Amihud Illiquidity Measure Explained (2026)

What the Amihud measure says

In January 2002, Yakov Amihud published Illiquidity and Stock Returns: Cross-Section and Time-Series Effects in the Journal of Financial Markets. Its central variable needs only two daily observations: absolute stock return and dollar trading volume.

The Amihud illiquidity measure, or ILLIQ, is the average absolute return per unit of dollar volume. Amihud described it as a rough measure of price impact. Rough is doing useful work. ILLIQ is an association observed over a day, not an identified coefficient telling a trader how far a new order of a given size will move the market.

That limitation is also its appeal. Quote and transaction histories are unavailable for many markets and older samples. Daily closes and volume reach much further back. ILLIQ trades microstructure precision for coverage, making it a common control and sorting variable in empirical asset pricing.

It complements Kyle's lambda, which is a structural price-on-signed-flow slope, and Roll's 1984 estimator, which uses serial covariance to infer bid-ask bounce.

Definition, units and scaling

For stock $i$ on trading day $d$ in period $P$, define

$$\operatorname{ILLIQ}_{iP} =\frac{1}{D_{iP}} \sum_{d=1}^{D_{iP}} \frac{|R_{id}|}{\operatorname{DVOL}_{id}},$$

where $R_{id}$ is the close-to-close return as a decimal, $\operatorname{DVOL}_{id}$ is price times shares traded in currency units and $D_{iP}$ is the number of valid days.

Amihud's original cross-sectional variable was annual. Monthly averaging is a later, common implementation choice, but it should not be described as the paper's original construction. The paper multiplied the annual ratio by $10^6$ for presentation:

$$\operatorname{ILLIQ}^{(6)}=10^6\operatorname{ILLIQ}.$$

Scaling changes the displayed number, not the ranking or economics. A paper using volume in millions of dollars has already built the $10^6$ factor into its denominator, so multiplying again would be an error.

Raw ILLIQ has units of inverse currency because return is dimensionless and dollar volume is currency. Suppose a stock moves $2\%$ on 10 million dollars of volume:

$$\frac{0.02}{10{,}000{,}000} =2\times10^{-9}\text{ dollars}^{-1}.$$

The $10^6$-scaled value is $0.002$. Equivalently, that day's observed ratio is 20 basis points per one million dollars of market-wide volume:

$$2\times10^{-9} \times1{,}000{,}000 \times10{,}000 =20\text{ bp}.$$

This conversion is descriptive. Multiplying ILLIQ by your proposed trade value does not, by itself, forecast your causal impact. Daily absolute return contains public news, overnight moves and other traders' orders; daily volume is unsigned total activity, not your net order.

A two-day example shows why the order of operations matters. Suppose day one has a 1% absolute return on 5 million dollars of volume, while day two has a 0.5% absolute return on 20 million dollars:

$$\operatorname{ILLIQ} =\frac{1}{2}\left( \frac{0.01}{5{,}000{,}000} +\frac{0.005}{20{,}000{,}000} \right) =1.125\times10^{-9}.$$

The $10^6$-scaled estimate is $0.001125$. By contrast, dividing total absolute return by total volume gives $0.015/25{,}000{,}000=6\times10^{-10}$. The second number is lower because the high-return, low-volume day receives less weight. It is not Amihud's estimator.

The distinction from market microstructure measures is simple:

A reproducible implementation

Data choices dominate small coding choices. Use adjusted returns that include split and delisting handling appropriate to the study, but do not combine split-adjusted shares with an unadjusted price when constructing dollar volume. Align the two series before division and treat zero volume as missing, not zero illiquidity.

import numpy as np
import pandas as pd

def amihud_illiq(
    returns: pd.Series,
    dollar_volume: pd.Series,
    frequency: str = "ME",
    min_days: int = 15,
    scale: float = 1e6,
) -> pd.Series:
    data = pd.concat(
        {"ret": returns, "dvol": dollar_volume}, axis=1
    ).replace([np.inf, -np.inf], np.nan)
    valid = data["dvol"].gt(0) & data["ret"].notna()
    ratio = data["ret"].abs().div(data["dvol"]).where(valid)

    grouped = ratio.resample(frequency)
    estimate = grouped.mean()
    return estimate.where(grouped.count() >= min_days) * scale

For annual replication of the original paper, use an annual period and its sample rules rather than the monthly default above. Amihud studied NYSE stocks from 1963 to 1997. The return regressions ran from 1964 to 1997 because lagged prior-year characteristics were used. Eligible stocks needed more than 200 return-and-volume days in the prior year, a prior year-end price above 5 dollars, year-end market capitalisation data and exclusion from the top and bottom 1% of the ILLIQ distribution.

That is different from a generic rule to drop every stock-month below 5 dollars or below 15 days. Those may be defensible modern filters, but they are not Amihud's exact annual protocol.

A useful practitioner workflow keeps both raw and scaled columns, records the currency and winsorises only after preserving the unaltered estimate. For cross-country work, convert volume into a common currency before comparing levels. Exchange rates rescale ILLIQ mechanically.

Portfolio tests also need a lag. A December 2025 annual ILLIQ estimate can be used to explain returns beginning in January 2026 because all of its inputs are then known. Sorting January 2026 returns on an ILLIQ value that includes those same January returns creates look-ahead and a mechanical return-in-the-signal relation. Monthly strategies usually delay the signal by at least one complete measurement window.

Corporate actions deserve their own check. A stock split should leave dollar volume economically comparable, but mixed adjusted and unadjusted fields can create a false jump. Delisting returns should not be discarded simply because they are extreme, while stale zero returns should not automatically be read as abundant liquidity. The data policy should be fixed before examining the liquidity premium.

Empirical meaning and limitations

Amihud's main evidence was not a claim that the highest ILLIQ decile mechanically earned a fixed 7% to 9% premium. The paper estimated Fama-MacBeth cross-sectional regressions and aggregate time-series relations. Across NYSE stocks over 1964 to 1997, lagged illiquidity had a positive, highly significant relation with expected return after controls. Over time, expected market illiquidity was positively related to subsequent market excess return, while unexpected illiquidity was associated with a contemporaneous price decline.

The cross-sectional result is a characteristic relation: stocks that were harder to trade subsequently offered higher gross returns on average. It does not prove that bearing innovation in aggregate liquidity is the only priced risk. Acharya and Pedersen's 2005 liquidity-adjusted CAPM separates expected trading cost from covariances involving market liquidity and returns. That is a different question from whether the level of a stock's ILLIQ predicts its return.

Nominal units create another long-sample issue. Because the denominator is dollar volume, changing price levels and currency units rescale raw ILLIQ mechanically. In the cross-sectional regressions, Amihud divided each stock's annual ILLIQ by that year's cross-sectional mean; the time-series tests used the logarithm of aggregate annual ILLIQ. Modern replications should document any deflation or market-wide normalisation rather than compare nominal raw levels across decades.

Always retain the sign-free nature of the variable in interpretation. ILLIQ uses $|R|$, so it measures magnitude, not whether buying pressure lifted price or selling pressure lowered it. A directional impact question needs signed order flow.

The sample design matters. ILLIQ was more strongly related to smaller firms, and the original analysis pre-dates US equity decimalisation in 2001. Trading technology, tick sizes and volume reporting have changed. A coefficient from that period should not be carried into a 2026 cost model without re-estimation.

There are four recurring interpretation errors.

First, ILLIQ confounds information and liquidity. A large earnings surprise can generate a large return and heavy volume without measuring the price concession required to execute a marginal order.

Second, the ratio is noisy in thin names. One stale close, erroneous volume record or corporate action can dominate a monthly average. Minimum-observation rules, corporate-action checks and documented tail treatment are part of the estimator.

Third, volume is endogenous. News can raise both $|R|$ and volume. ILLIQ is not the slope from a controlled experiment and should not be labelled a causal impact coefficient.

Fourth, aggregation is not innocent. The mean of daily ratios is not the ratio of average absolute return to average volume:

$$\frac{1}{D}\sum_d\frac{|R_d|}{\operatorname{DVOL}_d} \neq \frac{\sum_d|R_d|}{\sum_d\operatorname{DVOL}_d}.$$

The left-hand side gives low-volume days more influence and is Amihud's definition. Replacing it with the right-hand side creates a different measure.

For portfolio work, ILLIQ is best used for relative ranking, capacity screens and liquidity-regime monitoring. A pre-trade model should add spread, participation, volatility, order direction and horizon. Almgren-Chriss execution makes those scheduling assumptions explicit.

The measure survives because it is cheap, transparent and available. It becomes misleading only when its convenience is mistaken for identification.

Frequently Asked Questions

What is the Amihud illiquidity measure?

It is the average of absolute daily return divided by daily dollar volume over a chosen period. Higher values indicate more observed price movement for a given level of trading activity.

Is ILLIQ calculated monthly or annually?

Amihud's 2002 paper used annual stock-level ILLIQ. Monthly ILLIQ is now common, especially for portfolio sorts, but researchers should state the aggregation period.

Why multiply ILLIQ by one million?

Raw values are very small. Multiplication by $10^6$ is a display convention; it does not change rankings. Do not apply it twice when volume is already expressed in millions.

Can I multiply ILLIQ by my order size to predict impact?

Not as a causal forecast. The product is a rough scale calculation, but daily ILLIQ uses unsigned market-wide volume and price moves driven by many sources. A transaction-cost model needs order-specific calibration.

How should zero-volume days be handled?

Treat the ratio as missing and report the observation rule. Setting it to zero falsely labels a no-trade day as perfectly liquid; dividing by zero creates an infinite estimate.

Which paper should I cite?

Cite Yakov Amihud (2002), Illiquidity and Stock Returns: Cross-Section and Time-Series Effects, Journal of Financial Markets 5(1), 31 to 56.