The Trader's Arithmetic · Lesson 6 of 6

The Cost Tax: Arithmetic's Final Word

Your expectancy has a silent partner who takes their cut on every single trade, win or lose.

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Every formula so far assumed your wins and losses arrive intact. They do not. Spread, commission, overnight swap and slippage skim every trade — and because the skim is per-trade, it plugs straight into the expectancy formula as a constant negative term:

Real expectancy = (Win% × avg win) − (Loss% × avg loss) − average cost

That last term looks trivial — a pip and a half, perhaps. Now watch it eat a system. Take a genuinely profitable setup: 55% win rate, 25-pip target against a 40-pip stop... wait — that is below the 61.5% hurdle from lesson two, so make it 65%: expectancy = (0.65 × 25) − (0.35 × 40) = 16.25 − 14 = +2.25 pips per trade before costs. A real edge. Subtract 1.5 pips of costs: +0.75 remains — two-thirds of the edge gone. Now let the trader get "more active", taking marginal setups with a 62% rate: gross +1.0, net −0.5. The same skills, the same market, tipped into slow guaranteed loss by frequency alone.

Three consequences worth tattooing somewhere:

Costs punish thin edges hardest. A monster edge shrugs at 1.5 pips; a marginal one is erased. Since most real edges are thin, cost discipline is not accounting — it is often the entire difference between the winning and losing version of the same trader.

Frequency is a bill, not a virtue. Two trades a day at 1.5 pips is ~720 pips a year paid before profit — several months of good trading, spent on activity itself. The cheapest trade is the marginal one you decline.

Timeframe sets the tax rate. On a 10-pip scalp, 1.5 pips of cost is 15% of the move; on a 100-pip swing it is 1.5%. The shorter your timeframe, the greater the share of your edge the machinery consumes — which is precisely why the industry, paid per trade, markets the fast styles hardest.