Mykola Babiak, Jozef Baruník, Josef Kurka
9 min
This paper uncovers a powerful new predictor for stock market returns: skewness dispersion, the cross-sectional spread in how asymmetric individual stock returns are. Using high-frequency intraday data from nearly 7,000 U.S. stocks (2000-2022), authors Babiak, Baruník, and Kurka show that when firms' return distributions vary widely in their 'tailedness'—some highly positively skewed (lottery-like upside), others negatively skewed (crash-prone)—future aggregate market returns tend to be low. High dispersion signals investor disagreement on asymmetric risks, which resolves slowly, especially around macro news, dragging down near-term equity risk premiums.
Unlike prior work focusing on average firm skewness (Jondeau et al., 2019), dispersion captures heterogeneity. Think of it as measuring chaos in skewness opinions across stocks: low dispersion means uniform asymmetry (everyone agrees on the shape), high means wild differences. This beats 49 out of 50 established predictors (e.g., dividend yield, VIX) in out-of-sample tests and delivers massive portfolio gains.
Realized skewness is computed daily for each firm from 5-minute intraday returns: it's the standardized third moment, capturing asymmetry in high-frequency price jumps. Dispersion is the inter-percentile range (e.g., 90th minus 10th percentile) across all firms that day. This uses a 'five-minute grid'—last price per bin—to balance noise and precision, alongside realized variance (sum of squared returns) for scaling.
Intuition: Positive skewness means more extreme upside moves; negative means downside crashes. High dispersion periods show a polarized cross-section—some stocks lottery-like, others crash-prone—reflecting heterogeneous beliefs or risks not yet priced in.
Skewness dispersion negatively predicts market returns 1-12 months ahead (e.g., 1-standard-deviation increase cuts 5-10% annualized returns). It's robust:
Power concentrates around FOMC announcements: dispersion spikes pre-meeting on unresolved macro uncertainty, resolves post, driving predictability via slow news diffusion.
A mean-variance investor tilting allocations based on dispersion forecasts reaps huge rewards: certainty-equivalent gains of 709-875 basis points annually, Sharpe ratios 0.82-0.91 vs. buy-and-hold's ~0.4. This holds with transaction costs, varying risk aversion—pure alpha from timing market exposure.
Rational: High dispersion ties to elevated aggregate risk (positively with VIX), as heterogeneous asymmetries amplify tail risks. Behavioral: Links to sentiment (e.g., AAII bullishness)—predictability strengthens in optimistic regimes, when investors overweight skewed stocks.
Overall, dispersion proxies investor belief heterogeneity, gradual macro incorporation, and risk premia adjustments. It fills a gap: higher moments matter for aggregates via variation, not just means.
Cross-sectional dispersion in firm-level realized skewness is significantly and negatively related to future stock market returns. The predictive power of skewness dispersion is robust to in-sample and out-of-sample estimation and is incremental over a broad set of existing predictors, with only a few alternatives retaining independent explanatory ability. Skewness dispersion also delivers substantial economic gains in portfolio allocation. Its forecasting power is concentrated in months with monetary policy announcements, reflecting an information-based mechanism. The empirical evidence suggests that skewness dispersion captures the gradual incorporation of macro news into prices, which is driven by variation in aggregate risk and valuation adjustments.
Alex: Okay, so it holds up on its own reliably. What happens when they pit it against the other predictors head-to-head?
Sam: In bivariate regressions, they paired dispersion with each of over fifty established signals—like average skewness across stocks, investor sentiment gauges, or macro variables—one at a time. The dispersion's negative link stayed strong and significant in nearly every case, while most others became insignificant when added alongside it.
Alex: That suggests it's not redundant—it's adding something new to the mix.
Alex: That in-sample robustness is promising, but as you mentioned earlier, most predictors crumble out-of-sample. How does this dispersion measure hold up there?
Sam: Out-of-sample tests check if a predictor works on fresh data never seen during its development, like training a game AI on one level and seeing if it handles new ones without retraining. They used an expanding window starting December 2005, estimating the link each month and forecasting ahead. The paper compares squared prediction errors—how far off the guesses are—to a simple benchmark of just the historical average return. Out-of-sample R-squared ranges from about 2% to 9% across measures and horizons, reliably better than the benchmark.
Alex: So it beats the naive average by a meaningful margin on new data. Does that edge hold when paired with those other predictors in out-of-sample tests too?
Sam: Yes. In bivariate out-of-sample setups—one dispersion plus one other signal at a time—it still delivers lower errors than the historical average or the other signal alone for most pairings. This underscores its unique content from clashing investor views on risks.
Alex: Interesting—ties back to heterogeneous beliefs getting resolved. And you said its power clusters around FOMC announcements; is that sharper out-of-sample?
Sam: The evidence points to yes. Predictive strength concentrates in monetary policy announcement months, where macro news like FOMC decisions slowly seeps into prices, unifying mismatched skewness views. Out-of-sample, this timing signal persists.
Alex: So that timing around FOMC holds out-of-sample too. But for investors actually using this, how does it translate to real portfolio decisions—like, does it beat the historical average in terms of actual returns after risk?
Sam: Investors often decide how much to put in stocks versus safe assets by forecasting returns and volatility ahead. They use a formula that balances expected gain against risk aversion—like tilting more toward stocks if the forecast looks good, but pulling back if it signals trouble. The paper tests this with a mean-variance investor, who picks weights to maximize sure gains after accounting for ups and downs. Using dispersion forecasts yields certainty equivalent return gains of several hundred basis points annually at one month, compared to just following the historical average.
Alex: Certainty equivalent return—wait, so that's the steady payoff they'd take instead of the risky portfolio?
Sam: Yes. It's the risk-free rate an investor would accept over the portfolio's mix of average return minus half the risk aversion times variance. Higher means the strategy's worth it. Here, dispersion portfolios also hit Sharpe ratios up to 0.91, a clear step above buy-and-hold's 0.57.
Alex: You've mentioned belief clashes and policy timing a few times. Is the paper pinning this down to investors being too optimistic, or something about actual risks changing?
Sam: The authors check both angles. For risks: when dispersion is high, it lines up with lower overall market ups-and-downs—measured by summing squares of tiny price changes throughout the day—and with less agreement in how stocks move together. This suggests high dispersion flags times of actually lower risk. On the behavioral side, it correlates positively with surveys of everyday investors' optimism, like the American Association of Individual Investors poll. Stronger links show up when those surveys tilt bullish, hinting at over-optimism that corrects later.
Alex: So both rational lower risk and behavioral cheerfulness explain the negative link to future returns?
Sam: Yes. The direct survey ties closer, with predictive power doubling in bullish periods versus bearish ones. This mix gets resolved when big news hits. They split months into before, during, after FOMC, and none. The negative link shines in FOMC months but near zero outside. It starts pre-announcement as positions build, stays strong during, and fades post.
Alex: That gradual seep-in makes sense for why it times policy events well.
Sam: To test if it's really about lopsidedness in returns rather than just extreme ups and downs overall, the authors checked kurtosis dispersion—how much stocks differ in the thickness of their price tails, those rare big jumps or drops. High spread there also predicts lower future returns. But it fades more quickly compared to the skewness version, likely because tail extremes are noisier from odd outliers.
Alex: So kurtosis spread backs up the pattern, but points to asymmetry being the cleaner signal?
Sam: Exactly. Kurtosis is more prone to spurious spikes from single weird events, making it less reliable long-term.
Alex: Any other catches, like with the data itself?
Sam: A key one is reliance on high-speed price ticks every five minutes, using the last price in each slot to average out trading glitches—what's termed microstructure noise from bid-ask bounces or fleeting orders. This can muddy precise tail reads if not handled carefully. Predictability also softens beyond six months, as signals from belief clashes resolve mainly short-term around news.
Alex: Right, so strengths in timing short windows, but horizons and data noise are limits to watch.
Sam: Overall, the evidence suggests skewness dispersion offers a robust, unique tool for investors—delivering better forecasts than historical averages or most rivals out-of-sample, with portfolio edges like twice the risk-adjusted returns of passive holding in key tests. It enables real-time tilts around policy news, where traditional macro cues often miss. For the field, it highlights high-frequency views on asymmetries as a path to smarter equity timing.
Alex: That's a solid takeaway—incremental progress on what drives returns through investor mismatches. Thanks for breaking it down, Sam.
Sam: My pleasure, Alex. This paper adds meaningfully to understanding market predictability. Thanks for listening to ResearchPod.