2. Lecture 8 Risk and Return Managerial Finance FINA 6335 Ronald F. Singer

3. 8-2 Topics Covered  Markowitz Portfolio Theory  Risk and Return Relationship  Testing the CAPM  CAPM Alternatives

4. 8-3 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. efficient portfolios  The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.

5. 8-4 Markowitz Portfolio Theory Price changes vs. Normal distribution Microsoft - Daily % change 1986-1997 # of Days (frequency) Daily % Change

6. 8-5 Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment C % probability % return

7. 8-6 Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment D % probability % return

8. 8-7 Markowitz Portfolio Theory Bristol-Myers Squibb McDonald’s Standard Deviation Expected Return (%) 45% McDonald’s Expected Returns and Standard Deviations vary given different weighted combinations of the stocks.

9. 8-8 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.

10. 8-9 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 T S

11. Efficient Frontier Correlation Coefficient = 0.4 Stocks  % of Portfolio Avg. Return ABC Corp 2860% 15% Big Corp 42 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

12. Efficient Frontier Correlation Coefficient =.3 Stocks  % of PortfolioAvg. Return Portfolio28.150% 17.4% New Corp30 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

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

14. Efficient Frontier A B N Return Risk AB

15. Efficient Frontier A B N Return Risk AB ABN

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

17. Efficient Frontier Return Risk Low Risk High Return High Risk High Return Low Risk Low Return High Risk Low Return

18. Efficient Frontier Return Risk A B N AB ABN

19. Security Market Line Return Risk. rfrf Efficient Portfolio Risk Free Return =

20. Security Market Line Return Risk. rfrf Risk Free Return = Market Return = r m Efficient Portfolio

21. Security Market Line Return Risk. rfrf Risk Free Return = Market Return = r m Efficient Portfolio

22. Security Market Line Return BETA. rfrf Risk Free Return = Market Return = r m Efficient Portfolio 1.0

23. Security Market Line Return BETA rfrf Risk Free Return = Market Return = r m 1.0 Security Market Line (SML)

24. Security Market Line Return BETA rfrf 1.0 SML SML Equation = r f + B ( r m - r f )

25. Capital Asset Pricing Model R = r f + B ( r m - r f ) CAPM

26. Testing the CAPM Avg. Risk Premium 1931-65 Portfolio Beta 1.0 SML 30 20 10 0 Investors Market Portfolio Beta vs. Average Risk Premium

27. Testing the CAPM Avg. Risk Premium 1966-91 Portfolio Beta 1.0 SML 30 20 10 0 Investors Market Portfolio Beta vs. Average Risk Premium

28. Testing the CAPM Average Return (%) Company size SmallestLargest Company Size vs. Average Return

29. Testing the CAPM Average Return (%) Book-Market Ratio HighestLowest Book-Market vs. Average Return

30. 8-29 Consumption Betas Vs. Market Betas Stocks (and other risky assets) Wealth = market portfolio Market risk makes wealth uncertain. Stocks (and other risky assets) Consumption Wealth Wealth is uncertain Consumption is uncertain Standard CAPM Consumption CAPM

31. Arbitrage Pricing Theory Alternative to CAPM Expected Risk Premium = r - r f = B factor1 (r factor1 - r f ) + B f2 (r f2 - r f ) + … Return= a + b factor1 (r factor1 ) + b f2 (r f2 ) + …

32. Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978-1990)