Inventory Management for Market Makers

A market maker earns the spread by quoting both sides, as in Fair Value and Quoting — but every trade leaves a footprint. Buy from a seller and you're now long. Sell to a buyer and you're now short. That leftover position is called your inventory, and it is the market maker's occupational hazard: while you sit on it, the price can move against you and erase far more than the pennies of spread you collected. The whole discipline of inventory management is keeping that position small, and steering it back toward flat.

The lever you have is your own quote. You don't have to center it on fair value. If you're uncomfortably long, you can skew the whole market down — lower both your bid and your ask. A lower ask is more tempting to buyers, so you sell off your excess faster; a lower bid is less tempting to sellers, so you stop piling on more. Skew up when you're short. The point you center on is your reservation price, and it drifts away from fair value in the direction that unwinds your position.

The reservation price, in one formula

The standard model (The Avellaneda-Stoikov Model) writes the reservation price as

$$r = s - q\,\gamma\,\sigma^2\,(T - t).$$

In words: start from the true mid $s$, then shift it by an amount that grows with your inventory $q$ (positive when long), your risk aversion $\gamma$ (how much you hate holding risk), the variance $\sigma^2$ of the price (a jumpier asset is scarier to hold), and the time $T - t$ you might be stuck with the position. The more of any of these, the harder you shade. You then quote your bid and ask around $r$ instead of around $s$.

Worked example: unwinding a long book

Fair value is $100.00. Flat, you quote 99.90 bid / 100.10 ask — a symmetric 20-cent market. Two buyers lift your offer in quick succession; you've now sold 2 lots you didn't have and are short 2... no — you sold, so buyers took your ask and you are now short. Let's instead say two sellers hit your bid, so you bought 2 lots and are long 2.

You decide each lot of inventory should shade your center by 5 cents. Long 2 lots shifts your reservation price to $100.00 - 2 \times 0.05 = 99.90$. You re-quote around 99.90: 99.80 bid / 100.00 ask. Look what happened to the ask — it's now 100.00, a full dime below fair value. A buyer who thinks the thing is worth 100 will happily lift it, and you offload your excess. Meanwhile your 99.80 bid is stingy, so fresh sellers pass, and you stop accumulating. You've deliberately given up a little edge on the ask to buy down your risk. Once you're flat, you recenter on 100 and collect the full spread again.

Pitfalls and guardrails

• Position limits. Skewing nudges inventory; hard limits stop it from running away. Real desks cap the maximum long or short and simply pull a side of the quote at the limit.
• Adverse selection compounds inventory. If the flow hitting you is informed (Adverse Selection), your inventory grows precisely when the price is about to move against it — the worst possible correlation. Widen, don't just skew.
• Skewing doesn't beat a trend. Inventory tools assume price is roughly a random walk around fair value. In a strong directional move, shading down while the market keeps falling still loses; skew manages noise-driven inventory, not a genuine repricing.
• Your own skew moves the price. Lifting your quotes to attract flow is itself Market Impact; shade too hard and you signal your position to sharper players.

In an interview, if you're asked to keep making a market as trades come in, narrate the inventory: "I'm now long two, so I'll shade my market down a nickel to encourage buyers and slow the selling." That single sentence shows you understand the job is managing a position, not just naming a mid.