Backing out the informed flow from imbalance

Over a session you take 100 fills: your bid is hit 80 times (customers sell to you) and your offer is lifted 20 times (customers buy). You believe uninformed customers split 50/50 between buying and selling, while every informed customer is a seller (they know the price should fall). Each informed sell picks you off for a $1.00 loss; each uninformed fill earns you your $0.25 half-spread. Infer how many fills were informed, then compute your net session P&L (in dollars).

Show hints (2)+
  1. Uninformed flow is symmetric - solve 100−I2+I=80\frac{100-I}{2} + I = 80 for the informed sells II.
  2. Then net 60×(−1.00)60\times(-1.00) against 40×(+0.25)40\times(+0.25).

Answer

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