Assessing Sorting Portfolios

Abstract

This paper investigates the role of sorting portfolios in evaluating asset pricing models. With the rising number of empirical studies about asset pricing models, the comparability of these e ffects suffers from (1) di fferent aggregational levels of firm returns, (2) di fferent models, i.e. Capital Asset Pricing Model (CAPM) vs. the Fama and French model, and (3) time varying factor risk loadings causing uncertainty. Our objective is to address these issues by providing valuable insights into how sorting portfolios influence the performance of asset pricing models and compare these e ffects in an up-to-date study.We consider four distinct types of aggregation levels of returns, i.e.industry-level as well as beta-sort, beta-size-sort, and size-book-to-market-sort portfolios. By using a recent twenty year sample of U.S. stock market data, the CAPM and several multi-factor models are investigated using diff erent regression methods and tests.We provide evidence that sorting portfolios can highly improve the performance of the models. In particular, we nd that beta-sorting improves the performance of the CAPM, while portfolios built according to size and book-to-market enhance the Fama and French model. For all analyzed types of portfolios the three-factor model turns out to be superior to the CAPM both statistically and economically. Applying state-of-the-art median regression analysis, we also find that the role of the unspeci fied part (alpha) of the CAPM changes when looking at the tails of the return distribution.We conclude that the success of the three-factor model is not restricted to its factor-mimicking portfolios. Our fi ndings support claims toward using multi-factor models instead of the classic CAPM. This holds not only on average but for large parts of the conditional return distribution, meaning that there is a strong empirical evidence in favor of the location-shift hypothesis.