Tightness, Depth and Resiliency: The Dimensions of Liquidity

Everyone calls a market "liquid" and almost nobody says what they mean. Cheap for 100 shares but ruinous for 100,000? Cheap right now, but only until somebody else has just bought? Two stocks can quote the identical one-cent spread and one of them will cost you four times as much to trade. The word hides at least three separate questions, and Kyle (1985) is the standard way to pull them apart.

• Tightness — what does an instant round trip cost? That is the spread.
• Depth — how much size can you push through before the price itself moves?
• Resiliency — once you have knocked the book over, how fast does it stand back up?

A fourth, immediacy, is sometimes added: how long until you can trade at all. In continuous markets that is nearly free, so the working set is the three above.

Tightness: the price of impatience

Tightness is the quoted spread $s = a - b$, or better, the effective spread actually paid, $2|p - m|$ for a trade at price $p$ against a mid $m$. It is the toll for demanding immediacy on a small order. If your whole order fits inside the size showing at the touch, tightness is the only dimension you care about — you pay half the spread and you are done.

Depth: what happens when you don't fit

Depth is the size resting at and near the touch, and the honest way to express it is a cost-to-trade curve: the volume-weighted price you would pay for 1,000 shares, 5,000, 50,000. Two books with identical spreads can have wildly different curves.

Here are two names, both quoting a one-cent spread with a $20.005 mid. You want to buy 5,000 shares of each.

	Stock A (thin)	Stock B (deep)
Ask 20.01	600	4,000
Ask 20.02	800	6,000
Ask 20.03	1,000	—
Ask 20.04	1,200	—
Ask 20.05	1,400	—
Bid 20.00	500	4,200

In Stock A the market buy walks five levels: 600 at 20.01, 800 at 20.02, 1,000 at 20.03, 1,200 at 20.04, 1,400 at 20.05. Total cost $= 12{,}006 + 16{,}016 + 20{,}030 + 24{,}048 + 28{,}070 = 100{,}170$, so the average fill is $20.034. Against the $20.005 mid that is 2.9 cents per share, or 14.5 bps.

In Stock B the same order takes 4,000 at 20.01 and 1,000 at 20.02: $80{,}040 + 20{,}020 = 100{,}060$, an average fill of $20.012, which is 0.7 cents or 3.5 bps.

Same tightness, same mid, same order — four times the cost. Judging liquidity by the spread alone would have told you these were identical markets.

Resiliency: how fast it heals

After that sweep of Stock A, the ask side is empty out to $20.06 and the spread is six cents wide. Resiliency asks how quickly market makers repost. Track the spread after the sweep:

Time after sweep	Spread	Excess over the 1-cent norm
0.0 s	6.0¢	5.0¢
1.5 s	3.5¢	2.5¢
3.0 s	2.25¢	1.25¢
6.0 s	1.3¢	0.3¢

The excess halves every 1.5 seconds. Fit the standard exponential

$s_t - s_\infty = (s_0 - s_\infty)\,e^{-t/\tau}$

which says the gap between today's spread and its normal level shrinks by a constant fraction each second. Here the half-life is 1.5 s, so $\tau = 1.5/\ln 2 \approx 2.2$ s. That is a resilient book. A name where the same 5-cent wound takes four minutes to close is not resilient, however tight it looks in a screenshot — and if you are slicing a large order, resiliency is the dimension that decides how fast you can send the next child order.

The dimensions disagree, and that is the point

Tick size forces a trade-off: when the spread is pinned at one tick it cannot get tighter, so competition spills into size and queues grow enormous. Large-tick stocks are therefore deep but relatively wide; small-tick stocks are tight but thin. Stress hits all three at once — in March 2020 spreads widened, displayed depth collapsed, and replenishment slowed together, which is why "liquidity vanished" is a fair description of a crisis and a lazy one on a normal day.

In interviews

The classic prompt is "define liquidity" — a one-word answer marks you out. Name the three dimensions, then immediately show the Stock A / Stock B contrast: identical spreads, four-times cost difference. Expect a follow-up on measurement: tightness from quoted and effective spreads, depth from the cost-to-trade curve or Amihud Illiquidity as a daily proxy, resiliency from spread and depth recovery half-lives after sweeps. A strong finish is noting that the three tend to move together in stress, which makes liquidity risk far less diversifiable than it looks. See Market Impact for what depth costs you once you start pushing.