The Capital Asset Pricing Model.ppt

1、CHAPTER 9,The Capital Asset Pricing Model,9-2,It is the equilibrium model that underlies all modern financial theory Derived using principles of diversification with simplified assumptions Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development,Capital Asset Pricing Model

2、 (CAPM),9-3,Assumptions,Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes and transaction costs,Information is costless and available to all investors Investors are rational mean-variance optimizers There are homogeneou

3、s expectations,9-4,All investors will hold the same portfolio for risky assets market portfolio Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value,Resulting Equilibrium Conditions,9-5,Risk premium on the market depen

4、ds on the average risk aversion of all market participants Risk premium on an individual security is a function of its covariance with the market,Resulting Equilibrium Conditions,9-6,Figure 9.1 The Efficient Frontier and the Capital Market Line,9-7,Market Risk Premium,The risk premium on the market

5、portfolio will be proportional to its risk and the degree of risk aversion of the investor:,9-8,The risk premium on individual securities is a function of the individual securitys contribution to the risk of the market portfolio. An individual securitys risk premium is a function of the covariance o

6、f returns with the assets that make up the market portfolio.,Return and Risk For Individual Securities,9-9,GE Example,Covariance of GE return with the market portfolio: Therefore, the reward-to-risk ratio for investments in GE would be:,9-10,GE Example,Reward-to-risk ratio for investment in market p

7、ortfolio: Reward-to-risk ratios of GE and the market portfolio should be equal:,9-11,GE Example,The risk premium for GE: Restating, we obtain:,9-12,Expected Return-Beta Relationship,CAPM holds for the overall portfolio because: This also holds for the market portfolio:,9-13,Figure 9.2 The Security M

8、arket Line,9-14,Figure 9.3 The SML and a Positive-Alpha Stock,9-15,The Index Model and Realized Returns,To move from expected to realized returns, use the index model in excess return form: The index model beta coefficient is the same as the beta of the CAPM expected return-beta relationship.,9-16,F

9、igure 9.4 Estimates of Individual Mutual Fund Alphas, 1972-1991,9-17,Is the CAPM Practical?,CAPM is the best model to explain returns on risky assets. This means: Without security analysis, is assumed to be zero. Positive and negative alphas are revealed only by superior security analysis.,9-18,Is t

10、he CAPM Practical?,We must use a proxy for the market portfolio. CAPM is still considered the best available description of security pricing and is widely accepted.,9-19,Econometrics and the Expected Return-Beta Relationship,Statistical bias is easily introduced. Miller and Scholes paper demonstrate

11、d how econometric problems could lead one to reject the CAPM even if it were perfectly valid.,9-20,Extensions of the CAPM,Zero-Beta Model Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks Consideration of labor income and non-traded assets,9-21,Extensions of

12、 the CAPM,Mertons Multiperiod Model and hedge portfolios Incorporation of the effects of changes in the real rate of interest and inflation,Consumption-based CAPM Rubinstein, Lucas, and Breeden Investors allocate wealth between consumption today and investment for the future,9-22,Liquidity and the C

13、APM,Liquidity: The ease and speed with which an asset can be sold at fair market value Illiquidity Premium: Discount from fair market value the seller must accept to obtain a quick sale. Measured partly by bid-asked spread As trading costs are higher, the illiquidity discount will be greater.,9-23,F

14、igure 9.5 The Relationship Between Illiquidity and Average Returns,9-24,Liquidity Risk,In a financial crisis, liquidity can unexpectedly dry up. When liquidity in one stock decreases, it tends to decrease in other stocks at the same time. Investors demand compensation for liquidity risk Liquidity be

15、tas,9-25,CHAPTER 10,Arbitrage Pricing Theory and Multifactor Models of Risk and Return,9-26,Single Factor Model,Returns on a security come from two sources: Common macro-economic factor Firm specific events Possible common macro-economic factors Gross Domestic Product Growth Interest Rates,9-27,Sing

16、le Factor Model Equation,ri = Return on security i= Factor sensitivity or factor loading or factor beta F = Surprise in macro-economic factor (F could be positive or negative but has expected value of zero) ei = Firm specific events (zero expected value),9-28,Multifactor Models,Use more than one fac

17、tor in addition to market return Examples include gross domestic product, expected inflation, interest rates, etc. Estimate a beta or factor loading for each factor using multiple regression.,9-29,Multifactor Model Equation,ri = Return for security i GDP = Factor sensitivity for GDP IR = Factor sens

18、itivity for Interest Rate ei = Firm specific events,9-30,Multifactor SML Models,GDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP IR = Factor sensitivity for Interest Rate RPIR = Risk premium for Interest Rate,9-31,Interpretation,The expected return on a security is the sum of:,The risk-

19、free rate The sensitivity to GDP times the risk premium for bearing GDP risk The sensitivity to interest rate risk times the risk premium for bearing interest rate risk,9-32,Arbitrage Pricing Theory,Arbitrage occurs if there is a zero investment portfolio with a sure profit.,Since no investment is r

20、equired, investors can create large positions to obtain large profits.,9-33,Arbitrage Pricing Theory,Regardless of wealth or risk aversion, investors will want an infinite position in the risk-free arbitrage portfolio.,In efficient markets, profitable arbitrage opportunities will quickly disappear.,

21、9-34,APT & Well-Diversified Portfolios,rP = E (rP) + bPF + eP F = some factor For a well-diversified portfolio, eP approaches zero as the number of securities in the portfolio increases and their associated weights decrease,9-35,Figure 10.1 Returns as a Function of the Systematic Factor,9-36,Figure

22、10.2 Returns as a Function of the Systematic Factor: An Arbitrage Opportunity,9-37,Figure 10.3 An Arbitrage Opportunity,9-38,Figure 10.4 The Security Market Line,9-39,APT Model,APT applies to well diversified portfolios and not necessarily to individual stocks. With APT it is possible for some indiv

23、idual stocks to be mispriced - not lie on the SML. APT can be extended to multifactor models.,9-40,APT and CAPM,APT,Equilibrium means no arbitrage opportunities. APT equilibrium is quickly restored even if only a few investors recognize an arbitrage opportunity. The expected returnbeta relationship

24、can be derived without using the true market portfolio.,CAPM,Model is based on an inherently unobservable “market” portfolio. Rests on mean-variance efficiency. The actions of many small investors restore CAPM equilibrium. CAPM describes equilibrium for all assets.,9-41,Multifactor APT,Use of more t

25、han a single systematic factor Requires formation of factor portfolios What factors? Factors that are important to performance of the general economy What about firm characteristics?,9-42,Two-Factor Model,The multifactor APT is similar to the one-factor case.,9-43,Two-Factor Model,Track with diversified factor portfolios: beta=1 for one of the factors and 0 for all other factors. The factor portfolios track a particular source of macroe