金融學(xué)教學(xué)課件bodie2echapter13

1、 牛牛文庫文檔分享1Chapter 13: Capital Market EquilibriumObjectiveThe Theory of the CAPMUse of CAPM in benchmarking Using CAPM to determine correct rate for discounting 牛牛文庫文檔分享2IntroductionCAPM is a theory about equilibrium prices in the markets for risky assetsIt is important because it providesa justifica

2、tion for the widespread practice of passive investing called indexinga way to estimate expected rates of return for use in evaluating stocks and projects. 牛牛文庫文檔分享3IntroductionRelationship between CAPM and other contents we have learned so far. In part III we learned the valuation of securities and

3、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

4、 us a tool of valuation WITH risk. 牛牛文庫文檔分享4Chapter 13 Contents13.1 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 Return1

5、3.6 Modifications and Alternatives to the CAPM 牛牛文庫文檔分享513.1 The Capital Asset Pricing Model in BriefDeveloped 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, ri

6、sk, and correlations all chose their portfolios according the principles of efficient diversification 牛牛文庫文檔分享6So whats wrong with ms-analysisThe 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-retur

7、n if the present model aint broke? 牛牛文庫文檔分享7ms-analysis: EstimationWe 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

8、 (big problem) 牛牛文庫文檔分享8ms-analysis: EstimationAll 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 牛牛文庫文檔分享9ms-analysis: Estimation

9、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 param

10、eters will be in error 牛牛文庫文檔分享10ms-analysis: EstimationThe 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 牛牛文庫文檔分享11ms-anal

11、ysis: WishesAfter 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 fu

12、tures by computing individual interactions 牛牛文庫文檔分享12Guidance Principles for SimplificationAn 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

13、 to quadratic models 牛牛文庫文檔分享13The Astrophysics of FinanceIn 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 clo

14、ud then close stars need individual analysisdistant stars may be treated homogeneously 牛牛文庫文檔分享14CAPM: basic ideaThe 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

15、. 牛牛文庫文檔分享15Specifying the ModelIn 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 牛牛文庫文檔分享16Specifying the ModelWe also observed that in the limit as the number of secu

16、rities 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 牛牛文庫文檔分享17Specifying the ModelIn the homogenous model, we saw that there was individual- and market-riskAssume that each

17、equitys return is the composition of two random variables:one associated with the markets returnone associated with the company-specific return 牛牛文庫文檔分享18AssumptionsCompany-specific return on any stock xis not correlated to the company-specific return on any other stock yis correlated with the marke

18、t returnThe risk-free rate is constant during the investment period 牛牛文庫文檔分享19AssumptionsInvestors 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

19、 behave optimally In equilibrium, prices adjust so that aggregate demand for each security is equal to its supply 牛牛文庫文檔分享20Market PortfolioSince 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 pr

20、oportions in which they are valued in the market place Market Portfolio: a portfolio that holds all assets in proportion to their observed market values. 牛牛文庫文檔分享21CML and the CAPMCAPM says that in equilibrium, any investors relative holding of risky assets will be the same as in the market portfoli

21、oDepending on their risk aversions, different investors hold portfolios with different mixes of riskless asset and the market portfolio 牛牛文庫文檔分享22CAPM Formula 牛牛文庫文檔分享23The Capital Market Line 牛牛文庫文檔分享24Active v. Passive ManagementCAPM implies that, on average, the performance of active portfolio ma

22、nagers 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 neces

23、sary to induce them to perform their work. 牛牛文庫文檔分享25Reward Only for Market RiskThe 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 牛牛文

24、庫文檔分享2613.2 Determining the Risk Premium on the Market PortfolioCAPM 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 牛牛文庫文檔分享27CommentCAPM explains the difference betwee

25、n 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 consu

26、mptionEtc. 牛牛文庫文檔分享28Example: To Determine A 牛牛文庫文檔分享2913.3 Risk Premiums on Individual Securities: SMLWith 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 r

27、isk 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 th

28、e market portfolio. 牛牛文庫文檔分享30Comment: 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 牛牛文庫文檔分享31Comment: b 1 A security with a b 1 on

29、 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 牛牛文庫文檔分享32Comment: b 1 A security with a b 1 on average r

30、ises 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 牛牛文庫文檔分享33CAPM Risk Premium on any AssetAccording to CAPM, in equilib

31、rium, 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 牛牛文庫文檔分享34The Security Market Linehorizontal-betaVertical-excess returnSlope-risk premium on the market portfolioM-securities with ave

32、rage riskUpper part from M-aggressive securitiesLower part from M-defensive securitiesJ-over-priced security 牛牛文庫文檔分享35Moving toward SMLThe 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 o

33、r 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 pric

34、e 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) 牛牛文庫文檔分享36Portfolio lies on CML v. security lies on SMLAny portfolio lies on CML (portfolio formed by mixing the market portfolio and the

35、 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. 牛牛文庫文檔分享37Decomposition of total riskFor any ris

36、ky 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 t

37、he 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 undiversifia

38、ble risk. 牛牛文庫文檔分享38Sigma v. betaWhen 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 牛牛文庫文檔分享39Computing BetaHere are some useful formulae for computing beta 牛牛文庫文檔分

39、享4013.4 Using the CAPM in Portfolio SelectionWhether 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 牛牛文庫文檔分享41CML v. SMLAs weve known, CML uses a por

40、tfolio 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 whol

41、e portfolio.For measuring performance of such managers, the CAPM suggests a different benchmark: the SML. 牛牛文庫文檔分享42s-risk and b-riskAs 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

42、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 r

43、elation is called alpha 牛牛文庫文檔分享43How to judge a fund managers performanceIf a portfolio manager can consistently produce a positive alpha, then her performance is judged to be superior, even if the managed portfolio does not outperform the CML as a stand-alone investment. 牛牛文庫文檔分享44An exampleRisk-f

44、ree rate: 6%Risk premium on the market portfolio: 8%The SD on the market portfolio: 20%The alpha fund is a managed fund with a beta of 0.5, and alpha of 1%, and a SD of 15% 牛牛文庫文檔分享45Alpha Fund and the Security Market LineAlpha lies above the SML. Alpha-funds is measured as the vertical distance bet

45、ween alpha and SML.Apparently alpha-fund performs well. 牛牛文庫文檔分享46Alpha + market portfolio marketAlpha lies below CML, therefore it is not efficient.Alpha-fund would never be held by any investor as a total portfolio because investors could achieve lower risk and/or higher expected return by mixing

46、the market portfolio and the risk-free asset.However, by combing alpha fund with the market portfolio in certain optimal proportions, investors can achieve points that lie above CML.So, if you can find a portfolio manager with a positive alpha, you can beat the market. 牛牛文庫文檔分享47Alpha Fund and the C

47、apital Market LineAlpha lies below CML.Point Q corresponds to the optimal combination of alpha fund and the market portfolio.By mixing this portfolio with the risk-free asset, investors can achieve risk-return combinations anywhere along the line connecting points F and Q, which lies above CML. 牛牛文庫

48、文檔分享4813.5 Valuation and Regulating Rates of ReturnBeta may be used to obtain the discount factor for a projectAssume a project is similar to the projects undertaken by another firm, BetafulBetaful is financed by 20% short-term debt, and 80% equity, and its b is 1.3 (assume debt is risk-free)Your op

49、timal capital structure is 40% (risk-free) debt, and 60% equity 牛牛文庫文檔分享49Valuation and Regulating Rates of ReturnAssume the market rate is 15%, and the risk-free rate is 5%Compute the beta of Betafuls operations 牛牛文庫文檔分享50Valuation and Regulating Rates of ReturnBeta of Betafuls operations is equal

50、to the beta of our new operationTo find the required return on the new project, apply the CAPM 牛牛文庫文檔分享51Valuation and Regulating Rates of ReturnAssume that your company is just a vehicle for the new project, then the beta of your unquoted equity is 牛牛文庫文檔分享52Valuation and Regulating Rates of Return

51、Assume that your company has an expected dividend of $6 next year, and that it will grow annually at a rate of 4% forever, the value of a share is 牛牛文庫文檔分享53Valuation and Regulating Rates of ReturnRegulators use the CAPM to establish a fair rate of return on invested capital in public utilities, given the level of risk 牛牛文庫文檔分享5413.6 Modifications and Alternatives to the CAPMStarting in the 1970s researchers found that CAPM did not seem to fully explain the structure of expected r