®1999 South-Western College Publishing 1 Chapter 9 Risk And Return: The Linear Relationships And The Capital Asset Pricing Model

®1999 South-Western College Publishing 2 Characteristics Of Indifference Curves All Combinations [E(R),  R ]All Combinations [E(R),  R ] –Provide the investor with the same level of utility Moving to a Higher Indifference CurveMoving to a Higher Indifference Curve –Increases the investors utility SubjectiveSubjective –Slopes differ from one investor to another

®1999 South-Western College Publishing 3 Capital Market Theory: An Overview Capital market theory extends portfolio theory and develops a model for pricing all risky assetsCapital 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 assetCapital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset

®1999 South-Western College Publishing 4 Assumptions of Capital Market Theory 1. All investors are Markowitz efficient investors who want to target points on 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.

®1999 South-Western College Publishing 5 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.

®1999 South-Western College Publishing 6 Assumptions of Capital Market Theory 3. All investors have homogeneous expectations; that is, they estimate identical probability distributions for future rates of return. –Again, this assumption can be relaxed. As long as the differences in expectations are not vast, their effects are minor.

®1999 South-Western College Publishing 7 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.

®1999 South-Western College Publishing 8 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.

®1999 South-Western College Publishing 9 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.

®1999 South-Western College Publishing 10 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.

®1999 South-Western College Publishing 11 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.

®1999 South-Western College Publishing 12 Assumptions of Capital Market Theory Some of these assumptions are unrealisticSome 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.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.Judge a theory on how well it explains and helps predict behavior, not on its assumptions.

®1999 South-Western College Publishing 13 Risk-Free Asset An asset with zero varianceAn asset with zero variance Zero correlation with all other risky assetsZero correlation with all other risky assets Provides the risk-free rate of return (RFR)Provides the risk-free rate of return (RFR) Will lie on the vertical axis of a portfolio graphWill lie on the vertical axis of a portfolio graph

®1999 South-Western College Publishing 14 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.

®1999 South-Western College Publishing 15 Combining a Risk-Free Asset with a Risky Portfolio Expected return the weighted average of the two returns This is a linear relationship

®1999 South-Western College Publishing 16 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

®1999 South-Western College Publishing 17 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.

®1999 South-Western College Publishing 18 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.

®1999 South-Western College Publishing 19 Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier RFR M C A B D

®1999 South-Western College Publishing 20 The efficient frontier is expanded when risk-free borrowing or lending is allowed. Slide 3

®1999 South-Western College Publishing 21 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

®1999 South-Western College Publishing 22 Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier RFR M CML Borrowing Lending

®1999 South-Western College Publishing 23 E(R) CML  E(R m ) [E(R m ) - r]/  m mm CML

®1999 South-Western College Publishing 24 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

®1999 South-Western College Publishing 25 The Market Portfolio Because the market is in equilibrium, all assets are included in this portfolio in proportion to their market value

®1999 South-Western College Publishing 26 The Market Portfolio Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away

®1999 South-Western College Publishing 27 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 change over time

®1999 South-Western College Publishing 28 Examples of Macroeconomic Factors Affecting Systematic Risk Variability in growth of money supplyVariability in growth of money supply Interest rate volatilityInterest rate volatility Variability inVariability in industrial production industrial production corporate earnings corporate earnings and cash flow and cash flow

®1999 South-Western College Publishing 29 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

®1999 South-Western College Publishing 30 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?

®1999 South-Western College Publishing 31 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

®1999 South-Western College Publishing 32 Number of Stocks in a Portfolio and the Standard Deviation of Portfolio Return 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

®1999 South-Western College Publishing 33 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 and invest the remainder in the market portfolio

®1999 South-Western College Publishing 34 The CML and the Separation Theorem Investors preferring more risk might borrow funds at the RFR and invest everything in the market portfolio

®1999 South-Western College Publishing 35 The CML and the Separation Theorem The decision of both investors is to invest in portfolio M along the CML (the investment decision)

®1999 South-Western College Publishing 36 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 (financing decision)

®1999 South-Western College Publishing 37 The CML and the Separation Theorem Tobin refers to this separation of the investment decision from the financing decision the separation theorem

®1999 South-Western College Publishing 38 Separation Property Two StagesTwo Stages –Find portfolio m objective –Maximize utility by borrowing and lending subjective Linear RelationshipLinear Relationship –Between E(R) and 

®1999 South-Western College Publishing 39 A Risk Measure for the CML Covariance with the M portfolio is the systematic risk of an asset The Markowitz portfolio model considers the average covariance with all other assets in the portfolio The only relevant portfolio is the M portfolio

®1999 South-Western College Publishing 40 A Risk Measure for the CML Together, this means the only important consideration is the asset’s covariance with the market portfolio

®1999 South-Western College Publishing 41 Systematic Risk Only Systematic Risk Is Relevant!

®1999 South-Western College Publishing 42 A Risk Measure for the CML 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

®1999 South-Western College Publishing 43 Variance of Returns for a Risky Asset

®1999 South-Western College Publishing 44 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 frontierThe existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant frontier An asset’s covariance with the market portfolio is the relevant risk measureAn 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 - the capital asset pricing model (CAPM)This can be used to determine an appropriate expected rate of return on a risky asset - the capital asset pricing model (CAPM)

®1999 South-Western College Publishing 45 The Capital Asset Pricing Model: Expected Return and Risk CAPM indicates what should be the expected or required rates of return on risky assetsCAPM 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 modelsThis helps to value an asset by providing an appropriate discount rate to use in dividend valuation models You can compare an estimated rate of return to the required rate of return implied by CAPM - over/ under valued ?You can compare an estimated rate of return to the required rate of return implied by CAPM - over/ under valued ?

®1999 South-Western College Publishing 46 The Security Market Line (SML) The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Cov i,m )The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Cov i,m ) This is shown as the risk measureThis is shown as the risk measure 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: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:

®1999 South-Western College Publishing 47 Graph of Security Market Line (SML) RFR SML

®1999 South-Western College Publishing 48 The Security Market Line (SML) The equation for the risk-return line is We then define as beta

®1999 South-Western College Publishing 49 Graph of SML with Normalized Systematic Risk SML Negative Beta RFR

®1999 South-Western College Publishing 50 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)

®1999 South-Western College Publishing 51 Risk Premium [E(R m ) - r] is the Risk Premium on the Portfolio m[E(R m ) - r] is the Risk Premium on the Portfolio m E(R m ) - r = [E(R m ) - r]  iE(R m ) - r = [E(R m ) - r]  i The Larger the , the Larger the Risk PremiumThe Larger the , the Larger the Risk Premium

®1999 South-Western College Publishing 52 Determining the Expected Rate of Return for a Risky Asset Assume: RFR = 6% (0.06) R M = 12% (0.12) R M = 12% (0.12) Implied market risk premium = 6% (0.06) E(R A ) = ( ) = = 10.2% E(R B ) = ( ) = = 12.0% E(R C ) = ( ) = = 12.9% E(R D ) = ( ) = = 14.4% E(R E ) = ( ) = = 4.2%

®1999 South-Western College Publishing 53 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

®1999 South-Western College Publishing 54 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

®1999 South-Western College Publishing 55 Price, Dividend, and Rate of Return Estimates

®1999 South-Western College Publishing 56 Comparison of Required Rate of Return to Estimated Rate of Return

®1999 South-Western College Publishing 57 Plot of Estimated Returns on SML Graph SML R m A B C D E

®1999 South-Western College Publishing 58 CAPM For Stock Selection Excess or Abnormal ReturnExcess or Abnormal Return [E(R p ) - r] =  i + [E(R m ) - r]  i[E(R p ) - r] =  i + [E(R m ) - r]  i –Alpha  i = excess return Market is EfficientMarket is Efficient –  i will disappear [E(R p ) - r] = [E(R m ) - r]  i[E(R p ) - r] = [E(R m ) - r]  i

®1999 South-Western College Publishing 59 CAPM AS A Screening Tool High-Alpha StocksHigh-Alpha Stocks Low-Alpha StocksLow-Alpha Stocks Final AnalysisFinal Analysis –Dividends –Growth –Earnings surprise –Other variables

®1999 South-Western College Publishing 60 Proof Of The CAPM SML Holds for all Efficient Portfolios Whose Returns are R pSML Holds for all Efficient Portfolios Whose Returns are R p E(R p ) = r + [E(R m ) - r]  p In EquilibriumIn Equilibrium –The linear relationship between E(R) and  hold SMLSML

®1999 South-Western College Publishing 61 EPCoR EquilibriumEquilibrium All Assets in the PortfolioAll Assets in the Portfolio –Contribute the same % to Portfolio risk Portfolio risk Portfolio risk premiumPortfolio risk premium

®1999 South-Western College Publishing 62 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

®1999 South-Western College Publishing 63 Scatter Plot of Rates of Return RMRM RiRi The characteristic line is the regression line of the best fit through a scatter plot of rates of return

®1999 South-Western College Publishing 64 What Is Beta (  )? Slope of the Characteristic LineSlope of the Characteristic Line Measures Risk SystematicMeasures Risk Systematic –Variance –Covariance of other assets in the portfolio –Individual assets –Portfolios The Larger the The Larger the  –The more the risk

®1999 South-Western College Publishing 65 What Is The Meaning Of  ?  i = 1 = Neutral Stock Market Stock  i = 1 = Neutral Stock Market Stock  i > 1 = Aggressive Stock  i > 1 = Aggressive Stock  i < 1 = Defensive Stock  i < 1 = Defensive Stock  r = 0 = Risk-Free Asset  r = 0 = Risk-Free Asset

®1999 South-Western College Publishing 66 E(R i )  1.0 E(R m ) SML Neutral Stocks Aggressive Stocks Defensive Stocks SML E(R m - r) E(R i ) = r + [E(R m ) - r]  i

®1999 South-Western College Publishing 67 Characteristic Line Defensive Neutral Aggressive RiRi RmRm

®1999 South-Western College Publishing 68 The Impact of the Time Interval Number of observations and time interval used in regression vary Value Line Investment Services (VL) uses weekly rates of return over five years Merrill Lynch, Pierce, Fenner & Smith (ML) uses monthly return over five years 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

®1999 South-Western College Publishing 69 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

®1999 South-Western College Publishing 70 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

®1999 South-Western College Publishing 71 World Market Portfolio Include International SecuritiesInclude International Securities Steeper CMLSteeper CML Less Than Perfect CorrelationLess Than Perfect Correlation ObjectiveObjective –Increase the number of assets available –Decrease market portfolio risk Practical ReasonsPractical Reasons

®1999 South-Western College Publishing 72 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:

®1999 South-Western College Publishing 73 Computation of Beta of Coca-Cola with Selected Indexes

®1999 South-Western College Publishing 74 Summary of CAPM Theory When you combine the risk-free asset with any risky asset on the Markowitz efficient frontier, you derive a set of straight-line portfolio possibilitiesWhen you combine the risk-free asset with any risky asset on the Markowitz efficient frontier, you derive a set of straight-line portfolio possibilities

®1999 South-Western College Publishing 75 Summary of CAPM Theory The dominant line is tangent to the efficient frontierThe 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

®1999 South-Western College Publishing 76 Summary of CAPM Theory All investors want to invest in the risky portfolio, so this market portfolio must contain all risky assetsAll 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

®1999 South-Western College Publishing 77 Summary of CAPM Theory The relevant risk measure for an individual risky asset is its systematic risk or covariance with the market portfolioThe 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

®1999 South-Western College Publishing 78 Summary of CAPM Theory 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 returnAssuming 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

®1999 South-Western College Publishing 79 Summary of CAPM Theory The Arbitrage Pricing Theory (APT) model makes simpler assumptions, and is more intuitive, but test results are mixed at this pointThe Arbitrage Pricing Theory (APT) model makes simpler assumptions, and is more intuitive, but test results are mixed at this point

®1999 South-Western College Publishing 80 Relaxing the Assumptions of the CAPM CAPM assumption: all investors can borrow or lend at the risk-free rate - unrealisticCAPM assumption: all investors can borrow or lend at the risk-free rate - unrealistic –Differential borrowing and lending rates –Unlimited lending at risk-free rate –Borrowing at higher rate

®1999 South-Western College Publishing 81 Investment Alternatives When The Cost of Borrowing is Higher Than The Cost of Lending Figure 10.1 E(R) RbRb RFR Risk (standard deviation  ) F G K

®1999 South-Western College Publishing 82 Relaxing the Assumptions of the CAPM Zero-beta portfolio: create a portfolio that is uncorrelated to the market (beta 0)Zero-beta portfolio: create a portfolio that is uncorrelated to the market (beta 0) –The return of the zero-beta portfolio may differ from the risk-free rate Any combination of portfolios on the efficient frontier will be on the frontierAny combination of portfolios on the efficient frontier will be on the frontier Any efficient portfolio will have associated with it a zero-beta portfolioAny efficient portfolio will have associated with it a zero-beta portfolio

®1999 South-Western College Publishing 83 Implications of Black’s Zero-beta model The expected return of any security can be expressed as a linear relationship of any two efficient portfoliosThe expected return of any security can be expressed as a linear relationship of any two efficient portfolios E(R i ) = E(R z ) +  i [E(R m ) - E(R z )] If CAPM defines the relationship between risk and return, then the return on the zero-beta portfolio should equal RFIf CAPM defines the relationship between risk and return, then the return on the zero-beta portfolio should equal RF To test this - identify a market portfolio and solve for the return of a zero-beta portfolioTo test this - identify a market portfolio and solve for the return of a zero-beta portfolio

®1999 South-Western College Publishing 84 Security Market Line With A Zero-Beta Portfolio Figure 10.2 E(R) E(R m ) i i SML M E(R z ) E(R m ) - E(R z )

®1999 South-Western College Publishing 85 Relaxing the Assumptions of the CAPM Transaction costsTransaction costs –affect mispricing corrections –affect diversification

®1999 South-Western College Publishing 86 Security Market Line With Transaction Costs Figure 10.3 E(R) E(R m ) i i SML E(R z ) E(RFR) or

®1999 South-Western College Publishing 87 Relaxing the Assumptions of the CAPM Heterogenous expectationsHeterogenous expectations –If all investors have different expectations about risk and return, each would have a unique CML and/or SML, and the composite graph would be a band of lines with a breadth determined by the divergence of expectations Planning periodsPlanning periods –CAPM is a one period model, and the period employed should be the planning period for the individual investor, which will vary by individual, affecting both the CML and the SML

®1999 South-Western College Publishing 88 GCAPM “General Capital Asset Pricing Model”“General Capital Asset Pricing Model” Each Investor Holds A Different PortfolioEach Investor Holds A Different Portfolio Each Portfolio Has Entails Different  ’sEach Portfolio Has Entails Different  ’s Asset’s  will be a weighted average of all of the portfolio  ’sAsset’s  will be a weighted average of all of the portfolio  ’s Allows Investors to Hold a Relatively Small Number of AssetsAllows Investors to Hold a Relatively Small Number of Assets Can be used in cases where the above three assumptions (transactions costs, heterogeneous expectations, different planning periods) may not holdCan be used in cases where the above three assumptions (transactions costs, heterogeneous expectations, different planning periods) may not hold

®1999 South-Western College Publishing 89 Empirical Testing of CAPM How stable is the measure of systematic risk (beta)?How stable is the measure of systematic risk (beta)? Is there a positive linear relationship as hypothesized between beta and the rate of return on risky assets?Is there a positive linear relationship as hypothesized between beta and the rate of return on risky assets? How well do returns conform to the SML equation?How well do returns conform to the SML equation?

®1999 South-Western College Publishing 90 Empirical Testing of CAPM Beta is not stable for individual stocks over short periods of time (52 weeks)Beta is not stable for individual stocks over short periods of time (52 weeks) Stability for portfolios increase significantlyStability for portfolios increase significantly The larger the portfolio and the longer the period, the more stable the beta of the portfolioThe larger the portfolio and the longer the period, the more stable the beta of the portfolio Betas tend to regress toward the meanBetas tend to regress toward the mean

®1999 South-Western College Publishing 91 Empirical Testing of CAPM Different estimates of beta for a stock vary typically in data usedDifferent estimates of beta for a stock vary typically in data used Value Line estimates use 260 weekly observationsValue Line estimates use 260 weekly observations Merrill Lynch estimates using 60 monthly observationsMerrill Lynch estimates using 60 monthly observations Securities market value affects the size and direction of the interval affectSecurities market value affects the size and direction of the interval affect

®1999 South-Western College Publishing 92 Relationship Between Systematic Risk and Return Sharpe and Cooper: positive, but non-linearSharpe and Cooper: positive, but non-linear Douglas: intercept higher than the risk-free rateDouglas: intercept higher than the risk-free rate Miller and Scholes: possible error in Douglas findingsMiller and Scholes: possible error in Douglas findings Black, Jensen, and Scholes: positive linear relationship between monthly excess return and portfolio betaBlack, Jensen, and Scholes: positive linear relationship between monthly excess return and portfolio beta Fama and McBeth: supported the CAPM with the intercept equal to the RFRFama and McBeth: supported the CAPM with the intercept equal to the RFR

®1999 South-Western College Publishing 93 Relationship Between Systematic Risk and Return Effect of skewness on the relationshipEffect of skewness on the relationship –preference for high risk and returns Effect of size, P/E and leverageEffect of size, P/E and leverage Effect of book-to-market valueEffect of book-to-market value –The Fama-French Study

®1999 South-Western College Publishing 94 Shortcomings Of CAPM  is Dead  is Dead  is Alive  is Alive  is Alive, but not well  is Alive, but not well

®1999 South-Western College Publishing 95 The Market Portfolio: Theory Versus Practice Difficult to test full marketDifficult to test full market Portfolio used as market proxy may be correlated to true market portfolioPortfolio used as market proxy may be correlated to true market portfolio Benchmark errorBenchmark error

®1999 South-Western College Publishing 96 Criticism of CAPM by Richard Roll Limits on tests: only testable implication from CAPM is whether the market portfolio lies on the efficient frontierLimits on tests: only testable implication from CAPM is whether the market portfolio lies on the efficient frontier Range of SML’s - infinite number of possible SML’s, each of which produces a unique estimate of betaRange of SML’s - infinite number of possible SML’s, each of which produces a unique estimate of beta

®1999 South-Western College Publishing 97 Criticism of CAPM by Richard Roll Market efficiency effects - substituting a proxy, such as the S&P 500 creates two problemsMarket efficiency effects - substituting a proxy, such as the S&P 500 creates two problems –Proxy does not represent the true market portfolio –Even if the proxy is not efficient, the market portfolio might be

®1999 South-Western College Publishing 98 Criticism of CAPM by Richard Roll Conflicts between proxies - different substitutes may be highly correlated even though some may be efficient and others are not, which can lead to different conclusions regarding beta risk/return relationshipsConflicts between proxies - different substitutes may be highly correlated even though some may be efficient and others are not, which can lead to different conclusions regarding beta risk/return relationships So, CAPM is not testable - but it still has value and must be used carefullySo, CAPM is not testable - but it still has value and must be used carefully Stephen Ross devised an alternative way to look at asset pricing - APTStephen Ross devised an alternative way to look at asset pricing - APT