Chapter 5 Modern Portfolio Concepts

1. Chapter 5 Modern Portfolio Concepts

2. Required computations (10-12) • Various return concepts (HPR, IRR, realized return, expected return) • Compute the average return and standard deviation on a time series using excel. • Compute the mean/expected return and standard deviation given scenarios with probabilities. • Compute the mean return, beta of a portfolio of multiple assets • Compute the standard deviation of a two-asset portfolio • Apply CAPM to compute required rate of return, return sensitivity to market moves, and market risk premium.

3. Rank investment projects and beyond • Suppose the riskfree rate (Rf) is 5%. We have two projects that we can invest in. Project A has a projected mean return of 10% and standard deviation of 20%. Project B has a projected mean return of 15% and standard deviation of 30%. • Which project(s) should you take? • Sharpe A=(10%-5%)/20%=1/4. B=(15%-5%)/30%=1/3. Choose B if I can only invest in one project. • Suppose I put half of my money in A and half in B, what’s my Sharpe? • Return=average return of the two =0.5*10%+0.5*15%=12.5%. • Standard deviation depends on correlation! • If the two move perfectly together, std=0.5*20%+0.5*30%=25%.

4. Correlation (r) • Correlation is a standardized measure of comovement between two securities: • Between -1 and 1. • -1 Move perfectly in opposite directions • 1 move perfectly together • 0 do not move together • Standard deviation of a 2-asset portfolio =Sqrt(w1^2 *s1^2 + w2^2 *s2^2 + 2*w1*s1*w2*s2*r) • Example: r=0, std=sqrt(0.5^2*0.2^2+0.5^2*0.3^2)=18%. Sharpe=(12.5%-5%)/18%=0.42 • The benefit of diversification: The risk of a portfolio is smaller than the average risk of the individual names in the portfolio • S1=s2, w1=w2=0.5, std=sqrt(0.5^2 s^2+0.5^2 s^2)=sqrt(0.5)*s=s/sqrt(2)

5. What is a Portfolio? • Portfolio is a collection of investments assembled to meet one or more investment goals. • Efficient portfolio • A portfolio that provides the highest return for a given level of risk • Requires search for investment alternatives to get the best combinations of risk and return

6. Portfolio Return and Risk Measures • The return on a portfolio is simply the weighted average of the individual assets’ returns in the portfolio • The standard deviation of a portfolio’s returns is more complicated, and is a function of the portfolio’s individual assets’ weights, standard deviations, and correlations with all other assets

7. Return on Portfolio

8. Correlation: Why Diversification Works! • Correlation is a statistical measure of the relationship between two series of numbers representing data • Positively Correlated items tend to move in the same direction • Negatively Correlated items tend to move in opposite directions • Correlation Coefficient is a measure of the degree of correlation between two series of numbers representing data

9. Correlation Coefficients • Perfectly Positively Correlated describes two positively correlated series having a correlation coefficient of +1 • Perfectly Negatively Correlated describes two negatively correlated series having a correlation coefficient of -1 • Uncorrelated describes two series that lack any relationship and have a correlation coefficient of nearly zero

10. Figure 5.1 The Correlation Between Series M, N, and P

11. Correlation: Why Diversification Works! • Assets that are less than perfectly positively correlated tend to offset each others movements, thus reducing the overall risk in a portfolio • The lower the correlation the more the overall risk in a portfolio is reduced • Assets with +1 correlation eliminate no risk • Assets with less than +1 correlation eliminate some risk • Assets with less than 0 correlation eliminate more risk • Assets with -1 correlation eliminate all risk

12. Figure 5.2 Combining Negatively Correlated Assets to Diversify Risk

13. Figure 5.3 Portfolios of IBM and Celgene

14. Figure 5.4 Risk and Return for Combinations of Two Assets with Various Correlation Coefficients

15. Why Use International Diversification? • Offers more diverse investment alternatives than U.S.-only based investing • Foreign economic cycles may move independently from U.S. economic cycle • Foreign markets may not be as “efficient” as U.S. markets, allowing true gains from superior research

16. International Diversification • Advantages of International Diversification • Broader investment choices • Potentially greater returns than in U.S. • Reduction of overall portfolio risk • Disadvantages of International Diversification • Currency exchange risk • Less convenient to invest than U.S. stocks • More expensive to invest • Riskier than investing in U.S.

17. Methods of International Diversification • Foreign company stocks listed on U.S. stock exchanges • Yankee Bonds • American Depository Shares (ADS’s) • Mutual funds investing in foreign stocks • U.S. multinational companies (typically not considered a true international investment for diversification purposes)

18. Components of Risk • Diversifiable (Unsystematic) Risk • Results from uncontrollable or random events that are firm-specific • Can be eliminated through diversification • Examples: labor strikes, lawsuits • Nondiversifiable (Systematic) Risk • Attributable to forces that affect all similar investments • Cannot be eliminated through diversification • Examples: war, inflation, political events

19. Components of Risk

20. Beta: A Popular Measure of Risk • A measure of undiversifiable risk • Indicates how the price of a security responds to market forces • Compares historical return of an investment to the market return (the S&P 500 Index) • The beta for the market is 1.0 • Stocks may have positive or negative betas. Nearly all are positive. • Stocks with betas greater than 1.0 are more risky than the overall market. • Stocks with betas less than 1.0 are less risky than the overall market.

21. Beta as a Measure of Risk Table 5.4 Selected Betas and Associated Interpretations

22. Interpreting Beta • Higher stock betas should result in higher expected returns due to greater risk • If the market is expected to increase 10%, a stock with a beta of 1.50 is expected to increase 15% • If the market went down 8%, then a stock with a beta of 0.50 should only decrease by about 4% • Beta values for specific stocks can be obtained from Value Line reports or websites such as yahoo.com

23. Interpreting Beta

24. Capital Asset Pricing Model (CAPM) • Model that links the notions of risk and return • Helps investors define the required return on an investment • As beta increases, the required return for a given investment increases

25. Capital Asset Pricing Model (CAPM) (cont’d) • Uses beta, the risk-free rate and the market return to define the required return on an investment

26. Capital Asset Pricing Model (CAPM) (cont’d) • CAPM can also be shown as a graph • Security Market Line (SML) is the “picture” of the CAPM • Find the SML by calculating the required return for a number of betas, then plotting them on a graph

27. Figure 5.6 The Security Market Line (SML)

28. Two Approaches to Constructing Portfolios Traditional Approach versus Modern Portfolio Theory

29. Traditional Approach • Emphasizes “balancing” the portfolio using a wide variety of stocks and/or bonds • Uses a broad range of industries to diversify the portfolio • Tends to focus on well-known companies • Perceived as less risky • Stocks are more liquid and available • Familiarity provides higher “comfort” levels for investors

30. Modern Portfolio Theory (MPT) • Emphasizes statistical measures to develop a portfolio plan • Focus is on: • Expected returns • Standard deviation of returns • Correlation between returns • Combines securities that have negative (or low-positive) correlations between each other’s rates of return

31. Key Aspects of MPT: Efficient Frontier • Efficient Frontier • The leftmost boundary of the feasible set of portfolios that include all efficient portfolios: those providing the best attainable tradeoff between risk and return • Portfolios that fall to the right of the efficient frontier are not desirable because their risk return tradeoffs are inferior • Portfolios that fall to the left of the efficient frontier are not available for investments

32. Figure 5.7 The Feasible or Attainable Set and the Efficient Frontier

33. Key Aspects of MPT: Portfolio Betas • Portfolio Beta • The beta of a portfolio; calculated as the weighted average of the betas of the individual assets the portfolio includes • To earn more return, one must bear more risk • Only nondiversifiable risk (relevant risk) provides a positive risk-return relationship

34. Figure 5.8 Portfolio Risk and Diversification

35. Key Aspects of MPT: Portfolio Betas Table 5.6 Austin Fund’s Portfolios V and W

36. Interpreting Portfolio Betas • Portfolio betas are interpreted exactly the same way as individual stock betas. • Portfolio beta of 1.00 will experience a 10% increase when the market increase is 10% • Portfolio beta of 0.75 will experience a 7.5% increase when the market increase is 10% • Portfolio beta of 1.25 will experience a 12.5% increase when the market increase is 10% • Low-beta portfolios are less responsive and less risky than high-beta portfolios. • A portfolio containing low-beta assets will have a low beta, and vice versa.

37. Interpreting Portfolio Betas Table 5.7 Portfolio Betas and Associated Changes in Returns

38. Reconciling the Traditional Approach and MPT • Recommended portfolio management policy uses aspects of both approaches: • Determine how much risk you are willing to bear • Seek diversification between different types of securities and industry lines • Pay attention to correlation of return between securities • Use beta to keep portfolio at acceptable level of risk • Evaluate alternative portfolios to select highest return for the given level of acceptable risk

39. Figure 5.9 The Portfolio Risk-Return Tradeoff