How trading costs compound over time

Small per-trade costs compound because they are paid on every trade just as the strategy’s edge is earned on every trade. Net expectancy equals gross edge minus average cost, so the break-even cost threshold is simply the gross edge per trade. When costs are modeled realistically in backtests, they reduce average returns and can materially depress the deflated Sharpe ratio, making thin-edge, high-turnover strategies especially vulnerable.

Transaction costs are the gap between a strategy’s gross results and its net results after execution. They include explicit fees and implicit trading frictions such as spread and market impact. For a strategy with a small expected edge per trade, these costs matter because they are paid repeatedly. A small cost applied once may look negligible. The same cost applied across hundreds of trades becomes a large cumulative drag.

The arithmetic is straightforward. Let expected gross profit per trade be E and average cost per trade be C. Net profit per trade is then E minus C. Over N trades, expected gross profit is N times E, total trading cost is N times C, and expected net profit is N times the difference between E and C. This means a strategy with a modest edge can move from positive to negative simply because the cost term is multiplied by the same trade count as the edge term.

A simple illustration shows the mechanism. Suppose a strategy has an expected gross edge of 4 basis points per trade and incurs 3 basis points of total cost per trade. Its expected net edge is 1 basis point per trade. Over 500 trades, the expected gross result is twenty percentage points in basis point terms, while total costs sum to 15 percentage points (based on published terms), leaving five percentage points before any additional modeling error or slippage variation. If total cost rises from 3 to 5 basis points per trade, the same 500 trades produce an expected net result of negative 5 percentage points in basis point terms. Nothing about the signal changed. The repeated cost erased the edge.

This gives a clear break-even threshold. The maximum average cost a strategy can tolerate before expected profit turns negative is equal to its expected gross edge per trade. If a system earns 2 basis points per trade before costs, then 2 basis points is its break-even cost threshold. At any average cost above that level, the expected net value of each trade becomes negative. Marginal strategies are therefore the most fragile. A one basis point forecasting error or a one basis point increase in realized execution cost can be enough to flip the sign of expected net returns.

The same logic applies to risk-adjusted performance. The Sharpe ratio falls when average returns are reduced by costs. Sonar’s glossary defines the deflated Sharpe ratio as a correction to the Sharpe ratio that accounts for multiple testing and non-normal returns, with the goal of estimating whether an observed Sharpe ratio is statistically distinguishable from luck. When transaction costs lower mean returns, the observed Sharpe ratio declines, and the deflated Sharpe ratio declines with it. A strategy that appears acceptable before costs can lose statistical credibility after realistic costs are applied, especially when the original edge is small.

Sonar’s backtest overfitting audit tool emphasizes that realistic backtesting must account for execution assumptions and the difference between in-sample appearance and out-of-sample robustness. That framing matters for costs. A backtest that omits or understates trading frictions can overstate both raw profitability and the statistical strength of the strategy. Adding realistic cost assumptions reduces average returns trade by trade, and that reduction accumulates over the full sample. The more frequently a strategy trades, the more sensitive it becomes to modest errors in cost modeling.

The core lesson is mechanical rather than anecdotal. Cost drag scales with turnover. If expected edge per trade is thin, repeated costs can dominate the strategy’s economics. The practical test is to compare expected gross edge per trade with a realistic estimate of total cost per trade, then multiply both by the planned number of trades. If the two values are close, the strategy has little room for error. In that case, even small increases in spread, fees, slippage, or market impact can turn a seemingly profitable system into a net losing one.

Drafted with AI assistance from cited sources. Reviewed and approved by Sonar Sciences Quant & Research Team.