hard · Quantitative Finance microstructure-arb

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 strictly smaller per trade than linear cost at any given trade size, so any strategy that already passes the linear cost screen will trivially pass the square-root screen too, meaning the ranking of strategies can never actually flip
3. The two cost models coincide exactly for all individual trade sizes once calibrated to produce equal average cost across the whole book, so an observed ranking flip between them must indicate a backtest implementation bug rather than a genuine economic effect
4. Linear cost is convex and square-root cost is concave in traded notional, so the square-root model systematically overcharges the strategy's small trades and undercharges its large ones, exactly reversing the usual intuition about small-trade penalties in a high-turnover book

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