The scenario formula and its units
Estimated impact in percent is I = Y × σd × sqrt(Q/Vd), where Y is the assumed dimensionless coefficient, σd is daily volatility entered as a percentage, Q is order quantity, and Vd is daily traded volume. Q and Vd must use matching base-asset units. If daily volatility is 3%, enter 3. The formula represents the selected impact component; commissions, spread crossing, funding, and directional market movement require separate assumptions.
Double size without doubling the output
For coefficient 0.5, daily volatility 3%, order quantity 100 units, and daily volume 10,000 units, participation in daily volume is 1%. Estimated impact is 0.5 × 3 × sqrt(0.01) = 0.15%, or 15 basis points. Increasing the order to 400 units raises that scenario to 0.30%, or 30 basis points. Four times the quantity doubles the estimate because the model uses a square root.
Treat the coefficient as an assumption to test
The same coefficient need not fit a liquid Bitcoin market and a thin token market. Execution horizon, urgency, volume measurement, and temporary versus persistent price effects all matter. Research also documents departures from a simple square-root relationship across size and participation regimes. Enter independently justified assumptions and compare several coefficients before using the result in a budget. A precise decimal output reflects deterministic arithmetic, not proof that a future execution cost is known. Multiplying full impact by reference notional gives the displayed cost proxy; it does not estimate average execution cost along a modeled fill path.