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The effects around the quarter end are also mostly picked up by liquidity variables.
By contrast, liquidity variables explain return seasonality by up to appr.
Concurrent, Lag, and Lead denote, respectively, to the same, previous, and next trading day observations of the market liquidity variables.
We regress daily percentage changes in liquidity variables for an individual stock on market measures of liquidity, begin{array}{*{20}l} DL_{j,t} = alpha_{j} + beta_{j} DL_{M,t} + epsilon_{t} end{array} (1).
Table 4 Absolute daily proportional changes in liquidity variables Mean Median Standard deviation |SPR| 0.142 0.098 0.157 |PSPR| 0.103 0.065 0.127 |DEP| 0.268 0.125 0.862 |ESPR| 0.742 0.658 1.682 |PESPR| 0.728 0.595 1.714 SPR is the quoted spread, PSPR is the proportional spread, DEP is the depth, ESPR is the effective spread, and PESPR is the proportional effective spread.
The interacted variables in columns 4 to 7 show that liquidity variables are the more important driver for the TOM effect when compared to the economic effects of order imbalance (see parameters (M_{-,2, t}) to (M_{+, 2, t}) in columns 4 to 6 compared to column 7).
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In another word, the liquidity variable is significant at the threshold of 1% for both ratios of debt.
For example, there is no "liquidity" variable in the Black-Scholes formula for option pricing, but now it is becoming the key component in modern markets.
Panel A denotes the cross-sectional averages of the regression only with the concurrent market liquidity measure, Panel B contains the cross-sectional average coefficients of the regression with the concurrent market liquidity variable and a lag term, and Panel C contains the cross-sectional average of the regression with the concurrent market liquidity variable, and lead and lag market term.
Table 7 Dependence of the magnitude of order imbalance on size and liquidity Variable Coefficient t statistic p value (tilde{C}_{i,t}) 0.00 1.50 0.1326 (tilde{S}_{i,t}) 0.01 3.59 0.0003 Fixed-effects panel regression, Eq. (12).
where D L j,t, is, for stock j, the percentage change (D) from trading day t−1 to day t in liquidity variable L (L = SPR, PSPR, etc)., D L j,t =(L j,t −L j,t−1)/L j,t−1, and ε t ∼N 0,1) is Gaussian or white noise.
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