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Breakeven volume

Market makingMedium

A contract has a known fair value of $55$ . A market maker buys at $54.2$ on every trade and pays a fee of $0.2$ per unit. The market maker has a fixed daily cost of $90$ . How many units must be traded per day for the expected net profit to cover the fixed cost exactly?

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Hint

Net edge per unit is the edge minus the fee.

Solution

The edge per unit is $55 - 54.2 = 0.8$ .
After the fee the net edge per unit is $0.8 - 0.2 = 0.6$ .
The break-even volume is $90 \div 0.6 = 150$ .

Answer: $150$

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