Bid, Ask and the Spread

The bid-ask spread is compensation for providing liquidity and bearing risk, not free profit.

1. The idea

A market maker quotes a bid price $b$ (where they buy) and an ask price $a$ (where they sell), with $a > b$ . The spread $a - b$ compensates the maker for two costs: the risk of holding inventory before offsetting it, and the risk of trading with someone who knows more than they do.

If every trade were with an uninformed counterparty and the maker could instantly offset, the spread would be pure profit. In practice some counterparties are informed (adverse selection) and offsetting takes time (inventory risk), so the spread must be wide enough to cover expected losses from both.

The midpoint $m = (a + b) /2$ is the maker's best estimate of fair value. Quoting symmetrically around $m$ is a starting point; real quotes skew based on inventory and order-flow information, covered in later lessons.

2. Why it matters

Nearly every trading interview question about market making starts from 'why does a spread exist' — you need a crisp two-part answer: inventory cost and adverse selection.

3. Core mathematics

Spread

S = a - b

Always quoted so $a > b$ ; half-spread is $S /2$ .

Midpoint / fair value estimate

m = \frac{a + b}{2}

Round-trip capture

profit per round trip = a - b (if both sides fill at quoted prices)

4. How to recognize it

Think of this when…

Question mentions a market maker quoting two-sided prices
Asks why the spread can't be zero or why it's not pure profit
Involves a dealer buying low and selling high on the same asset

5. Worked example

Worked example

A stock has fair value $100. A market maker quotes bid $99.90 / ask $100.10. If they buy one share at the bid and later sell one share at the ask, with fair value unchanged, what is their profit?

1
The round-trip profit equals the spread captured when both sides trade at quoted prices.
$profit = 100.10 - 99.90$
2
Compute the spread.
$0.20$
Answer: $0.20 per share, the full spread — assuming fair value did not move and no informed trader was involved.

6. Common mistakes

Treating the spread as guaranteed profit rather than compensation for risk
Forgetting that fair value can move between the buy and the sell, eroding or reversing the gain
Ignoring that only one side of the quote may get filled, leaving inventory exposure

7. Quick check

If bid = $49.80 and ask = $50.20, the spread is:

A zero-risk, zero-information market would drive the equilibrium spread toward:

8. Practice

17 QuantSolve questions use this concept.

Practice this concept

9. Related methods

Bayes' Theorem

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