Inventory Risk and Quote Skewing

A market maker with unwanted inventory skews quotes to encourage trades that reduce risk, even at a worse expected price.

1. The idea

Holding inventory exposes a market maker to price risk unrelated to adverse selection — even with no informed trading, a large long position loses money if the price drifts down before it's sold. Risk-averse makers therefore want to keep inventory near a target (often zero).

The standard response is to skew both quotes in the direction that reduces inventory: a maker who is long lowers both bid and ask, making it more attractive for others to buy (reducing the maker's position) and less attractive to sell to the maker.

This skew is separate from adverse-selection-driven spread widening: skewing shifts the center of the quotes, while adverse selection widens the spread around the center. Both often happen together in practice.

A common simplified skew is linear in inventory: for inventory $q$ (positive = long), shift the quoted midpoint by $- k q$ for some sensitivity $k > 0$ , reflecting increasing risk aversion or risk-adjusted valuation as $∣ q ∣$ grows (as in Avellaneda-Stoikov style models).

2. Why it matters

Inventory skewing is the most commonly asked 'how do you manage risk as a market maker' interview question, and it tests whether you separate risk management from information reasoning.

3. Core mathematics

Skewed midpoint

m^{'} = m - k q

$q$ = current inventory (positive = long), $k$ = skew sensitivity

Skewed quotes

b^{'} = m^{'} - \frac{S}{2}, a^{'} = m^{'} + \frac{S}{2}

4. How to recognize it

Think of this when…

Mentions a market maker who is 'long' or 'short' and wants to flatten the position
Asks how quotes should change as inventory builds
Involves risk aversion or a soft position limit

5. Worked example

Worked example

Fair value is $50.00, base half-spread $0.10, skew sensitivity $k = 0.01$ per share. The maker is currently long 20 shares. What are the new bid and ask?

1
Compute the skewed midpoint.
$m^{'} = 50.00 - 0.01 \times 20 = 49.80$
2
Apply the half-spread around the skewed midpoint.
$b^{'} = 49.80 - 0.10 = 49.70, a^{'} = 49.80 + 0.10 = 49.90$
Answer: New quotes: bid $49.70, ask $49.90 — both lower than fair value, making the maker more eager to sell (offloading inventory) and less eager to buy more.

6. Common mistakes

Confusing inventory skew (shifts the midpoint) with adverse-selection spread widening (widens around the midpoint)
Skewing in the wrong direction — a long position should lower quotes, not raise them
Ignoring that skew should scale with position size and risk aversion, not be a fixed amount

7. Quick check

A market maker who is short (negative inventory) should skew quotes:

Inventory skew primarily addresses:

8. Practice

No linked practice questions yet.

9. Related methods

Dynamic Programming / Continuation Value Conditional Expectation

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