1. Portfolio Theory and the Capital Asset Pricing Model 723g28 Linköpings Universitet, IEI 1

2. We have learned from last chapter risk and return: (that for an individual investor) Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation. Rational investors maximize the expected return given risks. Or minimize risks given expected return. 2

3. Markowitz Portfolio Theory Efficient portfolio provides the highest return for a given level of risk Efficient portfolio provides the highest return for a given level of risk, or least risk for a given level of return. The market portfolio is the one that has the highest Sharpe ratio with the return and risk. The Sharpe ratio is a measure of risk premium per unit of risk in an investment asset or a trading strategy 3

4. Effect of diversification on variance 4

5. Markowitz Portfolio Theory Price changes vs. Normal distribution IBM - Daily % change 1988-2008 Proportion of Days Daily % Change 5

6. Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment A % probability % return 6

7. Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment B % probability % return 7

8. Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment C % probability % return 8

9. 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 9

10. A two asset portfolio constructed with % of both assets, allow short selling of one assets 10

11. Efficient Frontier TABLE 8.1 Examples of efficient portfolios chosen from 10 stocks. Note: Standard deviations and the correlations between stock returns were estimated from monthly returns January 2004-December 2008. Efficient portfolios are calculated assuming that short sales are prohibited. Efficient Portfolios – Percentages Allocated to Each Stock StockExpected ReturnStandard DeviationABCD Amazon.com22.8%50.9%10019.110.9 Ford19.047.219.911.0 Dell13.430.915.610.3 Starbucks9.030.313.710.73.6 Boeing9.523.79.210.5 Disney7.719.68.811.2 Newmont7.036.19.910.2 ExxonMobil4.719.19.718.4 Johnson & Johnson3.812.67.433.9 Soup3.115.88.433.9 Expected portfolio return22.814.110.54.2 Portfolio standard deviation50.922.016.08.8 11 Try graph the efficient frontier and find the market portfolio with the highest Sharpe Ratio!

12. Efficient Frontier 4 Efficient Portfolios all from the same 10 stocks 12

13. 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 S T 13 The red line is the Capital Market Line, where you can hold a combination of the risk free assets and the market portfolio and get any returns you like. Minimum variance portfolio

14. Efficient Frontier Another 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 14

15. Efficient Frontier A B Return Risk (measured as  ) 15

16. Efficient Frontier A B Return Risk AB 16

17. Efficient Frontier A B N Return Risk AB 17

18. Efficient Frontier A B N Return Risk AB ABN 18

19. Efficient Frontier A B N Return Risk AB Goal is to move up and left. WHY? ABN 19

20. Efficient Frontier The ratio of the risk premium to the standard deviation is the Sharpe ratio. In a competitive market, the expected risk premium varies in proportion to portfolio standard deviation. P denotes portfolio. Along the Capital Market Line one holds the risky assets and a risk free loan. 20

21. Capital Asset Pricing Model CAPM 21

22. Security Market Line Stock Return. rfrf Market Portfolio Market Return = r m BETA risk 1.0 Risk Free Return = (Treasury bills) 22 2,0 riri

23. Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return 23

24. Capital Market Line Return Risk. rfrf Risk Free Return = (Treasury bills) Market Portfolio Market Return = r m 24 Tangent portfolio

25. Security Market Line Return. rfrf Market Portfolio Market Return = r m BETA1.0 Risk Free Return = (Treasury bills) 25

26. Market Risk Premium: Example Example: Market Portfolio (market return = 12%)

27. Security Market Line: depicts the CAPM Return BETA rfrf 1.0 SML SML Equation = r f + β( r m - r f ) 27 Security Market Line

28. Expected Returns StockBeta (β)Expected Return [r f + β(r m – r f )] Amazon2.1615.4 Ford1.7512.6 Dell1.4110.2 Starbucks1.168.4 Boeing1.148.3 Disney.967.0 Newmont.634.7 ExxonMobil.554.2 Johnson & Johnson.503.8 Soup.302.4 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. 28

29. 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 money and put the balance in the market portfolio. And instead of buying stock B, they would prefer to borrow and invest in the market portfolio. (lend=save, borrow is leveraging.) risk free assets and the market portfolio can span the whole Security market line) 29 Higher risk lower return

30. Testing the CAPM Average Risk Premium 1931-2008 Portfolio Beta 1.0 SML 20 12 0 Investors Market Portfolio Beta vs. Average Risk Premium: low beta portfolio fared better than high beta portfolio 1931-2008 30

31. Testing the CAPM Portfolio Beta 1.0 SML 12 8 4 0 Investors Market Portfolio Beta vs. Average Risk Premium Average Risk Premium 1966-2008 31

32. Testing the CAPM: Return vs. Book-to- Market High-minus low book-to-market Dollars (log scale) Small minus big http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 2008 32 Cumulated difference of Small minus big firm stocks Cumulated difference of High minus low book-to-market firm stocks