Portfolio theory and the capital asset pricing model 8 Portfolio theory and the capital asset pricing model 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 weighted- average calculation Correlation coefficients make possible Various weighted combinations of stocks that create specific standard deviation constitute set of efficient portfolios

Figure 8.1 daily price changes, ibm

Figure 8.2a standard deviation versus expected return

Figure 8.2b standard deviation versus expected return

Figure 8.2c standard deviation versus expected return

FIGURE 8.3 EXPECTED RETURN AND STANDARD DEVIATION, HEINZ, AND EXXON MOBIL

Table 8.1 examples of efficient portfolios Efficient Portfolios—Percentages Allocated to Each Stock Stock Expected Return Standard Deviation A B C Dow Chemical 16.4% 40.2% 100 6 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 1 Pfizer 8.0 20.8 Starbucks 10.4 26.2 Walmart 6.3 13.8 9 42 ExxonMobil 10.0 21.9 Expected portfolio return 16.4 6.7 Portfolio standard deviation 40.2 18.4 11.8

Figure 8.4 four efficient portfolios from ten stocks

8-1 harry markowitz and the birth of portfolio theory Efficient Frontier Each half-ellipse represents possible weighted combinations for two stocks Composite of all stock sets constitutes efficient frontier Expected return (%) Standard deviation

Figure 8.5 lending and borrowing

8-1 harry markowitz and the birth of portfolio theory Example Correlation Coefficient = .18 Stocks s % of Portfolio Average Return Heinz 14.6 60% 6.0% ExxonMobil 21.9 40% 10.0% Standard deviation = weighted average = 17.52 Standard deviation = portfolio = 15.1 Return = weighted average = portfolio = 7.6% Higher return, lower risk through diversification

8-1 harry markowitz and the birth of portfolio theory Example Correlation Coefficient = .4 Stocks s % of Portfolio Average Return ABC Corp 28 60% 15% Big Corp 42 40% 21% Standard deviation = weighted average = 33.6 Standard deviation = portfolio = 28.1 Return = weighted average = portfolio = 17.4%

8-1 harry markowitz and the birth of portfolio theory Example, continued Correlation Coefficient = .3 Add new stock to portfolio Stocks s % of Portfolio Average Return Portfolio 28.1 50% 17.4% New Corp 30 50% 19% Standard deviation = weighted average = 31.80 Standard deviation = portfolio = 23.43 Return = weighted average = portfolio = 18.20%

8-1 harry markowitz and the birth of portfolio theory Return Risk (measured as s)

8-1 harry markowitz and the birth of portfolio theory Return Risk B AB

8-1 harry markowitz and the birth of portfolio theory Return Risk AB

8-1 harry markowitz and the birth of portfolio theory Return Risk AB ABN

8-1 harry markowitz and the birth of portfolio theory Goal is to move up and left—less risk, more return A B N Return Risk AB ABN

8-1 harry markowitz and the birth of portfolio theory Sharpe Ratio Ratio of risk premium to standard deviation

8-1 harry markowitz and the birth of portfolio theory Return Risk Low Risk High Return High Risk Low Return

8-1 harry markowitz and the birth of portfolio theory Return Risk Low Risk High Return High Risk Low Return

8-1 harry markowitz and the birth of portfolio theory Return Risk A B N AB ABN

8-2 the relationship between risk and return . rf Market portfolio Market return = rm

Figure 8.6 security market line Return . rf Market portfolio Market return = rm BETA 1.0 Security market line (SML)

8-2 the relationship between risk and return BETA rf 1.0 SML SML Equation: rf + β(rm − rf)

8-2 the relationship between risk and return Capital Asset Pricing Model (CAPM)

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. Stock Beta Expected Return Dow Chemical 1.78 14.50 Bank of America 1.54 12.80 Ford 1.53 12.70 ExxonMobil 0.98 8.86 Starbucks 0.95 8.68 IBM 0.80 7.62 Newmont Mining 0.75 7.26 Pfizer 0.66 6.63 Walmart 0.42 4.92 Heinz 0.40 4.78

Figure 8.7 security market line equilibrium In equilibrium, no stock can lie below the security market line

Figure 8.8 capital asset pricing model

Figure 8.9b beta versus average return

Figure 8.10 return versus book-to-market

8-4 Alternative Theories Alternative to CAPM

8-4 Alternative Theories Estimated risk premiums (1978-1990)

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.)

Table 8.3 expected equity returns