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Portfolio theory and the capital asset pricing model

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1 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.

2 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

3 Figure 8.1 daily price changes, ibm

4 Figure 8.2a standard deviation versus expected return

5 Figure 8.2b standard deviation versus expected return

6 Figure 8.2c standard deviation versus expected return

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

8 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

9 Figure 8.4 four efficient portfolios from ten stocks

10 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

11 Figure 8.5 lending and borrowing

12 8-1 harry markowitz and the birth of portfolio theory
Example Correlation Coefficient = .18 Stocks s % of Portfolio Average Return Heinz % % ExxonMobil % % Standard deviation = weighted average = 17.52 Standard deviation = portfolio = 15.1 Return = weighted average = portfolio = 7.6% Higher return, lower risk through diversification

13 8-1 harry markowitz and the birth of portfolio theory
Example Correlation Coefficient = .4 Stocks s % of Portfolio Average Return ABC Corp % % Big Corp % % Standard deviation = weighted average = 33.6 Standard deviation = portfolio = 28.1 Return = weighted average = portfolio = 17.4%

14 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 % % New Corp % % Standard deviation = weighted average = 31.80 Standard deviation = portfolio = Return = weighted average = portfolio = 18.20%

15 8-1 harry markowitz and the birth of portfolio theory
Return Risk (measured as s)

16 8-1 harry markowitz and the birth of portfolio theory
Return Risk B AB

17 8-1 harry markowitz and the birth of portfolio theory
Return Risk AB

18 8-1 harry markowitz and the birth of portfolio theory
Return Risk AB ABN

19 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

20 8-1 harry markowitz and the birth of portfolio theory
Sharpe Ratio Ratio of risk premium to standard deviation

21 8-1 harry markowitz and the birth of portfolio theory
Return Risk Low Risk High Return High Risk Low Return

22 8-1 harry markowitz and the birth of portfolio theory
Return Risk Low Risk High Return High Risk Low Return

23 8-1 harry markowitz and the birth of portfolio theory
Return Risk A B N AB ABN

24 8-2 the relationship between risk and return
. rf Market portfolio Market return = rm

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

26 8-2 the relationship between risk and return
BETA rf 1.0 SML SML Equation: rf + β(rm − rf)

27 8-2 the relationship between risk and return
Capital Asset Pricing Model (CAPM)

28 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

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

30 Figure 8.8 capital asset pricing model

31 Figure 8.9b beta versus average return

32 Figure 8.10 return versus book-to-market

33 8-4 Alternative Theories
Alternative to CAPM

34 8-4 Alternative Theories
Estimated risk premiums ( )

35 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.)

36 Table 8.3 expected equity returns

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