Definition. Cross-sectional predictability: a signal ranks assets against each other — high-signal names outperform low-signal names, market direction unknown and hedged away by the long-short construction. Time-series predictability: a signal forecasts an asset against its own history — direction itself, no hedge from construction. “Momentum works” means both claims to different papers (relative winners keep winning; assets with positive 12-month returns keep rising), and they are so different in mechanics and evidence that treating them as one is a category error with a P&L attached.
The worked example: same signal, two strategies, different worlds
Take 12-month past return on 500 stocks. Cross-sectional use: rank monthly, long the top decile, short the bottom. Every month contributes ~500 ranked observations; the market factor nets out; the classic failure is the momentum crash — the short leg (junk that cratered) rips upward in sharp reversals, delivering brutal negative skew while beta stays near zero. Time-series use: hold each asset long when its own 12-month return is positive, else flat/short. Each month contributes ~1 effective observation per regime (all 500 signals agree during broad trends — correlated bets, one bet); you carry structural beta most of the time; the failure mode is whipsaw at trend turns. Same input, different risk factory.
The evidence asymmetry follows: cross-sectional claims accumulate effective sample size fast (N assets × T periods, though cross-correlated), while time-series claims lean on far fewer independent regime episodes — a time-series result on 30 years of one index may rest on a dozen genuine trend cycles. Hold the two to different significance standards; most published time-series evidence is thinner than its t-stats look.
The checklist when a paper claims “predictability”
- ☐ Which claim is it? Long-short-ranked = cross-sectional; own-history-conditioned = time-series. If the paper mixes constructions across tables, evaluate each separately.
- ☐ Effective sample size computed accordingly: cluster cross-sectional stats by period; count time-series stats in regime episodes, not months.
- ☐ Beta accounting: time-series strategies must report performance against their embedded market exposure — a long-biased trend rule “predicting” equities in a bull sample is beta with a story.
- ☐ Crash mode identified: skew and worst-drawdown by construction — reversal spikes (cross-sectional) vs whipsaw regimes (time-series). A paper silent on its construction’s known failure mode hasn’t met its own literature.
- ☐ Costs match the construction: cross-sectional needs shorting and borrow costs; time-series needs turnover-at-regime-turns accounting.
- ☐ Breadth honesty: cross-sectional edges scale with breadth (many independent names); time-series edges scale with independent markets — 50 correlated equity indices are not 50 bets.
Questions to ask while reading
- If I hedged the market factor out of this result, what remains?
- How many independent episodes (not observations) support the claim?
- Does the paper test the same signal in the other construction — and if the effect exists in only one, does the mechanism story explain why?
- For ML papers: is the model predicting ranks or levels? Loss-function choice silently picks a claim type.
What our scoring captures — and misses
Our rigor scoring evaluates whether a paper’s evidence supports its claim, but the claim-type distinction itself is carried in the paper’s construction — and our archive shows the genres cluster: cross-sectional work dominates factor investing, time-series work runs through the trend and volatility literatures, and ML papers switch constructions between tables more than any other genre. When browsing hubs, read the portfolio-construction sentence before the results table; it tells you which evidence standard to load.
Companions: Momentum’s two families → · Evaluating factor papers → · Sample-size honesty →