Fig. 1. Autocorrelations of liquidity factors. Common factors are extracted separately for returns and different measures of liquidity using the APC method. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread measured, as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance, measured as the ratio of the net sum of signed trading volume through the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price-impact components PV, PF, TV, TF, as measured in Sadka (2006). The figure plots the autocorrelation of each of the first principal components. The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Fig. 2. Time series of liquidity shocks (APC). The first common factor is extracted separately for different measures of liquidity using the APC method. In addition, an across-measure common factor is extracted for all the liquidity measures jointly (ALL). The factor shocks plotted above are calculated as the residuals of an AR(2) model (estimated using a monthly expanding window). The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread measured, as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price-impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each liquidity variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Fig. 3. The time series of liquidity shocks of Fig. 2 over the subperiod January 1998–December 1999.

Fig. 4. The time series of liquidity shocks of Fig. 2 over the subperiod October 1996 through March 1998.

Fig. 5. Lead-lag correlations of liquidity shocks (first component). Common factors are extracted separately for returns and different measures of liquidity using the APC method. Factor shocks are calculated as the residuals of an AR(2) model (estimated using a monthly expanding window). The figure plots the pairwise correlation between the leads and lags of first principal component shocks. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance, measured as the ratio of the net sum of signed trading volume through the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each liquidity variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Fig. 6. Lead-lag canonical correlations of liquidity shocks. Three common factors are extracted separately for returns and different measures of liquidity using the APC method. Factor shocks are calculated as the residuals of an AR(2) model (estimated using a monthly expanding window). The table reports the first canonical correlation between the leads and lags of two groups of common factors. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance, measured as the ratio of the net sum of signed trading volume through the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each liquidity variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Fig. 7. Risk-adjusted returns and liquidity loadings. Across-measure common factors are extracted jointly for different measure of liquidity measures using the APC method. Factor shocks are then proxied with AR(2) residuals calculated using a monthly expanding window. Twenty portfolios are sorted each month by the across-measure liquidity loading estimated using the past 36 months (the loading is computed while controlling for Fama-French four factors). The risk-adjusted returns of each portfolio p, α_p, are calculated using Fama-French four factors. In addition, the loading of each portfolio on the across-measure liquidity factor, β_LIQ,p, is calculated using a time-series regression of returns (excess of the risk-free rate) including the Fama-French four factors. The points on the graph plot the risk-adjusted returns against the liquidity loadings. The line plots the fitted regression model

Diagnostics of within-measure common factors

This table reports distribution statistics of time-series regressions. Within-measure common factors are extracted separately for returns and different measures of liquidity using the APC method (Panel A) and the EM method (Panel B). Then, for each variable and each stock, a time-series regression of the variable on its common factors is executed. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid/ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance, measured as the ratio of the net sum of signed trading volume over the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price-impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors and regression analysis, for each stock, each variable (excluding return and order imbalance) is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The table reports the average R² and the average adjusted-R² of these regressions using one, two, and three factors. The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Persistence of aggregate liquidity

Within-measure common factors are extracted separately for different measures of liquidity using the APC method. In addition, across-measure common factors are extracted for all the liquidity measures jointly. Then, for each first principal component we apply an AR(2) model (coefficients Ro1 and Ro2 along with t-statistics in brackets below). The 6-month and 12-month values of the impulse response function applied to each a time series are also reported. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors and time-series analysis, for each stock, each variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Canonical contemporaneous correlations (raw time series)

Three common factors are extracted separately for returns and different measures of liquidity using the APC method. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance, measured as the ratio of the net sum of signed trading volume through the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price-impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable (excluding order imbalance) is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The table reports the first canonical correlation (contemporaneous) between each two groups of common factors. The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months). Statistical significance of 5% and 1% correspond to correlations of 0.13 and 0.18, respectively.

Canonical contemporaneous correlations (fitted AR(2))

Three common factors are extracted separately for returns and different measures of liquidity using the APC method. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance, measured as the ratio of the net sum of signed trading volume through the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable (excluding order imbalance) is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The table reports the first canonical correlation (contemporaneous) between each two groups of common factors. The table uses the residuals of a second order autocorrelation model for each factor (using a monthly expanding window). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months). Statistical significance of 5% and 1% correspond to correlations of 0.13 and 0.18, respectively.

Canonical lead-lag correlations (raw time series)

Three common factors are extracted separately for returns and different measures of liquidity using the APC method. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint, the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance, measured as the ratio of the net sum of signed trading volume through the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable (excluding order imbalance) is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The table reports the first canonical auto- and cross-correlations (one lag) between each two groups of common factors. Each column contains the canonical correlations between the common factors of the variable of that column and the lag common factors of each of the other variables (pair wise). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months). Statistical significance of 5% and 1% correspond to correlations of 0.13 and 0.18, respectively.

Canonical lead–lag correlations (fitted AR(2))

Three common factors are extracted separately for returns and different measures of liquidity using the APC method. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; order imbalance measured as the ratio of the net sum of signed trading volume through the month scaled by the number of shares outstanding (the sign of each trade is determined by the classification scheme introduced by Lee and Ready (1991)); and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable (excluding order imbalance) is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The table reports the first canonical auto- and cross-correlations (one lag) between each two groups of common factors. Each column contains the canonical correlations between the common factors of the variable of that column and the lag common factors of each of the other variables (pair wise). The table uses the residuals of a second order autocorrelation model for each factor (using a monthly expanding window). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months). Statistical significance of 5% and 1% correspond to correlations of 0.13 and 0.18, respectively.

Percent of firms with significant exposure to across-measure and within-measure factors

This table reports distribution statistics of time-series regressions. Within-measure common factors are extracted separately for different measures of liquidity using the APC method (Panel A) and EM method (Panel B). In addition, across-measure common factors are extracted for all the liquidity measures jointly. Then, for each liquidity measure of each stock, a time-series regression of the variable on the across-measure common factor (the first principal component) and the within-measure common factor (the first principal component) of the particular liquidity measure is executed (the within-measure common factor is first projected on the across-measure common factor to orthogonalize the two factors). The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The table reports the percentage of firms in the sample that exhibit significant coefficients at the 1% and 5% statistical significance levels, as well as the joint significance (F-statistic). The average R² and the average adjusted-R² of these regressions are also reported below. The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Variance decomposition

Within-measure common factors are extracted separately for different measures of liquidity using the APC method (Panel A) and EM method (Panel B). In addition, across-measure common factors are extracted for all the liquidity measures jointly. Then, for each liquidity measure of each stock, a time-series regression of the variable on the across-measure common factor (the first principal component) and the within-measure common factor (the first principal component) of the particular liquidity measure is executed (the within-measure common factor is first projected on the across-measure common factor to orthogonalize the two factors). The table reports the composition of the part of the variance explained by the model. The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price–impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Performance of across-measure-liquidity-loading-sorted portfolios

Across-measure common factors are extracted jointly for different measure of liquidity measures using the APC method. Factor shocks are then proxied with AR(2) residuals calculated using a monthly expanding window. Twenty portfolios are sorted each month by the across-measure liquidity loading estimated using the past 36 months (the loading is computed while controlling for Fama-French four factors). The time-series mean return (excess of risk-free rate) and risk-adjusted returns (using Fama-French four factors) of each portfolio are presented below (Newey-West adjusted t-statistics in parentheses). Portfolio returns are quoted in percent. In addition, the table reports the across-measure liquidity factor loading of each portfolio (post formation), calculated through a time-series regression of each portfolio returns on the Fama-French four factors and the across-measure liquidity factor. The liquidity measures used for the analysis are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask divided by the bid-ask midpoint; and four price-impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).

Pricing liquidity in the cross-section

Within-measure factors are extracted separately for different measures of liquidity using the APC method. In addition, across-measure common factors are extracted for all the liquidity measures jointly. Factor shocks are then proxied with AR(2) residuals calculated using a monthly expanding window. Factor loadings are calculated using time-series regressions of returns to 50 portfolios on the Fama-French four factors, the across-measure common factor (the first principal component) and the within-measure common factor (the first principal component) of the particular liquidity measure (the within-measure common factor is first projected on the across-measure common factor to orthogonalize the two factors). The portfolios are sorted each month by the across-measure liquidity loading estimated using the past 36 months (the loading is computed while controlling for the Fama-French four factors). Each month a stock is assigned the factor loadings of the portfolio to which it has assigned at the end of the prior month. The results of Fama-MacBeth regressions of individual stock returns on the factor loadings are reported below (Newey-West adjusted t-statistics in parentheses). The liquidity measure (estimated the previous month) of each stock (ILLIQ) is also added to the cross-sectional regressions, as well as the natural logarithm of market capitalization (in millions of dollars) (Size) and book-to-market ratio (as of the previous month) (B/M). The liquidity measures analyzed are: The Amihud (2002) measure, defined as the monthly average of daily absolute value of return divided by dollar volume; turnover, defined as the ratio of monthly volume and shares outstanding; the average monthly quoted spread, measured as the ratio of the quoted bid-ask spread and the bid-ask midpoint; the average monthly effective spread, measured as the absolute value of the difference between the transaction price and the midpoint of quoted bid and ask, divided by the bid-ask midpoint; and four price-impact components PV, PF, TV, TF, as measured in Sadka (2006). Prior to the extraction of common factors, for each stock, each variable is normalized every month by its mean and standard deviation calculated up to the prior month (with at least three prior monthly observations). While added to the cross-sectional regressions, the liquidity measures are not normalized; the Amihud measure, PV, and TV are multiplied by 10⁵, and quoted and effective spreads, PF, and TF are multiplied by 100. The return premium estimates are reported in percent. The sample includes 4,055 NYSE-listed stocks with available intraday data from ISSM and TAQ for the period January 1983 until December 2000 (216 months).