Quoting a Market When You Have a Position Limit

Here's a scenario an interviewer might put in front of you: you're making a two-sided market in a stock you believe is fairly worth $100. You can hold at most 1,000 shares long or 1,000 shares short — hit that limit and you must stop quoting on that side entirely. Right now you're already long 800 shares. How should your bid and ask differ from a symmetric quote around $100? Think it through before reading on: the honest answer is not "quote $99.90 / $100.10 like always," and the why matters more than the what.

The trap: quoting the same market regardless of inventory

A market maker with no position and no limit can just quote symmetrically around fair value — say $99.95 bid, $100.05 offer — and be indifferent to which side gets hit next. The mistake is carrying that same symmetric habit into a situation where inventory is already skewed. If you're long 800 out of a 1,000-share limit and someone lifts your offer for another 300, you'd be forced to refuse the trade or break your limit — and even before that hard wall, every additional share you buy is riskier than the last, because you have less room left to absorb more.

Skewing the quote

The fix is to make your quote reflect not just fair value but how much inventory room you have left on each side. Being long 800 of a 1,000 limit means you have only 200 shares of buying room left and 1,800 shares of selling room (you could sell down to -1,000). Two things should happen to your quote:

• Skew the whole quote down, off the $100 fair value, so your bid and offer are both a little below $100. This makes your offer more attractive (closer to fair, easier to hit) and your bid less attractive (further from fair, harder to hit) — nudging the market to sell to you less and buy from you more, working your position back toward flat.
• Widen the side you're closer to the limit on. Your bid — the side that adds to an already-large long position — should be pulled back further than the offer is pushed forward, because a fill there costs you disproportionately: it eats into your last 200 shares of room and pushes you toward a forced stop.

Concretely, you might quote something like $99.85 bid / $99.98 offer instead of a symmetric $99.95 / $100.05: both numbers shifted down (skew), and the bid pulled back more than the offer (asymmetric widening reflecting the 200-vs-1,800 room imbalance).

Position	Room to buy more	Room to sell more	Quote shape
Flat (0)	1,000	1,000	Symmetric around fair value
Long 800	200	1,800	Skewed down, bid pulled back hardest
Long 950	50	1,950	Sharply skewed down, bid near-prohibitive
Short 800	1,800	200	Skewed up, offer pulled back hardest

An interviewer will often push further: what happens right at the limit? At exactly 1,000 long, the honest answer is you can't take on any more long risk at all — your bid should effectively be pulled so far back it's not competitive (or you simply stop quoting that side), while your offer can stay reasonably tight since selling only helps you.

Where this shows up

This is the everyday reality of running an options or ETF market-making book: quotes aren't static, they move continuously with the position you're already carrying, which is why two market makers with identical fair-value models can be showing meaningfully different prices at the same moment — they're carrying different inventory.