The three dimensions of liquidity

The spread was one tick and the fill was awful. Or the book looked deep, absorbed your order without moving, and then sat several increments away for the next ten minutes.

Both are ordinary, and both happen because “liquid” is a summary of at least three separate properties that do not have to move together. Once they are separated, a book that seemed to misbehave usually turns out to have been described by the wrong one.

What the word is doing

Liquidity is the capacity to trade a quantity quickly at a price close to the prevailing one. That definition contains three independent variables — the quantity, the speed, and the price concession — and collapsing them into a single adjective is what makes the term unreliable.

The conventional decomposition splits it into tightness, depth and resiliency. Each is observable in the book, each is measured differently, and each constrains a different kind of order.

Tightness

Tightness is the cost of an immediate round trip at the smallest size: the spread.

It is the only one of the three that is visible at a glance, which is why it dominates casual descriptions of a market. It is also the only one with a hard floor, since the best bid and best ask must be at least one tick apart or they would cross.

What tightness tells you is bounded and specific: it is the concession for trading right now, in a size no larger than the quantity resting at the touch. It says nothing about a larger order, because a larger order does not trade at the touch.

Depth

Depth is quantity available near the current price — how much you could trade before the price you are trading at has moved by some amount you care about.

Depth is a function, not a number. The honest form of the question is “how far does the price move if I take five units”, and the answer is a curve: the cumulative quantity available at each increasing distance from the touch. A single figure like the size at the touch is one point on that curve and a poor summary of it.

Two properties matter mechanically. Depth is asymmetric — there is no reason the bid side and the ask side should hold similar quantity at any moment. And depth is a lower bound, because hidden and reserve quantity is not shown, so the displayed curve understates what is really there by an unknown amount.

Resiliency

Resiliency is how fast the book returns to its previous shape after being consumed.

This is the dimension with no display at all. When an incoming order clears the top two levels, the question of whether those levels are replaced in the next moment or in the next hour is not answerable from a snapshot. It is a property of the population of participants standing behind the book, and it is only visible over time.

Resiliency is what determines the difference between temporary and permanent impact. In a resilient book the displacement your order caused fades as new orders arrive; in a book with low resiliency, the hole you made stays a hole, and the next order to arrive pays the widened spread you created.

It also explains a specific pair of surprises. A large order can execute with modest impact and be followed by a market that stays displaced — depth was adequate, resiliency was not. And a market can show a thin book and absorb size repeatedly without moving, because quantity is being replaced as fast as it is taken.

The mechanism

THE MECHANISM — the three dimensions

  · Small order, tight spread
                    → tightness governs. Cost is
                      roughly half the spread.

  · Order larger than the touch quantity
                    → depth governs. Tightness stops
                      describing your cost entirely.

  · Repeated orders over time
                    → resiliency governs. Whether the
                      book refills between them decides
                      the total concession.

  · A one-tick spread
                    → NO GUARANTEE of depth. The
                      tightest possible quote can sit
                      on the smallest possible size.

  · Displayed depth curve
                    → a lower bound. Hidden quantity
                      and unposted interest are both
                      invisible.

  · Resiliency
                    → NOT OBSERVABLE from a snapshot.
                      It is a property of arrival over
                      time, not of book state.

  · Which figure a venue publishes as
    "liquidity", and over what window
                    → VENUE-SPECIFIC. Spread, top-level
                      size and traded volume are all
                      used, and they disagree.

Worked example

Illustrative figures, synthetic throughout. Consider two books on the same nominal asset.

Book A: best bid 40,000 for 0.1 units, best ask 40,000.5 for 0.1 units, then nothing until 40,100. The spread is 0.5 — one tick in this illustration, the tightest expressible. A buy for 0.1 units costs almost nothing above the touch. A buy for 1.0 units walks to 40,100, an average concession of roughly 90 per unit.

Book B: best bid 39,990 for 20.0 units, best ask 40,010 for 20.0 units. The spread is 20 — forty times wider than Book A. A buy for 0.1 units costs 10 above the mid, which is worse than Book A. A buy for 1.0 units also costs 10 per unit, because the level absorbs it entirely.

By tightness, A is forty times better. By depth at one unit, B is nine times better. Neither book is “more liquid” without naming the size, and a comparison that quotes only the spread ranks them backwards for every order above 0.1 units.

Now add resiliency. Suppose in Book B the 20.0 at the ask is replaced within a moment of being consumed, and in Book A the 0.1 is not replaced for minutes. Someone working through 5.0 units in small pieces pays roughly 10 per unit in B throughout, and in A pays the walk to 40,100 on the first piece and then waits. The third dimension changed the answer again, and it was invisible in both snapshots.

Where the three come apart

Tightness without depth is the common case in markets with a fine tick and automated quoting: a one-increment spread on a very small size, quoted continuously. The visible number is excellent and describes almost no quantity.

Depth without tightness appears where a coarse tick forces a wide spread and concentrates interest at a few levels. Small orders pay more; large orders pay less than they would elsewhere.

Depth without resiliency is the one that surprises people executing size. The book was there, you took it, and it did not come back, so the second half of your order met a different market from the first half.

None of these is a defect. They are consequences of tick size, of who is quoting, and of how quickly those participants replace what is taken — and the ranking between two venues flips depending on which dimension the question is about.

The failure mode

Liquidity is not a property a book has; it is a property of a specific order meeting a specific book. The failure mode is treating a measurement taken at one size as a statement about all sizes.

It bites hardest in the direction of confidence. A tight spread reads as reassurance, and it is evidence about the smallest possible trade only. Depth reads as capacity, and it is a lower bound on a snapshot that participants may withdraw before you arrive — a resting order is an offer, not a commitment, and displayed quantity can vanish rather than trade.

The one statement that survives all three dimensions: the cost of demanding immediacy rises with the quantity you demand it for, and there is no size at which it is zero.