[This article develops an intertemporal, discrete-time, competitive equilibrium version of the arbitrage pricing theory (APT) and explores the econometric implications of this model under various restrictions on investor preferences and on the dynamic behavior of dividends. We describe conditions under which the econometric techniques typically used for estimating and testing the APT can be shown to be consistent with our economic model. We relate our intertemporal version of the APT to the static APT and to Merton's intertemporal capital asset pricing model.]

This unusual book is not intended chiefly as a textbook for investment courses. The book's principal target audience is quantitatively inclined investment management professionals with some masters-level knowledge of finance. However, it could make an excellent textbook for a second-year MBA course in quantitative portfolio management; the authors mention this as a possible use of the book. Be warned: anyone teaching a course based on this book would need to make a substantial commitment to mastering and expositing a large body of unfamiliar, analytical material. The payoff would be a class full of students who could not complain that the course was not practically relevant. Alternatively, the book could play a valuable supporting role in an investments course as optional outside reading. Many M.B.A. students query the usefulness of modern portfolio theory in business applications. In this book the authors nearly describe how to build a fully functional investment management business, and it is all done on a foundation of modern portfolio theory.

An important issue in applications of multifactor models of asset returns is the appropriate number of factors. Most extant tests for the number of factors are valid only for strict factor models, in which diversifiable returns are uncorrelated across assets. In this paper, the authors develop a test statistic to determine the number of factors in an approximate factor model of asset returns, which does not require that diversifiable components of returns be uncorrelated across assets. They find evidence for one to six pervasive factors in the cross section of New York Stock Exchange and American Stock Exchange stock returns.

This paper develops a new estimation procedure for characteristic-based factor models of stock returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving as time-varying weights and a set of univariate nonparametric functions relating security characteristic to the associated factor betas. We use a time-series and cross-sectional pooled weighted additive nonparametric regression methodology to simultaneously estimate the factor returns and characteristic-beta functions. By avoiding the curse of dimensionality, our methodology allows for a larger number of factors than existing semiparametric methods. We apply the technique to the three-factor Fama–French model, Carhart’s four-factor extension of it that adds a momentum factor, and a five-factor extension that adds an own-volatility factor. We find that momentum and own-volatility factors are at least as important, if not more important, than size and value in explaining equity return comovements. We test the multifactor beta pricing theory against a general alternative using a new nonparametric test

We evaluate the performance of various methods for estimating factor returns in an approximate factor model. Differences across estimators are most pronounced when there is cross-sectional heteroscedasticity or when cross-sectional sample sizes, n, have fewer than 4,000 assets. Estimators incorporating either cross-sectional or time-series heteroscedasticity outperform the other estimators when those types of heteroscedasticity are present. The differences are most pronounced when the cross-sectional sample is small. Received December 2, 2015; editorial decision May 16, 2017 by Editor Jeffrey Pontiff.

We use an asymptotic principal components technique to estimate the pervasive factors influencing asset returns and to test the restrictions imposed by static and intertemporal equilibrium versions of the arbitrage pricing theory (APT) on a multivariate regression model. The empirical techniques allow for fairly arbitrary time variation in risk premiums. We find that the APT provides a better description of the expected returns on assets than the capital asset pricing model (CAPM). However, some statistically reliable mispricing of assets by the APT remains.

This paper develops a theory and econometric method of portfolio performance measurement using a competitive equilibrium version of the Arbitrage Pricing Theory. We show that the Jensen coefficient and the appraisal ratio of Treynor and Black are theoretically compatible with the Arbitrage Pricing Theory. We construct estimators for the two performance measures using a new principal components technique, and describe their asymptotic distributions. The estimators are computationally feasible using a large number of securities. We also suggest a new approach to testing for the correct number of factors.

This article develops an intertemporal, discrete-time, competitive equilibrium version of the arbitrage pricing theory (APT) and explores the econometric implications of this model under various restrictions on investor preferences and on the dynamic behavior of dividends. We describe conditions under which the econometric techniques typically used for estimating and testing the APT can be shown to be consistent with our economic model. We relate our intertemporal version of the APT to the static APT and to Merton’s intertemporal capital asset pricing model.

1. Preferences Representation and Risk Aversion. 2. Stachastic Dominance. 3. Mathematics of the Portfolio Frontier. 4. Two Fund Separation and Linear Valuation. 5. Allocative Efficiency and the Valuation of State Contingent Securities. 6. Valuation of Complex Securities and Options with Preference Restrictions. 7. Multiperiod Securities Markets I: Equilibrium Valuation. 8. Multiperiod Securities Markets II: Valuation by Arbitrage. 9. Financial Markets with Differential Information. 10. Econometric Issues in Testing the Capital Asset Pricing Model.

Two-pass cross-sectional regression (TPCSR) is frequently used in estimating factor risk premia. Recent papers argue that the common practice of grouping assets into portfolios to reduce the errors-in-variables (EIV) problem leads to loss of efficiency and masks potential deviations from asset pricing models. One solution that allows the use of individual assets while overcoming the EIV problem is iterated TPCSR (ITPCSR). ITPCSR converges to a fixed point regardless of the initial factors chosen. ITPCSR is intimately linked to the asymptotic principal components (APC) method of estimating factors since the ITPCSR estimates are the APC estimates, up to a rotation.