Sign-flip Simpson: order size and fill quality

Question

Pooling all your trades, a scatter of order size against fill quality slopes upward: larger orders are associated with better fills (lower cost per share). But when you split trades by the stock's liquidity tier, within every tier the slope is downward: larger orders get worse fills.

Reconcile the positive pooled slope with the negative within-tier slopes. Which relationship should guide how you size an order?

Accepted Answer

This is Simpson's paradox in continuous form: the pooled regression slope has the opposite sign of every within-group slope. The confounder is liquidity. What is happening. Liquid stocks have deep order books, so they both (a) receive your larger orders, because you are comfortable sizing up where depth exists, and (b) deliver better fills, because depth absorbs trades cheaply. Illiquid stocks get small orders and worse fills. Across tiers, "big order" travels with "liquid name," and liquid names fill well, so the between-tier pattern is strongly positive and dominates the pooled cloud, dragg…

Sign-flip Simpson: order size and fill quality

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