A thicker queue at a round dollar buys no extra time in Intel and SoFi. Across all five Nasdaq stocks studied, round dollars attract more resting size than nearby prices. In those two names, price also leaves sooner. Lallouache and Abergel (2014), cited in the paper, already documented the concentration of limit orders at round prices. Jung and Lee's contribution is the shorter visit after matching on displayed depth. Conditioning on depth keeps the queue-size finding from explaining away the duration result.
What counts as a visit?
The familiar barrier argument starts with a thicker queue: more orders take longer to consume, so price should linger. The authors ask whether that holds at the same displayed depth. They call a longer stay at a round level "residual stickiness". Both round-number price clustering and the concentration of limit orders there are already familiar.
The authors build their price series from the best bid whenever the spread is exactly one tick. They use Nasdaq TotalView-ITCH level-1 data covering Apple, Cisco, Intel, SoFi and American Airlines across 250 trading days of 2025. A visit lasts as long as this series remains at a single level. Counts range from 291,109 visits for American Airlines to 4,363,496 for Apple.
In the theory section, tick size multiplied by the departure count serves as discrete local time. Multiplying departures by tick squared and dividing by time spent at the level gives a tick-grid Florens-Zmirou volatility estimator. In practical terms, the ratio measures queue depletion. The empirical analysis uses survival methods.
A piecewise-exponential hazard regression models duration using depth at entry, with six-degree-of-freedom splines fitted separately for bid and ask. Each stock has 3,232 day-by-half-hour strata. Round-level indicators distinguish a round bid from a round ask. The main statistic, the residual stickiness index, compares mean visit duration at round and control levels after matching entry depth. Removing the depth splines produces the raw index. Dividing raw by residual gives the composition factor, which measures how much of the duration difference depth alone explains. A separate logit models the direction of single-tick departures.
Thick queues, quicker departures
Separating duration from direction keeps three questions distinct. Do round levels attract deeper queues? Does price remain there longer? Do departures tend to go a particular way? Those are questions about order placement, hazard and direction, respectively. All five stocks show depth concentration, two show a directional push (Intel, SoFi), and none shows longer holding after adjusting for depth.
Round-dollar quotes have more displayed size in every stock. Cisco's bid/ask ratios are 1.07 and 1.12, compared with 1.47 on both sides for Intel and 1.50/1.46 for SoFi. Every interval excludes one.
Duration runs the other way: nine of ten round-dollar residual indices are below one. Intel's round-bid estimate is 0.94 [0.90, 0.98]; its round-ask estimate is 0.93 [0.89, 0.97]. The corresponding Benjamini-Hochberg adjusted p values are 0.01 and 0.004. SoFi records 0.93 [0.90, 0.96] on each side. Mean visits are roughly 6% to 7% shorter than at comparable prices.
Depth accounts for little of that gap. Composition factors range from 0.98 to 1.02, and controlling for depth takes Intel's bid index from 0.96 to 0.94. Half again as much resting size still buys no extra time.
The direction result is sharper. For Intel, 54% of single-tick departures go upward when the round dollar is the best bid, versus 46% when it is the best ask. An upward move from a round bid takes the quote pair away from the round price; a downward move from a round ask does the same. Adjusted log-odds are 0.11 [0.05, 0.16] and -0.09 [-0.15, -0.03]. Near a coin flip, that amounts to about two and a half points. SoFi's estimates are 0.06 [0.00, 0.11] and -0.08 [-0.13, -0.04], with the bid side touching zero. Neither stock shows a significant directional effect at placebo levels three cents above the dollar.
Repeller is a fair name for it: price leaves a thick queue faster, moving away from the round number.
The gap fades after the first second
The departure-rate difference is concentrated early. During the first 0.01 seconds of a visit, inverse hazard ratios range from 0.90 to 0.91 for Intel and equal 0.85 for SoFi. The authors distinguish this timing result from the directional finding: it describes departure rates and does not establish when the directional bias appears. Neither side differs from one beyond one second in Intel or beyond 0.1 seconds in SoFi.
The first hour also carries the time-of-day result. Intel's ask index is 0.87 [0.81, 0.93], while SoFi records 0.89 on each side. Every interval over 10:30 to 15:00 includes one.
This timing matters when reading the headline 0.93. The reported index comes from a flat-baseline fit. It equals a mean-duration ratio when the baseline hazard stays constant within each stratum. The authors flag the distinction and show its size in their own simulation: an inverse hazard ratio of 2.84 accompanies a mean-duration ratio of 1.88. The headline therefore deserves to be read as a flat-baseline summary of an effect concentrated in the opening milliseconds.
Intel's result is less settled than SoFi's. Its bid interval includes one when distance bands are removed (0.95 [0.89, 1.02]), when distance receives a smooth control (0.97 [0.92, 1.02]), and on common depth support (0.96 [0.92, 1.01]). SoFi remains between 0.93 and 0.96, with every interval excluding one.
Apple and Cisco have directional log-odds within 0.03 of zero. Apple's intervals, [-0.05, 0.01] at the bid and [-0.02, 0.04] at the ask, exclude the Intel and SoFi estimates. American Airlines alone remains inconclusive. Apple's duration finding is less secure: the spread is one tick for only 28.7% of session time, the filters retain 66.8%, and the authors decline to interpret its 0.94 bid index.
American Airlines supplies about 2,700 round-dollar visits per side. The paper estimates its power to detect a directional effect the size of Intel's at about one half for the bid and one third for the ask. Across stocks, the pattern fits a tick-size account. Within stocks, it does not. Intel's bid-side direction interaction has the wrong sign, at -0.059 per basis point [-0.105, -0.012], and the authors note that both prices rose during the year. The evidence comes entirely from the Nasdaq book. As the authors caution, it need not carry over to the consolidated market.
One methodological choice earns its place. In the authors' queue simulation, controlling for contemporaneous depth erased a planted replenishment effect: the estimate was 1.006 against a true 1.882. The main specification therefore fixes depth at entry. With splines, the simulation recovers 1.869 against 1.882. The authors note that this recovery depends on liquidity working only through entry depth.
On the desk
The use is execution context. The paper measures departures of the quote pair and never measures fills, queue position or P&L. Consider a passive buyer at an Intel round-dollar bid. The 54% upward-move share describes price leaving without a fill, with the buyer behind a queue about 47% deeper. That supports more cautious pricing of passive round-dollar orders in the first hour. It supplies no signal with a net return.
We could not test any of these results. Constructing one-tick visits and measuring entry depth requires event-level bid and ask quotes with displayed queue sizes. Our equity data consist of one-minute OHLCV bars. They cannot recover sub-second visits or the depth behind them.
A sixth stock with a three-to-four basis point tick and no opposite-signed log-odds at the round bid and ask would change my mind.