RiskandReturn(投资分析与投资组合管理).pptx

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 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 Return What are the empirical test results related to the APT? Why do some authors 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 Return What are multifactor models and how are related to the APT? What are the steps necessary in developing a usable multifactor model? What are 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 benchmark An alternative pricing theory with fewer assumptions was developed: Arbitrage Pricing TheoryArbitrage 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 CAPMThat Were Not Required by APTAPT does not assume A market portfolio that contains all risky assets, and is mean-variance efficient Normally distributed security returns Quadratic utility function Arbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time periodikikiiiittbbbER.21RiArbitrage Pricing Theory (APT) For i = 1 to N where: = return on asset i during a specified time period= expected return for asset iikikiiiittbbbER.21RiEiArbitrage 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 factorikikiiiittbbbER.21RiEibikArbitrage 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 assetsikikiiiittbbbER.21RiEibikkArbitrage 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 assets= a unique effect on asset is return that, by assumption, is completely diversifiable in large portfolios and has a mean of zeroikikiiiittbbbER.21RiEibikkiArbitrage 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 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 assetsikikiiiittbbbER.21RiEibikkiNArbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets:kArbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets: InflationArbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets: Inflation Growth in GNPArbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets: Inflation Growth in GNP Major political upheavalsArbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets: Inflation Growth in GNP Major political upheavals Changes in interest ratesArbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets: Inflation Growth in GNP Major political upheavals Changes in interest rates And many more.Arbitrage Pricing Theory (APT)Multiple factors expected to have an impact on all assets: Inflation Growth in GNP Major political upheavals Changes in interest rates And many more.Contrast with CAPM insistence that only beta is relevantArbitrage 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 to the CAPM, the unique effects are independent and will be diversified away in a large portfolioArbitrage 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 away The expected return on any asset i (Ei) can be expressed as:Arbitrage Pricing Theory (APT)where:= the expected return on an asset with zero systematic risk whereikkiiibbbE.22110001EEi00E1= 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-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 rate1)01.(1= 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-risk asset (zero beta: boj=0) is 3 percent2)02.(2)03.(33Example of Two Stocks and a Two-Factor Model= the response of asset X to changes in the rate of inflation is 0.501xb)50.(1xb= the response of asset Y to changes in the rate of inflation is 2.00)50.(1yb1yb= 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 1.752xb2yb)50. 1(2xb)75. 1(2ybExample 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%22110iiibbERoll-Ross StudyThe methodology used in the study is as follows:1.Estimate the expected 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 conclusiveExtensions of the Roll-Ross Study Cho, Elton, and Gruber examined the number of factors in the return-generating process that were priced Dhrymes, Friend, and Gultekin (DFG) reexamined techniques and their limitations and found the number of factors varies with the size of the portfolioThe APT and Anomalies Small-firm effectReinganum - results inconsistent with the APTChen - supported the APT model over CAPM January 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 APT If returns are not explained by a model, it is not considered rejection of a model; however if the factors do explain returns, it is considered support APT has no advantage because the factors need not be observable, so equivalent sets may conform to different factor structures Empirical formulation of the APT may yield different implications regarding the expected returns for a given set of securities Thus, the theory cannot explain differential returns between securities because it cannot identify the relevant factor structure that explains the differential returnsAlternative Testing Techniques Jobson proposes APT testing with a multivariate linear regression model Brown and Weinstein propose using a bilinear paradigm Others propose new methodologiesMultifactor Models and Risk EstimationIn a multifactor model, the investor chooses the exact number and identity of risk factorsMultifactor Models and Risk EstimationMultifactor Models in Practice Macroeconomic-Based Risk Factor ModelsMultifactor Models and Risk EstimationMultifactor Models in Practice Macroeconomic-Based Risk Factor Models Microeconomic-Based Risk Factor ModelsMultifactor Models and Risk EstimationMultifactor Models in Practice Macroeconomic-Based Risk Factor Models Microeconomic-Based Risk Factor Models Extensions of Characteristic-Based Risk Factor ModelsEstimating Risk in a Multifactor Setting: Examples Estimating Expected Returns for Individual StocksEstimating Risk in a Multifactor Setting: Examples Estimating Expected Returns for Individual Stocks Comparing Mutual Fund Risk ExposuresThe InternetInvestments OnlineFuture topicsChapter 10 Analysis of Financial Statements