Costs versus edge: how much of a 55% strategy survives the spread
hypothesess.com, AI-assisted writing ยท
A backtest with a 55% win rate looks like a result. Add the costs and, in the example this entry works through, half of the edge is gone before a single real trade. This entry is the arithmetic to do first: how much of an edge survives the spread and the commission, and why the strategies that trade the most are the ones costs hurt most.
Why the edge is so small
The first number that matters is not the win rate. It is the expectancy: what the strategy earns on an average trade. With wins and losses of the same size, a 55% win rate earns 0.55 × 1% − 0.45 × 1% = 0.10% a trade [1]. That is the whole edge in this example. The rest of each trade's movement is noise that cancels out over many trades.
Seen that way, a cost of 0.05% a round trip, in the same example, is not small: it is half of everything the strategy earns [1]. The win rate does not change when you add costs; the expectancy does, and it was the only thing paying you.
What costs do, step by step
Here is the same strategy at five levels of cost, all assumptions for illustration [1]:
| Cost per round trip | Net edge per trade | Edge kept | Net over 250 trades, added up |
|---|---|---|---|
| 0.02% | 0.08% | 80% | 20% |
| 0.05% | 0.05% | 50% | 12.5% |
| 0.08% | 0.02% | 20% | 5% |
| 0.10% | 0.00% | 0% | 0% |
| 0.15% | −0.05% | −50% | −12.5% |
The break-even cost is exactly the gross edge: at 0.10% a round trip, a 55% strategy is a coin flip with extra steps [1]. Past it, the more you trade, the faster you lose: a cost you can barely see on one trade decides the whole year.
Trading more does not dilute costs
A tempting thought is that a strategy trading very often can afford costs because it has so many chances. The arithmetic says the opposite. Costs are paid on every trade, exactly like the edge is earned on every trade, so the ratio between them does not change with frequency [1].
What frequency does change is how clearly the result shows. With no costs, this strategy's yearly Sharpe ratio is about 0.7 at 50 trades a year, 1.6 at 250 and 3.2 at 1,000 [1]. A 0.05% cost halves every one of those, because it halves the mean while leaving the spread of results nearly unchanged [1]. More trades make a real edge easier to see. They make a cost-eaten edge easier to see too.
This is where costs meet the problems in the other notebook entries. A smaller net edge needs more trades to tell apart from luck (Edge or luck?), produces longer losing streaks relative to what it earns (Is a win due?), and is easier to fake by testing many variations (The best of many).
Nerd corner
The expectancy per trade is E = p × W − (1 − p) × L, with p the win rate and W and L the average win and loss. A round-trip cost c turns it into E − c, so the share of the edge kept is (E − c) / E and the break-even cost is E itself [2].
The Sharpe ratio of N independent trades a year is about E / σ × √N, with σ the spread of a single trade's result, close to 1% here. Costs barely move σ, so the Sharpe ratio scales with E − c: halve the net edge and you halve the Sharpe ratio at any trading frequency [2].
Real costs are not one number. The spread widens in fast markets, slippage grows with order size, and a strategy that trades on the open or the close pays the most. A backtest that charges a flat cost on every trade is the optimistic case.
Check yourself
A strategy wins 60% of its trades, with average wins of 0.5% and average losses of 0.6%. What is its edge per trade? 0.06%: 0.60 × 0.5% − 0.40 × 0.6% = 0.30% − 0.24% [1]. In this example, a cost of 0.03% a round trip would take half of it [1].
You double how often a strategy trades without changing its edge per trade. Do costs matter less? No. The cost per trade and the edge per trade keep the same ratio; you just get the same share of the edge, twice as many times [1].
Say, as an example, your backtest charges 0.02% a round trip but your broker's spread is often 0.06%. What happens to the 55% example? Its edge falls from 0.08% to 0.04% after costs, half of what the backtest promised [1].
An example strategy, not trading advice. A lab notebook entry for hypothesess.com, written with AI and checked by hand; every figure is computed from the stated assumptions, and the box above recomputes them for yours.