Amihud Illiquidity: Formula, Data, and Interpretation

The Amihud illiquidity ratio measures how much a stock’s price moves per dollar of trading volume. Yakov Amihud introduced it in a 2002 paper in the Journal of Financial Markets, and it has become the standard low-frequency proxy for trading cost because it needs only daily returns and daily volume, both readily available from the 1960s onward.¹ A high value means small trades push the price around. A low value means the market can absorb big orders without much disruption.

What the Ratio Measures

Every trade puts some pressure on price. A large buy nudges the price up, a large sell nudges it down. The Amihud ratio estimates the size of that pressure by comparing how much a stock moved on a given day to how much money flowed through it.

Earlier trading-cost measures relied on intraday bid-ask spreads or tick data, which barely exist before the 1980s. Using only daily returns and daily volume opened up decades of market history to liquidity research, and that is why the measure spread so quickly.¹

The Formula

The calculation divides the absolute value of a stock’s daily return by its dollar trading volume for the same day, then averages that daily figure across the period you care about. For stock i over period y:

ILLIQ = (1 / D) × Σ ( |R_d| / DVOL_d )

where |R_d| is the absolute return on day d, DVOL_d is the dollar volume that day, and D is the number of valid trading days in the period.²

How to Calculate It Step by Step

Compute the daily return as the percentage change in closing price from one day to the next.
Take the absolute value. A 3% loss and a 3% gain both become 0.03; you care about magnitude, not direction.
Compute dollar volume by multiplying shares traded that day by the closing price.
Divide absolute return by dollar volume. That is the daily illiquidity ratio.
Repeat for every valid trading day in your window, sum, and divide by the count of days.

For a monthly figure you’re averaging roughly 20 to 22 daily ratios. A typical NYSE month has between 19 and 22 trading sessions depending on holidays.³ Amihud’s original study used annual averages; later researchers have used monthly windows.⁴

Scaling the Output

The raw ratio produces tiny numbers for actively traded stocks because dollar volumes run into the millions or billions. To make results readable, researchers commonly multiply by 10⁶, or express dollar volume in units of 100 million. NYU Stern’s V-Lab, for instance, scales dollar volume into 100-million-dollar units before computing the ratio.⁵ Whichever convention you pick, apply it consistently across every security you’re comparing.

Zero-Volume Days

If a stock records zero shares traded on a day, the ratio is undefined. The standard fix is to exclude those days from the calculation and reduce D accordingly. Amihud’s original study also required at least 200 days of return and volume data in a given year, which filters out the thinnest names where zero-volume days would dominate.²

Data You Need

Two data points per trading day: the stock’s daily return (or a closing price you can turn into a return) and shares traded. That’s all.

The Center for Research in Security Prices (CRSP) database at the University of Chicago, now part of Morningstar, is the gold standard for U.S. equity research. It provides clean, split-adjusted daily returns and volume for NYSE, AMEX, and NASDAQ stocks going back to 1925, and access requires an institutional subscription.⁶

Without institutional access, Yahoo Finance carries historical price and volume for most listed securities, generally starting around 1970. Downloading CSVs requires a Yahoo Finance Gold subscription, and not every instrument is available due to licensing.⁷ Open-source Python libraries such as yfinance pull the same data from Yahoo’s public API for personal use, subject to Yahoo’s terms.

Whatever source you use, work with split-adjusted prices and volumes. A 2-for-1 split doubles share count and halves price overnight, which would inject a phantom 50% return and an artificial volume spike into your series if left unadjusted.

Cleaning the Data

Raw data almost always needs work before you compute the ratio. The steps that matter most:

Filter out low-priced stocks. Amihud excluded shares priced below $5 because the tick size at the time ($0.125) created artificial noise in returns for cheap stocks. Most researchers still apply some price floor.²
Trim outliers. The original study dropped stocks whose annual ILLIQ fell in the top or bottom 1% of the distribution. A single anomalous day can otherwise distort the full-period average.
Require a minimum number of observations. At least 200 valid trading days per year, or roughly 15 per month for monthly windows, keeps the average from riding on a handful of prints.
Adjust for inflation or volume growth. Over long horizons, nominal dollar volume climbs with inflation and market expansion. Deflating dollar volume, or taking the natural log of the ratio, neutralizes currency scaling.⁴

Skip these and your estimates will be driven by data artifacts rather than genuine trading frictions.

Reading the Output

The ratio tells you, roughly, how much price impact one dollar of trading volume produces. Higher means the stock is harder to trade in size without moving the price against you. Lower means the market can absorb size with minimal disruption.

Comparing absolute values across stocks works fine as long as the scaling convention is the same for all of them. Comparing values across time is harder. Nominal dollar volume has grown enormously since the 1960s because of inflation, market growth, and decimalization, so the raw ratio drifts downward over decades even if true liquidity conditions are unchanged. Log-transforming the ratio or deflating volume handles this.

Where the measure is strongest is in cross-sectional ranking: sorting stocks from most liquid to least liquid within the same time period. That ranking is robust and underpins most of the academic work that uses the measure.

What the Ratio Doesn’t Capture

Amihud acknowledged the limitations in the original paper. The ones worth knowing:

Size confounding. The ratio correlates heavily with market capitalization. Small stocks have low dollar volume and high price impact, so a high Amihud value may just be telling you the company is small. In Amihud’s own data, the correlation between ILLIQ and the log of market cap was −0.614.²
Inflation and volume drift. The denominator grows in nominal terms; any multi-decade study needs to correct for that or the trend will swamp the signal.
Non-trading days. Days a stock didn’t trade are excluded from the average, which can bias the estimate for thinly traded names where non-trading is itself a liquidity signal the ratio fails to record.
Coarseness. Averaging over a full day cannot distinguish a single large block from thousands of small trades that produce the same return and volume. Intraday measures like the Kyle lambda or the effective spread capture microstructure the Amihud ratio misses.

None of these kill the measure. They explain why researchers use it alongside other proxies rather than as a final answer.

Why the Ratio Matters for Expected Returns

The reason the measure draws so much attention is what Amihud found when he ran it. Across NYSE stocks from 1963 to 1997, higher expected illiquidity predicted higher expected stock returns. The illiquidity coefficient carried a t-statistic of 6.55, the relationship held even after excluding January, and the effect was strongest among small caps, which are the names most exposed to liquidity shocks.²

That finding supports a liquidity premium: investors demand extra return for holding stocks that are hard to sell quickly. If the market dries up, you’re stuck in a position you can’t exit without taking a loss. Amihud’s time-series results pointed the same way. When unexpected illiquidity rose, stock prices fell, with the sharpest declines in the smallest, least liquid names.

For portfolio construction the implication is direct. A stock that looks cheap on standard valuation metrics may simply be paying investors to hold something illiquid. Treating that compensation as alpha overstates the skill in a strategy that loads on illiquid names.

1
ScienceDirect. Illiquidity and Stock Returns: Cross-Section and Time-Series Effects
2
Elsevier Science. Journal of Financial Markets – Illiquidity and Stock Returns: Cross-Section and Time-Series Effects
3
NYSE. Trading Days
4
ICMA. Price Impact or Trading Volume: Why is the Amihud (2002) Illiquidity Measure Priced?
5
V-Lab. Liquidity Analysis Documentation
6
Center for Research in Security Prices. CRSP Research Data Products
7
Yahoo Help. Download Historical Data in Yahoo Finance