Liquidity Risk Models (Amihud, Roll, LOT)
Liquidity Risk Measures (Amihud, Roll, LOT) · Also known as: Amihud illiquidity, Roll spread estimator, LOT spread measure, Lesmond-Ogden-Trzcinka measure, Likidite Risk Modelleri (Amihud, Roll, LOT)
Liquidity Risk Models are a family of measures that quantify how easily an asset trades by capturing its price impact, its effective bid-ask spread, and a holding-period adjustment. The family brings together the Amihud illiquidity ratio (Amihud, 2002), the Roll serial-covariance spread estimator (Roll, 1984), and the LOT (Lesmond-Ogden-Trzcinka) realised-spread measure.
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When to use it
Use these models when you have continuous price-and-volume data for an asset, in either time-series or cross-sectional form, and at least about 60 observations. They are appropriate for describing, comparing, or predicting liquidity across stocks or over time. The Amihud measure relies on the daily absolute-return-to-volume ratio as a proxy for illiquidity; the Roll estimator assumes the spread can be read from the serial covariance of returns, and works best when market impact is negligible for small trades. For liquidity-adjusted value-at-risk the holding period should be scaled to the liquidity horizon.
Strengths & limitations
- Require only readily available price and volume data, with no need for high-frequency tick or quote feeds.
- Provide intuitive, directly comparable liquidity scores across assets and over time.
- Combine complementary views: price impact (Amihud), implied spread (Roll), and a holding-period-adjusted realised spread (LOT).
- The Roll estimator breaks down when the serial covariance of price changes is positive, leaving the spread undefined and conventionally set to zero.
- The Amihud ratio can be distorted by zero-volume days and by extreme returns, so it must be cleaned before averaging.
- These are proxies, not direct measurements; market impact is assumed negligible for small trades, which can fail in stressed or thin markets.
Frequently asked
What does a high Amihud illiquidity value mean?
It means a relatively small amount of trading volume already moves the price substantially, so the asset is illiquid. A low value means trades are absorbed with little price impact, indicating a liquid asset.
Why does the Roll estimator sometimes give a spread of zero?
The Roll spread is twice the square root of the negative serial covariance of consecutive price changes. When that covariance is positive, the formula has no real solution, so by convention the spread is set to zero. This is a known limitation, not evidence that the asset is perfectly liquid.
Do I need high-frequency or quote data to use these models?
No. A key appeal of the Amihud, Roll, and LOT measures is that they are low-frequency proxies: they work from daily prices and volumes, without needing intraday tick or bid-ask quote feeds.
How much data do I need?
These models expect continuous price and volume data with at least about 60 observations, in either time-series or cross-sectional form, so that the averages and covariances are estimated reliably.
Sources
- Amihud, Y. (2002). Illiquidity and Stock Returns: Cross-Section and Time-Series Effects. Journal of Financial Markets, 5(1), 31-56. DOI: 10.1016/S1386-4181(01)00024-6 ↗
- Roll, R. (1984). A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market. Journal of Finance, 39(4), 1127-1139. DOI: 10.1111/j.1540-6261.1984.tb03897.x ↗
How to cite this page
ScholarGate. (2026, June 1). Liquidity Risk Measures (Amihud, Roll, LOT). ScholarGate. https://scholargate.app/en/finance/liquidity-risk-models
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