《金融学教学课件》bodie2e-cha.ppt

Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,1,Chapter 13:Capital Market Equilibrium,ObjectiveThe Theory of the CAPMUse of CAPM in benchmarking Using CAPM to determine correct rate for discounting,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,2,Introduction,CAPM is a theory about equilibrium prices in the markets for risky assetsIt is important because it providesa justification for the widespread practice of passive investing called indexinga way to estimate expected rates of return for use in evaluating stocks and projects.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,3,Introduction,Relationship between CAPM and other contents we have learned so far.In part III we learned the valuation of securities and projects,by using NPV-rule,but we didnt consider the influence of risk.In part IV we learned that risk should be managed by the mean-variance method,in which risk should get its reward,and would influence the valuation of portfolios or projects.CAPM would combine the previous 2 parts,and give us a tool of valuation WITH risk.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,4,Chapter 13 Contents,13.1 The Capital Asset Pricing Model in Brief13.2 Determining the Risk Premium on the Market Portfolio 13.3 Risk Premiums on Individual Securities:SML13.4 Using the CAPM in Portfolio Selection13.5 Valuation&Regulating Rates of Return13.6 Modifications and Alternatives to the CAPM,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,5,13.1 The Capital Asset Pricing Model in Brief,Developed in the 1960s by Sharp,and independently by Lintner,and MossinIt answers the questionWhat would equilibrium risk premiums be if people had the same set of forecasts of expected returns,risk,and correlations all chose their portfolios according the principles of efficient diversification,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,6,So whats wrong with ms-analysis,The assumptions of the last chapter appeared fully acceptableIn fact it may appear to be pedantic to mention them at allWhy develop a new model for risk-return if the present model aint broke?,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,7,ms-analysis:Estimation,We did not spell it out,but if you recall the mnemonic for obtaining the portfolio volatility in the ms-model,(given n-shares in the portfolio,)we needed n-means(no problem)n-standard deviations(no problem)n*(n-1)/2 correlations(big problem),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,8,ms-analysis:Estimation,All parameters need estimation,and there are n*(n+1)/2+n parametersAssume a portfolio of,say,2,000 shares represent the market,then we need to estimate more than 2,000,000 parameters,most of which are correlations,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,9,ms-analysis:Estimation,Recall that when you estimate parameters,it is done with only a given level of confidence(confidential interval)Confidence improves with the number of observationsIn practice the parameters have time dependence,so old data introduces errorFor 2,000 shares,and a 99%confidence,about 20,000 parameters will be in error,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,10,ms-analysis:Estimation,The errors may,or may not,be significant to your investment decision,but their existence calls for further analysisIn any case,the data collection,verification,and processing,is a significant use of analytical resources,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,11,ms-analysis:Wishes,After we have the estimated parameters,finding the optimal portfolio requires quadratic programming,and this again requires heavy use of computational resourcesThe problem is similar to knowing the position and velocity of every star in the Milky Way,and attempting to predict their futures by computing individual interactions,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,12,Guidance Principles for Simplification,An important principle of financial modeling is to create equations that capture the key factors parsimoniouslyAnother important principle is to attempt to develop simple modelsLinear models are then preferred to quadratic models,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,13,The Astrophysics of Finance,In the Milky Way problem,an astronomer should specify exactly what needs to be predicted,and give attention to the variables that most affect itSo,if he wants to know when the next star will come close enough to Sol to disturb the Oort cloud then close stars need individual analysisdistant stars may be treated homogeneously,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,14,CAPM:basic idea,The fundamental idea of CAPM is that in equilibrium the market rewards people for bearing risk,or,the old saying:high income with high risk.But not every kind of risk would be rewarded.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,15,Specifying the Model,In the last chapter we examined diversifying a homogenous portfolio,and we observed that there were two kinds of riskdiversifiable or individual riskNondiversifiable or market risk,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,16,Specifying the Model,We also observed that in the limit as the number of securities becomes large,we obtained the formulaThis formula tells us that the correlations are of crucial importance in the relationship between a portfolio risk and the stock risk,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,17,Specifying the Model,In the homogenous model,we saw that there was individual-and market-riskAssume that each equitys return is the composition of two random variables:one associated with the markets returnone associated with the company-specific return,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,18,Assumptions,Company-specific return on any stock xis not correlated to the company-specific return on any other stock yis correlated with the market returnThe risk-free rate is constant during the investment period,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,19,Assumptions,Investors forecasts agree with respect to expectations,standard deviations,and correlations of the returns of risky securitiesTherefore all investors hold risky assets in the same relative proportionsInvestors behave optimally In equilibrium,prices adjust so that aggregate demand for each security is equal to its supply,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,20,Market Portfolio,Since every investors relative holdings of risky assets is the same,the only way the asset market can clear is if those optimal relative proportions are the proportions in which they are valued in the market place Market Portfolio:a portfolio that holds all assets in proportion to their observed market values.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,21,CML and the CAPM,CAPM says that in equilibrium,any investors relative holding of risky assets will be the same as in the market portfolioDepending on their risk aversions,different investors hold portfolios with different mixes of riskless asset and the market portfolio,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,22,CAPM Formula,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,23,The Capital Market Line,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,24,Active v.Passive Management,CAPM implies that,on average,the performance of active portfolio managers is equal to that of passive managers employing just the market portfolio and the risk-free securityDiligent managers do outperform passive managers,but only to the degree that their diligence is rewarded.Because over time the competition among them reduces those rewards to the minimum necessary to induce them to perform their work.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,25,Reward Only for Market Risk,The risk premium on any individual security is proportional only to its contribution to the risk of the market portfolio,and does not depend on its stand-alone riskInvestors are rewarded only for bearing market risk,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,26,13.2 Determining the Risk Premium on the Market Portfolio,CAPM states that the equilibrium risk premium on the market portfolio is the product ofvariance of the market,s2Mweighted average of the degree of risk aversion of holders of risk,A,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,27,Comment,CAPM explains the difference between the riskless interest rate and the expected rate of return on the market portfolio,but not their absolute levelsThe absolute level of the equilibrium expected rate of return on the market portfolio is determined by such factors asexpected productivityhousehold inter-temporal preferences for consumptionEtc.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,28,Example:To Determine A,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,29,13.3 Risk Premiums on Individual Securities:SML,With the idea that investors must be compensated in terms of expected return for bearing risk,we define the risk of a security by the size of its equilibrium expected return.As weve learned,the risk of an efficient portfolio is measured by.Hence,the general measure of a securitys risk is its beta,which describes the marginal contribution of that securitys return to the SD of the market portfolios return:,where denotes the covariance between the return on security j and the return on the market portfolio.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,30,Comment:b=1,A security with a b=1 on average rises and falls with the marketa 10%(say)unexpected rise(fall)in the market return premium will,on average,result in a 10%rise(fall)in the securitys return premium,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,31,Comment:b 1,A security with a b 1 on average rises and falls more than the marketWith a b=1.3,a 10%(say)unexpected rise(fall)in the market return premium will,on average,result in a 13%rise(fall)in the securitys return premiumSuch a security is said to be aggressive,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,32,Comment:b 1,A security with a b 1 on average rises and falls less than the marketWith a b=0.7,a 10%(say)unexpected rise(fall)in the market return premium will,on average,result in a 7%rise(fall)in the securitys return premiumSuch a security is said to be defensive,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,33,CAPM Risk Premium on any Asset,According to CAPM,in equilibrium,the risk premium on any asset is equal the product of b(or Beta)the risk premium on the market portfolioThis is called the security market line(SML)relation,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,34,The Security Market Line,horizontal-betaVertical-excess returnSlope-risk premium on the market portfolioM-securities with average riskUpper part from M-aggressive securitiesLower part from M-defensive securitiesJ-over-priced security,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,35,Moving toward SML,The existence of J contradicts CAPM,because it implies either that the market is not in equilibrium or that investors do not agree on the distribution of returns or that investors are not behaving as mean-variance optimizers.Under the assumptions of CAPM,investors could improve their portfolios by investing less in security J and more in other securities.Therefore,there is excess supply of J and excess demand for other securities,which would cause Js price to fall and its expected return to rise,until M.By CAPM theory,all securities(not just efficient portfolios)must fall precisely on the SML(hence its name),Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,36,Portfolio lies on CML v.security lies on SML,Any portfolio lies on CML(portfolio formed by mixing the market portfolio and the riskless asset)has a beta equal to the fraction of the portfolio invested in the market portfolio.For example:an efficient portfolio with 150%risky securities-50%riskless asset would have a beta of 1.5,and would be considered to be aggressive.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,37,Decomposition of total risk,For any risky security,its undiversifiable risk is given by,whereas the diversifiable risk can be found as the residual by subtracting the undiversifiable risk from the total risk:For example:a security with a beta+1 would have undiversifiable risk(and offer and expected risk premium)equal to that of the market portfolio.This means that when held as part of the market portfolio its diversifiable risk would have been eliminated and therefore be of no concern,but when held otherwise(especially when held alone)the holder would subject to both risks,while only being rewarded for the undiversifiable risk.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,38,Sigma v.beta,When determining the risk of a portfolio using standard deviation(portfolio perspective)results in a formula thats quite complexusing beta(security perspective),the formula is linear,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,39,Computing Beta,Here are some useful formulae for computing beta,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,40,13.4 Using the CAPM in Portfolio Selection,Whether or not CAPM is a valid theory,indexing is attractive to investors becausehistorically it has performed better than most actively managed portfoliosit costs less to implement that active management,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,41,CML v.SML,As weve known,CML uses a portfolio perspective,and SML uses a security perspective.The CML provides a convenient benchmark for measuring the performance of an investor s entire portfolio of assets.However,households and pension funds often use several different portfolio managers,each of whom manages only a part of the whole portfolio.For measuring performance of such managers,the CAPM suggests a different benchmark:the SML.,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,42,s-risk and b-risk,As weve already known,a security has two kinds of risk:risk that may be diversified away,and risk that is associated with the marketThe CAPM theory states that the lower return on the s-riskier security implies that it has a lower level of market b-risk,and this is the only relevant riskThe s-riskier security contains relatively more(irrelevant)security-specific riskThe difference between the average rate of return on a security or a portfolio and its SML relation is called alpha,Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall,43,How to judge a fund