The long-short option return looks easiest to collect from the quoting side of the market. The authors report 0.22% to 0.45% per half-day, gross of costs. A delta-hedged option that performs well overnight tends to lose ground during the next trading day, then perform well the following night. Same-session continuation remains visible 20 business days back: the lag-40 slopes are 0.030 intraday and 0.040 overnight. That long memory is the paper's new finding, and the evidence for it holds up. Who can collect the return is the harder question.
The returns are the P&L on a delta-hedged single-stock option in separate intraday and overnight windows. Intraday runs from 10:00 to 16:00; overnight runs from 16:00 to 10:00 the next morning. Each window predicts its own next return and reverses the other. A strong night, for example, forecasts a strong next night and a weak next day.
The authors locate the source in market making. End users persist in pushing one way, while dealers with limited capacity absorb that flow and adjust quotes around the session boundary. The evidence comes from CBOE 30-minute NBBO snapshots from 2004 to 2021.
The half-day pattern
Bali, Goyal, Mörke and Weigert assign the first half hour of trading to overnight, an explicit choice in their split between 16:00 to 10:00 and 10:00 to 16:00. They revise the intraday hedge every 30 minutes. Returns follow the Muravyev and Ni delta-hedging method and use NBBO mid-quotes from CBOE 30-minute snapshots. Their universe consists of at-the-money contracts with 5 to 50 days to expiry, averaged per underlying, from January 2004 to December 2021.
Fama-MacBeth regressions across 40 half-day lags show how the pattern changes with time. At lag 1, the prior overnight return has an intraday slope of -0.152 (t = -30.48); the prior intraday return has an overnight slope of -0.229 (t = -40.70). The slopes switch sign at lag 2, when the observation comes from the same session one day earlier: 0.094 intraday and 0.095 overnight. At lag 40, they remain 0.030 (t = 6.99) and 0.040 (t = 12.63). Decile long-short portfolios formed on the last five days of same-session returns earn 0.23% per half-day intraday (t = 19.85) and 0.42% overnight (t = 19.34). Cross-session reversal sorts earn -0.25% and -0.28%. Tian-Wu alphas for momentum are close to the raw returns, at 0.21% and 0.37%.
The demand evidence comes from Nasdaq signed non-market-maker volume from 2009 to 2021. Intraday order imbalance has a lag-2 slope near 0.09; it declines to about 0.02 by lag 20, with every lag positive. "Buyers tend to remain buyers, and sellers remain sellers," the authors write. They read the combination of persistent demand and alternating returns as evidence of market-maker capacity strained at the session boundary.
How far back does the finding reach?
Muravyev and Ni already documented the unconditional day-night sign flip, as this paper acknowledges. The authors also cite two recent intraday studies. Da, Goyenko and Zhang find that a straddle's 30-minute return predicts its return in the same interval tomorrow. Beckmeyer, Filippou, Zhou and Zhou find that the overnight return negatively predicts the 10:00 to 10:30 return. Their finding overlaps with this paper's lag-1 reversal.
That reversal is concentrated almost entirely at lag 1. Once the most recent five days of opposite-session returns are dropped (lags 11 to 19), the intraday return is -0.05% (t = -9.41). Extending the window to 20 days reduces the five-day -0.25% to -0.13%. Momentum lasts longer. Skipping the last ten days (lags 22 to 40) still produces 0.12% intraday and 0.28% overnight. Among the studies this paper cites, none reports same-session continuation through 20 business days.
What about the underlying stock?
Stocks also show day-night periodicity, which makes inherited stock returns an obvious concern. The delta hedge strips out first-order exposure. Adding controls, including the underlying stock return, changes the intraday lag-1 slope from -0.152 to -0.170. A spanning regression gives a more direct check: the authors regress the option-sorted long-short return on an option portfolio sorted by past stock half-day returns. Intraday five-day momentum retains an alpha of 0.23% (t = 26.07), with a beta of -0.03 (t = -0.54) and an R2 of 0.03%. Every R2 in that table is below 1%.
The day-night volatility ratio has little economic effect on the result. Intraday five-day momentum earns 0.15% in its low tercile and 0.16% in its high tercile. The 0.01 difference has a t of 2.85 and is economically negligible; the overnight difference is 0.01 (t = 1.38). On stock-return inheritance, the paper makes a convincing case.
Where quotes are thinnest
The liquidity, size and venue-concentration sorts put the largest returns in the least inviting places to trade. Overnight five-day momentum earns 0.47% in the top tercile of bid-ask spread volatility, against 0.07% in the bottom (difference t = 25.79). Where trading is concentrated on few exchanges, it earns 0.63%; where trading is fragmented, 0.15%. The venue test uses a Herfindahl-Hirschman index of exchange volume shares, orthogonalized to volume, over 2012 to 2019. Small underlyings earn 0.46% against 0.06% for large ones. Options trading fewer than 10 contracts a day earn 0.57% in a quintile sort. Pooling all options that pass the filters lifts overnight momentum to 1.01%, roughly twice the main specification's 0.42%, although the authors describe the result as unchanged. The three-year rolling overnight spread rose from about 0.10% to nearly 1.00%.
Every return there is gross.
The authors acknowledge the cost issue: "Even if our strategy's alpha is zero after costs, the existence of systematic intraday and overnight return predictability is economically informative about return formation and the role of market frictions," they write. Gross returns can show compensation for providing liquidity in quoted prices. Their defence works as an account of price formation, and our reading of the spread-volatility and exchange-concentration sorts also turns on frictions. Yet their filter allows spreads as wide as 70% of mid or $3. A 0.42% mid-to-mid edge in that setting describes where quotes sit; a taker must pay the spread to trade against them.
A persistent stock-specific difference between the 16:00 quote and the 10:00 quote could also generate the signature: positive same-session autocorrelation, negative cross-session autocorrelation, and a slow decay. The bid-to-bid and ask-to-ask checks address bounce, their intended target. A lean that moves both sides of the quote together would pass those checks. This possibility sits close to the authors' supply account. A market maker leaning closing quotes in a concentrated, wide-spread name could produce the same result. The clearest claim on the long-short return still belongs to whoever sets the quote.
Two text slips deserve correction. The prose calls -23.2bp overnight and -20bp intraday the medians, though Table 1 places those values in the first quartile; the medians are -0.050% and -0.019%. The introduction calls 0.46% the limits-to-arbitrage gap. It is the high-tercile level, while Table 7 reports a difference of 0.37.
Why we did not backtest half-day option momentum
This signal requires option mid-quotes at 10:00 and 16:00 each day, as well as prices for the 30-minute re-hedges between them. Our option data contain end-of-day quotes and Greeks. Minute stock bars can cover the hedge leg, but they cannot provide option prices at the session boundary.
We did not find value-weighted portfolio sorts or a test executed at the bid and ask. Either could establish whether the result is a trade or a map of where quotes become less competitive. For now, we read it as the latter, and as useful evidence for anyone making markets in single-name options trading fewer than 10 contracts a day.