One Ratio to Measure Liquidity: Amihud's ILLIQ

Everyone agrees liquidity matters. Almost nobody agrees on how to measure it.

You could use the quoted bid-ask spread, but that needs intraday data that did not exist for most of history and still does not exist for most of the world's assets. You could use Kyle's price impact coefficient, but estimating it properly requires trade-by-trade data and a model. You could use trading volume, but volume is a terrible proxy: a stock can trade a lot precisely because it is being pushed around.

Amihud's 2002 paper offers a way out that is almost embarrassingly simple, and that simplicity is exactly why it took over.

The problem: liquidity is easy to feel and hard to count

Liquidity, in the sense that matters to a trader, means: can I move size without moving the price?

A liquid stock absorbs a large order and barely flinches. An illiquid one lurches. That is the intuition, and it is really a statement about a ratio: how much price movement do you get per unit of trading?

Kyle had already formalized exactly this idea as a coefficient, often called lambda, which is the slope of price with respect to order flow. But lambda is expensive to estimate. You need signed order flow, which you have to infer, and you need a lot of intraday data. In 2002, and for most assets even today, you simply do not have that.

The key idea via analogy: how much does the boat rock per passenger?

Picture two boats. One is a supertanker, one is a canoe. Ask a passenger to walk from one side to the other. The tanker does not notice. The canoe nearly capsizes.

You do not need instruments to know which is which. You just need to watch how much the boat rocked and divide by how many people walked. Big rock per person means small boat.

That is Amihud's measure, exactly. For each day, take:

• how much the boat rocked: the absolute value of the stock's return that day, ignoring direction, because you only care about the magnitude of the lurch
• how many people walked: the dollar volume traded that day

Divide the first by the second, and average the ratio over a year. The result is the ILLIQ measure. Big number means a stock whose price moves a lot for very little trading, which is precisely what "illiquid" means.

The beauty is in what it does not need. No quotes. No bid, no ask. No intraday data. No trade classification. No model to estimate. Just daily returns and daily volume, which exist for essentially every stock in every market for as far back as records go. It is, in effect, a poor man's Kyle lambda, and it turns out to be a remarkably good one.

Why it mattered

Amihud used ILLIQ to make two distinct claims, and it is worth separating them because they are different in kind.

The cross-sectional claim. Illiquid stocks earn higher average returns than liquid ones, even after you control for size, book-to-market and beta. This confirmed and extended the Amihud and Mendelson (1986) argument: illiquidity is compensated. If you are willing to hold hard-to-trade assets, the market pays you for it.

The time-series claim, which is the more original and more interesting one. Amihud showed that market-wide illiquidity predicts future market returns. When the whole market becomes illiquid, expected returns going forward rise. Read that carefully, because it contains a mechanism: if investors suddenly demand more compensation for illiquidity, then prices must fall today to deliver that higher future return. In other words, a liquidity shock is not just an inconvenience for traders, it is a repricing event for the entire market. He also documented that this hits small, illiquid stocks harder than large liquid ones, which is the "flight to liquidity" phenomenon that every crisis since has confirmed.

That second finding is why the paper is cited by people who have never thought about a bid-ask spread in their lives. It connects the plumbing of trading to the level of the stock market.

Beyond the findings, ILLIQ became infrastructure. It is the default liquidity control variable in thousands of empirical finance papers, precisely because it can be computed anywhere, for anything, from data everyone already has. Its ubiquity is its own kind of contribution.

The honest limitations

• It is a proxy, and a crude one. Absolute return divided by dollar volume is not price impact. It is a correlate of price impact. On days with big news, the return is large for reasons that have nothing to do with order flow, and ILLIQ will register that as illiquidity when it is really just information arriving. The measure cannot tell a lurch caused by a big order from a lurch caused by a press release.
• It is unstable for low-volume stocks. On days with very little trading, the denominator is tiny, and the ratio explodes. Since these are exactly the stocks you most want to measure, this is awkward. Practitioners handle it with winsorising, log transforms and filters, all of which are judgement calls that affect the answer.
• Volume is not comparable across venues or eras. A share of volume in 2002 meant something different than it does now, when the same economic order gets sliced into hundreds of small prints across a dozen venues. The measure's level is not comparable over time without care, and cross-market comparisons are worse.
• Liquidity and size are stubbornly entangled. The illiquidity premium in the cross-section is concentrated in small stocks, and disentangling "illiquid" from "small" from "neglected" from "risky" remains genuinely unresolved. Some researchers argue much of the ILLIQ premium is really a microcap effect that is hard to actually capture after paying the very trading costs the measure describes, which is a delicious and uncomfortable irony.
• The strategy eats itself. To harvest the illiquidity premium you must buy illiquid stocks, which means paying a large spread and moving the price. The premium is real, but a meaningful chunk of it is not accessible to anyone trading at scale.

The one-line takeaway

Amihud measured illiquidity as how much the price moves per dollar traded, computable from daily data alone, and used it to show both that illiquid stocks earn a premium and that when the whole market turns illiquid, prices fall and future expected returns rise.