**4. Empirical Results**

#### *4.1. Spread Benchmarks and Spread Proxies*

#### 4.1.1. Spread Benchmarks and Spread Proxies

Panel A of Table 1 presents the median spread benchmarks and median spread proxies for each of the 21 emerging markets in our sample. The reported quoted spread displays rich cross-country variation. For example, Venezuela has the highest median quoted spread at 6.76%, while China has the lowest median quoted spread at 0.18%. In fact, for many countries, the median quoted spreads are substantial, reaching as high as 3%. Meanwhile, not all emerging markets have large transaction costs. There are a number of markets with substantially low spreads. While South Korea has the second largest number of sample stocks, its median quoted spread is only 0.30%. Spreads are generally higher in South America than in other regions.

The median quoted spreads that are shown in Table 1 are significantly smaller than those reported by Lesmond (2005). There are two possible reasons for this substantial difference. First, quoted spreads that are reported in Lesmond's study are based on daily closing quotes, which could overstate the median quoted spread level during the day. The median quoted spreads in our sample are all complied from intraday quotes. Second, our stringent requirements in the sampling and the data filtering process may exclude many firms with extremely large spreads.

The effective spread also exhibits rich cross-sectional dispersion across markets. As expected, a substantial gap exists between the quoted spread and the effective spread for most countries. Furthermore, the proportion of the effective spread to the quoted spread differs dramatically from country to country. In the case of the Czech Republic, the effective spread is slightly more than one-third, or 37% (0.612%/1.672%) of the quoted spread. China is at the other extreme, with an effective spread to quoted spread ratio of 98% (0.177%/0.180%). The median proportion for the whole sample is 76%, which indicates that, in general, post-trade transaction costs are significantly smaller than pre-trade transaction costs. The realized spread also displays an interesting cross-country distribution. The realized spread is interpreted as the proportion of the effective spread attributable to the cost of immediacy. The proportion of the realized spread in the effective spread also shows large variations, ranging from 11% (0.273%/2.471%) for Brazil to 56% (0.524%/0.929%) for Malaysia.

Panel A of Table 1 also reports the medians of the three low-frequency proxies of the spreads. Among the three proxies, *ROLL* and *HASB* display the least amount of cross-country dispersion. Both measures are generally between 1% and 2% for most countries. This is in contrast to the rich cross-country dispersion in the effective spread, in which both measures are intended proxies. The *LOT* measure displays greater variation. For example, the median *LOT* measure for Venezuela (8.64) is

much larger than the median *LOT* measure for China (0.18). While the magnitudes of the proxies differ significantly from market to market, they show some consistency in that countries with a larger *ROLL* measure also have generally larger *HASB* and *LOT* measures.

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

Now, we turn to the summary statistics for price impact benchmarks and price impact proxies. Panel B of Table 1 shows the medians of both high-frequency benchmarks (*LAMBDA*, *IMP*, and *ASC*) and low-frequency proxies (*AMIHUD*, 1/*AMIVEST*, and *PASTOR*). Rich cross-country dispersion is evident in the price impact benchmarks. *IMP* and *ASC* are quite similar in magnitude, while *LAMBDA* is somewhat different from *IMP* and *ASC*. Greece has the largest *LAMBDA* with a value of 12.52. Venezuela has the largest *IMP* at 2.49 and the largest *ASC* at 2.29. The larger the price impact measures, the more illiquid the market is.

With respect to price impact proxies, Peru has the largest *AMIHUD* at 31.92. A larger value of *AMIHUD* indicates greater illiquidity. It does not take much volume to move the stock price and generate large returns. On the other hand, *AMIVEST* measures liquidity. South Korea has the highest *AMIVEST* at 4.42, and the lowest *AMIHUD* value at 0.00. This indicates that South Korea is the most liquid market among the 21 countries in our sample. A high *PASTOR* value indicates illiquidity. Peru has the highest *PASTOR* value at 0.89. While Pástor and Stambaugh (2003) warn against using their measure for individual stocks, the *PASTOR* measure is constructed keeping in mind liquidity at the portfolio level.

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

Panel C of Table 1 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 or it is zero otherwise. The trading mechanism takes the value one for a pure limit-order system, and zero for a dealer or a hybrid system. Panel D of Table 1 reports the minimum tick size, whether tick size varies by stock price, currency code, and the average month-end exchange rates during our sample period.

#### *4.2. The Best Liquidity Proxies*

#### 4.2.1. The Best Spread Proxies

In this section, we examine which liquidity proxies act as the best proxies for liquidity benchmarks. We first partition all countries four groups (G1 to G4) based on the average daily turnover of each country.<sup>7</sup> G1, which has the highest turnover, includes China, South Korea, Taiwan, and Thailand. G2 includes Brazil, Hungary, Indonesia, Israel, Mexico, and Poland. G3 includes Argentina, Czech Republic, Egypt, Greece, India, Malaysia, and South Africa. G4, which has the lowest turnover, includes Chile, Peru, Philippines, and Venezuela. The number of stocks in each group are 530, 180, 370, and 103, respectively.

To examine which among *ROLL*, *HASB*, and *LOT* more accurately proxy spread benchmarks (*ES*, *QS*, and *RS*), we calculate a minimum gap measure, which is the smallest absolute difference between the median spread proxy and median spread benchmark.

> *GAPROLL* = |*Median* (*ROLLi*) − *Median* (*Benchmarki*)|, *GAPHASB* = |*Median* (*HASBi*) − *Median* (*Benchmarki*)|, *GAPLOT* = |*Median* (*LOTi*) − *Median* (*Benchmarki*)|,

<sup>7</sup> Turnover is calculated as the daily average number of traded shares divided by market capitalization.

where the median is calculated using sample stocks in each group, for example, *i =* 1, 2, ... , 530 for the G1 group. The results are reported in Panel A of Table 2 under the headings *ROLL*, *HASB*, and *LOT*. For each group, the spread proxy that has the smallest gap is indicated by \*\*. The three proxies exhibit stark differences in their effectiveness. The *LOT* measure is by far the most effective one, dominating the other two proxies in three out of the four groups when the spread benchmark is *ES*. Furthermore, *LOT* dominates the other two proxies in two out of the four groups when the spread benchmark is *QS*, and in three out of the four groups when the spread benchmark is *RS*. Thus, it appears that *LOT* is more effective, particularly in active and liquid markets from Groups G1 to G3.

**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 *GAPLOT* = |*Median* (*LOT*i) − *Median* (*ES*i)| is smallest in G1. Furthermore, in Panel B, the gap *GAPAMIHUD* = |*Median* (*AMIHUDi*) − *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.


Now, we repeat the analysis and calculate *GAPROLL*, *GAPHASB*, and *GAPLOT* 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.

**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. *GAPROLL* = |*Median* (*ROLLi*) − *Median* (*ESi*)|, *GAPHASB* = |*Median* (*HASBi*) − *Median* (*ESi*)|, and *GAPLOT* = |*Median* (*LOTi*) − *Median* (*ESi*)|, where the median is calculated from sample stocks indexed by subscript *i* in each country.

Figure 1 also suggests that *LOT* is more accurate in markets with the highest turnover. For each of the four markets in Group G1, i.e., China, Korea, Taiwan, and Thailand, with the highest turnover, *LOT* is the dominating proxy for ES. The number of stocks in G1 is 530. This accounts for 45% of the total sample of 1183 stocks. *ROLL* is the dominating proxy for *ES* in Venezuela and Peru, while *HASB* is the dominating proxy for *ES* in Philippines, Mexico, Egypt, Indonesia, and Brazil.

#### 4.2.2. The Best Price Impact Proxies

To examine which among *AMIHUD*, 1/*AMIVEST*, and *PASTOR* is a more accurate proxy for price impact benchmarks (*LAMBDA*, *IMP*, and *ASC*), we also calculate the following minimum gap measures:

$$GAP\_{AMIHUD} = |Median\ (AMIHIDD\_i) - Median\ (BendmRT\_i)|\_\prime$$

$$GAP\_{1/AMIVEST} = |Median\ (1/AMIVEST\_i) - Median\ (BendmRT\_i)|\_\prime$$

$$GAP\_{PATOR} = |Median\ (PASTOR\_i) - Median\ (BendmRT\_i)|\_\prime$$

where the median is calculated using sample stocks in each group. The results are reported in Panel B of Table 2 under the headings *AMIHUD*, 1/*AMIVEST*, and *PASTOR*. Here, notice that we use the inverse of *AMIVEST* because this has a positive correlation with *AMIHUD*. For each group, the price impact proxy that has the smallest gap is indicated by \*\*. The pattern is clear. *AMIHUD* is by far the most effective measure, dominating the other two proxies in three out of the four groups, when the price impact benchmark is *LAMBDA*. *AMIHUD* also dominates the other two proxies in three out of the four groups when the price impact measures are *IMP* and *ASC*, respectively.

Similarly, we repeat the analysis and calculate *GAPAMIHUD*, *GAP1/AMIVEST*, and *GAPPASTOR* 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.

**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*. *GAPAMIHUD* = |*Median* (*AMIHUDi*) − *Median* (*LAMBDA*i)|, *GAP*1/*AMIVEST* = |*Median* (1/*AMIVEST*i) − *Median* (*LAMBDA*i)|, and *GAPPASTOR* = |*Median* (*PASTOR*i) − *Median* (*LAMBDA*i)|, where the median is calculated from sample stocks indexed by subscript *i* in each country.

Figure 2 also suggests that *AMIHUD* is more accurate in markets with the highest turnover. For each of the four markets in Group G1, i.e., China, Korea, Taiwan, and Thailand, with the highest turnover, *AMIHUD* is the dominating proxy for *LAMBDA*.

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

#### 4.3.1. Effectiveness of Spread Proxies

An analysis of the accuracy of the spread proxies in Figures 1 and 2 is descriptive, without any formal statistical test. To see whether the pattern that is described above is statistically discernible, we calculate the absolute difference (*MERR*) between the spread proxies (*ROLL*, *HASB*, and *LOT*), and spread benchmarks (*ES*, *QS*, and *RS*) for each stock *i*, as follows:

$$MERR\_{ROLL,i} = |ROLL\_i - Benchmark\_i|\_\prime$$

$$MERR\_{HASB,i} = |HASB\_i - Benchmark\_i|\_\prime$$

$$MERR\_{LOT,i} = |LOT\_i - Benchmark\_i|\_\prime$$

*MERR* is similar to the *GAP* measure introduced earlier except that, for each group from G1 to G4, *GAP* calculates the difference in cross-sectional medians between a spread proxy and a spread benchmark, while *MERR* calculates the difference for each individual stock.

Panel A of Table 3 displays the median *MERR* for each stock group partitioned by turnover. The results are generally consistent with those that are displayed in Panel A of Table 2 and Figure 1. LOT is the most accurate proxy for *ES*, *QS*, and *RS*. For example, in the top section of Panel A where the spread benchmark is *ES*, and the turnover is the highest (G1), the median |*LOT*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.

**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, *MERRROLL*,<sup>i</sup> = |*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, *MERRAMIHUD*,<sup>i</sup> = |*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.



**Table 3.** *Cont.*

#### 4.3.2. Effectiveness of Price Impact Proxies

Now, we calculate the absolute difference (*MERR*) between the price impact proxies (*AMIHUD*, 1/*AMIVEST*, and *PASTOR*), and price impact benchmarks (*LAMBDA*, *IMP*, and *ASC*) for each stock *i,* asfollows:

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Panel B of Table 3 displays the median *MERR* for each stock group partitioned by turnover. The results are notably different from those displayed in Panel B of Table 2 and Figure 2, wherein *AMIHUD* is the dominating proxy for the price impact benchmarks *LAMBDA*, *IMP*, and *ASC*. When we examine the effectiveness of the price impact proxies at the individual stock level, there is no clear winner, when the price impact benchmark is *LAMBDA* in the top section of Panel B. However, there is some evidence that when the price impact benchmark is either *IMP* or *ASC*, *PASTOR* turns out to be the winner for less liquid markets in G3 and G4. We conjecture that the results might be driven by larger dispersion in price impact proxy measures, as compared to the results for spread proxy measures. We examine this issue further when we analyze the correlation structure and conduct regression analysis.
