Essays on predicting downside risk in firms

Abstract

Understanding and predicting downside risk is central to asset pricing, risk management, and corporate governance. This chapter includes three studies that investigate different dimensions and informational sources of downside risk in equity markets. While all three chapters focus on large, downward movements in stock price, each study investigates a different explanation: managerial discretion, dispersion in investors’ beliefs, and directional positioning in the options market.
The first study examines the determinants of the skewness risk premium (SRP), defined as the difference between risk-neutral skewness and realized skewness. SRP reflects the compensation earned by investors who sell crash risk, typically by shorting out-of-the-money (OTM) options. In normal conditions, SRP is positive because realized skewness tends to be smaller than the market's ex-ante expectation. However, when large negative returns occur, realized skewness increases sharply and may exceed the anticipated level, resulting in a negative SRP. This chapter shows that managerial discretion, proxied by discretionary accruals, predicts negative SRP. When firms delay the release of bad news through earnings management, the market underestimates the probability of large negative returns. Once the accumulated bad news is eventually disclosed, realized skewness becomes more negative than expected, resulting in a negative SRP. Accordingly, firms that hoard bad news, as reflected by higher levels of earnings management, are more likely to exhibit lower or negative SRP. The effect is especially pronounced around earnings announcement periods. These findings suggest that financial reporting distortions impair the option market’s ability to accurately assess and price downside risk.
The second study explores how investor disagreement, measured from options data, predicts stock price crashes. The key variable is dispersion in investors’ beliefs (IDISP), a model-free proxy that reflects the divergence in beliefs among option market participants. High IDISP indicates increased demand for deep out-of-the-money and deep in-the-money options, often driven by investor concern over extreme downside risk. The analysis shows that IDISP significantly predicts future stock price crashes. This relation reflects a buildup of divergent views that cannot be fully expressed due to market frictions, similar to the mechanism behind other disagreement measures in the stock market. This predictive power remains robust after accounting for firm characteristics and alternative controls. The study also investigates several mechanisms that may amplify this relation. It finds stronger effects when financial reporting quality is low, short-sale constraints are tight, investor sentiment is elevated, or around earnings announcements. These results suggest that belief dispersion interacts with market frictions to increase crash risk.
The third study builds on the previous chapter by shifting the focus from non-directional belief dispersion to directional positioning in the options market. While disagreement captures the extent of divergence in investor opinions, it does not indicate whether informed traders anticipate downside risk. This study examines whether trading patterns in strike asymmetry, particularly in out-of-the-money (OTM) put options, can reveal such directional expectations. The key variable is option strike asymmetry, a model-free measure constructed from strike price and trading volume across different option categories. The analysis covers various combinations of moneyness and option type, with the strongest predictive power observed in deep OTM puts. Lower strike asymmetry, reflecting heavier trading in lower-strike options, is associated with a higher likelihood of future crashes. This relationship remains robust across alternative crash definitions, firm-level controls, and disagreement proxies. The study further explores mechanisms including short-sale constraints, financial reporting quality, and investor sentiment. The findings suggest that directional option positioning reveals private downside beliefs and provides early warnings of crash risk.
Overall, this chapter contributes to the understanding of downside risk by examining how firm-level financial reporting behavior and option market signals relate to large negative stock returns. The three chapters study earnings management as an internal source of crash risk, and use belief dispersion and strike-level positioning to capture investor expectations about potential crashes. The results show that these signals help identify when crashes are more likely to occur. These findings offer useful insights for researchers and investors seeking to better understand and manage the risk of sharp price declines.