PARTIAL · execution
Hypothesis
Price impact is linear in signed order flow with slope $\lambda$ (Kyle); estimating $\lambda$ per symbol lets us cap order size so impact stays below expected edge.
Math — Kyle's lambda
Mid-price moves linearly in net signed volume:
$$ \Delta P = \lambda\, Q + \text{noise} $$
Cap participation so expected impact $<$ expected edge:
$$ Q_{\max} = \frac{\alpha_{\text{edge}}}{2\lambda} $$
Method
Estimate $\lambda$ by regressing mid-moves on signed volume per symbol/hour; size orders to keep modeled impact under a fraction of expected edge.
Results
| Impact model $R^2$ | 0.4–0.6 |
| Slippage vs naive sizing | lower |
| Directional edge | none (execution tool) |
No alpha, but a real execution improvement: knowing $\lambda$ per symbol caps size before impact eats the edge, materially cutting slippage on thin alts. Adopted in the sizing layer.
Every signal has a capacity set by price impact. Estimating $\lambda$ tells you the size at which your own order destroys the edge you found.