Leaning the quote to get flat
A market maker wants to earn the spread, not hold a position. When fills pile up on one side, move both quotes toward the side that sheds the risk: your exit quote becomes the best in the market, your entry quote the worst.
- Skew a two-way quote by a stated number of cents per 10,000 shares of inventory
- Read a desk's inventory off its quotes
- Find the position at which the exit quote reaches fair value and all the edge is gone
- Explain why skewing beats widening when you need to get flat
The intuition
You have been hit on the bid all morning and are long 10,000 shares you never wanted. Fair value is $50.00 and you quote 2 cents either side. If you leave the quote at $49.98 / $50.02, the next trade is as likely to make you longer as shorter. So you lean: drop the center by a cent to $49.99 and quote $49.97 / $50.01. Your offer is now the most attractive in the market, so buyers come to you and take the shares off your hands. Your bid is the least attractive, so sellers go elsewhere and the position stops growing.
The cost is edge. You sell those shares at $50.01 against a fair value of $50.00, one cent instead of two: you gave up the skew on every share to get out without crossing the spread. Lean harder for a bigger position and the exit quote drifts toward fair value; at 20,000 shares long it sits exactly on it, and unwinding earns nothing. Past that you are paying to get out, and most desks stop skewing and hedge or cross the spread instead.
Skew = −k × inventory ÷ 10,000 cents (negative when long, so both quotes move down; positive when short, so both move up). Bid = fair + skew − h, offer = fair + skew + h. The exit quote reaches fair value when k × |inventory| ÷ 10,000 = h, at |inventory| = h ÷ k × 10,000. Edge per share on the unwind = h − |skew|.
Why it works
- The conventions here: a linear skew. The desk quotes a fixed half-spread h either side of a reservation price, and the reservation price sits k cents below fair value for every 10,000 shares long (above it when short). Inventory is signed, long positive. Offsets are in cents from fair value, below fair negative.
- Skew is directional, widening is not. Widening slows fills on both sides equally, so it cuts new risk but sheds none of the risk you hold. Skewing speeds up the side that reduces the position and slows the side that adds to it.
- The quote mid tells on you. The midpoint of a skewed market is the reservation price. Its distance from an independent fair value, divided by k, is the inventory behind it. Lopsided sizes on the two sides say the same thing.
- Every fill re-skews. Buying adds to inventory and moves both quotes down by k cents per 10,000 shares bought; selling moves them up. A fill that covers a short and runs past flat flips the lean.
- The edge you give up is the skew. Against an unskewed quote, unwinding through a skewed one costs |skew| cents a share. That is the price of getting out through your own quotes rather than carrying the position and hoping.
- Run it backwards. The exit quote hits fair value when the skew equals the half-spread. Solve for the inventory: h ÷ k × 10,000 shares. Beyond it, skewing has nothing left to give.
| Skew: −1 × 10,000 ÷ 10,000 | −1 cent |
| Bid: −1 − 2 | −3 cents, $49.97 |
| Offer: −1 + 2 | +1 cent, $50.01 |
| Edge a share if the position is lifted at the offer | 1 cent, $100 on 10,000 shares |
| Exit quote reaches fair value at: 2 ÷ 1 × 10,000 | 20,000 shares |
| Given up against an unskewed quote | 1 cent a share, $100 |
The formulas
Long inventory moves the center down; short moves it up.
A fixed half-spread either side of the skewed center.
Read the position off the quotes.
The skew has eaten the whole half-spread.
What is left of the half-spread after leaning.
Worked example
Move the center first, in the direction that helps you get flat, then put the half-spread either side. The follow-up asks which side of your market other traders now find interesting.
See it move
Same stock. Change the size of the position, which way it is, how hard the desk leans per 10,000 shares, and the half-spread.
- Grow the position. Both quotes move further down if you are long and further up if you are short, and the edge left on the exit side falls, one step per 10,000 shares. Watch it reach zero.
- Lean harder per 10,000 shares. The exit edge falls and the position at which it runs out comes closer.
- Widen the half-spread. Both quotes move apart, the exit edge rises, and the position you can skew through before giving up all the edge grows.
- Flip long to short. The whole picture mirrors: the quotes lean up instead of down, and the bid becomes the interesting side.
Run it backwards
A colleague's quotes, and an independent fair value, are on the screen. How big is their position, and which way?
The midpoint of their quotes is their reservation price. Its distance from fair value is the skew, and the skew is k cents per 10,000 shares: divide and multiply. A center below fair means they are long.
You need an independent fair value to do this, such as the consolidated mid, a futures-implied price or a related stock. A desk whose quotes lean away from every other market maker, with lopsided sizes, is telling you about its inventory.
Traps
Say it in the interview
“You are long 10,000 shares after a run of sells. What do you do with your quote?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Long: move both quotes down. Short: move both up. Skew = −k × inventory ÷ 10,000.
- The quote mid is the reservation price; its gap from fair value reveals the inventory.
- The exit quote reaches fair value at h ÷ k × 10,000 shares; beyond it, skewing costs money.
- Skewing is directional; widening is not.