Bid-Ask Spread & Edge

Medium3–4 hrsBid-AskEdgeMarket MakingFair Value

Overview

Market making is about capturing the spread while managing the risk that you're trading against someone who knows more than you. The core skill: estimate fair value quickly and accurately, then quote a spread wide enough to be profitable but narrow enough to attract flow. In Optiver and IMC interviews, they'll make you actually quote prices on live dice rolls — practice this!

How to Recognize

→You're asked to quote a two-sided market on a game or asset
→'What would you buy and sell this for?' in an interview simulation
→Estimating fair value under uncertainty
→Questions about profit per trade and volume

Step-by-Step Approach

1.Step 1: Estimate fair value (FV) — E[payoff] or expected outcome
2.Step 2: Set spread around FV: bid = FV − s/2, ask = FV + s/2
3.Step 3: Spread must cover: adverse selection + inventory risk + target profit
4.Step 4: Widen spread if you're uncertain about FV
5.Step 5: Update FV when new information arrives mid-trade

Key Formulas

\text{bid} = \text{FV} - \frac{s}{2},\quad \text{ask} = \text{FV} + \frac{s}{2}

\text{Edge per trade} = \frac{s}{2}

(if flow is uninformed)

\text{P\&L} = (\text{ask}-\text{FV}) \cdot Q_{\text{sell}} + (\text{FV}-\text{bid}) \cdot Q_{\text{buy}}

04Break-even spread:

s \geq 2 \cdot E[\text{adverse selection cost}]

Worked Examples

0Quick Example

FV of a d6 roll = 3.5. Quote 3.2/3.8 (spread = 0.6). Expected edge = $0.30 per uninformed trade.

Problem

You are a market maker. Your client wants to bet on the outcome of rolling a fair die. How do you quote a market for the cash value of the roll?

Solution

Step 1: Fair value = E[die] = (1+2+3+4+5+6)/6 = 21/6 = 3.5.

Step 2: Decide on spread. You want to profit, so bid < 3.5 < ask.

Step 3: If you quote 3.3/3.7, your edge = 0.2 on each side. If both buy and sell happen equally, you earn $0.20 per completed round-trip.

Step 4: Consider your uncertainty. FV of 3.5 is certain here (uniform die). If FV were uncertain, widen the spread.

Quote: 3.3 / 3.7. If client buys from you at 3.7: you sell them the bet. If die rolls 1–3 (p=1/2), you profit. If 4–6 (p=1/2), you pay up. Your edge: 3.7 − 3.5 = $0.20 on average.

Answer

Quote 3.3/3.7 (or any spread centered on 3.5). Edge per trade = half the spread = $0.20. The key: FV first, then spread around it.

Common Mistakes

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Setting bid = ask = FV. That's a zero-spread, you capture nothing. You need bid < FV < ask.
!
Making the spread too wide: clients won't trade with you. The spread must be competitive.
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Not updating on flow information. Consecutive buys or sells signal something — update your FV.
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Forgetting that your edge is per HALF of the spread, not the full spread.

Practice Problems

Click "Show Answer" to reveal

Make a market on the following game: roll 2 dice, win the product. What is FV? What would you quote?

Hint: E[product] = E[die1] × E[die2] (independence). FV = 3.5 × 3.5.

You're making a market on a coin flip: heads pays $10, tails pays$ 0. Fair coin. Client asks for a 'bulk' deal: 100 flips. How should your pricing change?

Hint: Think about variance. Single flip: E=

5, Var=

25. 100 flips: E=

500, SD =

50. LLN helps you.

Back to Study Plan

Auction Theory Adverse Selection