Three Essays on the Skewness of Discrete Stock Returns

Abstract

In the first chapter, we develop an estimator of the physical skewness of an asset's discrete return over any time horizon based on the assumption that the asset's price follows a stochastic process from the affine stochastic volatility (ASV) model class. Conceptually, our estimator improves upon others by (i) focusing on discrete returns; (ii) allowing us to capture compounding and leverage effects; yielding (iii) horizon-consistent (iv) unconditional and conditional (i.e., in-sample and out-of-sample) estimates; and (v) not requiring ad-hoc conditioning variables. Our simulation exercise shows that our estimator is highly precise even when the true data-generating process partially deviates from that assumed by the estimator, and that it comfortably beats others advocated in recent studies. Using options data, we further show that our estimator best captures time-series variations in the risk-neutral conditional skewness of the S&P 500 index. In the second chapter, we apply our newly developed skewness estimator to U.S. single-stock data. We first show that our estimates easily beat those of other estimators from the literature. We next identify those stocks more likely to exhibit a U-shaped skewness-return horizon relation or an explosive skewness. Moreover, we show that while historical and forward-looking skewness align over long return horizons, historical skewness is a weak predictor of forward-looking skewness over short horizons, with the spread conditioned by various firm fundamentals and the economic state. We next reveal how our estimates relate to firm fundamentals and firm-fundamental-based skewness estimators. We finally estimate the term structure of forward-looking skewness premiums orthogonal to firm characteristics. In the third chapter, we empirically show that retail investors' preference for skewed assets meaningfully affects the skewness premiums of single stocks. Measuring the skewness premium as the difference between forward-looking skewness obtained from our newly developed skewness estimator and risk-neutral skewness obtained from options data, we report that the skewness premium of the average single stock significantly drops from the start of the COVID-19 pandemic. Exploiting the profound rise in retail investing over the same period, we establish that these drops in skewness premiums occur only for those stocks which observed the largest increases in their retail holdings.

Date of Award	1 Aug 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Kevin Aretz (Supervisor) & Yifan Li (Supervisor)