NBER WORKING PAPER SERIES TESTS OF MUTLIFACTOR PRICING MODELS, VOLATILITY BOUNDS AND PORTFOLIO PERFORMANCE Wayne E.Ferson Working Paper 9441 http://www.nber.org/papers/w9441 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge,MA 02138 January 2003 The author acknowledges financial support from the Collins Chair in Finance at Boston College and the Pigott- PACCAR professorshipat the University of Washington.He is also grateful to George Constantinides and Ludan Liu for helpful comments and suggestions.The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. 2003 by Wayne E.Ferson.All rights reserved.Short sections of text not to exceed two paragraphs,may be quoted without explicit permission provided that full credit including.notice,is given to the source
NBER WORKING PAPER SERIES TESTS OF MUTLIFACTOR PRICING MODELS, VOLATILITY BOUNDS AND PORTFOLIO PERFORMANCE Wayne E. Ferson Working Paper 9441 http://www.nber.org/papers/w9441 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 January 2003 The author acknowledges financial support from the Collins Chair in Finance at Boston College and the PigottPACCAR professorship at the University of Washington. He is also grateful to George Constantinides and Ludan Liu for helpful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. ©2003 by Wayne E. Ferson. All rights reserved. Short sections of text not to exceed two paragraphs, may be quoted without explicit permission provided that full credit including . notice, is given to the source
Tests of Multifactor Pricing Models,Volatility Bounds and Portfolio Performance Wayne E.Ferson NBER Working Paper No.9441 January 2003 JEL No.G000,G110,G120,G140 ABSTRACT Three concepts:stochastic discount factors,multi-beta pricing and mean variance efficiency,are at the core of modern empirical asset pricing.This paper reviews these paradigms and the relations among them,concentrating on conditional asset pricing models where lagged variables serve as instruments for publicly available information.The different paradigms are associated with different empirical methods.We review the variance bounds of Hansen and Jagannathan (1991),concentrating on extensions for conditioning information.Hansen's(1982)Generalized Method of Moments(GMM) is briefly reviewed as an organizing principle.Then,cross-sectional regression approaches as developed by Fama and MacBeth (1973)are reviewed and used to interpret empirical factors,such as those advocated by Fama and French(1993,1996).Finally,we review the multivariate regression approach, popularized in the finance literature by Gibbons(1982)and others.A regression approach,with a beta pricing formulation,and a GMM approach with a stochastic discount factor formulation,may be considered competing paradigms for empirical work in asset pricing.This discussion clarifies the relations between the various approaches.Finally,we bring the models and methods together,with a review of the recent conditional performance evaluation literature,concentrating on mutual funds and pension funds. Wayne E.Ferson Boston College Carroll School of Management 140 Commonwealth Avenue,330B Chestnut Hill,MA 02467 and NBER wayne.ferson@bc.edu
Tests of Multifactor Pricing Models, Volatility Bounds and Portfolio Performance Wayne E. Ferson NBER Working Paper No. 9441 January 2003 JEL No. G000, G110, G120, G140 ABSTRACT Three concepts: stochastic discount factors, multi-beta pricing and mean variance efficiency, are at the core of modern empirical asset pricing. This paper reviews these paradigms and the relations among them, concentrating on conditional asset pricing models where lagged variables serve as instruments for publicly available information. The different paradigms are associated with different empirical methods. We review the variance bounds of Hansen and Jagannathan (1991), concentrating on extensions for conditioning information. Hansen's (1982) Generalized Method of Moments (GMM) is briefly reviewed as an organizing principle. Then, cross-sectional regression approaches as developed by Fama and MacBeth (1973) are reviewed and used to interpret empirical factors, such as those advocated by Fama and French (1993, 1996). Finally, we review the multivariate regression approach, popularized in the finance literature by Gibbons (1982) and others. A regression approach, with a beta pricing formulation, and a GMM approach with a stochastic discount factor formulation, may be considered competing paradigms for empirical work in asset pricing. This discussion clarifies the relations between the various approaches. Finally, we bring the models and methods together, with a review of the recent conditional performance evaluation literature, concentrating on mutual funds and pension funds. Wayne E. Ferson Boston College Carroll School of Management 140 Commonwealth Avenue, 330B Chestnut Hill, MA 02467 and NBER wayne.ferson@bc.edu
CONTENTS I.Introduction 2.Multi-factor Asset Pricing Models:Review and Integration 2.1 The Stochastic Discount Factor Representation Expected Risk Premiums Return Predictability 2.2 Consumption-based Asset Pricing Models 2.3 Multi-beta pricing Models Relation to the Stochastic Discount Factor Relation to Mean variance efficiency A"Large Markets"Interpretation 2.4 Mean variance efficiency with conditioning information Conditional versus Unconditional Efficiency Implications for Tests 2.5 Choosing the factors 3.Modern Variance Bounds 3.1 The Hansen Jagannathan Bounds 3.2 Variance bounds with conditioning information Efficient-portfolio bounds Optimal bounds Discussion 3.3 The Hansen Jagannathan Distance 4.Methodology and Tests of Multifactor Asset Pricing Models 4.1 The Generalized Method of Moments Approach 4.2 Cross-sectional Regression Methods The Fama-MacBeth approach Interpreting the estimates A Caveat Errors in Betas 4.3 Multivariate Regression and beta pricing models Comparing the Beta Pricing and stochastic discount factor approaches
CONTENTS I. Introduction 2. Multi-factor Asset Pricing Models: Review and Integration 2.1 The Stochastic Discount Factor Representation Expected Risk Premiums Return Predictability 2.2 Consumption-based Asset Pricing Models 2.3 Multi-beta pricing Models Relation to the Stochastic Discount Factor Relation to Mean variance efficiency A "Large Markets" Interpretation 2.4 Mean variance efficiency with conditioning information Conditional versus Unconditional Efficiency Implications for Tests 2.5 Choosing the factors 3. Modern Variance Bounds 3.1 The Hansen Jagannathan Bounds 3.2 Variance bounds with conditioning information Efficient-portfolio bounds Optimal bounds Discussion 3.3 The Hansen Jagannathan Distance 4. Methodology and Tests of Multifactor Asset Pricing Models 4.1 The Generalized Method of Moments Approach 4.2 Cross-sectional Regression Methods The Fama-MacBeth approach Interpreting the estimates A Caveat Errors in Betas 4.3 Multivariate Regression and beta pricing models Comparing the Beta Pricing and stochastic discount factor approaches
3 5.Conditional Performance Evaluation 5.1 Stochastic Discount Factor formulation Invariance to the number of funds 5.2 Beta pricing formulation 5.3 Using portfolio weights Conditional Performance Attribution Interim Trading Bias 5.4 Conditional market timing models 5.5 Empirical Evidence on Conditional Performance 6.Conclusions
3 5. Conditional Performance Evaluation 5.1 Stochastic Discount Factor formulation Invariance to the number of funds 5.2 Beta pricing formulation 5.3 Using portfolio weights Conditional Performance Attribution Interim Trading Bias 5.4 Conditional market timing models 5.5 Empirical Evidence on Conditional Performance 6. Conclusions
I.Introduction The asset pricing models of modern finance describe the prices or expected rates of return of financial assets,which are claims traded in financial markets.Examples of financial assets are common stocks, bonds,options,futures and other "derivatives,"so named because they derive their values from other, underlying assets.Asset pricing models are based on two central concepts.The first is the no arbitrage principle,which states that market forces tend to align prices so as to eliminate arbitrage opportunities.An arbitrage opportunity arises when assets can be combined in a portfolio with zero cost,no chance of a loss and positive probability of a gain.The second central concept in asset pricing is financial market equilibrium.Investors'desired holdings of financial assets derive from an optimization problem.In equilibrium the first order conditions of the optimization problem must be satisfied,and asset pricing models follow from these conditions.When the agent considers the consequences of the investment decision for more than a single period in the future,intertemporal asset pricing models result. The present paper reviews multi-factor asset pricing models from an empiricists'perspective. Multi-factor models can be motivated by either the no arbitrage principle or by an equilibrium model. Their distinguishing feature is that expected asset returns are determined by a linear combination of their covariances with variables representing the risk factors.This paper has two main objectives.The first is to integrate the various empirical models and their tests in a self contained discussion.The second is to review the application to the problem of measuring investment performance. This paper concentrates heavily on the role of conditioning information,in the form of lagged variables that serve as instruments for publicly available information.I think that developments in this area,conditional asset pricing,represent some of the most significant advances in empirical asset pricing research in recent years. The models described in this paper are set in the classical world of perfectly efficient financial
I. Introduction The asset pricing models of modern finance describe the prices or expected rates of return of financial assets, which are claims traded in financial markets. Examples of financial assets are common stocks, bonds, options, futures and other "derivatives," so named because they derive their values from other, underlying assets. Asset pricing models are based on two central concepts. The first is the no arbitrage principle, which states that market forces tend to align prices so as to eliminate arbitrage opportunities. An arbitrage opportunity arises when assets can be combined in a portfolio with zero cost, no chance of a loss and positive probability of a gain. The second central concept in asset pricing is financial market equilibrium. Investors' desired holdings of financial assets derive from an optimization problem. In equilibrium the first order conditions of the optimization problem must be satisfied, and asset pricing models follow from these conditions. When the agent considers the consequences of the investment decision for more than a single period in the future, intertemporal asset pricing models result. The present paper reviews multi-factor asset pricing models from an empiricists' perspective. Multi-factor models can be motivated by either the no arbitrage principle or by an equilibrium model. Their distinguishing feature is that expected asset returns are determined by a linear combination of their covariances with variables representing the risk factors. This paper has two main objectives. The first is to integrate the various empirical models and their tests in a self contained discussion. The second is to review the application to the problem of measuring investment performance. This paper concentrates heavily on the role of conditioning information, in the form of lagged variables that serve as instruments for publicly available information. I think that developments in this area, conditional asset pricing, represent some of the most significant advances in empirical asset pricing research in recent years. The models described in this paper are set in the classical world of perfectly efficient financial