Cross-sectional methods for empirical asset pricing

Abstract

This thesis develops new methods in empirical asset pricing which are valid when a large number of assets is available for the analysis. The work is divided in three main chapters, each of them focusing on different aspects and issues typically related to asset-pricing models. The fir st chapter introduces a methodology for estimating and testing beta-pricing models when a large number of assets is available for investment but the number of time-series observations is fixed. We first consider the case of correctly specified models with constant risk premia, and then extend our framework to deal with time-varying risk premia, potentially misspecified models, firm characteristics, and unbalanced panels. We show that our large cross-sectional framework poses a serious challenge to common empirical findings regarding the validity of beta-pricing models. Firm characteristics are found to explain a much larger proportion of variation in estimated expected returns than betas. The second chapter investigates the effect of model misspecification on mean-variance portfolios and show how asset-pricing theory and asymptotic analysis can mitigate misspeci cation. The analysis is founded on the Arbitrage Pricing Theory (APT), because it allows for pricing errors. The APT is extended to show it can capture not just small pricing errors unrelated to factors but also large pricing errors from mismeasured and missing factors. The key insight is that, instead of treating misspecification directly in the mean-variance portfolio, it is better to fi rst decompose the portfolio into a "beta" portfolio that depends only on factor risk premia and an "alpha" portfolio that depends only on pricing errors. Then, as the number of assets increases, we show that the weights of the alpha portfolio dominate those of the beta portfolio, leading to mean-variance portfolio weights that are immune to beta misspecification. For the alpha portfolio, misspecification is treated by imposing the APT restriction, which serves as an identification condition and a shrinkage constraint. Using simulations, we illustrate how our theoretical insights lead to a significant improvement in the out-of-sample performance of mean-variance portfolios. The third chapter analyzes the large cross-sectional properties of the standard two-pass methodology, when useless factors are included in the beta-pricing specification. When the number of time-series observations, T, is assumed to be fixed, and contrary to the conventional large-T framework, we find that the simple two-pass OLS estimator of risk premia exhibits desirable asymptotic properties that can be used to detect useless factors. In particular, we derived correctly-sized t-ratios, F-tests and goodness-of- t measures that allow us to implement a powerful statistical strategy to test for factors that can be potentially irrelevant for the analysis. The results hold also under the assumption of potential model misspecification. The validity of our results is assessed by means of simulation exercises.