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Net edge across trades

Market makingMedium

A contract has a known fair value of $80$ . A market maker makes $3$ trades. Trade $1$ buys $30$ units at $79.5$ . Trade $2$ sells $20$ units at $80.4$ . Trade $3$ buys $50$ units at $80.2$ . A fee of $0.05$ per unit applies to every trade. What is the total expected net profit?

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Hint

Compute the signed edge per unit of each trade, subtract the fee, then multiply by size.

Solution

Trade $1$ earns $30 \times (0.5 - 0.05) = 13.5$ and trade $2$ earns $20 \times (0.4 - 0.05) = 7$ .
Trade $3$ pays above fair value, so it earns $50 \times (- 0.2 - 0.05) = - 12.5$ .
The total is $13.5 + 7 - 12.5 = 8$ .

Answer: $8$

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