1 Introduction
2 Literature Review
2.1 Liquidity
2.2 Volatility
3 Methodology
3.1 Cross-Sectional Analysis
3.2 Evolution of Stock Liquidity and Volatility
3.3 Time-Series Framework
Variable | Definition | Measurement |
---|---|---|
Amihud illiquidity | The sum of the ratios of the daily absolute return to price times trading volume divided by the number of days that data is available | Amihud illiquidity = 1/Dq ΣQt=1 |Rt|/(Pricet × Volumet),where Dq is the number of days for which data are available and Rt, Pt and VOt are the daily return, daily price and daily volume, respectively |
Proportional bid-ask spread | The difference between ask and bid Main market prices to the average of the ask and bid prices (midpoint). Monthly average bid-ask spread is calculated as the average of the daily bid-ask spreads | Bid–Ask Spreadi,T = (1/Ni,T)Σ( Pask i,t − Pbid i,t)/(( Pask i,t + Pbid i,t)/2), where Bid–Ask Spread i, T is the average bid–ask spread of stock i in month T; Ni,T is the number of trading days for stock i in month T; Pask i,t is the ask price of stock i on day t; and Pbid i,t is the bid price of stock i on day t |
Total turnover ratio | The monthly average of the daily turnover ratios which are calculated as a ratio of the trading volume by value which is the result of the number of shares traded times the stock price divided by the stock’s market capitalization | TPtoMVi,T = (1/ Ni,T)Σ(VOi,T Pi,T /MVi,T), where TPto MVi,T is the average turnover ratio of stock i in month T; Ni,T is the number of trading days for stock i in month T; VOi,t is the number of shares traded on the Main Market of stock i on day t; Pi,T is the closing price of stock i on day t; and MVi,t is the market capitalization of stock i on day t |
Return volatility | The monthly standard deviation of the stock’s daily returns including dividend income | Volatility Ratioi,T = σi,T, where Volatility Ratioi,T is the firm-to-market volatility ratio of stock i or the monthly market-adjusted volatility of stock i’s daily returns in month T |
Volatility ratio | The ratio of monthly standard deviation of the stock’s daily total returns to the monthly standard deviation of daily total returns of the Main market | Volatility Ratioi,T = σi,T / σM(i),T, where Volatility Ratioi,T is the firm-to-market volatility ratio of stock i or the monthly market-adjusted volatility of stock i’s daily returns in month T; σi,T is the monthly standard deviation of stock i’s daily returns in month T; and σM(i),T, T is the monthly standard deviation of stock i’s Main Market daily returns in month T |
High-low ratio | The average of the daily high-low ratios which is the natural logarithm of the ratio of the highest stock price reached on the day to the lowest price attained on the day | High–Low Ratioi,T = (1/Ni,T)Σln(Phigh i,t /Plow i,t), where High–Low Ratioi,T is the average of the daily high–low ratios of stock i in month T; Ni,T is the number of trading days for stock i in month T; Phigh i,t is the highest price reached of stock i on day t; and Plow i,t is the lowest price attained by stock i on day t |
4 Findings and Results
Variable | Moving status | N observations | Mean | Mean difference from match | Min. | Max. | St. Dev. |
---|---|---|---|---|---|---|---|
Panel A: Dependent variables | |||||||
Amihud illiquidity | All | 48,470 | 0.251 | 0.000 | 53.958 | 1.045 | |
MAIN2AIM | 24,235 | 0.279 | 0.000*** | 0.000 | 24.634 | 1.074 | |
MATCH | 24,235 | 0.202 | 0.000 | 53.958 | 1.025 | ||
Bid–ask spread | All | 48,470 | − 0.062 | − 1.924 | 2 | 0.045 | |
MAIN2AIM | 24,235 | − 0.093 | 0.000*** | − 1.825 | 0.245 | 0.023 | |
MATCH | 24,235 | − 0.025 | − 1.924 | 2 | 0.052 | ||
Total Turnover ratio | All | 48,470 | 0.335 | 0.000 | 61.288 | 0.781 | |
MAIN2AIM | 24,235 | 0.297 | 0.000*** | 0.000 | 61.288 | 1.041 | |
MATCH | 24,235 | 0.372 | 0.000 | 34.182 | 0.704 | ||
Return volatility | All | 47,661 | 218.825 | 0.000 | 34,005.44 | 894.741 | |
MAIN2AIM | 24,235 | 85.127 | 0.000*** | 0.000 | 10,012.86 | 10,003.120 | |
MATCH | 23,426 | 324.843 | 0.009 | 34,005.44 | 1254.209 | ||
Volatility ratio | All | 48,470 | 0.450 | 0.000 | 860.637 | 7.191 | |
MAIN2AIM | 24,235 | 0.742 | 0.000*** | 0.009 | 860.637 | 9.167 | |
MATCH | 24,235 | 0.652 | 0.000 | 1.598 | 0.315 | ||
High–low ratio | All | 48,470 | − 0.005 | − 7.967 | 0.280 | 0.309 | |
MAIN2AIM | 24,235 | − 0.006 | 0.000*** | − 7.967 | 0.280 | 0.421 | |
MATCH | 24,235 | 0.008 | 0 | 0.105 | 0.012 | ||
Panel B: Firm characteristics | |||||||
Company size | All | 42,822 | 15,119,204 | 50 | 6,002,353,806 | 208,457,845 | |
MAIN2AIM | 21,411 | 62,845.04 | 0.000*** | 235 | 16,681,284.4 | 506,142.01 | |
MATCH | 21,411 | 28,745,811 | 50 | 6,002,353,806 | 286,900,729 | ||
Leverage | All | 39,004 | 0.412 | − 0.462 | 65.371 | 1.804 | |
MAIN2AIM | 19,502 | 0.523 | 0.000*** | − 0.462 | 65.371 | 2.824 | |
MATCH | 19,502 | 0.501 | 0.004 | 43.902 | 0.901 | ||
Total trading volume | All | 48,470 | 1365.215 | 0.004 | 637,982.9 | 15,140.01 | |
MAIN2AIM | 24,235 | 285.124 | 0.000*** | 0.004 | 95,608.02 | 1498.925 | |
MATCH | 24,235 | 2441.543 | 0.006 | 637,982.9 | 21,195.41 |
Probit | ||
---|---|---|
(1) | (2) | |
Company size | − 0.000*** (− 20.14) | − 0.000*** (− 15.01) |
Leverage | 0.045*** (4.15) | 0.014*** (2.00) |
IAS | − 0.596*** (− 42.58) | − 0.615*** (− 25.94) |
Trading volume | − 0.000*** (− 18.56) | − 0.000*** (− 16.88) |
Return volatility | − 0.000*** (− 15.55) | |
Volatility ratio | 0.854*** (0.013) | |
High–low ratio | − 2.846*** (− 7.014) | |
Amihud | 0.067*** (9.015) | |
Bid–ask spread | 8.549*** (49.45) | |
Total turnover ratio | − 0.045*** (− 3.18) | |
Constant | − 0.110*** (− 5.841) | − 0.417*** (− 19.42) |
N observations | 29,675 | 29,876 |
Pseudo R-squared | 0.103 | 0.284 |
Random effect | 2SLS | Heckman | |||||||
---|---|---|---|---|---|---|---|---|---|
Amihud | Bid–ask spread | Total turnover ratio | Amihud | Bid–ask spread | Total turnover ratio | Amihud | Bid–ask spread | Total turnover ratio | |
Company size | − 0.000 (− 0.14) | 0.000 (1.20) | − 0.000 (− 0.18) | − 0.000*** (− 4.74) | − 0.000** (− 3.01) | 0.000 (0.15) | − 0.000*** (− 14.22) | − 0.000*** (− 6.01) | 0.000*** (7.02) |
IAS | 0.174** (2.22) | 0.006 ( 0.98) | 0.274 (1.66) | − 0.887*** (− 13.41) | − 0.018*** (− 5.80) | 0.508 (0.88) | − 1.005*** (− 11.19) | − 0.034*** (− 5.74) | 9.157*** (7.67) |
Lambda | 2.41*** (17.52) | 0.078*** (12.51) | − 18.084*** (− 8.46) | ||||||
Volume | − 0.000 (− 0.41) | 0.000 (1.54) | 0.000 (0.59) | − 0.000*** (− 8.20) | − 0.000 (− 1.12) | 0.000 (0.98) | − 0.000*** (− 13.12) | − 0.000*** (− 7.03) | 0.003*** (7.25) |
Leverage | − 0.000 (− 0.16) | − 0.000 (− 1.20) | 0.006*** (47.01) | 0.000*** (5.01) | 0.000*** (17.66) | 0.006*** (42.22) | 0.000*** (3.25) | 0.000*** (13.54) | 0.005*** (23.12) |
Constant | 0.111* (1.54) | − 0.051*** (7.84) | 0.412*** (2.54) | 1.529*** (16.99) | 0.000 (0.08) | − 0.602 (− 0.58) | − 1.484*** (− 12.84) | − 0.151*** (− 33.03) | 11.413*** (8.41) |
N observations | 28,402 | 28,613 | 27,984 | 27,461 | 26,947 | 27,951 | 29,456 | 28,910 | 29,519 |
4.1 Liquidity
4.2 Volatility
Random effect | 2SLS | Heckman | |||||||
---|---|---|---|---|---|---|---|---|---|
Return volatility | Volatility ratio | High–low ratio | Return volatility | Volatility ratio | High–low ratio | Return volatility | Volatility ratio | High–low ratio | |
Total turnover | 0.051 (0.21) | 0. .271*** (125.71) | − 0.003*** (− 71.48) | − 1.315 (− 1.85) | 0.301*** (58.08) | − 0.004*** (− 129.03) | − 0.058 (− 0.54) | 0.345 (1.92) | − 0.005*** (− 87.09) |
IAS | − 6.004 (− 0.04) | − 0.049 (− 0.49) | 0.003 (0.76) | 1167.024*** (12.03) | 7.238*** (10.84) | − 0.016* (− 1.84) | 50.008*** | 0.854*** (43.01) | 0.020*** (3.57) |
Lambda | − 43.608*** (3.35) | 1.487*** (3.84) | − 0.039***(− 4.54) | ||||||
Volume | 0 .000 (0.39) | − 0.000 (− 0.24) | 0.000 (1.54) | 0.008*** (6.72) | 0.000*** (6.81) | 0.000 (0.81) | 0.002 (0.65) | 0.000 (1.83) | 0.000 (0.08) |
Leverage | 0.000 (0.06) | 0.001*** (27.00) | − 0.000*** (− 26.55) | − 0.125*** (5.87) | 0.001*** (8.49) | − 0.000*** (− 218.74) | − 0.007 (− 2.36) | 0.001*** (16.01) | − 0.000*** (156.58) |
Constant | 301.002 (5.59) | 0.301*** (6.77) | 0.064*** (8.23) | − 1812.149*** (10.25) | − 12.973*** (11.85) | 0.048*** (3.95) | 93.715*** (9.15) | 1.413*** (6.54) | − 0.001 (− 0.33) |
N observations | 28,941 | 29,413 | 28,974 | 28,782 | 28,749 | 28,782 | 28,782 | 28,749 | 28,782 |
Years around movement | ||||||||
---|---|---|---|---|---|---|---|---|
− 4Y | − 3Y | − 2Y | − 1Y | + 1Y | + 2Y | + 3Y | + 4Y | |
Panel A: Liquidity | ||||||||
Amihud | ||||||||
MAIN2AIM | − 0.129*** (− 4.08) | − 0.017*** (− 3.46) | − 0.082** (− 3.54) | − 0.038** (− 2.41) | 0.051 (1.97) | 0.084*** (3.65) | 0.063*** (2.21) | 0.146*** (5.14) |
Match | 0.032 (0.06) | 0.067 (1.27) | 0.029** (4.14) | − 0.009–0.67 | − 0.004 (− 0.31) | − 0.021 (− 0.34) | − 0.064 (− 1.01) | − 0.003 (− 1.00) |
Bid–ask spread | ||||||||
MAIN2AIM | − 0.010*** (− 6.12) | − 0.004*** (− 1.71) | 0.009*** (3.87) | 0.001 (1.14) | 0.008** (3.79) | − 0.006 (− 1.02) | − 0.004 (− 0.31) | 0.000 (0.64) |
Match | − 0.004***(− 3.87) | − 0.004*** (− 12.78) | − 0.005*** (0.004) | − 0.006*** (− 4.01) | − 0.006*** (− 4.29) | 0.002** (3.01) | 0.007*** (2.71) | 0.007*** (8.67) |
Total turnover ratio | ||||||||
MAIN2AIM | − 0.519 (− 0.21) | − 0.847 (− 2.07) | − 0.287 (− 1.45) | − 0.564 (− 0.74) | 1.026 (0.47) | − 0.347 (− 0.07) | 1.009 (− 1.89) | − 0.579 (− 0.74) |
Match | 0.049*** (7.29) | 0.064*** (5.14) | 0.014*** (2.31) | − 0.019 (− 1.87) | − 0.046 (− 2.41) | − 0.045** (− 2.87) | − 0.097*** (− 4.61) | − 0.035*** (− 5.03) |
Panel B: Volatility | ||||||||
Return volatility | ||||||||
MAIN2AIM | − 42.512 (32.59) | − 36.197*** (− 2.12) | − 12.410 (− 1.01) | 15.39** (1.02) | 8.197 (0.57) | 3.192 (0.27) | 19.197** (2.03) | 18.037*** (1.98) |
Match | − 88.034*** (− 3.41) | − 77.278*** (− 3.84) | − 82.650*** (− 2.87) | − 3.009 (− 0.09) | − 28.078 (− 1.88) | − 24.279 (− 1.54) | 78.194*** (5.01) | 165.697*** (6.24) |
Volatility ratio | ||||||||
MAIN2AIM | − 0.491 (− 1.03) | − 1.279*** (− 4.87) | − 0.501 (− 1.09) | − 0.357 (− 1.28) | 1.647*** (5.24) | − 0.547 (− 1.24) | 0.468** (2.03) | 0.716** (2.19) |
Match | − 0.016*** (− 3.05) | 0.019*** (4.54) | 0.018*** (5.78) | 0.035*** (8.15) | 0.026*** (7.87) | 0.006 (1.02) | − 0.035*** (− 8.09) | − 0.037*** (− 10.02) |
High–low ratio | ||||||||
MAIN2AIM | 0.015***(2.81) | 0.054*** (5.09) | 0.018 (2.14) | 0.016** (2.41) | − 0.035*** (− 5.39) | 0.000 (0.09) | − 0.020*** (− 2.24) | − 0.028*** (− 4.69) |
Match | − 0.000 (− 1.00) | 0.001*** (4.08) | 0.000 (1.78) | 0.000 (1.64) | − 0.001*** (− 2.87) | − 0.001** (− 2.49) | − 0.000** (− 2.90) | 0.001***(4.12) |
Mean difference from 1 | ||||
---|---|---|---|---|
Variable | Movement status | Mean | t-stats | Pr(t) |
Liquidity | ||||
Amihud ratio | MAIN2AIM | 3.659 | 6.128 | < .0001 |
MATCH | 2.503 | 5.228 | < .0001 | |
Bid‒ask spread ratio | MAIN2AIM | 1.946 | 8.641 | < .0001 |
MATCH | 0.854 | − 3.120 | 0.0040 | |
Turnover ratio | MAIN2AIM | 1.575 | 3.659 | 0.0003 |
MATCH | 1.959 | 4.259 | < .0001 | |
Volatility | ||||
Return volatility ratio | MAIN2AIM | 0.841 | − 2.801 | 0.007 |
MATCH | 5.022 | 10.211 | < .0001 | |
Volatility ratio | MAIN2AIM | 1.152 | 0.495 | 0.498 |
MATCH | 1.027 | 0.132 | 0.603 | |
High‒low ratio | MAIN2AIM | 0.701 | − 2.845 | 0.469 |
MATCH | 1.540 | 1.878 | 0.106 |
Liquidity | Volatility | |||||
---|---|---|---|---|---|---|
Amihud ratio | Bid‒ask spread ratio | Total turnover ratio | Return volatility ratio | Volatility ratio | High‒low ratio | |
Model (1) | ||||||
Movement status | 0.741*** (8.42) | 0.901*** (8.09) | 0.463 (1.87) | − 2.897*** (− 33.01) | 0.098*** (6.87) | − 2.138*** (− 58.82) |
Intercept | 2.284*** (5.87) | 0.581*** (7.80) | 1.901*** (11.04) | 5.137*** (9.12) | 1.549*** (11.08) | 2.479*** (8.82) |
Adj. R− sq | 0.021 | 0.081 | 0.001 | 0.041 | 0.019 | 0.137 |
Model (2) | ||||||
Movement status | 0.659*** (6.12) | 0.497*** (9.08) | 0.912*** (3.15) | − 0.887*** (− 10.59) | 0.113*** (4.87) | − 2.193*** (− 16.28) |
Company size ratio | − 3.208*** (− 6.87) | − 3.509*** (− 15.49) | 9.089*** (7.39) | 12.151*** (9.51) | − 0.209*** (− 2.88) | 0.401** (2.08) |
Trading volume ratio | − 0.001** (− 2.78) | 0.000 (0.58) | 0.018*** (7.32) | 0.001*** (3.22) | − 0.001*** (− 9.38) | 0.000 (0.21) |
Leverage ratio | − 0.241*** (− 4.15) | 0.137*** (15.45) | 0.228 (1.46) | 0.031 ( 0.91) | 0.028** (2.87) | 0.078*** (3.64) |
Intercept | 5.841*** (11.09) | 4.341*** (7.12) | − 8.114*** (− 5.81) | − 10.802*** (− 13.64) | 1.379*** (14.12) | 1.964*** (9.41) |
Adj. R-sq | 0.045 | 0.171 | 0.039 | 0.187 | 0.056 | 0.108 |
N observations | 31,184 | 31,184 | 31,184 | 29,342 | 29,342 | 29,342 |
N stocks | 476 | 476 | 476 | 476 | 476 | 476 |