Uninformed Spread Profit, Second Instance

Compute the market maker's profit for a buy trade and a sell trade separately against fair value.

Average the two profits since each is equally likely.

1. 1. Profit on each side

   On a buy at 100.20, profit is $100.20-100=0.20$. On a sell at 99.80, profit is $100-99.80=0.20$.

2. 2. Average

   Both sides give profit $0.20$, so the expected profit per trade is $0.20$.

   $$E[\text{profit}]=0.5(0.20)+0.5(0.20)=0.20$$

Answer: 0.20