Chapter 2: Measuring Liquidity
If Chapter 1 is the map of how markets are built, this chapter is the instrument panel — how to actually put a number on "how illiquid is this," using nothing but real trading data. It comes with a real ITG cost table, a real NASDAQ execution-quality report, and a real institutional-investor implementation shortfall of 10.1 percentage points.
- Source
- Extracted directly from the chapter text in /references
- Companion lecture
- Covers the same ground as Lecture 2 of the video course — read independently
- Book part
- Part I — foundations of market microstructure
Two kinds of trading cost
The chapter's own analogy: if market structure is the car's design, measuring liquidity is assessing its driving performance — several dimensions matter at once (trading cost, depth for large orders, execution speed, execution risk), the same way a car's performance isn't just top speed.
Trading costs split into two kinds. Explicit costs — broker commissions, transaction taxes, platform fees, clearing/settlement fees — are easy to measure because they're charged directly. Implicit costs are the ones this whole chapter is about: the gap between the execution price and a benchmark price (usually the midquote) that stands in for "what you'd have paid in a perfectly liquid market."
| Quarter | Delay cost | Impact cost | Comm. cost | Total |
|---|---|---|---|---|
| 2003 Q1 | 61 | 16 | 17 | 94 |
| 2005 Q1 | 41 | 8 | 16 | 65 |
| 2007 Q4 | 58 | 10 | 11 | 79 |
What this means: explicit costs (commissions) fell steadily from 2003 as competition and technology improved — but implicit costs are the bigger share throughout, and delay cost (the price moving against you before your broker even starts executing) dominates impact cost in every quarter shown. Then 2007 Q4 shows implicit costs spiking back up as the financial crisis hit — real evidence that illiquidity is exactly what dries up first when markets get stressed.
The quoted spread and the weighted-average spread
The most direct measure: S = a − b (ask minus bid), normalized by the midprice m = (a+b)/2 to get the relative quoted spread s = S/m. This is "the" bid-ask spread people usually mean — but it's only accurate for orders small enough to fill entirely at the best quote. For larger orders, Chapter 1's weighted-average spread s(q) applies: it rises with order size q, and how fast it rises is itself a measure of depth.
The effective spread
The quoted spread describes a hypothetical trade; the effective half-spread uses what actually happened: Sᵉ = d(p − m), where d is +1 for a buyer-initiated trade, −1 for seller-initiated, p is the execution price, and m is the midquote just before. Because it's built from real fills, it captures price improvement (trades inside the spread) that the quoted spread misses entirely — but being backward-looking, it can't tell you what a trade will cost before you place it.
The book's own worked example: a 1,000-share market buy executes at 75.50 when the midquote was 75.45. Effective half-spread = 75.50 − 75.45 = 0.05, or 0.067% of the midquote.
Trades inside the spread: a broker matching two client orders privately, or a dealer giving a favored client a price improvement. Trades outside: genuinely large orders that exhaust the best quote, or simply a recording-time mismatch, since electronic quote updates are typically faster than transaction reporting — Lee and Ready (1991) found reporting delays of up to five seconds are common. When the direction of a trade isn't recorded, the Lee-Ready algorithm classifies it as buyer-initiated if closer to the ask, seller-initiated if closer to the bid, and by the "uptick/downtick" of the previous price if exactly at the midpoint. Odders-White (2000), testing this on real NYSE TORQ data, found it 85% accurate — worse specifically at the midpoint, on small trades, and on large-cap, frequently-traded stocks.
The realized spread — why the effective spread overstates the dealer's profit
The book's own worked example makes this concrete: a dealer buys 75 shares at $326 when the market is $326 bid / $327 ask.
| Scenario | New bid/ask | Unwind at | Profit/sh. |
|---|---|---|---|
| Quotes unchanged | $326 / $327 | $327 (ask) | +$1.00 |
| Quotes decline | $325.50 / $326.50 | avg of $325.50/$326.50 | $0.00 |
What this means: the quoted/effective spread implied a $1.00 gain, but if prices simply drift down after the dealer buys — which is common, since buy-side pressure and sell-side pressure both tend to move prices in their own direction — the dealer's actual profit can be zero. The realized half-spread fixes this by comparing the trade price to the midquote some delay Δ later (5-10 minutes, long enough for quotes to adjust): Sʳ = d(pₜ − mₜ₊Δ). It's smaller than the effective spread whenever prices drift in the direction of the trade — which is the normal case, not the exception. If the effective spread were ever smaller than that adverse drift, dealers would lose money on average and exit the business — so in equilibrium, the effective spread has a floor set by exactly this adverse-selection cost.
Since 2000, US platforms must publish monthly "Dash-5" execution-quality reports (SEC rule 605) — average effective and realized spreads, and execution speed, by order size and type. The book shows a real 2005 NASDAQ report for Microsoft: realized spreads are smaller than effective spreads across every trade-size bucket except the very largest.
When you don't have quote data: VWAP, price impact, and non-trading measures
VWAP (volume-weighted average price) needs only transaction data, not quotes — the average trade price over a period, weighted by size. It's the standard benchmark for judging broker execution quality, but it's gameable: if a single order is a large share of the day's volume, its own execution price mechanically pulls VWAP toward itself, making the comparison close to meaningless for exactly the trades where it matters most.
Price impact: Δmₜ = λqₜ + εₜ, where qₜ is the dollar order imbalance (buy value minus sell value) over an interval. 1/λ is a depth measure — the book cites Stoll (2000)'s real finding: a 1-percentage-point order imbalance moves price by 0.75% for the lowest-capitalization NYSE/AMEX stocks, but only 0.52% for the highest-cap ones — bigger stocks really are deeper, as a number, not just a feeling.
When even signed order-imbalance data is unavailable, the Hasbrouck measure regresses absolute price change on total trading volume instead, and the Amihud ratio (|return|/volume) captures the same idea as a simple ratio rather than a regression slope.
Non-trading measures: in very thin markets (many emerging markets, some corporate bonds), the fraction of zero-return days can proxy for illiquidity — but it can also overstate illiquidity, since a very liquid market can absorb trades without moving price at all, which looks identical to "no trading happened."
Roll's measure — estimating the spread from prices alone
Roll (1984)'s model: the midquote follows a random walk (mₜ = mₜ₋₁ + εₜ); orders are a random 50/50 buy/sell mix uncorrelated with fundamentals; the spread is constant. Under these assumptions, transaction prices bounce between bid and ask ("bid-ask bounce"), which mechanically creates negative serial correlation in price changes — and that covariance converts directly into a spread estimate: Sᴿ = 2√(−cov(Δpₜ₊₁, Δpₜ)).
| Measure | NYSE | Nasdaq |
|---|---|---|
| Half quoted spread | 7.9¢ | 12.6¢ |
| Half effective spread | 5.6¢ | 10.7¢ |
| Half Roll's measure | 3.81¢ | 11.5¢ |
What this means: Roll's measure, built from price data alone, systematically underestimates both the quoted and effective spread — here by about half on the NYSE. That's expected: it relies on assumptions (balanced order flow, no autocorrelation, orders carry no information) that real markets violate to varying degrees, each violation biasing the estimate further downward. It's a useful estimate when quotes simply aren't available, not a substitute for real quote data when you have it.
Implementation shortfall — the measure that includes time
Every measure above prices one trade at one instant. Implementation shortfall (Perold, 1988) adds the dimension that actually matters for large institutional orders: the risk of not finishing at all, and the cost of the delay before execution even starts. Decide at time 0 to buy q shares at midquote m₀; by time t, a fraction κ is filled at average price p̄, while the stock has moved to mₜ.
IS = q(mₜ − m₀) − κq(mₜ − p̄)
= κq(p̄ − m₀) + (1 − κ)q(mₜ − m₀)
execution cost opportunity cost| Component | Calculation | Value |
|---|---|---|
| Filled: 3,000 sh. @ p̄=$101 | 3,000 × (101 − 100) | $3,000 |
| Unfilled: 7,000 sh., stock now $103 | 7,000 × (103 − 100) | $21,000 |
| Total implementation shortfall | $24,000 | |
What this means: $24,000 is 2.4% of the $1,000,000 paper-portfolio value (10,000 × $100) — a real, material cost. Only 30% of the order filled, so 87.5% of the loss ($21,000 of $24,000) is opportunity cost from the unfilled 70%, not execution cost on what was actually bought. The book cites a real-world case with the same shape: Leinweber (1995) found the Value Line newsletter portfolio's paper return was 26.2% over 1971-1991, but its actual, implemented return was 16.1% — a real 10.1-percentage-point implementation shortfall, purely from the gap between the strategy on paper and the cost of actually executing it.
- Context
- Execution cost and opportunity cost trade off directly against each other — patient (limit-order) execution lowers one and raises the other.
- Algo-relevant?
- Yes — this trade-off is the literal design problem execution algorithms exist to solve.
- What's applied
- An algorithm's speed of execution is a dial, not a fixed choice: faster execution pushes κ toward 1 (shrinking opportunity cost, which scales with 1−κ) at the cost of worse average fill prices (raising execution cost).
- Action
- The book notes the optimal speed depends on the broker's forecast of price direction and market resiliency — how fast liquidity replenishes after a large trade depletes it (a new named concept here, distinct from depth: depth is how much size sits at a price level right now, resiliency is how quickly that size comes back after being consumed).
- Why
- In a highly resilient market, an algorithm can execute faster and get both lower execution cost and lower opportunity cost — the trade-off softens. In a low-resiliency market, the trade-off is sharp and unavoidable, and the algorithm has to actually choose a point on it.
Before moving to Chapter 3
- 1
Using real quote and transaction data for a stock you trade, compute the quoted, effective, and realized (Δ=5-10 min) spreads side by side, the way this chapter's NASDAQ/Microsoft example does.
- 2
Compute your own implementation shortfall on a real order: your decision-time midquote, your average fill price, the fraction filled, and where the stock ended up — split it into execution cost and opportunity cost the way the $24,000 example does.
- 3
Chapter 3 turns to price determination theory — why the spread exists in the first place (inventory risk, adverse selection), which this chapter's realized-spread discussion already previewed.