Slippage and market impact

Every trade you make tells the market something and consumes liquidity. The cost shows up as the difference between the price you hoped for and the price you got.

Components of trading cost

Fees and commissions: explicit and known.
Half the spread: paid on every market order.
Market impact: the price moving away as your order executes, because you are pushing through the book and other participants react to your flow.
Timing / opportunity cost: the price drifting while you wait to trade.

The total, measured against the price when you decided to trade, is the implementation shortfall.

The square-root law

Across asset classes, empirical studies find that the average price impact of a large order (a “metaorder”, executed over time in pieces) scales roughly with the square root of its size relative to volume:

\frac{\Delta p}{p} \approx Y\,\sigma_{\text{daily}}\,\sqrt{\frac{Q}{V_{\text{daily}}}}

where $Q$ is the order size, $V$ the daily traded volume, $\sigma$ the daily volatility, and $Y$ a constant of order 1 (often estimated between about 0.5 and 1).

Worked example

You want to buy 1% of a coin’s daily volume. Daily volatility is 4% and $Y \approx 1$ . Expected impact is about $4\% \times \sqrt{0.01} = 0.4\%$ . Trading 4% of daily volume costs about $0.8\%$ : four times the size means twice the cost per unit, and therefore eight times the total cost.

The square root is concave: small orders are cheap, but cost per unit keeps rising with size. Part of the impact is temporary (it decays after you finish) and part is permanent (the market has learned something from your trade).

Capacity

Impact sets a strategy’s capacity — the capital at which it stops being worth running. If gross alpha per trade is $\alpha$ and cost per trade grows like $\sqrt{Q}$ , net profit per trade falls as size grows. Total profit, $Q(\alpha - c\sqrt{Q})$ , is maximised at

Q^* = \Big(\frac{2\alpha}{3c}\Big)^2

and falls back to zero at $Q = (\alpha/c)^2$ . Beyond the optimum, scaling up reduces total profit. High-turnover strategies on small assets hit this wall very quickly.

Common mistake

Applying a fixed slippage of a few basis points to every trade in a backtest, regardless of size or liquidity. That makes small-cap and altcoin strategies look scalable when they are not. Model cost as a function of order size relative to volume.

Next: how execution algorithms break large orders up to minimise these costs in execution.