A stock's average effective spread is 6 cents and the realized spread five minutes after each trade is 1.5 cents. The maker pays 0.4 cents a share of exchange and clearing costs on a round trip and charges itself 0.6 cents of inventory risk. Decompose the spread and give the adverse selection component.

A stock's average effective spread is 6 cents and the realized spread five minutes after each trade is 1.5 cents. The maker pays 0.4 cents a share of exchange and clearing costs on a round trip and charges itself 0.6 cents of inventory risk. Decompose the spread and give the adverse selection component.

Approach: Use the identity that the effective spread splits into the post-trade price move and the part the maker keeps, then split what is kept into its three cost components.

4.5 cents. The effective spread splits into adverse selection, measured by the post-trade price move, and the realized spread the maker keeps, so adverse selection is 6 - 1.5 = 4.5 cents. The realized 1.5 cents then splits into 0.4 cents of order processing cost, 0.6 cents of inventory cost and 0.5 cents of economic profit. Adverse selection at 75% of the spread says the flow in this stock is informed, so the quote is set by the information in the order flow and would barely move if fees fell to zero. Halving the tick would compress the 0.5 cent profit and part of the order processing cost, and it cannot compress the 4.5 cents of adverse selection, so the spread would not halve with the tick.

Follow-up: The realized spread is 1.5 cents at five minutes and 3 cents at thirty seconds. What does the difference say about the horizon of the information?

Key concepts: spread decomposition, adverse selection, realized spread, order processing cost, inventory cost.