Setting an Entry Price Also Sets the Probability That the Order Never Fills

A conditional entry order carries two decisions inside one instruction. The first is the price, and it gets nearly all the attention. The second is the probability that the order never becomes a position at all, and it is usually discovered later. Both are fixed the moment the order is entered, and the second is not a matter of patience or conviction. It is arithmetic, and it can be written down before the order is sent.

The starting point is a distinction the SEC's Office of Investor Education states plainly across its bulletins on order types: a guarantee of price and a guarantee of execution are separate things, and no single order type carries both.

What Each Order Type Guarantees, and What It Leaves Open

The wording in the SEC's investor materials is worth reading literally rather than in summary. On market orders: "A market order is an order to buy or sell a stock at the best available price. Generally, a market order will be executed immediately." Immediately, but not at a known price, because "the price at which a market order will be executed is not guaranteed."

On limit orders, the trade runs the other way. "A limit order is not guaranteed to execute," the same bulletin says, and it gives the condition: "A limit order can only be filled if the stock's market price reaches the limit price." FINRA's investor page on order types puts the same point in the negative: "if the market price fails to match or better your limit price while your order remains active, it will not be executed."

Stop orders sit between the two and are frequently misread as a price commitment. They are not: "The stop price is not the guaranteed execution price for a stop order," because once the stop price is reached the instruction becomes a market order. A stop-limit order restores the price control and gives back the certainty of trading, which the SEC notes directly, warning that such an order "may not be executed if the stock's price moves away."

Every entry method is therefore a choice about which of the two uncertainties to keep. That choice has a number attached to it, and the number can be estimated in advance.

The Non-Fill Rate Is Set at the Same Moment the Price Is

Take a stock quoted at $100.00 and a trader who would rather not pay $100.00. The instruction is a buy limit at some distance d below. To turn that into a probability, three assumptions have to be stated, because the result is a property of the assumptions and not a measurement of any market:

• The price follows a driftless random walk with a daily standard deviation of 1.5%.
• The order is live and continuously monitored for T trading days.
• A touch of the limit price counts as a full fill at that price.

Under those assumptions the probability that the price trades at or below the limit at least once before the order expires is P = 2 × N(-d / (sigma × sqrt(T))), where N is the standard normal distribution function. Everything depends on one ratio: the distance divided by the standard deviation scaled to the order's life. For a five-day order at 1.5% daily volatility that scaling factor is 1.5% × the square root of 5, or 3.35%.

Limit distance	Fill probability, 1 day	Fill probability, 5 days	Fill probability, 20 days	Expected improvement per attempt, 5 days
0.50%	73.9%	88.1%	94.1%	0.44%
1.00%	50.5%	76.6%	88.1%	0.77%
1.50%	31.7%	65.5%	82.3%	0.98%
2.00%	18.2%	55.1%	76.6%	1.10%
2.50%	9.6%	45.6%	70.9%	1.14%
3.00%	4.6%	37.1%	65.5%	1.11%
4.00%	0.8%	23.3%	55.1%	0.93%
5.00%	0.1%	13.6%	45.6%	0.68%
6.00%	0.0%	7.4%	37.1%	0.44%

The right-hand column is the distance multiplied by the probability of getting it: the improvement the instruction earns per attempt, averaged over the attempts that fill and the attempts that do not. It rises, flattens, and falls.

The turn is not an accident of the chosen numbers. Writing x = d / (sigma × sqrt(T)), the expected improvement is proportional to x × 2N(-x), which reaches its maximum at x of about 0.75 regardless of the volatility assumed or the horizon chosen. At 1.5% daily volatility and a five-day life that lands at roughly 2.5% below the reference price, where the order fills 45.6% of the time. Past that point the instruction is asking for a larger discount and collecting it less often, and the product of the two shrinks.

None of that is a recommendation. Expected improvement is not expected profit: the calculation assigns zero value to the trades that never happen, which is the one quantity it cannot supply. Whether a 54.4% non-fill rate is acceptable depends on what the missed exposure was worth, and that is a question about the strategy, not the order.

The Same Distance Is a Different Order at a Different Horizon

A limit 2.00% below the reference price fills 18.2% of the time if it is live for a single session, 55.1% over five sessions, and 76.6% over twenty. The price in the instruction did not change. The time-in-force did, and the time-in-force is the other half of the arithmetic. A trader who describes an entry only by its price has specified about half of it.

Touching the Price and Receiving the Shares Are Different Events

The table above is deliberately generous, because it treats a touch as a fill. In practice the touch is the first of several conditions, and each of the others can fail on its own.

The first is whether the order is visible at all. SEC Rule 604 (17 CFR 242.604) requires that customer limit orders priced better than a market maker's quote be displayed, but the rule carries a list of exceptions in paragraph (b): orders executed on receipt, orders where the customer expressly requests no display, odd-lot orders, block size orders "unless a customer placing such order requests that the order be displayed," orders routed immediately to another venue, and "all or none" orders. An order that qualifies for one of those exceptions can sit at the right price without ever advertising itself.

The second is rank at that price. Exchange rulebooks set an explicit ordering. NYSE Rule 7.36 defines priority categories in which unexecuted market orders "have priority over all other same-side orders with the same working price," displayed non-marketable limit orders come second, and non-displayed interest, including the hidden portion of reserve orders, comes third. Resting behind that stack means the price can print without the order being reached. Venues also differ in how they allocate within a category, so a general assumption of pure first-in, first-out is not safe across markets.

The third is size. A print at the limit price clears only the quantity it carried, so a resting order larger than the volume traded at its price comes back as a partial fill: a position of unplanned size rather than the one that was sized in advance.

How Long the Order Lives Is Not Entirely the Trader's Choice

The horizon T in the arithmetic is usually assumed to be whatever the platform's time-in-force menu says. It is worth checking what that menu promises.

Investor.gov defines a good-til-cancelled order as one "to buy or sell a stock that lasts until the order is completed or canceled," and then adds the qualification that matters: "Brokerage firms typically limit the length of time an investor can leave a GTC order open. This time frame may vary from broker to broker."

At the venue level the picture has been narrowing rather than widening. The New York Stock Exchange filed in 2015 to "eliminate GTC Orders (which are also defined as 'Open' Orders) and Stop Orders," with conforming changes across fifteen other rules, on the stated ground of streamlining its order type offerings. More recently, Nasdaq filed to discontinue the good-til-cancelled time-in-force attribute in its equities market entirely, deleting the GTC definition at Equity 4, Rule 4703(a)(3) and removing the "one year after entry" expiry option from Rule 4703(a). The filing states the exchange "currently intends to discontinue GTC Orders on February 2, 2026," that orders resting on the book at the close on January 30, 2026 were to be cancelled by the exchange, and that "any new GTC Orders sent to the Exchange will be rejected" afterward. The reason given was usage: "very few Participants avail themselves of the GTC TIF."

The practical reading is not that long-dated entry orders have disappeared. It is that a long-dated entry order is generally an instruction held by a broker and released to a venue when its conditions approach, rather than a claim on a queue position that has been accruing since the day it was entered. The horizon in the arithmetic is set by the broker's own cap, and that cap is a documented number that differs between firms.

Events That Change the Order While It Waits

An unfilled order is not a frozen object. FINRA Rule 5330 requires members to adjust open orders on the ex-date of a dividend or distribution. For a cash dividend, "unless marked 'Do Not Reduce,' open order prices shall be first reduced by the dollar amount of the dividend," with the result rounded down to the next lower minimum quotation variation. Distributions of less than one cent are excluded. For stock dividends and forward splits, both the price and, unless marked "Do Not Increase," the share quantity are adjusted by the split ratio, with the size rounded to the next lowest share. For a reverse split the rule is categorical: "the order (buy or sell) shall be cancelled." The rule also lists what falls outside it, including open stop orders to buy, open sell orders, and orders governed by the rules of a registered exchange.

So the distance d that was chosen on entry can be moved by a corporate action the trader had no part in, the share count can change, and in the reverse-split case the order can cease to exist without anyone cancelling it.

Volatility controls interrupt the other side of the assumption. Under the national market system plan governing extraordinary volatility, price bands are set around a reference price at 5% for Tier 1 securities above $3.00, 10% for Tier 2 securities above $3.00, 20% for securities priced from $0.75 up to and including $3.00, and the lesser of $0.15 or 75% below that, with the bands doubled during the last 25 minutes of the regular session. If quoting stays at a band edge for 15 seconds, the primary listing exchange declares a five-minute trading pause, which can be extended by another five minutes. During a pause the model's assumption of continuous monitoring is simply false, and the guarantee that a market order executes immediately is suspended along with it.

What Would Invalidate This

The arithmetic above is a frame, and there are clear conditions under which it stops describing anything useful.

• Drift and volatility clustering. The formula assumes no drift and constant volatility. Real return series show neither. In an instrument with a strong directional tendency over the order's life, the touch probability computed here can be badly wrong in either direction, and the error grows with the horizon.
• Gaps. Continuous monitoring is an idealisation. An order that is live only during regular hours faces overnight moves that can open through the limit, in which case the fill is better than the limit price and the "improvement equals d" assumption understates it, or can reverse before the session opens, in which case the touch never registers at all.
• Depth relative to order size. For a small order in a heavily traded name, the display, ranking and size conditions almost never bind, and the touch probability is close to the whole story. For a large order, or a thin one, they can dominate everything the price model says.
• The purpose of the entry. If the strategy's edge is in the entry price itself, a low fill rate is the intended output rather than a defect. If the edge is in being present for a move, the same low fill rate removes the edge. The same number reads in opposite directions depending on which of those is true, and the arithmetic cannot tell them apart.
• Order handling that is not modelled here. All-or-none conditions, minimum-quantity conditions, and broker-held conditional orders all behave differently from the plain resting limit assumed above.

Concrete Framework

1. Write down both halves of the entry. Record the limit price and the time-in-force together. An entry described only by its price has left the more consequential half unstated.
2. Compute the ratio before sending the order. Divide the intended distance by an estimate of the instrument's standard deviation over the order's life. The ratio x = d / (sigma × sqrt(T)), not the distance in dollars, is what determines the fill probability.
3. Convert the ratio to a non-fill rate and read it out loud. At x near 0.75 the arithmetic above gives roughly a 46% fill rate, which is another way of saying the instruction is designed to do nothing more often than it does something.
4. Decide, in advance, what a non-fill means. Whether the plan calls for re-entering at market, moving the limit, or letting the setup pass is a decision that is cheaper to make before the order exists than while the price is leaving.
5. Check the venue and broker terms rather than assuming them. Confirm the firm's maximum life for a resting entry order, whether it is held at the broker or sent to a venue, and how the platform handles stop and stop-limit triggers.
6. Check the calendar against the order. Note any ex-dividend date, split, or reverse split falling inside the order's intended life, since FINRA Rule 5330 can reprice, resize, or cancel the order without further instruction.
7. Log the non-fills as entries in the record. A journal that records only executed trades measures the fill rate at 100% by construction, and a fill rate is not something a strategy can be evaluated without.
8. Re-derive the numbers when volatility changes. The same limit distance is a different order at 1.0% daily volatility than at 2.5%, and nothing in the order ticket announces that it has changed.

The frame holds only under the assumptions listed, and the figures throughout are calculated from those assumptions rather than measured from market data. What survives the assumptions is narrower and harder to argue with: an entry condition specific enough to be worth setting is also specific enough to be missed, and the rate at which it is missed was chosen at the same time as the price.