Aggregate stock market returns display negative skewness, the propensity to generate negative returns with greater probability than suggested by a symmetric distribution. A large body of literature has aimed to explain this stylized fact about the distribution of aggregate stock returns (e.g., Fama, 1965, Black, 1976, Christie, 1982, Blanchard and Watson, 1982, Pindyck 1984, French et al., 1987, Hong and Stein, 2003). The evidence on aggregate returns contrasts with another stylized fact, namely, that firm-level returns are positively skewed. For this reason, theories of negative skewness that model single-firm stock markets necessarily depict an incomplete picture. In this paper I provide a unified theory for both stylized facts by explicitly modeling firm level heterogeneity and present evidence consistent with the theory.
The implications from the disconnect between firm-level return skewness and aggregate return skewness are best illustrated using the definition of sample skewness of a portfolio return. Skewness of a portfolio return is the sum of mean firm-return skewness and coskewness terms. Because mean firm skewness is positive, negative portfolio-return skewness must be caused by negative co-skewness terms. The co-skewness terms capture the average co-movement in one firm’s return with the variance of the portfolio that comprises the remaining firms. Thus, co-skewness depends on the cross-sectional heterogeneity of firm comovement, which makes the observed negative skewness in aggregate returns a cross-sectional phenomenon.
This paper argues that the behavior of stock prices around certain firm announcement events is consistent with the existence of positive skewness in firm returns and that cross-sectional heterogeneity in these events can account for the negative skewness in aggregate returns.
The paper provides a stationary asset pricing model of cash payout and earnings announcement events that captures the basic stylized facts on volatility and mean returns around such events. When cash payouts are periodic, cash flow news is discounted according to the time remaining until the next payout. The impact of news on the conditional return volatility is thus greater for news released closer to the payout. This gives rise to a pattern of increasing conditional return volatility, despite homoskedastic news shocks. In addition, discounting also implies that the conditional return volatility increases at an increasing rate.
The presence of a risk-return trade-off in the model implies that these properties apply to con-ditional mean returns and induces positive skewness in conditional mean returns. Similarly, the model predicts conditionally higher return volatility and mean returns around earnings announcement events due to large contemporaneous information flows. Firm returns may thus display sporadic and short-lived periods of high volatility and high mean returns around earnings announcements and positive skewness in conditional mean returns.
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Skewness in Stock Returns: Reconciling the Evidence on Firm versus Aggregate Returns
