Make Me a Market on a Die

Question

I'm going to roll a fair six-sided die and pay the winner of the contract its face value in dollars. Make me a market: give me a bid and an offer, and be ready to defend them. (This is the single most common live exercise in trading interviews.)

Accepted Answer

Theo first: mathbbE[textroll] = 3.5. A good market: 3.30 bid / 3.70 offer (or 3.25 at 3.75). Both sides have +0.20 of expected edge for you; the width reflects that one die roll has real variance (std dev approx 1.71) and the game is one-shot. What the interviewer probes next, and what you should already be thinking: - "I buy at 3.70." You're now short one contract at +0.20 EV. Expected P&L per trade is fine; risk is the roll comes 5 or 6. - "Make me another market." Convention: having sold once, skew quotes up if you want to discourage further buying or manage inventory: e.g. 3.40 / 3.80. If they keep lifting your offer, either they're price-insensitive (keep selling, collect edge) or they know something (is the die loaded?), say this out loud; recognizing potential adverse selection is the point of the exercise. - "Tighter." You can quote 3.45/3.55, but articulate that tighter = less edge per trade; you'd want flow or information in exchange. Grading criteria interviewers actually use: Did you compute theo immediately? Is your market symmetric around it? Do you know your position and P&L after each trade? Do you skew after trading? Do you ask why the counterparty keeps trading?

Make Me a Market on a Die

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