Market Liquidity Measures - Amihud Illiquidity Ratio (Examples)

Understanding the Amihud illiquidity ratio

The Amihud illiquidity ratio, introduced by Yakov Amihud in 2002, measures the average daily price response associated with one dollar of trading volume. The ratio helps quantify an asset's liquidity by examining the price impact of trades.

The basic formula is:

$ILLIQ = \frac{|R_{t}|}{VOL_{t}}$

Where:

• $|R_{t}|$ is the absolute return on day t
• $VOL_{t}$ is the trading volume in dollars on day t

For practical implementation over a time period T, the average is calculated:

$ILLIQ_i = \frac{1}{T} \sum_{t=1}^T \frac{|R_{it}|}{VOL_{it}}$

Applications in market microstructure

The ratio is particularly valuable in market microstructure analysis because it:

1. Captures price impact relative to volume
2. Requires only daily data, making it accessible for most markets
3. Correlates well with more sophisticated intraday measures

The Amihud ratio is especially useful for analyzing less liquid markets where high-frequency tick data may not be available.

Implementation considerations

When implementing the Amihud ratio, several factors need consideration:

Data requirements

• Daily price changes
• Daily trading volumes
• Currency adjustments for cross-market comparisons

Time period selection

The measurement period should be appropriate for the asset class and market conditions being analyzed:

Relationship with trading costs

The Amihud ratio has important implications for transaction cost modeling. Higher ratios typically indicate:

1. Larger bid-ask spreads
2. Higher market impact costs
3. Greater difficulty in executing large orders

Limitations and considerations

While widely used, the measure has several limitations:

1. Assumes a linear price-volume relationship
2. May not capture all dimensions of liquidity
3. Can be sensitive to extreme volume events

Applications in portfolio management

The ratio serves several purposes in portfolio management:

Risk management

• Liquidity screening for portfolio construction
• Risk monitoring during market stress periods
• Portfolio rebalancing cost estimation

Trading strategy development

• Asset selection for statistical arbitrage
• Execution timing optimization
• Market impact forecasting

Modern extensions and variations

Recent developments have introduced modifications to the basic ratio:

1. Volume-weighted variants
2. Intraday calculations
3. Adjustments for market capitalization

These adaptations help address specific market contexts and trading needs while maintaining the fundamental insight of price impact per unit of volume.