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Liquidity Riskadvanced

Amihud Illiquidity Ratio

The Amihud illiquidity measure (Amihud, 2002) captures the price impact of trading: how much the price moves per dollar traded. For each day it is the absolute return divided by the dollar volume, ILLIQt=∣Rt∣/Volumet\mathrm{ILLIQ}_t = |R_t| / \mathrm{Volume}_t, and the stock’s illiquidity is the average of this ratio over a period. The reading is directional and easy to get backwards: a higher ratio means a given dollar of trading moves the price more, so the stock is less liquid. A low ratio means large volume barely budges the price, the hallmark of a deep, liquid market. Its great appeal is that it needs only daily return and volume data, available almost everywhere, rather than high-frequency quotes.

Try it yourself

Stock liquidity — measuring tightness, depth and price impact

Is this stock liquid? Read the spread and the Amihud ratio.

A tight spread is cheap to round-trip and a low Amihud ratio means a dollar of trading barely moves the price. Both point to a liquid name. The Amihud ratio is the one to watch: higher Amihud = more price impact per dollar = LESS liquid.

Quoted spread %
0.08%
= US$0.04 / mid US$50.00
Amihud ILLIQ (×10⁶)
1.60e-5Liquid
raw 1.60e-11 per US$ traded
Spread costs and turnover (% of mid-price / float)
Quoted spread0.08%Effective spread0.04%Turnover0.50%
Mid-price Pₘᵢ𝒹 = (ask + bid)/2US$50.00
Quoted spread Pₐₛₖ − P_bidUS$0.04 (0.08%)
Effective spread 2·|Pₑₓₑ𝒸 − Pₘᵢ𝒹|US$0.02 (0.04%)
Turnover Volume / Shares out.0.50% / day
Daily dollar volume P · VolumeUS$500100000
Amihud ILLIQ |Rₜ| / (P·Volume)1.60e-11 (×10⁶ = 1.60e-5)
A tight spread of 0.08% and a low Amihud ratio mark this as a liquid name: a dollar of trading barely nudges the price.
Spread % 0.08%Turnover 0.50%Amihud verdict Liquid
Try this. Load the small-cap, then drag daily volume up toward the blue-chip level. Watch the Amihud ratio collapse: same price move, far more dollars traded, so each dollar moves the price less. Then drop the daily |return| and notice the spread is unaffected — spread (tightness) and Amihud (price impact) are separate dimensions of liquidity.
Reflect: two stocks share the same quoted spread. Which measure would still tell you they differ in how much a large order moves the price?

Why it matters

Amihud asks a simple question: how much does the price jump for each dollar that trades? If a tiny trade sends the price flying, the stock is illiquid, fragile, easily pushed around. If a huge trade barely moves it, the stock is liquid and deep. So a big number is bad (illiquid) and a small number is good (liquid). The beauty is that you do not need a fancy data feed of bids and asks. Daily returns and daily volume, which everyone has, are enough to rank thousands of stocks by how easily their prices are moved.

Formulas

Daily Amihud ratio
ILLIQt  =  ∣Rt∣Volumet\mathrm{ILLIQ}_t \;=\; \dfrac{|R_t|}{\mathrm{Volume}_t}
∣Rt∣|R_t| is the absolute daily return and Volumet\mathrm{Volume}_t is daily dollar volume. The ratio is price impact per dollar traded: higher means the price moves more for the same volume, so the stock is less liquid.
Period average (the Amihud measure)
ILLIQ  =  1D∑t=1D∣Rt∣Volumet\mathrm{ILLIQ} \;=\; \dfrac{1}{D}\sum_{t=1}^{D} \dfrac{|R_t|}{\mathrm{Volume}_t}
Averaging the daily ratio over DD trading days (often a month or a year) gives the stock’s illiquidity. A larger average ILLIQ identifies a less liquid stock.

Worked examples

Scenario

On a given day, Stock A has a 1% return on 100 million dollars of volume; Stock B has a 1% return on 2 million dollars of volume. Which is more illiquid?

Solution

ILLIQ for A = 0.01 / 100,000,000 = 1.0 × 10⁻¹⁰. ILLIQ for B = 0.01 / 2,000,000 = 5.0 × 10⁻⁹, fifty times larger. Stock B has the higher Amihud ratio, so the same 1% price move was generated by far less trading: its price is easily pushed, meaning Stock B is the less liquid name. Higher ratio, more price impact, less liquidity. This is the direction students most often reverse.

Scenario

The GameStop episode of January 2021. How would the Amihud ratio behave during the squeeze?

Solution

During the squeeze the price swung violently while a coordinated rush of retail orders met very few willing sellers, so even though volume was high, the price impact per dollar was extreme and erratic. On days where huge absolute returns coincided with order flow that the available depth could not absorb, the daily ILLIQ spiked, signalling that the stock had become hard to trade without enormous price moves. The episode shows that a stock can post record volume yet still display severe price impact, because liquidity is about impact per dollar, not raw volume.

Common mistakes

  • ✗A higher Amihud ratio means a more liquid stock. The opposite: a higher ratio means more price impact per dollar traded, so the stock is LESS liquid. This is the most common error and the one to fix.
  • ✗The Amihud measure needs intraday bid-ask data. Its key advantage is using only daily absolute returns and dollar volume, so it can be computed for long histories and for markets without high-frequency data.
  • ✗High trading volume always lowers the Amihud ratio. Volume is the denominator, but the numerator is the absolute return; a volatile, news-driven day can keep the ratio high even with heavy volume, as in the GameStop squeeze.
  • ✗It is a single-day statistic. The Amihud measure is the average of the daily ratio over many days, which smooths out noise and gives a stable illiquidity ranking.

Revision bullets

  • •Amihud ILLIQ = average of |daily return| / daily dollar volume
  • •Measures price impact: how far the price moves per dollar traded
  • •HIGHER ratio = more impact = LESS liquid (state the direction)
  • •Needs only daily returns and volume, not high-frequency quotes
  • •Averaged over many days for a stable illiquidity ranking

Quick check

Stock A has an Amihud ILLIQ of 8 × 10⁻⁹ and Stock B has 3 × 10⁻¹⁰. Which stock is more liquid?

The numerator and denominator of the daily Amihud ratio are

A key practical advantage of the Amihud measure over spread-based measures is that it

Connected topics

Stock LiquidityLiquidity RiskTrading VolumeBid-Ask Spread

Sources

  1. Amihud (2002)
    Amihud, Y. "Illiquidity and Stock Returns: Cross-Section and Time-Series Effects." Journal of Financial Markets, 5(1), 31–56, 2002.
    Introduces the ILLIQ ratio (average of |return| / dollar volume) and shows illiquidity carries a positive return premium.
  2. Vo & Bui (2016)
    Vo, X. V., & Bui, H. T. "Liquidity, Liquidity Risk and Stock Returns: Evidence from Vietnam." International Journal of Monetary Economics and Finance, 9(1), 67-89, 2016.
    Applies the Amihud illiquidity measure to Ho Chi Minh Stock Exchange data (2007-2012), the emerging-market context of FIN302.
How to cite this page
Dr. Phil's Quant Lab. (2026). Amihud Illiquidity Ratio. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-amihud-illiquidity
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