Chapter 8 PORTFOLIO THEORY AND THE CAPITAL ASSET PRICING MODEL Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY • Combining stocks into portfolios can reduce standard deviation below simple weightedaverage calculation • Correlation coefficients make possible • Various weighted combinations of stocks that create specific standard deviation constitute set of efficient portfolios 8-2 FIGURE 8.1 DAILY PRICE CHANGES, IBM 8-3 FIGURE 8.2A STANDARD DEVIATION VERSUS EXPECTED RETURN 8-4 FIGURE 8.2B STANDARD DEVIATION VERSUS EXPECTED RETURN 8-5 FIGURE 8.2C STANDARD DEVIATION VERSUS EXPECTED RETURN 8-6 FIGURE 8.3 EXPECTED RETURN AND STANDARD DEVIATION, HEINZ, AND EXXON MOBIL 8-7 TABLE 8.1 EXAMPLES OF EFFICIENT PORTFOLIOS Efficient Portfolios—Percentages Allocated to Each Stock Stock Expected Standard Return Deviation Dow Chemical 16.4% 40.2% Bank of America 14.3 30.9 10 Ford 15.0 40.4 8 Heinz 6.0 14.6 11 35 IBM 9.1 19.8 18 12 Newmont Mining 8.9 29.2 6 1 Pfizer 8.0 20.8 10 8 Starbucks 10.4 26.2 12 Walmart 6.3 13.8 9 ExxonMobil 10.0 21.9 8 A B 100 C 6 42 Expected portfolio return 16.4 10.0 6.7 Portfolio standard deviation 40.2 18.4 11.8 8-8 FIGURE 8.4 FOUR EFFICIENT PORTFOLIOS FROM TEN STOCKS 8-9 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY • Efficient Frontier • Each half-ellipse represents possible weighted combinations for two stocks Expected return (%) • Composite of all stock sets constitutes efficient frontier Standard deviation 8-10 FIGURE 8.5 LENDING AND BORROWING 8-11 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY • Example Correlation Coefficient = .18 Stocks s Heinz 14.6 60% 6.0% ExxonMobil 21.9 40% 10.0% % of Portfolio Average Return • Standard deviation = weighted average = 17.52 • Standard deviation = portfolio = 15.1 • Return = weighted average = portfolio = 7.6% • Higher return, lower risk through diversification 8-12 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY • Example Correlation Coefficient = .4 Stocks s ABC Corp 28 60% 15% Big Corp 42 40% 21% % of Portfolio Average Return • Standard deviation = weighted average = 33.6 • Standard deviation = portfolio = 28.1 • Return = weighted average = portfolio = 17.4% 8-13 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY • Example, continued Correlation Coefficient = .3 • Add new stock to portfolio Stocks s Portfolio 28.1 50% 17.4% New Corp 30 50% 19% % of Portfolio Average Return • Standard deviation = weighted average = 31.80 • Standard deviation = portfolio = 23.43 • Return = weighted average = portfolio = 18.20% 8-14 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Return B A Risk (measured as s) 8-15 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Return B AB A Risk 8-16 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Return B AB N A Risk 8-17 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Return B ABN AB N A Risk 8-18 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Goal is to move up and left—less risk, more return Return B ABN AB N A Risk 8-19 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY • Sharpe Ratio • Ratio of risk premium to standard deviation Sharpe ratio rp r f sp 8-20 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Return Low Risk High Risk High Return High Return Low Risk High Risk Low Return Low Return Risk 8-21 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Return Low Risk High Risk High Return High Return Low Risk High Risk Low Return Low Return Risk 8-22 8-1 HARRY MARKOWITZ AND THE BIRTH OF PORTFOLIO THEORY Return B ABN AB N A Risk 8-23 8-2 THE RELATIONSHIP BETWEEN RISK AND RETURN Return Market return = rm . Market portfolio rf Risk 8-24 FIGURE 8.6 SECURITY MARKET LINE Return Security market line (SML) . r Market return = m Market portfolio rf 1.0 BETA 8-25 8-2 THE RELATIONSHIP BETWEEN RISK AND RETURN Return SML rf BETA 1.0 SML Equation: rf + β(rm − rf) 8-26 8-2 THE RELATIONSHIP BETWEEN RISK AND RETURN • Capital Asset Pricing Model (CAPM) r rf (rm rf ) 8-27 TABLE 8.2 ESTIMATES OF RETURNS • Returns estimates in January 2012 based on capital asset pricing model. Assume 2% for interest rate rf and 7% for expected risk premium rm − rf. tock S Dow Chemical Bank of America Ford ExxonMobil Starbucks IBM Newmont Mining Pfizer Walmart Heinz Beta 1.78 Expected Return 14.50 1.54 1.53 0.98 0.95 0.80 0.75 0.66 0.42 0.40 12.80 12.70 8.86 8.68 7.62 7.26 6.63 4.92 4.78 8-28 FIGURE 8.7 SECURITY MARKET LINE EQUILIBRIUM • In equilibrium, no stock can lie below the security market line 8-29 FIGURE 8.8 CAPITAL ASSET PRICING MODEL 8-30 FIGURE 8.9B BETA VERSUS AVERAGE RETURN 8-31 FIGURE 8.10 RETURN VERSUS BOOK-TO-MARKET 8-32 8-4 ALTERNATIVE THEORIES • Alternative to CAPM Return a b1 (rfactor1 ) b2 (rfactor2 ) b3 (rfactor3 ) .... noise Expected risk premium r rf b1 (rfactor1 rf ) b2 (rfactor2 rf ) ... 8-33 8-4 ALTERNATIVE THEORIES • Estimated risk premiums (1978-1990) Factor Estimated Risk Premium Yield spread (rfactor rf ) 5.10% Interest rate Exchange rate - .61 - .59 Real GNP Inflation .49 - .83 Market 6.36 8-34 8-4 ALTERNATIVE THEORIES • Three-Factor Model • Identify macroeconomic factors that could affect stock returns • Estimate expected risk premium on each factor ( rfactor1 − rf, etc.) • Measure sensitivity of each stock to factors ( b1, b2, etc.) 8-35 TABLE 8.3 EXPECTED EQUITY RETURNS 8-36