RiskandReturn(投资分析与投资组合管理)(40页PPT).pptx

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

2、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 authors contend

3、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 are the multifa

4、ctor 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 Pricing TheoryAr

5、bitrage 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 indexes Assumptions of CAPM

6、That 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 specified time periodRiArbitra

7、ge Pricing Theory(APT)For i=1 to N where:=return on asset i during a specified time period=expected return for asset iRiEiArbitrage 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 commo

8、n factorRiEibikArbitrage 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 all assetsRiEibikArbitrage Pricing

9、 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 all assets=a unique effect on asset is return that,by assumption,i

10、s completely diversifiable in large portfolios and has a mean of zeroRiEibikArbitrage 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

11、 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 assetsRiEibikNArbitrage Pricing Theory(APT)Multiple factors expected to have an impact on all assets:Arbitrage Pricing Theory(A

12、PT)Multiple factors expected to have an impact on all assets:InflationArbitrage Pricing Theory(APT)Multiple factors expected to have an impact on all assets:InflationGrowth in GNPArbitrage Pricing Theory(APT)Multiple factors expected to have an impact on all assets:InflationGrowth in GNPMajor politi

13、cal upheavalsArbitrage Pricing Theory(APT)Multiple factors expected to have an impact on all assets:InflationGrowth in GNPMajor political upheavalsChanges in interest ratesArbitrage Pricing Theory(APT)Multiple factors expected to have an impact on all assets:InflationGrowth in GNPMajor political uph

14、eavalsChanges 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 ratesAnd many more.Contrast with CAPM insistence that only beta is relevantArbitrage Pricing Theory(A

15、PT)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 to the CAPM,the unique effects are independent and will be diversified away in a large portfolioArbitr

16、age 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 any asset i(Ei)can be expressed as:Arbitrage Pricing Theory(APT)where:=the expected return on an asset with

17、 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 risk premium and asset i-that is how responsive asset i is to this common factor KExample of Two Stocks and a Two-Facto

18、r 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 risk premium related to this factor is 2 percent for every 1 percent change in the rate=the rate of return on a zero-systematic-

19、risk asset(zero beta:boj=0)is 3 percentExample 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 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 re

20、sponse of asset Y to changes in the growth rate of real GNP is 1.75Example of Two Stocks and a Two-Factor Model =.03+(.01)bi1 +(.02)bi2 Ex=.03+(.01)(0.50)+(.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:1.Estimate the expect

21、ed returns and the factor coefficients from time-series data on individual asset returns2.Use these estimates to test the basic cross-sectional pricing conclusion implied by the APTThe authors concluded that the evidence generally supported the APT,but acknowledged that their tests were not conclusi

22、veExtensions of the Roll-Ross StudyCho,Elton,and Gruber examined the number of factors in the return-generating process that were pricedDhrymes,Friend,and Gultekin(DFG)reexamined techniques and their limitations and found the number of factors varies with the size of the portfolioThe APT and Anomali

23、esSmall-firm effectReinganum-results inconsistent with the APTChen-supported the APT model over CAPMJanuary anomalyGultekin-APT not better than CAPMBurmeister and McElroy-effect not captured by model,but still rejected CAPM in favor of APTShankens Challenge to Testability of the APTIf returns are no

24、t explained by a model,it is not considered rejection of a model;however if the factors do explain returns,it is considered 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 d

25、ifferent implications regarding the expected returns for a given set of securitiesThus,the theory cannot explain differential returns between securities because it cannot identify the relevant factor structure that explains the differential returnsAlternative Testing TechniquesJobson proposes APT te

26、sting with a multivariate linear regression modelBrown and Weinstein propose using a bilinear paradigmOthers propose new methodologiesMultifactor Models and Risk EstimationIn a multifactor model,the investor chooses the exact number and identity of risk factorsMultifactor Models and Risk EstimationM

27、ultifactor Models in PracticeMacroeconomic-Based Risk Factor ModelsMultifactor Models and Risk EstimationMultifactor Models in PracticeMacroeconomic-Based Risk Factor ModelsMicroeconomic-Based Risk Factor ModelsMultifactor Models and Risk EstimationMultifactor Models in PracticeMacroeconomic-Based R

28、isk Factor ModelsMicroeconomic-Based Risk Factor ModelsExtensions of Characteristic-Based Risk Factor ModelsEstimating Risk in a Multifactor Setting:ExamplesEstimating Expected Returns for Individual StocksEstimating Risk in a Multifactor Setting:ExamplesEstimating Expected Returns for Individual St

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