A Penny a Share and the Arithmetic of Small Targets

Buy 1,000 shares of a $44 stock, sell them a penny higher, and the account gains $10 before costs. Do that 40 times in a day and the gross is $400. Pay a few tenths of a cent per share in fees on each side and a good part of that vanishes before lunch.

Scalping is the practice of harvesting moves that small, hundreds or thousands of times, with positions held for seconds or minutes. It looks like easy money because each trade is so modest in risk. The mathematics says otherwise, and the reason is that the target and the cost live on the same scale. When a trade aims for five cents and costs one, the cost is a fifth of the prize.

The topic has fresh relevance as of May 2020. Volatility is still elevated after the March collapse, and the large brokers dropped commissions on stock trades last fall. Many new accounts have arrived with the idea that free commissions make short-term trading free. They don't, because commissions were never the largest cost of a scalp.

The practice itself is old. Floor traders and exchange specialists lived on the bid-ask spread long before screens existed, and the first electronic market makers copied their arithmetic. What has changed is that anyone with a laptop can now attempt the same trade, usually without the rebates, the fast connections or the queue priority that make the arithmetic work for professionals.

This post walks through the numbers: break-even win rates, the random walk that governs most short-term price moves, how trade counts magnify both skill and error, and what it all means for names like C, MS, GS, EFA and META.

Break-Even Win Rates When Costs Loom Large

Start with the simplest accounting. Let W be the gross gain on a winning trade, L the gross loss on a losing one, c the round-trip cost per share and p the fraction of trades that win. Expected profit per share is p × W − (1 − p) × L − c.

Set that to zero and the break-even win rate is (L + c) / (W + L). With a five-cent target, a five-cent stop and a one-cent cost, the answer is 6/10, or 60%. A trader who wins half the time loses a cent per share on average, and no amount of discipline changes the sign.

Change the proportions of the bracket and the requirement moves. A ten-cent target with a five-cent stop and the same one-cent cost needs only 6/15, or 40%. Wider targets dilute the cost, which is why many short-term traders drift toward larger moves after their first month of tracking real fills.

The common misconception runs the other way. Many people judge a scalping method by its hit rate, and strategies that win 80% of the time feel wonderful. Take a two-cent target, a ten-cent stop and a one-cent cost. The break-even win rate is 11/12, about 91.7%, so an 80% winner loses 1.4 cents per share on average (0.8 × 2 − 0.2 × 10 − 1).

That pattern, many small wins and an occasional large loss, is a classic trap. Every day ends green except the day it doesn't, and one bad afternoon erases weeks. A tight target paired with a wide stop feels safe because it is rarely wrong, yet the arithmetic charges for that comfort.

Costs also need an honest definition. Commissions and exchange fees are the visible part. Crossing the spread costs half the quoted spread on entry and half on exit, and slippage on fast markets adds more. For liquid large caps the spread dominates the fee, so it belongs in c from the start.

Random Walks, Barriers and the Clock on Every Scalp

A scalp has two exits, a profit target and a stop. If prices follow a driftless random walk, the chance of touching the target a ticks above before the stop b ticks below is b / (a + b). A symmetric bracket wins half the time. A target of ten ticks with a stop of five wins 5/15, about one trade in three.

Plug that into expected profit and the gross result is zero for every bracket: (1/3) × 10 − (2/3) × 5 = 0. Wide target, narrow stop, tight target, wide stop, the expectation stays at zero before costs and goes negative after them. The bracket only changes how the outcomes are distributed, giving frequent small wins or rare big ones.

This is the central discipline of the subject. Exit rules cannot create positive expectancy in a pure random walk. A scalper needs a forecast, some reason to believe the next few cents are more likely up than down, or a structural payment such as an exchange rebate for providing liquidity.

The same model gives a clock. The expected number of steps before a walk hits one of the two barriers is a × b. A ten-tick target with a five-tick stop takes about 50 steps on average. If a liquid stock changes its quote 30 times a minute, that is under two minutes, which is why scalping is a game of speed and repetition.

Real prices depart from the pure model in useful ways. Quotes bounce between bid and ask, so a trade at the bid is slightly more likely to be followed by an uptick. Order imbalance, meaning more resting size on the bid than the offer, carries some short-horizon predictive power. These effects are small, often a fraction of a cent, and they are the raw material of every working scalping strategy.

They are also the territory where professionals compete. A fraction of a cent of predictability is worth capturing only if fees and slippage stay below it, and firms with exchange memberships pay far less than a retail account does. The retail trader's forecast has to be better to compensate for the higher cost.

Why Trade Count Magnifies Both Skill and Error

Suppose a method earns a net 0.2 cent per share per trade with a standard deviation of five cents per share on each trade. The per-trade information ratio is 0.002 / 0.05 = 0.04, which looks like nothing. Because independent trades accumulate with the square root of their number, 40 trades a day over 252 days is 10,080 trades, and the annualized Sharpe ratio becomes 0.04 × √10,080, about 4.0.

That is how scalping desks report Sharpe ratios that look impossible next to a stock fund. The number is real in the sense that the arithmetic holds, but it depends entirely on the 0.2 cent being real. Trim the expectancy to 0.1 cent and the Sharpe ratio halves. Add 0.2 cent of extra slippage and it goes negative.

Here is the harder question: how would a trader know the 0.2 cent exists? The standard error of an average is the standard deviation divided by √n. To see 0.2 cent at two standard errors with a five-cent trade deviation, n must satisfy 0.002 = 2 × 0.05 / √n, so √n = 50 and n = 2,500 trades.

At 40 trades a day that is about 63 sessions, roughly three months. A trader who judges the method after two weeks has seen 800 trades and a standard error of 0.18 cent, nearly as large as the claimed advantage. A lucky fortnight and an unlucky fortnight are both entirely compatible with zero skill.

Tails matter too. The five-cent standard deviation hides the occasional gap, such as a halt, a headline or a stop that fills 15 cents away instead of five. A handful of those per quarter can remove weeks of small gains, so the stop-loss distance in the model should come from observed fills, not from the order ticket.

Position size interacts with all of this. Doubling shares doubles both the expected dollar gain and the dollar variance, but market impact and queue position get worse with size. In liquid names the first few hundred shares fill at the quote, and thousands of shares start moving it.

Where C, EFA, MS, META and GS Fit

Different securities charge different amounts for the same cent target. Citigroup (C) and Morgan Stanley (MS) both traded in the $40s in mid-May 2020, and each usually quotes a one-cent spread with deep size. One cent on a $44 stock is about 2.3 basis points. Goldman Sachs (GS) at roughly $195 often quotes a spread of several cents, which is still only a basis point or two of price, but the cents-based arithmetic above bites harder.

Take a scenario on C. A trader posts passive orders on both sides and captures the one-cent spread plus a rebate of 0.2 cent per side, for 1.4 cents gross per round trip. Suppose 30% of fills are adverse, meaning the price moves through the order and the trade closes at a net loss of 1.6 cents after rebates. Expected profit is 0.7 × 1.4 − 0.3 × 1.6 = 0.5 cent per share, or $5 on 1,000 shares.

Now let the adverse fraction rise to 45%, which happens when faster participants pick off resting orders. Expected profit becomes 0.55 × 1.4 − 0.45 × 1.6 = 0.05 cent, or 50 cents per 1,000 shares. A fifteen-point shift in one behavioral parameter removed 90% of the profit. Most retail accounts also receive only part of the exchange rebate, which makes the true starting point worse.

Now a liquidity-taking scalp on GS. Suppose the spread is five cents and fees add 0.6 cent round trip, so costs measured from the midpoint come to about 5.6 cents. A symmetric ten-cent bracket then needs a win rate of (10 + 5.6) / 20 = 78%. No short-term signal we know of gets close to that reliably, which explains why spread-crossing in wider-quoted names rarely survives a proper test.

The iShares MSCI EAFE ETF (EFA) is a different animal. It quotes a penny spread near $58 with heavy volume, but it holds foreign stocks whose home markets close before the US session ends. Price discovery in the afternoon can lag the true value of the basket, and arbitrageurs trading against that gap will happily take the other side of a naive scalp.

META, the company that traded as Facebook in 2020, moves in larger increments at roughly $200 a share. A five-cent stop gets hit by ordinary noise, so brackets have to scale with volatility, perhaps 15 to 25 cents, which changes the cost ratio in the trader's favor but raises risk per share. Position size must shrink to keep dollar risk constant.

Risk sits in the financials too. C, MS and GS tend to move together on news about rates, credit losses or regulation, so three simultaneous positions behave like one larger position. A diversified-looking book of bank scalps can lose in a single move.

Testing a Scalping Method Before Real Money Touches It

Build the test around fills, not charts. Record the time, intended price, actual fill, shares and every fee for each trade. A paper-trading account that fills at the last price flatters the results, because live orders at the bid wait in a queue and often never execute when the price turns.

Once real fills exist, compute the average net result per share and the standard error described earlier. Wait for the test to cover at least 2,500 trades before treating a small positive average as evidence. Until then, size the account so that a run of losses consistent with zero skill does not end the experiment.

Costs deserve a separate ledger. Track the spread paid, the fees and the slippage against the intended price as three separate columns. When a method stops working, the cause is nearly always one column growing, and the columns show which.

Regulation and taxes add friction. Accounts under $25,000 face the pattern day trader rule, which limits a margin account to three day trades in five business days. Gains on positions held under a year are taxed at ordinary rates, and the wash-sale rule disallows losses when the same stock is repurchased within 30 days, which catches nearly every active scalper in the same name.

Time of day matters. The first 30 minutes after the 9:30 open carry the widest spreads and fastest moves, and the last half hour has heavy volume from index funds and closing orders. Midday is quieter, with narrower ranges, which suits tight brackets but offers less to capture.

Finally, set a daily loss limit before the session and respect it. A scalper in a drawdown tends to raise trade frequency to recover, which raises costs and removes the rest from the process. A fixed stop on the day, say 1% of the account, cuts the loop.

Turning the Arithmetic into a Plan

The central result is short. Gross expectancy in a random walk is zero, costs make it negative, and only a real forecast or a structural payment can lift it above zero. Everything else, the bracket shape, the hit rate, the speed of the platform, is a way of distributing outcomes around that starting point.

A few concrete steps follow. Write down the break-even win rate for the chosen target, stop and total cost, and compare it with the win rate observed in fills. If the required rate is above what the data supports, widen the target or drop the method.

Trade one liquid name first, such as C or MS, where a one-cent spread keeps costs measurable. Add GS, EFA or META only after the cost ledger for the first name is clean, because each has its own spread, volatility and timing quirks. Keep the number of shares small enough that fills match the quote.

Collect at least 2,500 trades before drawing conclusions, and compute the standard error alongside the average. If the confidence interval includes zero, the honest reading is that there is no demonstrated advantage yet. Scalping rewards patience about evidence more than speed about execution.

Finally, hold a realistic view of the competition. Professional firms see the same penny and pay less to capture it. A retail trader can still find a niche, for example in the wider moves after earnings or in names too small for the large firms, but it starts with the numbers above, run honestly on real fills.