Quantitative Finance
Amihud (ILLIQ) Illiquidity Ratio Formula: Return Impact per $1M Volume
Measure stock market illiquidity from standard daily bars using Amihud’s (2002) ratio ILLIQ = (1 / D) * Sum(|R_t %| / DollarVolume_MUSD_t) without requiring tick-level order-book data.
Quantify price impact per million dollars traded from daily OHLCV data!
When intraday bid-ask quote feeds are unavailable across decades or international markets, Amihud (2002) showed that averaging daily absolute percentage return divided by daily dollar volume ($ millions)—ILLIQ = (1 / D) * Sum(|R_t %| / V_MUSD_t)—captures the exact spirit of Kyle’s price-impact lambda: how many percentage points the price moves per $1,000,000 of trading volume!
Liquid large-cap equities exhibit tiny ILLIQ values (< 0.01% per $1M), whereas thinly traded micro-caps exhibit high ILLIQ (> 0.40% per $1M), demanding wider execution schedules and an illiquidity return premium.
| Trading Day | Abs Daily Return |R_t| (%) | Dollar Volume ($M) | Daily Impact (%/M$) |
|---|---|---|---|
| Day 1 | 1.20% | $4.00M | 0.3000 |
| Day 2 | 0.80% | $2.00M | 0.4000 |
| Day 3 | 2.50% | $5.00M | 0.5000 |
| Day 4 | 1.50% | $3.00M | 0.5000 (Mean ILLIQ = 0.4250) |
Mean Amihud Illiquidity Ratio (% Move per $1M Traded)
Averages B2:B5 / C2:C5 across D = COUNT(B2:B5) positive-volume sessions using SUMPRODUCT.
=IF(MIN(C2:C5) <= 0, "Zero Volume Day Detected", ROUND(SUMPRODUCT(B2:B5 / C2:C5) / COUNT(B2:B5), 4))Estimated Linear Price Impact (bps) for Order Size Q ($M)
Multiplies ILLIQ (% per $1M) by 100 bps/% and order size B6 ($M).
=IF(OR(MIN(C2:C5) <= 0, B6 < 0), 0, ROUND(100 * B6 * (SUMPRODUCT(B2:B5 / C2:C5) / COUNT(B2:B5)), 2))Try the example
Use the original values or change them to test your understanding.