,Return,Risk,.,rf,Risk Free Return = (Treasury bills),Market Portfolio,Security Market Line,Return,.,rf,Market Portfolio,BETA,1.0,Risk Free Return = (Treasury bills),Security Market Line,Return,.,rf,Risk Free Return =,BETA,Security Market Line (SML),Security Market Line,Return,BETA,rf,1.0,SML,SML Equation = rf + B ( rm - rf ),Capital Asset Pricing Model,CAPM,Expected Returns,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 .,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 mone