Transaction Cost Models: Spread, Impact, and the Square-Root Law

Successful quants estimate that transaction costs absorb 20–50% of their gross alpha . The transaction cost model's job is not to minimise trading costs — that is the execution algorithm's job — but to tell the portfolio construction engine how much it will cost to make any candidate trade, so the engine can decide whether the alpha benefit clears the cost hurdle. Getting this number wrong in either direction degrades the strategy: underestimating costs leads to over-trading; overestimating leads to positions held too long past their signal peak.

This note develops the four types of transaction cost models from flat to quadratic, grounds the square-root law for market impact, and shows how each cost type enters the portfolio construction objective function.

• identify the three cost components (commissions, slippage, market impact) and state which dominates at quant scale;
• describe the flat, linear, piecewise-linear, and quadratic cost models and state when each is appropriate;
• apply the square-root impact law to estimate the cost of a given order;
• compute the break-even trade threshold that governs whether a signal improvement justifies the round-trip cost.

1. 1. Three components of transaction costs
2. 1. Four types of transaction cost models
3. 1. The square-root law for market impact
4. 1. Break-even trade threshold