*2.4. Illiquidity Measure*

The Amihud illiquidity (ILLIQ) ratio (Amihud 2002) is a common measure used to calculate the degree of stock liquidity. Here, we applied this measure to compute and compare the liquidity of cryptocurrencies during bull and bear markets. We could also interpret this ratio as a measure of price impact because it represents an hourly price response associated with one dollar of trading volume. This illiquidity measure was chosen for its simplicity and robustness as it requires only high-frequency trade data. More importantly, other liquidity measures require microstructure data on cryptocurrencies, and these data are not freely available, as the market is still in its infancy. The Amihud illiquidity ratio is defined as

$$ILLIQ\_{iT} = 1/D\_{iT} \sum\_{t=1}^{D\_{iT}} \frac{|\ R\_{it}|}{VOLD\_{it}} \, , \tag{1}$$

where *DiT* denotes the number of traded hours in cryptocurrency *i* in year *T*, *Rit* is the hourly return on cryptocurrency *i* in hour *t* in USD, and *VOLDit* is the hourly volume in dollars (price at time *t* × volume at time *t*) on cryptocurrency *i* in hour *t*.
