hard · Quantitative Finance

What is the correct quantitative reason the two cost models rank strategies differently, beyond average magnitude?

1. Square-root impact propto√(|q|) has decreasing marginal cost per share, so it penalizes the strategy's many small rebalancing trades far less than the linear model while still taxing large trades, changing the optimal trade-size distribution and thus the ranking
2. Square-root impact is always smaller per trade than linear cost, so any strategy passing the linear screen trivially passes the square-root screen and the ranking can never flip
3. The two models coincide for all trade sizes once calibrated to equal average cost, so an observed ranking flip must be a backtest bug rather than a real effect
4. Linear cost is convex and square-root is concave in notional, so the square-root model overcharges small trades and undercharges large ones, exactly reversing the intuition about small-trade penalties

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