# Which Liquidity Proxy Measures Liquidity Best in Emerging Markets?

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}. The regression originally includes only popular determinants of liquidity, such as stock price, firm size, country dummies, and industry dummies. Thereafter, we add liquidity proxies one at a time, and see how much the adjusted R

^{2}has improved.

^{2}) generate meaningful economic interpretation. This is because three spread proxies (ROLL, HASB, and LOT) measure round-trip trading costs as a percentage of stock price in a similar manner, and can be directly compared with three spread benchmarks (ES, QS, and RS). We can also arrive at meaningful economic interpretations of the second and third measures (correlation and incremental R

^{2}) when we compare the price impact benchmarks and price impact proxies. The first measure, which is absolute difference, is interpreted with care. For example, LAMBDA captures the sensitivity of return of the signed squared volume. IMP is measured as continuously compounded return. ASC is the percentage change of returns. AMIHUD captures the average ratio of absolute return to the U.S. dollar trading volume. The inverse of AMIVEST is similar to the AMIHUD measure. PASTOR captures the sensitivity of excess return on the lagged signed U.S. dollar trading volume. Therefore, in our empirical analysis of the price impact benchmark and price impact proxies, the correlation and incremental R

^{2}measures carry more weight.

## 2. Liquidity Variables

#### 2.1. Liquidity Benchmarks Using High-Frequency Data

#### 2.1.1. Spread Benchmarks

#### 2.1.2. Price Impact Benchmarks

#### 2.2. Liquidity Proxies from Low-Frequency Data

#### 2.2.1. Spread Proxies

#### 2.2.2. Price Impact Proxies

## 3. Data and Sample

- (1)
- Quotes and transactions are used only if they are recorded during the exchange opening hours, and if the quotes or trades have positive prices and positive shares.
- (2)
- Only valid quotes and trades are used, where a valid quote or trade is defined, as follows:
- (a)
- If a quote is not the first quote of the day, its price should be within the range of 50–150% of its previous quote.
- (b)
- If a trade is not the first trade of the day, its price should be within the range of 50–150% of the price of the trade prior to it.

- (3)
- To obtain a reliable time series average of the daily average spreads, we impose a condition that there should be at least 20 valid trading days for each stock during the entire investigation window. A valid trading day is a day that has at least one valid quoted spread and one valid effective spread. A valid quoted spread is a spread whose size in currency unit is within 0.2 $\times $ (quote midpoint) and a valid effective spread is an effective spread whose size in currency unit is within 0.2 $\times $ (quote midpoint in effect at the time of the trade).
- (4)
- For the quoted, effective, and realized spreads, we calculate the daily average spread first (an equal weight average of all spreads, not time weighted), and then calculate the average of these daily spreads over the entire period. For each stock, these average spreads in currency units must be smaller than 10% the time series average of the daily prices during the period.

## 4. Empirical Results

#### 4.1. Spread Benchmarks and Spread Proxies

#### 4.1.1. Spread Benchmarks and Spread Proxies

#### 4.1.2. Price Impact Benchmarks and Price Impact Proxies

#### 4.1.3. Firm Characteristics, Market Features, Minimum Tick Size, and Foreign Exchange Rate

#### 4.2. The Best Liquidity Proxies

#### 4.2.1. The Best Spread Proxies

_{ROLL}, GAP

_{HASB}, and GAP

_{LOT}for each of the 21 emerging markets. Figure 1 plots the dominating proxy against the average daily turnover in each market. If LOT dominates the other proxies in a specific market, then the market is plotted with a circle symbol (●) on the upper parallel line. If ROLL is dominant in a market, then the market is plotted with a triangular delta symbol (▲) on the middle parallel line. If HASB is dominant, then the market is plotted with a diamond symbol (♦) on the bottom parallel line. For example, South Korea, which has a daily turnover of 1.24, the highest among the countries in the sample, and, at the same time, has LOT as the dominating proxy, is plotted as a circle to the far right on the upper parallel line. The pattern in Figure 1 clearly indicates that LOT is the best proxy for effective spread ES in 14 out 21 emerging markets. Our unreported results indicate that LOT is the best proxy for quoted spread QS and realized spread RS in 14 and 16 out of 21 emerging markets, respectively.

#### 4.2.2. The Best Price Impact Proxies

_{AMIHUD}, GAP

_{1/AMIVEST}, and GAP

_{PASTOR}for each of the 21 emerging markets. Figure 2 plots the dominating proxy against the average daily turnover in each market. If PASTOR dominates the other proxies in a specific market, then the market is plotted with a circle symbol (●) on the upper parallel line. If 1/AMIVEST is dominant in a market, then the market is plotted with a triangular delta (▲) on the middle parallel line. If AMIHUD is dominant, then the market is plotted with a diamond symbol (♦) on the bottom parallel line. For example, South Korea, which has a daily turnover of 1.24, the highest among the countries in the sample, and, at the same time, has AMIHUD as the dominating proxy, is plotted with a circle to the far right on the lower parallel line. The pattern in Figure 2 clearly indicates that AMIHUD is the best proxy for the price impact benchmark LAMBDA in 16 out 21 emerging markets. Our unreported results indicate that AMIHUD is the best proxy for IMP and ASC in 14 and 12 out of 21 emerging markets, respectively.

#### 4.3. Wilcoxon Rank-Sum Tests for the Effectiveness of Liquidity Proxies

#### 4.3.1. Effectiveness of Spread Proxies

_{i}− ES

_{i}| is 0.181%. The median |ROLL

_{i}− ES

_{i}|, and |HASB

_{i}− ES

_{i}| are 1.029% and 2.193%, respectively. We implement the Wilcoxon rank-sum test to see if the median |ROLL

_{i}− ES

_{i}|, and the median |LOT

_{i}− ES

_{i}| are statistically different. The result indicates that the difference between 1.029% and 0.181% is highly significant. A significance level of *** is assigned to the corresponding number corresponding number in the |ROLL

_{i}− ES

_{i}| column. The median |HASB

_{i}− ES

_{i}| of 2.193% and the median |LOT

_{i}− ES

_{i}| of 0.181% are also statistically different. A significance level of *** is assigned to the corresponding number in the |HASB

_{i}− ES

_{i}| column.

#### 4.3.2. Effectiveness of Price Impact Proxies

#### 4.4. Correlation Analysis

#### 4.5. Incremental Regression R^{2}

#### 4.5.1. The Determinants of Spread Benchmarks

^{2}, ${R}_{ADJ1}^{2}$ from the above regressions. Subsequently, we run the following regressions, adding spread proxies:

^{2}is ${R}_{ADJ2}^{2}$. The incremental adjusted R

^{2}is calculated as:

^{2}of 0.325. When ROLL, HASB, and LOT are added one at a time as in Equation (2), then the corresponding estimates (t-statistics) are 0.296 (3.84), 0.256 (4.73), and 0.122 (3.94), respectively. Furthermore, the corresponding adjusted R

^{2}increases to 0.361, 0.343, and 0.464, respectively. The incremental R

^{2}are 0.036, 0.018, and 0.139, respectively. The notable largest incremental R

^{2}comes from adding LOT in the regression. The results that were obtained using QS and RS as dependent variables are similar. The largest incremental R

^{2}values, 0.134 and 0.082, respectively, again come from adding LOT in the regression. The conclusion from the incremental R

^{2}analysis is fully consistent with the conclusions drawn from measurement error and the correlation structure analysis.

#### 4.5.2. The Determinants of Price Impact Benchmarks

^{2}is calculated as in Equation (3).

^{2}of 0.087. When AMIHUD, 1/AMIVEST, and PASTOR are added one at a time as in Equation (5), the corresponding estimates (t-statistics) are 0.047 (1.51), 0.403 (3.12), and 0.914 (1.42), respectively. The corresponding adjusted R

^{2}increase to 0.160, 0.671, and 0.114, respectively. The incremental R

^{2}values are 0.073, 0.584, and 0.027, respectively. The notable largest incremental R

^{2}come from adding 1/AMIVEST in the regression.

^{2}values become 0.389, 0.396, and 0.319, respectively. Therefore, for emerging liquid markets in the G1 group, all three price impact proxies do a very good job in predicting the price impact benchmark, LAMBDA. The weak results are driven by less liquid markets. The notably large incremental R

^{2}value of 0.587, by adding 1/AMIVEST in the regression, is driven by stocks in the G3 group.

^{2}values at 0.018 and 0.098, respectively, come by adding PASTOR in the regression. Both of these results are driven by the stocks in the G3 group, where the countries are less liquid. To some extent, the conclusion regarding PASTOR is consistent with the measurement error analysis for price impact in Panel B of Table 3, where PASTOR turns out to be the better proxy for less liquid markets in the G3 and G4 groups.

#### 4.6. Firm and Market Characteristics and Accuracy of Liquidity Proxies

_{i}is the measurement error of a liquidity proxy, the smaller the error, the larger the value of Accuracy

_{i}. We apply log transformation because Accuracy

_{i}exhibits extreme distribution. The regression is run as follows:

^{2}exceeding 0.40. LOT portrays spread better when a firm has a higher stock price, a higher turnover, a smaller return volatility, a larger market capitalization, and is more accessible to foreigners.

^{2}values range from 0.529 to 0.816, much higher than the R

^{2}values from the regressions for spread proxies that range from 0.316 to 0.409. In general, the accuracy increases with turnover, firm size, and investability. The accuracy decreases with individual stock return volatility. The indicator variable for legal origin is positive and highly significant in all three regressions. This suggests that all the three price impact proxies are more effective in markets with common law legal systems. The indicator variable for the trading mechanism is positive and highly significant in all three regressions as well. This suggests that all three price impact proxies work better in a limit-order based system than in dealer or hybrid systems.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1 | Hasbrouck (2009) also evaluates the effectiveness of transaction costs estimated from daily data using the Bayesian Gibbs sampling approach that he developed (Hasbrouck 2004, 2009). |

2 | The selection of proxies is made from the set of low-frequency measures evaluated in Goyenko et al. (2009). |

3 | Roll (1984), and Goyenko et al. (2009) assign 0 to the value of the spread when the covariance is negative. |

4 | Gibbs sampler estimation programs are available at www.stern.nyu.edu/~jhasbrou. We draw 2000 times for each Gibbs sampler. Like Hasbrouck (2009), we discard the first 200 draws to “burn in the sampler” (Hasbrouck 2009, p. 1451). Hasbrouck points out that 1000 sweeps are sufficient to produce reliable estimates. |

5 | Lesmond et al. (1999) also develop measures (ZEROS and ZEROS2) that are similar to, but much simpler than the LOT measure, utilizing zero return days. ZEROS and ZEROS2 are based on the rationale that low liquidity and less-informed trading lead to a zero daily return. The result using ZEROS and ZEROS2 are slightly weaker than the results using the LOT measure. |

6 | Originally, Pástor and Stambaugh (2003) used the coefficient to measure the liquidity. They anticipated the minus (−) value of the coefficient, where the lower minus value represented the lower liquidity. We take the absolute value to measure the degree of illiquidity in this study. Moreover, we confirm that the latter performs better than the former in the analyses. |

7 | Turnover is calculated as the daily average number of traded shares divided by market capitalization. |

8 |

**Figure 1.**Turnover and the Best Proxy for Effective Spread in each Country. This figure plots the best proxy for the effective spread in each of the 21 emerging markets against the average daily turnover of the market. The spread proxies include ROLL, HASB, and LOT. The effectiveness, or minimum gap, is measured as the absolute difference in median values between the proxy, and the effective spread. GAP

_{ROLL}= |Median (ROLL

_{i}) − Median (ES

_{i})|, GAP

_{HASB}= |Median (HASB

_{i}) − Median (ES

_{i})|, and GAP

_{LOT}= |Median (LOT

_{i}) − Median (ES

_{i})|, where the median is calculated from sample stocks indexed by subscript i in each country.

**Figure 2.**Turnover and the Best Proxy for Price Impact LAMBDA in each Country. This figure plots the best proxy for the price impact LAMBDA in each of the 21 emerging markets against the average daily turnover of the market. The price impact proxies include AMIHUD, 1/AMIVEST, and PASTOR. The effectiveness, or minimum gap, is measured as the absolute difference in median values between the proxy, and the price impact LAMBDA. GAP

_{AMIHUD}= |Median (AMIHUD

_{i}) − Median (LAMBDA

_{i})|, GAP

_{1/AMIVEST}= |Median (1/AMIVEST

_{i}) − Median (LAMBDA

_{i})|, and GAP

_{PASTOR}= |Median (PASTOR

_{i}) − Median (LAMBDA

_{i})|, where the median is calculated from sample stocks indexed by subscript i in each country.

**Table 1.**Country-by-Country Summary Statistics. Panel A of Table 1 reports the cross-sectional medians of the spread benchmarks calculated using intraday data, and the spread proxies estimated using daily data. The high-frequency spread benchmarks include the quoted spread QS, effective spread ES, and realized spread RS. The low-frequency spread proxies include ROLL (Roll 1984), HASB (Hasbrouck 2009), and LOT (Lesmond et al. 1999). Panel B of the table reports the cross-sectional medians of price impact benchmarks calculated using intraday data and price impact proxies estimated using daily data. The high-frequency price impact benchmarks include LAMBDA (Hasbrouck 2009), IMP (Goyenko et al. 2009), and ASC (Huang and Stoll 1996). The low-frequency spread proxies include AMIHUD (Amihud 2002), AMIVEST (Cooper et al. 1985), and PASTOR (Pástor and Stambaugh 2003). Panel C of the table reports the cross-sectional median values of firm characteristics (stock price, firm size, turnover, volatility, and investability), and market features (market volatility, legal origin, and trading mechanism). The legal origin takes a value of one if the country’s legal system is based on common laws, and is considered zero otherwise. The trading mechanism takes the value of one for a pure limit-order system, and zero for a dealer or a hybrid system. Panel D of the table reports the minimum tick size, whether tick size varies by stock price, currency code, and average month-end exchange rates during our sample period. The sample covers 1183 firms from 21 emerging markets. The sample period is from February to May 2004.

Panel A: Spread Benchmarks and Spread Proxies | |||||||||

Market | High-Frequency Spread Benchmark | Low-Frequency Spread Proxy | |||||||

Region | Country | N | QS(%) | ES(%) | RS(%) | ROLL | HASB | LOT | |

Asia | China | 222 | 0.180 | 0.177 | 0.036 | 1.086 | 2.239 | 0.176 | |

India | 101 | 0.318 | 0.234 | 0.103 | 2.506 | 2.942 | 0.001 | ||

Indonesia | 43 | 2.973 | 1.996 | 1.036 | 2.246 | 3.372 | 4.075 | ||

South Korea | 145 | 0.301 | 0.273 | 0.096 | 1.539 | 2.654 | 0.515 | ||

Malaysia | 89 | 0.929 | 0.706 | 0.524 | 1.324 | 2.298 | 1.265 | ||

Philippines | 39 | 2.590 | 1.760 | 0.879 | 1.797 | 2.995 | 4.514 | ||

Taiwan | 106 | 0.464 | 0.463 | 0.211 | 1.956 | 2.841 | 0.674 | ||

Thailand | 57 | 0.710 | 0.656 | 0.262 | 1.593 | 2.632 | 1.030 | ||

Eastern Europe | Czech Republic | 7 | 1.672 | 0.612 | 0.241 | 1.526 | 2.092 | 0.263 | |

Greece | 63 | 0.740 | 0.647 | 0.238 | 1.176 | 2.192 | 0.554 | ||

Hungary | 13 | 0.916 | 0.765 | 0.378 | 1.691 | 2.550 | 0.473 | ||

Poland | 26 | 0.534 | 0.450 | 0.229 | 1.067 | 2.041 | 0.602 | ||

Latin America | Argentina | 12 | 0.938 | 0.643 | 0.141 | 1.694 | 1.573 | 0.527 | |

Brazil | 23 | 2.471 | 1.486 | 0.273 | 1.830 | 2.302 | 0.132 | ||

Chile | 35 | 1.933 | 1.568 | 0.583 | 0.732 | 1.905 | 1.333 | ||

Mexico | 35 | 1.053 | 0.701 | 0.145 | 1.076 | 1.967 | 0.269 | ||

Peru | 18 | 4.097 | 2.914 | 0.591 | 1.340 | 2.552 | 4.297 | ||

Venezuela | 11 | 6.761 | 4.500 | 1.211 | 1.150 | 3.748 | 8.635 | ||

Others | Egypt | 48 | 2.187 | 1.479 | 0.779 | 1.710 | 2.535 | 0.699 | |

Israel | 40 | 0.429 | 0.299 | 0.121 | 1.068 | 1.726 | 0.103 | ||

South Africa | 50 | 0.707 | 0.560 | 0.185 | 1.124 | 2.062 | 0.583 | ||

Panel B: Price Impact Benchmarks and Price Impact Proxies | |||||||||

Market | High-Frequency Price Impact Benchmark | Low-Frequency Price Impact Proxy | |||||||

LAMBDA | IMP | ASC | AMIHUD | AMIVEST | PASTOR | ||||

Asia | China | 222 | 1.216 | 0.140 | 0.136 | 0.140 | 0.017 | 0.011 | |

India | 101 | 1.477 | 0.177 | 0.119 | 0.233 | 0.027 | 0.007 | ||

Indonesia | 43 | 0.020 | 1.180 | 1.159 | 0.004 | 1.166 | 0.000 | ||

South Korea | 145 | 0.073 | 0.217 | 0.185 | 0.000 | 4.415 | 0.000 | ||

Malaysia | 89 | 1.984 | 0.241 | 0.182 | 1.639 | 0.002 | 0.070 | ||

Philippines | 39 | 0.438 | 0.968 | 0.832 | 4.292 | 0.001 | 0.059 | ||

Taiwan | 106 | 0.321 | 0.237 | 0.234 | 0.009 | 0.310 | 0.000 | ||

Thailand | 57 | 0.157 | 0.420 | 0.394 | 0.040 | 0.038 | 0.004 | ||

Eastern Europe | Czech Republic | 7 | 0.458 | 0.370 | 0.311 | 0.093 | 0.128 | 0.002 | |

Greece | 63 | 12.519 | 0.459 | 0.358 | 10.120 | 0.000 | 0.813 | ||

Hungary | 13 | 0.789 | 0.402 | 0.194 | 0.097 | 0.038 | 0.002 | ||

Poland | 26 | 2.869 | 0.293 | 0.226 | 1.385 | 0.002 | 0.045 | ||

Latin America | Argentina | 12 | 5.207 | 0.530 | 0.503 | 3.187 | 0.001 | 0.145 | |

Brazil | 23 | 0.046 | 1.281 | 0.954 | 0.253 | 0.010 | 0.020 | ||

Chile | 35 | 0.053 | 0.694 | 0.564 | 0.013 | 1.017 | 0.000 | ||

Mexico | 35 | 0.807 | 0.561 | 0.468 | 0.146 | 0.031 | 0.010 | ||

Peru | 18 | 11.545 | 1.703 | 1.712 | 31.924 | 0.000 | 0.893 | ||

Venezuela | 11 | 1.887 | 2.493 | 2.293 | 0.267 | 0.014 | 0.007 | ||

Others | Egypt | 48 | 4.924 | 0.534 | 0.487 | 7.518 | 0.000 | 0.512 | |

Israel | 40 | 0.140 | 0.266 | 0.162 | 0.366 | 0.009 | 0.015 | ||

South Africa | 50 | 0.054 | 0.382 | 0.340 | 0.231 | 0.030 | 0.008 | ||

Panel C: Firm and Market Characteristics | |||||||||

Market | Stock Price ($) | Firm Size ($ Million) | Turnover | Volatility | Investability | Market Volatility | Legal Origin | Trading Mechanism | |

Asia | China | 0.89 | 571 | 0.343 | 0.018 | 0.000 | 1.147 | 0 | 1 |

India | 5.70 | 719 | 0.123 | 0.032 | 0.490 | 2.210 | 1 | 1 | |

Indonesia | 0.07 | 166 | 0.168 | 0.026 | 0.000 | 1.742 | 0 | 1 | |

South Korea | 13.63 | 676 | 0.663 | 0.022 | 0.837 | 1.690 | 0 | 1 | |

Malaysia | 1.04 | 496 | 0.101 | 0.014 | 0.503 | 0.890 | 1 | 1 | |

Philippines | 0.28 | 228 | 0.024 | 0.018 | 0.000 | 1.155 | 0 | 1 | |

Taiwan | 0.78 | 1521 | 0.840 | 0.025 | 0.707 | 1.951 | 0 | 1 | |

Thailand | 0.40 | 507 | 0.296 | 0.023 | 0.435 | 1.933 | 1 | 1 | |

Eastern Europe | Czech Republic | 15.09 | 2658 | 0.218 | 0.019 | 0.569 | 1.133 | 0 | 0 |

Greece | 7.46 | 622 | 0.142 | 0.020 | 0.759 | 1.079 | 0 | 1 | |

Hungary | 18.13 | 289 | 0.241 | 0.015 | 0.000 | 1.342 | 0 | 0 | |

Poland | 13.94 | 656 | 0.147 | 0.014 | 0.684 | 1.124 | 0 | 1 | |

Latin America | Argentina | 1.18 | 427 | 0.048 | 0.020 | 0.000 | 2.561 | 0 | 0 |

Brazil | 0.93 | 949 | 0.126 | 0.023 | 0.923 | 2.211 | 0 | 0 | |

Chile | 1.90 | 986 | 0.047 | 0.014 | 0.643 | 0.634 | 0 | 1 | |

Mexico | 1.97 | 1612 | 0.110 | 0.016 | 0.718 | 1.184 | 0 | 1 | |

Peru | 0.56 | 181 | 0.039 | 0.027 | 0.000 | 0.983 | 0 | 0 | |

Venezuela | 0.26 | 189 | 0.005 | 0.021 | 0.000 | 0.906 | 0 | 1 | |

Others | Egypt | 2.97 | 86 | 0.121 | 0.022 | 0.000 | 0.602 | 0 | 1 |

Israel | 10.58 | 698 | 0.243 | 0.014 | 0.663 | 0.904 | 1 | 1 | |

South Africa | 3.48 | 909 | 0.166 | 0.014 | 0.877 | 1.007 | 1 | 1 | |

Panel D: Minimum Tick Size and Foreign Exchange Rates | |||||||||

Market | Minimum Tick in Local Currency | Minimum Tick in US Currency (Cents) | Tick Size Varies by Stock Price | Local Currency | Exchange Rate (Local Currency/USD) | ||||

Asia | China | 0.01 | 0.1208 | No | CNY | 8.28 | |||

India | 0.01/0.05 | 0.0224/0.1120 | Yes | INR | 44.63 | ||||

Indonesia | 1 | 0.0114 | Yes | IDR | 8768.88 | ||||

South Korea | 1 | 0.0858 | Yes | KRW | 1165.19 | ||||

Malaysia | 0.005 | 0.1316 | Yes | MYR | 3.80 | ||||

Philippines | 0.0001 | 0.0002 | Yes | PHP | 56.10 | ||||

Taiwan | 0.01 | 0.0301 | Yes | TWD | 33.21 | ||||

Thailand | 0.01 | 0.0251 | Yes | THB | 39.79 | ||||

Eastern Europe | Czech Republic | 0.01 | 0.0377 | Yes | CZK | 26.50 | |||

Greece | 0.001 | 0.1220 | Yes | EUR | 0.82 | ||||

Hungary | 1 | 0.4852 | Yes | HUF | 206.12 | ||||

Poland | 0.01 | 0.2564 | Yes | PLN | 3.90 | ||||

Latin America | Argentina | 0.001 | 0.0345 | Yes | ARS | 2.90 | |||

Brazil | 0.01 | 0.3367 | No | BRL | 2.97 | ||||

Chile | 0.001 | 0.0002 | Yes | CLP | 616.77 | ||||

Mexico | 0.001 | 0.0089 | Yes | MXN | 11.26 | ||||

Peru | 0.001 | 0.0288 | Yes | PEN | 3.48 | ||||

Venezuela | 0.01 | 0.0004 | No | VEF | 3067.58 | ||||

Others | Egypt | 0.01 | 0.1616 | No | EGP | 6.19 | |||

Israel | 0.01 | 0.2203 | Yes | ILS | 4.54 | ||||

South Africa | 1 | 15.1286 | No | ZAR | 6.61 |

**Table 2.**The Best Spread Proxies and Price Impact Proxies of Countries sorted by Turnover. All countries are partitioned into four groups (G1 to G4) based on the average daily turnover of each country. G1, which has the highest turnover, includes China, South Korea, Taiwan, and Thailand. G2 includes Brazil, Hungary, Indonesia, Israel, Mexico, and Poland. While G3 includes Argentina, Czech Republic, Egypt, Greece, India, Malaysia, and South Africa, G4, which has the lowest turnover, incudes Chile, Peru, Philippines, and Venezuela. Panel A of the table reports the cross-sectional medians of spread benchmarks and spread proxies. Spread benchmarks include QS, ES, and RS. Spread proxies include ROLL, HASB, and LOT. Panel B of the table reports the cross-sectional medians of price impact benchmarks, and price impact proxies. Price impact benchmarks include LAMBDA, IMP, and ASC. Price impact proxies include AMIHUD, the inverse of AMIVEST, and PASTOR. The median spread (price impact) proxy that best approximates the median spread (price impact) benchmark in each group is indicated by **. In Panel A for example, the gap GAP

_{LOT}= |Median (LOT

_{i}) − Median (ES

_{i})| is smallest in G1. Furthermore, in Panel B, the gap GAP

_{AMIHUD}= |Median (AMIHUD

_{i}) − Median (LAMBDA

_{i})| is smallest in G1. The sample covers 1183 firms from 21 emerging markets. The sample period is from February to May 2004.

Panel A: Spread Benchmarks and Spread Proxies | ||||

Group | ES(%) | ROLL | HASB | LOT |

G1 | 0.274 | 1.380 | 2.490 | 0.396 ** |

G2 | 0.760 | 1.423 | 2.204 | 0.454 ** |

G3 | 0.599 | 1.532 | 2.422 | 0.522 ** |

G4 | 1.909 | 1.210 | 2.492 ** | 3.368 |

QS (%) | ||||

G1 | 0.297 | 1.380 | 2.490 | 0.396 ** |

G2 | 1.074 | 0.423 ** | 2.204 | 0.454 |

G3 | 0.792 | 1.532 | 2.422 | 0.522 ** |

G4 | 2.620 | 1.210 | 2.492 ** | 3.368 |

RS (%) | ||||

G1 | 0.096 | 1.380 | 2.490 | 0.396 ** |

G2 | 0.263 | 1.423 | 2.204 | 0.454 ** |

G3 | 0.313 | 1.532 | 2.422 | 0.522 ** |

G4 | 0.783 | 1.210 ** | 2.492 | 3.368 |

Panel B: Price Impact Benchmarks and Price Impact Proxies | ||||

Group | LAMBDA | AMIHUD | 1/AMIVEST | PASTOR |

G1 | 0.365 | 0.029 ** | 0.010 | 0.002 |

G2 | 0.184 | 0.213 ** | 0.046 | 0.007 |

G3 | 2.087 | 1.135 ** | 0.336 | 0.054 |

G4 | 0.268 | 0.404 | 0.225 ** | 0.008 |

IMP | ||||

G1 | 0.191 | 0.029 ** | 0.010 | 0.002 |

G2 | 0.560 | 0.213 ** | 0.046 | 0.007 |

G3 | 0.277 | 1.135 | 0.336 ** | 0.054 |

G4 | 0.955 | 0.404 ** | 0.225 | 0.008 |

ASC | ||||

G1 | 0.179 | 0.029 ** | 0.010 | 0.002 |

G2 | 0.390 | 0.213 ** | 0.046 | 0.007 |

G3 | 0.224 | 1.135 | 0.336 ** | 0.054 |

G4 | 0.832 | 0.404 ** | 0.225 | 0.008 |

**Table 3.**Measurement Errors of Spread Proxies and Price Impact Proxies of Countries sorted by Turnover. All countries are partitioned into four groups (G1 to G4) based on the average daily turnover of each country. Panel A of the table reports the median values of the measurement error (MERR) between the spread benchmarks (ES, QS, and RS), and spread proxies (ROLL, HASB, and LOT), respectively. For example, MERR

_{ROLL}

_{,i}= |ROLL

_{i}− ES

_{i}|. Panel A then implements the Wilcoxon rank-sum tests for equality between (i) the median |ROLL

_{i}− ES

_{i}| and median |LOT

_{i}− ES

_{i}|, and (ii) the median |HASB

_{i}− ES

_{i}| and median |LOT

_{i}− ES

_{i}|. The significance levels are assigned to the |ROLL

_{i}− ES

_{i}| and |HASB

_{i}− ES

_{i}| columns, respectively. Panel B reports the measurement error between the price impact benchmarks (LAMBDA, IMP, and ASC), and price impact proxies (AMIHUD, 1/AMIVEST, and PASTOR), respectively. For example, MERR

_{AMIHUD}

_{,i}= |AMIHUD

_{i}− LAMBDA

_{i}|. Panel B also implements the Wilcoxon rank-sum tests for equality between (i) the median |AMIHUD

_{i}− LAMBDA

_{i}| and median |1/AMIVEST

_{i}− LAMBDA

_{i}|, and (ii) the median |AMIHUD

_{i}− LAMBDA

_{i}| and median |PASTOR

_{i}– LAMBDA

_{i}|. The significance levels are assigned to the |1/AMIVEST

_{i}− LAMBDA

_{i}| and |PASTOR

_{i}− LAMBDA

_{i}| columns, respectively. The sample covers 1183 firms from 21 emerging markets. The sample period is from February to May 2004. *, **, and *** represent statistical significance at 10%, 5%, and 1%, respectively.

Panel A: Spread Proxies | |||

Group | Median Measurement Error | ||

|ROLL_{i} − ES_{i}| | |HASB_{i} − ES_{i}| | |LOT_{i} − ES_{i}| | |

G1 | 1.029 *** | 2.193 *** | 0.181 |

G2 | 0.811 *** | 1.316 *** | 0.464 |

G3 | 0.877 *** | 1.673 *** | 0.300 |

G4 | 1.008 ** | 1.195 *** | 1.604 |

|ROLL_{i} − QS_{i}| | |HASB_{i} − QS_{i}| | |LOT_{i} − QS_{i}| | |

G1 | 1.003 *** | 2.165 *** | 0.181 |

G2 | 0.892 * | 1.162 *** | 0.656 |

G3 | 0.752 *** | 1.545 *** | 0.399 |

G4 | 1.760 | 1.199 | 1.442 |

|ROLL_{i} − RS_{i}| | |HASB_{i} − RS_{i}| | |LOT_{i} − RS_{i}| | |

G1 | 1.273 *** | 2.388 *** | 0.290 |

G2 | 1.066 *** | 1.839 *** | 0.256 |

G3 | 1.149 *** | 1.997 *** | 0.328 |

G4 | 0.921 *** | 1.793 ** | 2.398 |

Panel B: Price Impact Proxies | |||

Group | Median Measurement Error | ||

|AMIHUD_{i} − LAMBDA_{i}| | |1/AMIVEST_{i} − LAMBDA_{i}| | |PASTOR_{i} − LAMBDA_{i}| | |

G1 | 0.326 | 0.360 | 0.366 |

G2 | 0.355 | 0.188 * | 0.145 * |

G3 | 1.515 | 1.645 | 2.028 |

G4 | 0.957 | 0.740 | 0.682 |

|AMIHUD_{i} − IMP_{i}| | |1/AMIVEST_{i} − IMP_{i}| | |PASTOR_{i} − IMP_{i}| | |

G1 | 0.184 | 0.171 | 0.185 ** |

G2 | 0.598 | 0.522 | 0.524 |

G3 | 0.847 | 0.265 *** | 0.230 *** |

G4 | 1.902 | 0.953 | 0.928 *** |

|AMIHUD_{i} − ASC_{i}| | |1/AMIVEST_{i} − ASC_{i}| | |PASTOR_{i} − ASC_{i}| | |

G1 | 0.170 | 0.156 | 0.171 * |

G2 | 0.546 | 0.423 ** | 0.372 *** |

G3 | 0.878 | 0.265 *** | 0.183 *** |

G4 | 1.702 | 0.874 | 0.784 *** |

**Table 4.**Cross-Sectional Correlations between Liquidity Benchmarks and Liquidity Proxies. All countries are partitioned into four groups (G1 to G4) based on the average daily turnover of each country. Panel A of the table reports the Spearman cross-sectional correlations between spread benchmarks (ES, QS, and RS), and spread proxies (ROLL, HASB, and LOT). Panel B reports the Spearman cross-sectional correlations between price impact benchmarks (LAMBDA, IMP, and ASC), and price impact proxies (AMIHUD, 1/AMIVEST, and PASTOR). Among the spread proxies that have a significant correlation, the ones larger than 0.50 are in bold. The sample covers 1183 firms from 21 emerging markets. The sample period is from February to May 2004. ** indicates statistical significance at the 5% level.

Panel A: Correlation between Spread and Spread Proxies | ||||

Spread | Spread Proxy | |||

Benchmark | ROLL | HASB | LOT | |

G1 | ES | 0.274 ** | 0.255 ** | 0.582 ** |

QS | 0.265 ** | 0.246 ** | 0.575 ** | |

RS | 0.210 ** | 0.118 ** | 0.544 ** | |

G2 | ES | 0.351 ** | 0.609 ** | 0.622 ** |

QS | 0.311 ** | 0.578 ** | 0.576 ** | |

RS | 0.260 ** | 0.503 ** | 0.691 ** | |

G3 | ES | −0.081 | 0.062 | 0.636 ** |

QS | −0.077 | 0.054 | 0.551 ** | |

RS | −0.084 | 0.055 | 0.620 ** | |

G4 | ES | 0.261 ** | 0.449 ** | 0.818 ** |

QS | 0.258 ** | 0.438 ** | 0.802 ** | |

RS | 0.060 | 0.211 ** | 0.457 ** | |

Panel B: Correlation between Price Impact and Price Impact Proxies | ||||

Price Impact | Price Impact Proxy | |||

Benchmark | AMIHUD | 1/AMIVEST | PASTOR | |

G1 | LAMBDA | 0.800 ** | 0.787 ** | 0.713 ** |

IMP | −0.113 | −0.115 | −0.168 ** | |

ASC | −0.079 | −0.080 | −0.137 ** | |

G2 | LAMBDA | 0.606 ** | 0.633 ** | 0.550 ** |

IMP | 0.069 | 0.006 | −0.026 | |

ASC | −0.049 | −0.090 | −0.098 | |

G3 | LAMBDA | 0.715 ** | 0.759 ** | 0.716 ** |

IMP | 0.705 ** | 0.613 ** | 0.583 ** | |

ASC | 0.636 ** | 0.563 ** | 0.534 ** | |

G4 | LAMBDA | 0.487 ** | 0.490 ** | 0.504 ** |

IMP | 0.510 ** | 0.475 ** | 0.467 ** | |

ASC | 0.534 ** | 0.502 ** | 0.498 ** |

**Table 5.**Incremental Regression R

^{2}s. Panel A of the table examines the incremental explanatory power of spread proxies in predicting spread benchmarks, after controlling for stock price and firm size. In the first regression, the dependent variable is one of the spread benchmarks (ES, QS, and RS), while the independent variables are the control variables, namely the stock price (PRICE) and firm size (SIZE). The corresponding adjusted R

^{2}is ${R}_{ADJ1}^{2}$. In the second regression, the dependent variable is one of the spread benchmarks (ES, QS, and RS), while the independent variables are the control variables, stock price and firm size in addition to one of the spread proxies (ROLL, HASB, and LOT). The corresponding adjusted R

^{2}is ${R}_{ADJ2}^{2}$. The incremental adjusted R

^{2}is calculated as: ${R}_{ADJ2}^{2}-{R}_{ADJ1}^{2}$. Panel B examines the incremental explanatory power of price impact proxies (AMIHUD, 1/AMIVEST, and PASTOR) in predicting price impact benchmarks (LAMBDA, IMP, and ASC). The sample covers 1183 firms from 21 emerging markets. The sample period is from February to May 2004. The t-statistics are in parenthesis. *, **, and *** represent statistical significance at 10%, 5%, and 1% levels, respectively.

Panel A: The Incremental Explanatory Power of Spread Proxies | ||||||||

Intercept | PRICE | SIZE | ROLL | HASB | LOT | Adjusted R^{2} | Incremental R^{2} | |

ES | 5.956 *** | 0.009 | −0.306 *** | 0.325 | ||||

(10.23) | (0.22) | (−6.48) | ||||||

5.345 *** | 0.022 | −0.252 *** | 0.296 *** | 0.361 | 0.036 | |||

(8.97) | (0.57) | (−7.17) | (3.84) | |||||

4.879 *** | 0.023 | −0.265 *** | 0.256 *** | 0.343 | 0.018 | |||

(8.45) | (0.53) | (−5.66) | (4.73) | |||||

3.699 *** | −0.001 | −0.175 *** | 0.122 *** | 0.464 | 0.139 | |||

(5.69) | (−0.01) | (−5.61) | (3.94) | |||||

QS | 8.852 *** | 0.026 | −0.402 *** | 0.439 | ||||

(11.26) | (0.63) | (−8.24) | ||||||

8.242 *** | 0.040 | −0.348 *** | 0.295 ** | 0.463 | 0.024 | |||

(10.15) | (1.02) | (−9.12) | (3.74) | |||||

7.671 *** | 0.041 | −0.357 *** | 0.280 *** | 0.453 | 0.014 | |||

(9.88) | (0.98) | (−7.34) | (4.91) | |||||

6.197 *** | 0.015 | −0.248 *** | 0.144 *** | 0.573 | 0.134 | |||

(7.79) | (0.57) | (−6.91) | (4.27) | |||||

RS | 2.431 *** | 0.017 | −0.187 *** | 0.133 | ||||

(4.32) | (0.49) | (−4.59) | ||||||

1.971 *** | 0.027 | −0.146 *** | 0.223 *** | 0.165 | 0.032 | |||

(3.52) | (0.83) | (−4.87) | (3.19) | |||||

1.860 *** | 0.024 | −0.165 *** | 0.136 *** | 0.140 | 0.007 | |||

(3.15) | (0.69) | (−4.00) | (2.75) | |||||

1.042 | 0.011 | −0.107 *** | 0.075 *** | 0.215 | 0.082 | |||

(1.44) | (0.41) | (−3.95) | (2.94) | |||||

Panel B: The Incremental Explanatory Power of Price Impact Proxies | ||||||||

Intercept | PRICE | SIZE | AMIHUD | 1/AMIVEST | PASTOR | Adjusted R^{2} | Incremental R^{2} | |

LAMBDA | 19.550 *** | −1.313 * | −3.495 ** | 0.087 | ||||

(2.73) | (−1.76) | (−2.25) | ||||||

15.592 *** | −1.454 * | −2.724 ** | 0.047 | 0.160 | 0.073 | |||

(2.62) | (−1.91) | (−2.15) | (1.51) | |||||

6.907 *** | −0.713 ** | −0.767 ** | 0.403 *** | 0.671 | 0.584 | |||

(2.69) | (−2.18) | (−2.23) | (3.12) | |||||

17.158 ** | −1.274 * | −3.007 ** | 0.914 | 0.114 | 0.027 | |||

(2.45) | (−1.72) | (−1.98) | (1.42) | |||||

IMP | 6.561 *** | 0.024 | −0.159 *** | 0.405 | ||||

(3.48) | (0.64) | (−5.99) | ||||||

6.534 *** | 0.023 | −0.153 *** | 0.001 | 0.406 | 0.001 | |||

(3.46) | (0.62) | (−5.72) | (0.71) | |||||

6.486 *** | 0.028 | −0.142 *** | 0.002 * | 0.414 | 0.009 | |||

(3.43) | (0.74) | (−5.44) | (1.93) | |||||

6.471 *** | 0.026 | −0.140 *** | 0.034 *** | 0.423 | 0.018 | |||

(3.43) | (0.68) | (−5.41) | (3.92) | |||||

ASC | 3.433 *** | −0.009 | −0.111 *** | 0.523 | ||||

(6.12) | (−0.63) | (−7.59) | ||||||

3.383 *** | −0.011 | −0.101 *** | 0.001 | 0.539 | 0.016 | |||

(6.00) | (−0.76) | (−7.51) | (1.06) | |||||

3.337 *** | −0.004 | −0.090 *** | 0.003 * | 0.569 | 0.046 | |||

(5.91) | (−0.31) | (−7.34) | (1.72) | |||||

3.310 ** | −0.007 | −0.086 *** | 0.047 *** | 0.621 | 0.098 | |||

(5.85) | (−0.50) | (−7.24) | (14.54) |

**Table 6.**Determinants of accuracy of Liquidity Proxies. The table presents the coefficients (t-statistics) from the cross-sectional regressions of the accuracy measures of liquidity proxies on firm and market characteristics. The accuracy measure is calculated as log(1/|Proxy − Benchmark|). The spread benchmark is ES. The spread proxies include ROLL, HASB, and LOT. The price impact benchmark is LAMBDA. The price impact proxies include AMIHUD, 1/AMIVEST, and PASTOR. Firm characteristics include stock price, turnover, return volatility, firm size, and investability. Market characteristics include market volatility, legal origin, and trading mechanism. Country dummies and industry dummies are also included. *, **, and *** represent statistical significance at the 10%, 5%, and 1% levels, respectively. The sample covers 1183 firms from 21 emerging markets. The sample period is from February to May 2004.

The Dependent Variable Is log(1/|Proxy − Benchmark|) | ||||||
---|---|---|---|---|---|---|

Proxy = ROLL | Proxy = HASB | Proxy = LOT | Proxy = AMIHUD | Proxy = 1/AMIVEST | Proxy = PASTOR | |

Benchmark = ES | Benchmark = ES | Benchmark = ES | Benchmark = LAMBDA | Benchmark = LAMBDA | Benchmark = LAMBDA | |

Intercept | −2.079 *** | −2.625 *** | −2.90 *** | −6.163 *** | −4.189 ** | −5.389 *** |

(−2.58) | (−3.46) | (−3.56) | (−8.93) | (−5.02) | (−10.14) | |

Stock Price | 0.052 | 0.004 | 0.120 *** | −0.046 | 0.038 | −0.016 |

(1.15) | (0.08) | (2.64) | (−1.19) | (0.82) | (−0.53) | |

Turnover | 5.186 | 6.535 | 22.193 *** | 34.789 *** | 4.937 | 33.427 *** |

(0.64) | (0.85) | (2.70) | (5.00) | (0.59) | (6.23) | |

Stock Volatility | −13.734 *** | −11.402 ** | −15.984 *** | −2.128 | −12.097 ** | −11.668 *** |

(−2.71) | (−2.39) | (−3.12) | (−0.49) | (−2.31) | (−3.49) | |

Firm Size | 0.091 * | 0.158 *** | 0.158 *** | 0.699 *** | 0.042 | 0.599 *** |

(1.85) | (3.40) | (3.17) | (16.52) | (0.82) | (18.37) | |

Investability | 0.371 ** | 0.091 | 0.371 ** | 0.803 *** | 0.313 * | 0.532 *** |

(2.04) | (0.53) | (2.01) | (5.14) | (1.66) | (4.42) | |

Market Volatility | 1.437 *** | 1.775 *** | 1.253 ** | −0.857 * | 1.616 *** | −0.441 |

(2.64) | (3.46) | (2.28) | (−1.84) | (2.87) | (−1.23) | |

Legal Origin | 0.443 * | 0.481 ** | −0.032 | 1.952 *** | 1.119 *** | 1.656 *** |

(1.78) | (2.06) | (−0.13) | (9.16) | (4.35) | (10.09) | |

Trading Mechanism | −0.193 | −0.696 | 0.177 | 2.678 *** | 2.155 *** | 2.379 *** |

(−0.27) | (−1.04) | (0.25) | (4.40) | (2.93) | (5.07) | |

Country Dummies | Yes | Yes | Yes | Yes | Yes | Yes |

Industry Dummies | Yes | Yes | Yes | Yes | Yes | Yes |

R^{2} | 0.316 | 0.324 | 0.409 | 0.699 | 0.529 | 0.816 |

Observations | 1183 | 1183 | 1183 | 1183 | 1183 | 1183 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ahn, H.-J.; Cai, J.; Yang, C.-W.
Which Liquidity Proxy Measures Liquidity Best in Emerging Markets? *Economies* **2018**, *6*, 67.
https://doi.org/10.3390/economies6040067

**AMA Style**

Ahn H-J, Cai J, Yang C-W.
Which Liquidity Proxy Measures Liquidity Best in Emerging Markets? *Economies*. 2018; 6(4):67.
https://doi.org/10.3390/economies6040067

**Chicago/Turabian Style**

Ahn, Hee-Joon, Jun Cai, and Cheol-Won Yang.
2018. "Which Liquidity Proxy Measures Liquidity Best in Emerging Markets?" *Economies* 6, no. 4: 67.
https://doi.org/10.3390/economies6040067