RiskandReturn(投资分析与投资组合管理)ppt课件

1、Lecture Presentation Software to accompanyInvestment Analysis and Portfolio ManagementSeventh Editionby Frank K. Reilly & Keith C. BrownChapter 9.Chapter 9 Multifactor Models of Risk and ReturnQuestions to be answered:What is the arbitrage pricing theory (APT) and what are its similarities and diffe

2、rences relative to the CAPM?What are the major assumptions not required by the APT model compared to the CAPM?How do you test the APT by examining anomalies found with the CAPM?.Chapter 9 - Multifactor Models of Risk and ReturnWhat are the empirical test results related to the APT?Why do some author

3、s contend that the APT model is untestable?What are the concerns related to the multiple factors of the APT model?.Chapter 9 - Multifactor Models of Risk and ReturnWhat are multifactor models and how are related to the APT?What are the steps necessary in developing a usable multifactor model?What ar

4、e the multifactor models in practice?How is risk estimated in a multifactor setting?.Arbitrage Pricing Theory (APT)CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmarkAn alternative pricing theory with fewer assumptions was developed:Arbitrage P

5、ricing Theory.Arbitrage Pricing Theory - APTThree major assumptions:1. Capital markets are perfectly competitive2. Investors always prefer more wealth to less wealth with certainty3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexe

6、s .Assumptions of CAPMThat Were Not Required by APTAPT does not assume A market portfolio that contains all risky assets, and is mean-variance efficientNormally distributed security returns Quadratic utility function .Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a

7、specified time periodRi.Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period= expected return for asset iRiEi.Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period= expected return for asset i= react

8、ion in asset is returns to movements in a common factorRiEibik.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 is returns to movements in a common factor= a common factor with a zero mean that inf

9、luences the returns on all assetsRiEibik.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 is returns to movements in a common factor= a common factor with a zero mean that influences the returns on

10、 all assets= a unique effect on asset is return that, by assumption, is completely diversifiable in large portfolios and has a mean of zeroRiEibik.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

11、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 is return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero= number of assetsRiEibikN.Arbitrage Pricing Theory (AP

12、T) Multiple factors expected to have an impact on all assets:.Arbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets:Inflation.Arbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets:InflationGrowth in GNP.Arbitrage Pricing Theory (APT

13、)Multiple factors expected to have an impact on all assets:InflationGrowth in GNPMajor political upheavals.Arbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets:InflationGrowth in GNPMajor political upheavalsChanges in interest rates.Arbitrage Pricing Theory (APT)Mu

14、ltiple factors expected to have an impact on all assets:InflationGrowth in GNPMajor political upheavalsChanges in interest ratesAnd many more.Arbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets:InflationGrowth in GNPMajor political upheavalsChanges in interest rat

15、esAnd many more.Contrast with CAPM insistence that only beta is relevant.Arbitrage Pricing Theory (APT)Bik determine how each asset reacts to this common factorEach asset may be affected by growth in GNP, but the effects will differIn application of the theory, the factors are not identifiedSimilar

16、to the CAPM, the unique effects are independent and will be diversified away in a large portfolio.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 awayThe expected return on

17、 any asset i (Ei) can be expressed as:.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 riskbi = the pricing relationship between the r

18、isk premium and asset i - that is how responsive asset i is to this common factor K.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 ris

19、k 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: boj=0) is 3 percent.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

20、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.Example of Two Stocks and a Two-Factor Model = .03 + (.01)bi1 + (.02)bi2 Ex = .03 + (.01)(0.50) +

21、(.02)(1.50) = .065 = 6.5% Ey = .03 + (.01)(2.00) + (.02)(1.75) = .085 = 8.5%.Roll-Ross StudyThe methodology used in the study is as follows:Estimate the expected returns and the factor coefficients from time-series data on individual asset returnsUse these estimates to test the basic cross-sectional

22、 pricing conclusion implied by the APTThe authors concluded that the evidence generally supported the APT, but acknowledged that their tests were not conclusive.Extensions of the Roll-Ross StudyCho, Elton, and Gruber examined the number of factors in the return-generating process that were pricedDhr

23、ymes, Friend, and Gultekin (DFG) reexamined techniques and their limitations and found the number of factors varies with the size of the portfolio.The APT and AnomaliesSmall-firm effectReinganum - results inconsistent with the APTChen - supported the APT model over CAPMJanuary anomalyGultekin - APT

24、not better than CAPMBurmeister and McElroy - effect not captured by model, but still rejected CAPM in favor of APT.Shankens Challenge to Testability of the APTIf returns are not explained by a model, it is not considered rejection of a model; however if the factors do explain returns, it is consider

25、ed supportAPT has no advantage because the factors need not be observable, so equivalent sets may conform to different factor structuresEmpirical formulation of the APT may yield different implications regarding the expected returns for a given set of securitiesThus, the theory cannot explain differ

26、ential returns between securities because it cannot identify the relevant factor structure that explains the differential returns.Alternative Testing TechniquesJobson proposes APT testing with a multivariate linear regression modelBrown and Weinstein propose using a bilinear paradigmOthers propose new methodologies.Multifactor Models and Risk EstimationIn a multifactor model, the investor chooses the exact number and identity o