Abstract
We investigate the marginal predictive content of small versus large jump variation, when forecasting one-week-ahead cross-sectional equity returns, building on Bollerslev et al. (2020). We find that sorting on signed small jump variation leads to greater value-weighted return differentials between stocks in our highest- and lowest-quintile portfolios (i.e., high–low spreads) than when either signed total jump or signed large jump variation is sorted on. It is shown that the benefit of signed small jump variation investing is driven by stock selection within an industry, rather than industry bets. Investors prefer stocks with a high probability of having positive jumps, but they also tend to overweight safer industries. Also, consistent with the findings in Scaillet et al. (2018), upside (downside) jump variation negatively (positively) predicts future returns. However, signed (large/small/total) jump variation has stronger predictive power than both upside and downside jump variation. One reason large and small (signed) jump variation have differing marginal predictive contents is that the predictive content of signed large jump variation is negligible when controlling for either signed total jump variation or realized skewness. By contrast, signed small jump variation has unique information for predicting future returns, even when controlling for these variables. By analyzing earnings announcement surprises, we find that large jumps are closely associated with “big” news. However, while such news-related information is embedded in large jump variation, the information is generally short-lived, and dissipates too quickly to provide marginal predictive content for subsequent weekly returns. Finally, we find that small jumps are more likely to be diversified away than large jumps and tend to be more closely associated with idiosyncratic risks. This indicates that small jumps are more likely to be driven by liquidity conditions and trading activity.
Highlights
Theoretical models of the risk-return relationship anticipate that volatility should be priced, and that investors should demand higher expected returns for more volatile assets
When the truncation parameter used to differentiate small from large jumps is based on a 5 standard-deviation (i.e., α = 5) cutoff, we find that average return spreads are 10% higher when signed small jump variation is sorted on rather than signed total jump variation
As we show that small jumps are more likely to be associated with idiosyncratic risk, and since signed small jump variation has a negative relationship with future stock returns, our results help explain the idiosyncratic volatility puzzle
Summary
Theoretical models of the risk-return relationship anticipate that volatility should be priced, and that investors should demand higher expected returns for more volatile assets. In increased predictive ability, relative to the case where only signed total jump variation is used in return forecasting, for big firms This finding is interesting, given that the comparison of aggregated and weighted jump variation measures indicates that small jump variation captures idiosyncratic risk. As we show that small jumps are more likely to be associated with idiosyncratic risk, and since signed small jump variation has a negative relationship with future stock returns, our results help explain the idiosyncratic volatility puzzle This is because of agent’s preference for lottery-like returns (i.e., investors will accept lower returns for stocks with high probabilities of having positive jumps).
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