Three Essays on Predictability and Seasonality in the Cross-Section of Stock Returns

This thesis examines predictability and seasonality in the cross-section of stock returns. The first chapter, titled Infrequent Rebalancing, Return Autocorrelation, and Seasonality,'' shows that a model of infrequent rebalancing can explain specific predictability patterns in the time series and cross-section of stock returns. First, infrequent rebalancing produces return autocorrelations that are consistent with empirical evidence from intraday returns and new evidence from daily returns. Autocorrelations can switch sign and become positive at the rebalancing horizon. Second, the cross-sectional variance in expected returns is larger when more traders rebalance. This effect generates seasonality in the cross-section of stock returns, which can help explain available empirical evidence. The second chapter, titled Seasonalities in Anomalies,'' investigates return seasonalities in a set of well-known anomalies in the cross-section of U.S. stocks returns. A January seasonality goes beyond a size effect and strongly affects most anomalies, which can even switch sign in January. Both tax-loss selling and firm size are important in explaining the turn-of-the-year pattern. Return seasonality exists outside of January, with respect to the month of the quarter. Small stocks earn abnormally high average returns on the last day of each quarter, which significantly affects size, idiosyncratic volatility, and illiquidity portfolios. The results have implications for the interpretation and analysis of many anomalies, such as asset growth and momentum. The third chapter, titled ``The Cross-Section of Intraday and Overnight Returns,'' uses a thirty-year sample of U.S. stock returns to document substantial cross-sectional variation in returns over the trading day and overnight. Market closures have a large impact on returns. Small and illiquid stocks earn high average returns in the last thirty minutes of trading. In contrast, large and liquid stocks perform poorly at this time. I find support for institutional and information asymmetry theories. But these theories do not fully explain the cross-sectional evidence. Portfolios based on other characteristics, such as beta and idiosyncratic volatility, earn their return gradually throughout the trading dayâcontrary to the market and a benchmark based on random portfolios. These portfolios also tend to incur large negative returns overnight, consistent with mispricing at the open.

Portfolio construction under information asymmetry

Lionel Coulot

We introduce in this thesis the idea of a variable lookback model, i.e., a model whose predictions are based on a variable portion of the information set. We verify the intuition of this model in the context of experimental finance. We also propose a novel algorithm to estimate it, the variable lookback algorithm, and apply the latter to build investment strategies. Financial markets under information asymmetry are characterized by the presence of better-informed investors, also called insiders. The literature in finance has so far concentrated on theoretical models describing such markets, in particular on the role played by the price in conveying information from informed to uninformed investors. However, the implications of these theories have not yet been incorporated into processing methods to extract information from past prices and this is the aim of this thesis. More specifically, the presence of a time-varying number of insiders induces a time-varying predictability in the price process, which calls for models that use a variable lookback window. Moreover, although our initial motivation comes from the study of markets under information asymmetry, the problem is more general, as it touches several issues in statistical modeling. The first one concerns the structure of the model. Existing methods use a fixed model structure despite evidences from data, which support an adaptive one. The second one concerns the improper handling of the nonstationarity in data. The stationarity assumption facilitates the mathematical treatment. Hence, existing methods relies on some form of stationarity, for example, by assuming local stationary, as in the windowing approach, or by modeling the underlying switching process, for example, with a Markov chain of order 1. However, these suffer from certain limitations and more advanced methods that take explicitly into account the nonstationariry of the signal are desirable. In summary, there is a need to develop a method that constantly monitors what is the appropriate structure, when a certain model works and when not or when are the underlying assumptions of the model violated. We verify our initial intuition in the context of experimental finance. In particular, we highlight the diffusion of information in the market. We give a precise definition to the notion of the time of maximally informative price and verify, in line with existing theories, that the time of maximally informative price is inversely proportional to the number of insiders in the market. This supports the idea of a variable lookback model. Then, we develop an estimation algorithm that selects simultaneously the order of the process and the lookback window based on the minimum description length principle. The algorithm maintains a series of estimators, each based on a different order and/or information set. The selection is based on an information theoretic criterion, that accounts for the ability of the model to fit the data, penalized by the model complexity and the amount of switching between models. Finally, we put the algorithm at work and build investment strategies. We devise a method to draw dynamically the trend line for the time-series of log-prices and propose an adaptive version of the well-known momentum strategy. The latter outperforms standard benchmarks, in particular during the 2009 momentum crash.

EPFL2013

Portfolio construction under information asymmetry

Lionel Coulot

EPFL2013