1. 1 Chapter 5 Why Diversification Is a Good Idea

2. 2 The most important lesson learned is an old truth ratified. - General Maxwell R. Thurman

3. 3 Outline u Introduction u Carrying your eggs in more than one basket u Role of uncorrelated securities u Diversification and beta u Capital asset pricing model u Equity risk premium u Using a scatter diagram to measure beta u Arbitrage pricing theory

4. 4 Introduction u Diversification of a portfolio is logically a good idea u Virtually all stock portfolios seek to diversify in one respect or another

5. 5 Carrying Your Eggs in More Than One Basket u Investments in your own ego u The concept of risk aversion revisited u Multiple investment objectives

6. 6 Investments in Your Own Ego u Never put a large percentage of investment funds into a single security If the security appreciates, the ego is stroked and this may plant a speculative seed If the security never moves, the ego views this as neutral rather than an opportunity cost If the security declines, your ego has a very difficult time letting go

7. 7 The Concept of Risk Aversion Revisited u Diversification is logical If you drop the basket, all eggs break u Diversification is mathematically sound Most people are risk averse People take risks only if they believe they will be rewarded for taking them

8. 8 The Concept of Risk Aversion Revisited (cont’d) u Diversification is more important now Journal of Finance article shows that volatility of individual firms has increased –Investors need more stocks to adequately diversify

9. 9 Multiple Investment Objectives u Multiple objectives justify carrying your eggs in more than one basket Some people find mutual funds “unexciting” Many investors hold their investment funds in more than one account so that they can “play with” part of the total –E.g., a retirement account and a separate brokerage account for trading individual securities

10. 10 Role of Uncorrelated Securities u Variance of a linear combination: the practical meaning u Portfolio programming in a nutshell u Concept of dominance u Harry Markowitz: the founder of portfolio theory

11. 11 Variance of A Linear Combination u One measure of risk is the variance of return u The variance of an n-security portfolio is:

12. 12 Variance of A Linear Combination (cont’d) u The variance of a two-security portfolio is:

13. 13 Variance of A Linear Combination (cont’d) u Return variance is a security’s total risk u Most investors want portfolio variance to be as low as possible without having to give up any return Total RiskRisk from ARisk from BInteractive Risk

14. 14 Variance of A Linear Combination (cont’d) u If two securities have low correlation, the interactive risk will be small u If two securities are uncorrelated, the interactive risk drops out u If two securities are negatively correlated, interactive risk would be negative and would reduce total risk

15. 15 Portfolio Programming in A Nutshell u Various portfolio combinations may result in a given return u The investor wants to choose the portfolio combination that provides the least amount of variance

16. 16 Portfolio Programming in A Nutshell (cont’d) Example Assume the following statistics for Stocks A, B, and C: Stock AStock BStock C Expected return.20.14.10 Standard deviation.232.136.195

17. 17 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) The correlation coefficients between the three stocks are: Stock AStock BStock C Stock A1.000 Stock B0.2861.000 Stock C0.132-0.6051.000

18. 18 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) An investor seeks a portfolio return of 12%. Which combinations of the three stocks accomplish this objective? Which of those combinations achieves the least amount of risk?

19. 19 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution: Two combinations achieve a 12% return: 1)50% in B, 50% in C: (.5)(14%) + (.5)(10%) = 12% 2)20% in A, 80% in C: (.2)(20%) + (.8)(10%) = 12%

20. 20 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution (cont’d): Calculate the variance of the B/C combination:

21. 21 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution (cont’d): Calculate the variance of the A/C combination:

22. 22 Portfolio Programming in A Nutshell (cont’d) Example (cont’d) Solution (cont’d): Investing 50% in Stock B and 50% in Stock C achieves an expected return of 12% with the lower portfolio variance. Thus, the investor will likely prefer this combination to the alternative of investing 20% in Stock A and 80% in Stock C.

23. 23 Concept of Dominance u Dominance is a situation in which investors universally prefer one alternative over another All rational investors will clearly prefer one alternative

24. 24 Concept of Dominance (cont’d) u A portfolio dominates all others if: For its level of expected return, there is no other portfolio with less risk For its level of risk, there is no other portfolio with a higher expected return

25. 25 Concept of Dominance (cont’d) Example (cont’d) In the previous example, the B/C combination dominates the A/C combination: Risk Expected Return B/C combination dominates A/C

26. 26 Harry Markowitz: Founder of Portfolio Theory u Introduction u Terminology

27. 27 Introduction u Harry Markowitz’s “Portfolio Selection” Journal of Finance article (1952) set the stage for modern portfolio theory The first major publication indicating the important of security return correlation in the construction of stock portfolios Markowitz showed that for a given level of expected return and for a given security universe, knowledge of the covariance and correlation matrices are required

28. 28 Terminology u Security Universe u Efficient frontier u Capital market line and the market portfolio u Security market line u Expansion of the SML to four quadrants u Corner portfolio

29. 29 Security Universe u The security universe is the collection of all possible investments For some institutions, only certain investments may be eligible –E.g., the manager of a small cap stock mutual fund would not include large cap stocks

30. 30 Efficient Frontier u Construct a risk/return plot of all possible portfolios Those portfolios that are not dominated constitute the efficient frontier

31. 31 Efficient Frontier (cont’d) Standard Deviation Expected Return 100% investment in security with highest E(R) 100% investment in minimum variance portfolio Points below the efficient frontier are dominated No points plot above the line All portfolios on the line are efficient

32. 32 Efficient Frontier (cont’d) u The farther you move to the left on the efficient frontier, the greater the number of securities in the portfolio

33. 33 Efficient Frontier (cont’d) u When a risk-free investment is available, the shape of the efficient frontier changes The expected return and variance of a risk-free rate/stock return combination are simply a weighted average of the two expected returns and variance –The risk-free rate has a variance of zero

34. 34 Efficient Frontier (cont’d) Standard Deviation Expected Return RfRf A B C

35. 35 Efficient Frontier (cont’d) u The efficient frontier with a risk-free rate: Extends from the risk-free rate to point B –The line is tangent to the risky securities efficient frontier Follows the curve from point B to point C

36. 36 Capital Market Line and the Market Portfolio u The tangent line passing from the risk-free rate through point B is the capital market line (CML) When the security universe includes all possible investments, point B is the market portfolio –It contains every risky assets in the proportion of its market value to the aggregate market value of all assets –It is the only risky assets risk-averse investors will hold

37. 37 Capital Market Line and the Market Portfolio (cont’d) u Implication for investors: Regardless of the level of risk-aversion, all investors should hold only two securities: –The market portfolio –The risk-free rate Conservative investors will choose a point near the lower left of the CML Growth-oriented investors will stay near the market portfolio

38. 38 Capital Market Line and the Market Portfolio (cont’d) u Any risky portfolio that is partially invested in the risk-free asset is a lending portfolio u Investors can achieve portfolio returns greater than the market portfolio by constructing a borrowing portfolio

39. 39 Capital Market Line and the Market Portfolio (cont’d) Standard Deviation Expected Return RfRf A B C

40. 40 Security Market Line u The graphical relationship between expected return and beta is the security market line (SML) The slope of the SML is the market price of risk The slope of the SML changes periodically as the risk-free rate and the market’s expected return change

41. 41 Security Market Line (cont’d) Beta Expected Return RfRf Market Portfolio 1.0 E(R)

42. 42 Expansion of the SML to Four Quadrants u There are securities with negative betas and negative expected returns A reason for purchasing these securities is their risk-reduction potential –E.g., buy car insurance without expecting an accident –E.g., buy fire insurance without expecting a fire

43. 43 Security Market Line (cont’d) Beta Expected Return Securities with Negative Expected Returns

44. 44 Corner Portfolio u A corner portfolio occurs every time a new security enters an efficient portfolio or an old security leaves Moving along the risky efficient frontier from right to left, securities are added and deleted until you arrive at the minimum variance portfolio

45. 45 Capital Asset Pricing Model u Introduction u Systematic and unsystematic risk u Fundamental risk/return relationship revisited

46. 46 Introduction u The Capital Asset Pricing Model (CAPM) is a theoretical description of the way in which the market prices investment assets The CAPM is a positive theory

47. 47 Systematic and Unsystematic Risk u Unsystematic risk can be diversified and is irrelevant u Systematic risk cannot be diversified and is relevant Measured by beta –Beta determines the level of expected return on a security or portfolio (SML)

48. 48 Fundamental Risk/Return Relationship Revisited u CAPM u SML and CAPM u Market model versus CAPM u Note on the CAPM assumptions u Stationarity of beta

49. 49 CAPM u The more risk you carry, the greater the expected return:

50. 50 CAPM (cont’d) u The CAPM deals with expectations about the future u Excess returns on a particular stock are directly related to: The beta of the stock The expected excess return on the market

51. 51 CAPM (cont’d) u CAPM assumptions: Variance of return and mean return are all investors care about Investors are price takers –They cannot influence the market individually All investors have equal and costless access to information There are no taxes or commission costs

52. 52 CAPM (cont’d) u CAPM assumptions (cont’d): Investors look only one period ahead Everyone is equally adept at analyzing securities and interpreting the news

53. 53 SML and CAPM  If you show the security market line with excess returns on the vertical axis, the equation of the SML is the CAPM The intercept is zero The slope of the line is beta

54. 54 Market Model Versus CAPM u The market model is an ex post model It describes past price behavior u The CAPM is an ex ante model It predicts what a value should be

55. 55 Market Model Versus CAPM (cont’d) u The market model is:

56. 56 Note on the CAPM Assumptions u Several assumptions are unrealistic: People pay taxes and commissions Many people look ahead more than one period Not all investors forecast the same distribution u Theory is useful to the extent that it helps us learn more about the way the world acts Empirical testing shows that the CAPM works reasonably well

57. 57 Stationarity of Beta u Beta is not stationary Evidence that weekly betas are less than monthly betas, especially for high-beta stocks Evidence that the stationarity of beta increases as the estimation period increases u The informed investment manager knows that betas change

58. 58 Equity Risk Premium u Equity risk premium refers to the difference in the average return between stocks and some measure of the risk-free rate The equity risk premium in the CAPM is the excess expected return on the market Some researchers are proposing that the size of the equity risk premium is shrinking

59. 59 Using A Scatter Diagram to Measure Beta u Correlation of returns u Linear regression and beta u Importance of logarithms u Statistical significance

60. 60 Correlation of Returns u Much of the daily news is of a general economic nature and affects all securities Stock prices often move as a group Some stock routinely move more than the others regardless of whether the market advances or declines –Some stocks are more sensitive to changes in economic conditions

61. 61 Linear Regression and Beta u To obtain beta with a linear regression: Plot a stock’s return against the market return Use Excel to run a linear regression and obtain the coefficients –The coefficient for the market return is the beta statistic –The intercept is the trend in the security price returns that is inexplicable by finance theory

62. 62 Importance of Logarithms u Taking the logarithm of returns reduces the impact of outliers Outliers distort the general relationship Using logarithms will have more effect the more outliers there are

63. 63 Statistical Significance u Published betas are not always useful numbers Individual securities have substantial unsystematic risk and will behave differently than beta predicts Portfolio betas are more useful since some unsystematic risk is diversified away

64. 64 Arbitrage Pricing Theory u APT background u The APT model u Comparison of the CAPM and the APT

65. 65 APT Background u Arbitrage pricing theory (APT) states that a number of distinct factors determine the market return Roll and Ross state that a security’s long-run return is a function of changes in: –Inflation –Industrial production –Risk premiums –The slope of the term structure of interest rates

66. 66 APT Background (cont’d) u Not all analysts are concerned with the same set of economic information A single market measure such as beta does not capture all the information relevant to the price of a stock

67. 67 The APT Model u General representation of the APT model:

68. 68 Comparison of the CAPM and the APT u The CAPM’s market portfolio is difficult to construct: Theoretically all assets should be included (real estate, gold, etc.) Practically, a proxy like the S&P 500 index is used u APT requires specification of the relevant macroeconomic factors

69. 69 Comparison of the CAPM and the APT (cont’d) u The CAPM and APT complement each other rather than compete Both models predict that positive returns will result from factor sensitivities that move with the market and vice versa

70. 70 Sharpe and Treynor Measures u The Sharpe and Treynor measures:

71. 71 Sharpe and Treynor Measures (cont’d) u The Treynor measure evaluates the return relative to beta, a measure of systematic risk It ignores any unsystematic risk u The Sharpe measure evaluates return relative to total risk Appropriate for a well-diversified portfolio, but not for individual securities

72. 72 Sharpe and Treynor Measures (cont’d) Example Over the last four months, XYZ Stock had excess returns of 1.86%, -5.09%, -1.99%, and 1.72%. The standard deviation of XYZ stock returns is 3.07%. XYZ Stock has a beta of 1.20. What are the Sharpe and Treynor measures for XYZ Stock?

73. 73 Sharpe and Treynor Measures (cont’d) Example (cont’d) Solution: First compute the average excess return for Stock XYZ:

74. 74 Sharpe and Treynor Measures (cont’d) Example (cont’d) Solution (cont’d): Next, compute the Sharpe and Treynor measures:

75. 75 Jensen Measure u The Jensen measure stems directly from the CAPM:

76. 76 Jensen Measure (cont’d) u The constant term should be zero Securities with a beta of zero should have an excess return of zero according to finance theory u According to the Jensen measure, if a portfolio manager is better-than-average, the alpha of the portfolio will be positive

77. 77 Jensen Measure (cont’d) u The Jensen measure is generally out of favor because of statistical and theoretical problems

78. Copyright © 2005 Pearson Addison-Wesley. All rights reserved.14-78 Assessing Portfolio Performance u Portfolio Revision: the process of selling certain issues in a portfolio and purchasing new ones to replace them u Periodic reallocation and rebalancing are necessary u Reasons to revise portfolio: Major life event Proportion of one asset class increases or decreases substantially Expect to reach specific goal within two years Percentage allocation of asset class varies from original allocation by 10% or more.

79. Passive Management u Holding well diversified portfolio for a long term u Portfolio that resembles the overall market returns u Keeping each stock in proportion to stock index u Holding specified number of stocks 79

80. Active Management u Holding securities based on the forecast about the future u Pursue market strategy based on the “market timer” u Attractive stocks are given more weights and less attractive stocks are given less weights 80

81. Copyright © 2005 Pearson Addison-Wesley. All rights reserved.14-81 Timing Transactions (cont’d) u Constant-Ratio Plan Similar to constant-dollar plan, only the ratio between the speculative and conservative portions is fixed u Variable-Ratio Plan Similar to constant-ratio plan, only the ratio between the speculative and conservative portions is allowed to fluctuate to predetermined levels Moderately aggressive strategy which tries to “buy low and sell high”

82. u Formula Plans u Rupee Cost Averaging u Constant Rupee Plan u Constant Ratio Plan u Variable ration plan u Swaps 82

83. Copyright © 2005 Pearson Addison-Wesley. All rights reserved.14-83 Using Limit and Stop-Loss Orders u Limit Orders May be used to purchase additional securities only at desired purchase price or below u Stop-Loss Orders Used to limit downside loss or protect a profit by selling security when price falls below predetermined price

84. Copyright © 2005 Pearson Addison-Wesley. All rights reserved.14-84 Other Portfolio Considerations u Warehousing Liquidity Keep portion of portfolio in low-risk, highly liquid investments to protect against loss or to wait for future investment opportunities u Tax Consequences Use long-term capital gains when possible Use capital losses to offset capital gains u Achieving Investment Goals When an investment becomes more or less risky, or it does not meet its return objective, sell it Don’t hold out for top price; take your profits and reinvest in more suitable investment