1. Version 1.2 Copyright © 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department Harcourt, Inc. 6277 Sea Harbor Drive Orlando, Florida 32887-6777 Lecture Presentation Software to accompany Investment Analysis and Portfolio Management Sixth Edition by Frank K. Reilly & Keith C. Brown Chapter 9

2. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 9 - An Introduction to Asset Pricing Models Questions to be answered: What are the assumptions of the capital asset pricing model? What is a risk-free asset and what are its risk-return characteristics? What is the covariance and correlation between the risk-free asset and a risky asset or portfolio of risky assets?

3. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 9 - An Introduction to Asset Pricing Models What is the expected return when you combine the risk-free asset and a portfolio of risky assets? What is the standard deviation when you combine the risk-free asset and a portfolio of risky assets? When you combine the risk-free asset and a portfolio of risky assets on the Markowitz efficient frontier, what does the set of possible portfolios look like?

4. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 9 - An Introduction to Asset Pricing Models Given the initial set of portfolio possibilities with a risk-free asset, what happens when you add financial leverage (that is, borrow)? What is the market portfolio, what assets are included in this portfolio, and what are the relative weights for the alternative assets included? What is the capital market line (CML)? What do we mean by complete diversification?

5. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 9 - An Introduction to Asset Pricing Models How do we measure diversification for an individual portfolio? What are systematic and unsystematic risk? Given the capital market line (CML), what is the separation theorem? Given the CML, what is the relevant risk measure for an individual risky asset? What is the security market line (SML) and how does it differ from the CML?

6. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 9 - An Introduction to Asset Pricing Models What is beta and why is it referred to as a standardized measure of systematic risk? How can you use the SML to determine the expected (required) rate of return for a risky asset? Using the SML, what do we mean by an undervalued and overvalued security, and how do we determine whether an asset is undervalued or overvalued?

7. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 9 - An Introduction to Asset Pricing Models What is an asset’s characteristic line and how do you compute the characteristic line for an asset? What is the impact on the characteristic line when you compute it using different return intervals (e.g., weekly versus monthly) and when you employ different proxies (i.e., benchmarks) for the market portfolio (e.g., the S&P 500 versus a global stock index)?

8. Copyright © 2000 by Harcourt, Inc. All rights reserved. Chapter 9 - An Introduction to Asset Pricing Models What is the arbitrage pricing theory (APT) and how does it differ from the CAPM in terms of assumptions? How does the APT differ from the CAPM in terms of risk measure?

9. Copyright © 2000 by Harcourt, Inc. All rights reserved. Capital Market Theory: An Overview Capital market theory extends portfolio theory and develops a model for pricing all risky assets Capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset

10. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 1. All investors are Markowitz efficient investors who want to target points on the efficient frontier. –Also, they include all investable assets in their estimation of the efficient frontier –The exact location on the efficient frontier and, therefore, the specific portfolio selected, will depend on the individual investor’s risk-return utility function.

11. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 2. Investors can borrow or lend any amount of money at the risk-free rate of return (RFR). –Clearly it is always possible to lend money at the nominal risk-free rate by buying risk-free securities such as government T-bils. It is not always possible to borrow at this risk-free rate, but we will see that assuming a higher borrowing rate does not change the general results.

12. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 3. All investors have homogeneous expectations; that is, they estimate identical probability distributions for future rates of return. –This implies that everyone estimates the efficient frontier to be in the exact same location –Again, this assumption can be relaxed. As long as the differences in expectations are not vast, their effects are minor.

13. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 4. All investors have the same one-period time horizon such as one-month, six months, or one year. –The model will be developed for a single hypothetical period, and its results could be affected by a different assumption. A difference in the time horizon would require investors to derive risk measures and risk-free assets that are consistent with their time horizons.

14. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 5. All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of any asset or portfolio. –This assumption allows us to discuss investment alternatives as continuous curves. Changing it would have little impact on the theory.

15. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 6. There are no taxes or transaction costs involved in buying or selling assets. –This is a reasonable assumption in many instances. Neither pension funds nor religious groups have to pay taxes, and the transaction costs for most financial institutions are less than 1 percent on most financial instruments. Again, relaxing this assumption modifies the results, but does not change the basic thrust.

16. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 7. There is no inflation or any change in interest rates, or inflation is fully anticipated. –This is a reasonable initial assumption, and it can be modified.

17. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory 8. Capital markets are in equilibrium. –This means that we begin with all investments properly priced in line with their risk levels.

18. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Capital Market Theory Some of these assumptions are unrealistic Relaxing many of these assumptions would have only minor influence on the model and would not change its main implications or conclusions. Judge a theory on how well it explains and helps predict behavior, not on its assumptions.

19. Copyright © 2000 by Harcourt, Inc. All rights reserved. Risk-Free Asset In addition to investors who invest on the efficient frontier, CAPM also assumes the existence of a “risk-free asset,” which is … An investment with NO risk An asset with zero variance Zero correlation with all other risky assets Provides the risk-free rate of return (RFR) Will lie on the vertical axis of a portfolio graph

20. Copyright © 2000 by Harcourt, Inc. All rights reserved. Risk-Free Asset Covariance between two sets of returns is Because the returns for the risk free asset are certain, Thus R i = E(R i ), and Ri - E(Ri) = 0 Consequently, the covariance of the risk-free asset with any risky asset or portfolio will always equal zero. Similarly the correlation between any risky asset and the risk-free asset would be zero.

21. Copyright © 2000 by Harcourt, Inc. All rights reserved. Combining a Risk-Free Asset with a Risky Portfolio Expected return the weighted average of the two returns This is a linear relationship

22. Copyright © 2000 by Harcourt, Inc. All rights reserved. Combining a Risk-Free Asset with a Risky Portfolio Standard deviation The expected variance for a two-asset portfolio is Substituting the risk-free asset for Security 1, and the risky asset for Security 2, this formula would become Since we know that the variance of the risk-free asset is zero and the correlation between the risk-free asset and any risky asset i is zero we can adjust the formula

23. Copyright © 2000 by Harcourt, Inc. All rights reserved. Combining a Risk-Free Asset with a Risky Portfolio Given the variance formula the standard deviation is Therefore, the standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio.

24. Copyright © 2000 by Harcourt, Inc. All rights reserved. Combining a Risk-Free Asset with a Risky Portfolio Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets. This line is called the Capital Market Line (CML). The CML represents the relationship between expected return and volatility (  ) for well- diversified portfolios

25. Copyright © 2000 by Harcourt, Inc. All rights reserved. Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier Figure 9.1 RFR M C A B D

26. Copyright © 2000 by Harcourt, Inc. All rights reserved. Risk-Return Possibilities with Leverage To attain a higher expected return than is available at point M (in exchange for accepting higher risk) Either invest along the efficient frontier beyond point M, such as point D Or, add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M

27. Copyright © 2000 by Harcourt, Inc. All rights reserved. Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier Figure 9.2 RFR M CML Borrowing Lending

28. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Market Portfolio Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML Therefore this portfolio must include ALL RISKY ASSETS

29. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Market Portfolio Because the market is in equilibrium, all assets are included in this portfolio in proportion to their market value

30. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Market Portfolio Because it contains all risky assets, it is a completely diversified portfolio (once you already own everything, you can’t diversify any more!), which means that all the unique risk of individual assets (unsystematic risk) is diversified away (all the risk that’s left over is, by definition, systematic risk)

31. Copyright © 2000 by Harcourt, Inc. All rights reserved. Systematic Risk Only systematic risk remains in the market portfolio Systematic risk is the variability in all risky assets caused by macroeconomic variables Systematic risk can be measured by the standard deviation of returns of the market portfolio and can (and does) change over time

32. Copyright © 2000 by Harcourt, Inc. All rights reserved. Examples of Macroeconomic Factors that Affect Systematic Risk Variability in growth of money supply Interest rate volatility Variability in: industrial production corporate earnings and cash flow

33. Copyright © 2000 by Harcourt, Inc. All rights reserved. How to Measure Diversification All portfolios on the CML are perfectly positively correlated with each other and with the completely diversified market Portfolio M A completely diversified portfolio would have a correlation with the market portfolio of +1.00 Thus, can use regression R 2 of portfolio’s returns regressed on the “market” portfolio’s returns as a measure of the extent of diversification

34. Copyright © 2000 by Harcourt, Inc. All rights reserved. Diversification and the Elimination of Unsystematic Risk The purpose of diversification is to reduce the standard deviation of the total portfolio This assumes that imperfect correlations exist among securities As you add securities, you expect the average covariance for the portfolio to decline How many securities must you add to obtain a completely diversified portfolio?

35. Copyright © 2000 by Harcourt, Inc. All rights reserved. Diversification and the Elimination of Unsystematic Risk Observe what happens as you increase the sample size of the portfolio by adding securities that have some positive correlation

36. Copyright © 2000 by Harcourt, Inc. All rights reserved. Number of Stocks in a Portfolio and the Standard Deviation of Portfolio Return Figure 9.3 Standard Deviation of Return Number of Stocks in the Portfolio Standard Deviation of the Market Portfolio (systematic risk) Systematic Risk Total Risk Unsystematic (diversifiable) Risk

37. Copyright © 2000 by Harcourt, Inc. All rights reserved. The CML and the Separation Theorem The CML leads all investors to invest in the M portfolio Individual investors should differ in position on the CML depending on risk preferences How an investor gets to a point on the CML is based on financing decisions Risk averse investors will lend part of the portfolio at the risk-free rate (i.e., they will invest part of their portfolios in T-Bills, T-Notes, or T-Bonds) and invest the remainder in the market portfolio

38. Copyright © 2000 by Harcourt, Inc. All rights reserved. The CML and the Separation Theorem Investors preferring more risk might borrow funds at the RFR and invest everything (their own funds plus the borrowed funds) in the market portfolio In other words, more risk-seeking investors will still invest in the market portfolio, but will use margin to leverage up their holdings of this portfolio

39. Copyright © 2000 by Harcourt, Inc. All rights reserved. The CML and the Separation Theorem The decision of both investors is to invest in portfolio M along the CML (the investment decision) I.e., regardless of how risk averse or risk tolerant investors are, the equity portion of their holdings will still be invested in the exact same portfolio, the market portfolio (portfolio M) – this is “the investment decision”

40. Copyright © 2000 by Harcourt, Inc. All rights reserved. The CML and the Separation Theorem The decision to borrow or lend to obtain a point on the CML is a separate decision based on risk preferences (the financing decision) Where risk tolerance levels do make a difference is in whether investors decide to be conservative and put only part of their money in portfolio M and the rest in Treasury bonds (lending, to the federal govt.) or to be more aggressive and put all into M and leverage up their holdings using margin borrowing

41. Copyright © 2000 by Harcourt, Inc. All rights reserved. The CML and the Separation Theorem Tobin refers to this separation of the investment decision from the financing decision as “the separation theorem”

42. Copyright © 2000 by Harcourt, Inc. All rights reserved. A Risk Measure for the CML The Markowitz portfolio model considers the average covariance with all other assets in the portfolio Under capital market theory, the only relevant portfolio is the M portfolio The systematic risk of an asset is defined by its covariance with the completely diversified portfolio M

43. Copyright © 2000 by Harcourt, Inc. All rights reserved. A Risk Measure for the CML Together, this means the only important or relevant measure of an asset’s risk is its systematic risk or covariance with the market portfolio

44. Copyright © 2000 by Harcourt, Inc. All rights reserved. A Risk Measure for the CML: The Market Model Because all individual risky assets are part of the M portfolio, an asset’s rate of return in relation to the return for the M portfolio may be described using the following linear model: where: R it = return for asset i during period t a i = constant term for asset i b i = slope coefficient for asset i R Mt = return for the M portfolio during period t = random error term

45. Copyright © 2000 by Harcourt, Inc. All rights reserved. Variance of Returns for a Risky Asset

46. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Capital Asset Pricing Model: Expected Return and Risk The existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant investment frontier An asset’s covariance with the market portfolio is the relevant risk measure This can be used to determine an appropriate expected rate of return on a risky asset, leading to the Capital Asset Pricing Model (CAPM)

47. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Capital Asset Pricing Model: Expected Return and Risk CAPM indicates what should be the expected or required rates of return on risky assets This helps to value an asset by providing an appropriate discount rate to use in dividend valuation models Conversely, you can compare an estimated rate of return to the required rate of return implied by CAPM – over / under valued ?

48. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Security Market Line (SML) The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Cov i,m ) This is the risk measure for the SML, which describes the relationship between risk and expected return for all portfolios, whether well- diversified or not, as well as for all securities The return for the market portfolio should be consistent with its own risk, which is the covariance of the market with itself - or its variance:

49. Copyright © 2000 by Harcourt, Inc. All rights reserved. Graph of Security Market Line (SML) Figure 9.5 RFR SML

50. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Security Market Line (SML) The equation for the risk-return line is We then redefine as beta

51. Copyright © 2000 by Harcourt, Inc. All rights reserved. Graph of SML with Normalized Systematic Risk Figure 9.6 SML Negative Beta RFR

52. Copyright © 2000 by Harcourt, Inc. All rights reserved. Determining the Expected Rate of Return for a Risky Asset The expected rate of return of a risk asset is determined by the RFR plus a risk premium for the individual asset The risk premium is determined by the systematic risk of the asset (beta) and the prevailing market risk premium (R M -RFR)

53. Copyright © 2000 by Harcourt, Inc. All rights reserved. Determining the Expected Rate of Return for a Risky Asset Assume: RFR = 6% (0.06) R M = 12% (0.12) Implied market risk premium = 6% (0.06) E(R A ) = 0.06 + 0.70 (0.12-0.06) = 0.102 = 10.2% E(R B ) = 0.06 + 1.00 (0.12-0.06) = 0.120 = 12.0% E(R C ) = 0.06 + 1.15 (0.12-0.06) = 0.129 = 12.9% E(R D ) = 0.06 + 1.40 (0.12-0.06) = 0.144 = 14.4% E(R E ) = 0.06 + -0.30 (0.12-0.06) = 0.042 = 4.2%

54. Copyright © 2000 by Harcourt, Inc. All rights reserved. Determining the Expected Rate of Return for a Risky Asset In equilibrium, all assets and all portfolios of assets should plot on the SML Any security with an estimated return that plots above the SML is underpriced Any security with an estimated return that plots below the SML is overpriced A superior investor must derive value estimates for assets that are consistently superior to the consensus market evaluation to earn better risk-adjusted rates of return than the average investor

55. Copyright © 2000 by Harcourt, Inc. All rights reserved. Identifying Undervalued and Overvalued Assets Compare the required rate of return to the expected rate of return for a specific risky asset using the SML over a specific investment horizon to determine if it is an appropriate investment Independent estimates of return for the securities provide price and dividend outlooks

56. Copyright © 2000 by Harcourt, Inc. All rights reserved. Price, Dividend, and Rate of Return Estimates Table 9.1

57. Copyright © 2000 by Harcourt, Inc. All rights reserved. Comparison of Required Rate of Return to Estimated Rate of Return Table 9.2

58. Copyright © 2000 by Harcourt, Inc. All rights reserved. Plot of Estimated Returns on SML Graph Figure 9.7 SML.20.40.60.801.20 1.40 1.60 1.80 -.40 -.20.22.20.18.16.14.12 R m.10.08.06.04.02 A B C D E

59. Copyright © 2000 by Harcourt, Inc. All rights reserved. Calculating Systematic Risk: The Characteristic Line The systematic risk input of an individual asset is derived from a regression model, referred to as the asset’s characteristic line with the model portfolio: where: R i,t = the rate of return for asset i during period t R M,t = the rate of return for the market portfolio M during t

60. Copyright © 2000 by Harcourt, Inc. All rights reserved. Scatter Plot of Rates of Return Figure 9.8 RMRM RiRi The characteristic line is the regression line of the best fit through a scatter plot of rates of return

61. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Impact of the Time Interval Number of observations and time interval used in the regression vary Value Line Investment Services (VL) uses weekly rates of return over five years (260 obs.) Merrill Lynch, Pierce, Fenner & Smith (ML) uses monthly return over five years (60 obs.) There is no “correct” interval for analysis Weak relationship between VL & ML betas due to difference in intervals used Interval effect impacts smaller firms more

62. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Effect of the Market Proxy The market portfolio of all risky assets must be represented in computing an asset’s characteristic line Standard & Poor’s 500 Composite Index is most often used –Large proportion of the total market value of U.S. stocks –Value weighted series

63. Copyright © 2000 by Harcourt, Inc. All rights reserved. Weaknesses of Using S&P 500 as the Market Proxy –Includes only U.S. stocks –The theoretical market portfolio should include U.S. and non-U.S. stocks and bonds, real estate, coins, stamps, art, antiques, and any other marketable risky asset from around the world

64. Copyright © 2000 by Harcourt, Inc. All rights reserved. Comparing Market Proxies Calculating Beta for Coca-Cola using Morgan Stanley (M-S) World Equity Index and S&P 500 as market proxies results in a 1.27 beta when compared with the M-S index, but a 1.01 beta compared to the S&P 500 The difference is exaggerated by the small sample size (12 months) used, but selecting the market proxy can make a significant difference Here are the computations from page 303:

65. Copyright © 2000 by Harcourt, Inc. All rights reserved. Computation of Beta of Coca-Cola with Selected Indexes Table 9.3

66. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) CAPM is criticized because of, among other things, the difficulties in selecting a proxy for the market portfolio as a benchmark An alternative pricing theory with fewer assumptions was developed: Arbitrage Pricing Theory

67. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of Arbitrage Pricing Theory (APT) 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be presented as K factor model (to be described)

68. Copyright © 2000 by Harcourt, Inc. All rights reserved. Assumptions of CAPM That Were Not Required by APT APT does not assume: A market portfolio that contains all risky assets, and is mean-variance efficient Normally distributed security returns Quadratic utility function

69. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period RiRi

70. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period = expected return for asset i RiEiRiEi

71. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period = expected return for asset i = reaction in asset i’s returns to movements in a common factor R i E i b ik

72. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period = expected return for asset i = reaction in asset i’s returns to movements in a common factor = a common factor with a zero mean that influences the returns on all assets R i E i b ik

73. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period = expected return for asset i = reaction in asset i’s returns to movements in a common factor = a common factor with a zero mean that influences the returns on all assets = a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero R i E i b ik

74. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period = expected return for asset i = reaction in asset i’s returns to movements in a common factor = a common factor with a zero mean that influences the returns on all assets = a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero = number of assets R i E i b ik N

75. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets:

76. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: –Inflation

77. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: –Inflation –Growth in GNP

78. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: –Inflation –Growth in GNP –Major political upheavals

79. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: –Inflation –Growth in GNP –Major political upheavals –Changes in interest rates

80. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: –Inflation –Growth in GNP –Major political upheavals –Changes in interest rates –And potentially many more….

81. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: –Inflation –Growth in GNP –Major political upheavals –Changes in interest rates –And potentially many more…. Contrast with CAPM insistence that only beta is relevant

82. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) b ik determine how each asset reacts to this common factor Each asset may be affected by growth in GNP, but the effects will differ In application of the theory, the factors are not identified Similar to the CAPM, the unique effects (the  i ’s) are independent and will be diversified away in a large portfolio Caveat: impossible to completely diversify away unique risk if all the relevant systematic risk factors are not correctly identified

83. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic-risk portfolio is zero when the unique effects are diversified away The expected return on any asset i (E i ) can be expressed as:

84. Copyright © 2000 by Harcourt, Inc. All rights reserved. Arbitrage Pricing Theory (APT) where: = the expected return on an asset with zero systematic risk where = the risk premium related to each of the common factors - for example the risk premium related to interest rate risk b ij = the pricing relationship between the risk premium and asset i - that is how responsive asset i is to this common factor j

85. Copyright © 2000 by Harcourt, Inc. All rights reserved. Example of Two Stocks and a Two-Factor Model = changes in the rate of inflation. The risk premium related to this factor is 1 percent for every 1 percent change in the rate = percent growth in real GNP. The average risk premium related to this factor is 2 percent for every 1 percent change in the rate = the rate of return on a zero-systematic-risk asset (zero beta: b oj =0) is 3 percent

86. Copyright © 2000 by Harcourt, Inc. All rights reserved. Example of Two Stocks and a Two-Factor Model = the response of asset X to changes in the rate of inflation is 0.50 = the response of asset Y to changes in the rate of inflation is 2.00 = the response of asset X to changes in the growth rate of real GNP is 1.50 = the response of asset Y to changes in the growth rate of real GNP is 1.75

87. Copyright © 2000 by Harcourt, Inc. All rights reserved. Example of Two Stocks and a Two-Factor Model =.03 + (.01)b i1 + (.02)b i2 E x =.03 + (.01)(0.50) + (.02)(1.50) =.065 = 6.5% E y =.03 + (.01)(2.00) + (.02)(1.75) =.085 = 8.5%

88. Copyright © 2000 by Harcourt, Inc. All rights reserved. Empirical Tests of the APT Studies by Roll and Ross and by Chen support APT by explaining different rates of return with some better results than CAPM Reinganum’s study did not explain small- firm results Dhrymes and Shanken question the usefulness of APT because it was not possible to identify the factors

89. Copyright © 2000 by Harcourt, Inc. All rights reserved. Summary When you combine the risk-free asset with any risky asset on the Markowitz efficient frontier, you derive a set of straight-line portfolio possibilities

90. Copyright © 2000 by Harcourt, Inc. All rights reserved. Summary The dominant line is tangent to the efficient frontier –Referred to as the capital market line (CML) –All investors should target points along this line depending on their risk preferences

91. Copyright © 2000 by Harcourt, Inc. All rights reserved. Summary All investors want to invest in the risky portfolio, so this market portfolio must contain all risky assets –The investment decision and financing decision can be separated –Everyone wants to invest in the market portfolio –Investors finance based on risk preferences

92. Copyright © 2000 by Harcourt, Inc. All rights reserved. Summary The relevant risk measure for an individual risky asset is its systematic risk or covariance with the market portfolio –Once you have determined this Beta measure and a security market line, you can determine the required return on a security based on its systematic risk

93. Copyright © 2000 by Harcourt, Inc. All rights reserved. Summary Assuming security markets are not always completely efficient, you can identify undervalued and overvalued securities by comparing your estimate of the rate of return on an investment to its required rate of return

94. Copyright © 2000 by Harcourt, Inc. All rights reserved. Summary The Arbitrage Pricing Theory (APT) model makes simpler assumptions, and is more intuitive, but test results are mixed at this point

95. Copyright © 2000 by Harcourt, Inc. All rights reserved. The Internet Investments Online www.valueline.com www.barra.com www.stanford.edu/~wfsharpe.com

96. Copyright © 2000 by Harcourt, Inc. All rights reserved. End of Chapter 9 –An Introduction to Asset Pricing Models

97. Copyright © 2000 by Harcourt, Inc. All rights reserved. Future topics Chapter 10 Extensions of Capital Asset Pricing Model Relaxation of Assumptions –Effect on SML and CML Empirical Tests of the Theory

98. Copyright © 2000 by Harcourt, Inc. All rights reserved.