**1. Introduction**

The importance of liquidity extends far beyond the traditional domain of market microstructure research. There is mounting evidence that liquidity is important in asset pricing. Numerous studies document the pricing of illiquidity, and how it affects stock returns (Amihud and Mendelson 1986; Brennan and Subrahmanyam 1996; Chalmers and Kadlec 1998; Eleswarapu 1997; Amihud 2002), among others. Other studies report that liquidity commonality systematically affects expected returns (Acharya and Pedersen 2005; Pástor and Stambaugh 2003; Sadka 2006). The importance of liquidity is not limited to asset pricing; it is an important factor in corporate finance as well. When the liquidity of a company affects its required return and cost of capital, it has important implications for corporate financial policies. Empirical studies examine how liquidity is linked to capital structure decisions (Lesmond et al. 2008; Lipson and Mortal 2007; Bharath et al. 2009), payou<sup>t</sup> policies (Amihud and Li 2006; Banerjee et al. 2007), information disclosure (Coller and Yohn 1997), and corporate governance (Brockman and Chung 2003).

Most literature on liquidity, including the studies mentioned above, focuses on the markets in the United States (U.S.) or developed markets. However, liquidity may have even greater impacts on emerging markets, as emphasized by Bekaert et al. (2007). Emerging markets are generally characterized by low transparency and limited portfolio choices due to a lack of diversity in available securities (Bekaert et al. 2007). When compared to investors in developed markets, investors in emerging markets tend to be more short-term oriented. Short-term investors are more likely to be concerned about the liquidity of securities. Besides, corporations in emerging markets are characterized by more concentrated ownership than those in developed markets, and they often face severe corporate

governance problems. All of these considerations imply that liquidity may have a greater role to play in emerging markets than in developed markets.

While the role of liquidity is instrumental in emerging markets, research on emerging market liquidity is scant at best. This is in contrast to the attention being paid to liquidity in emerging markets lately, due to the dramatic growth of these markets, and the steady global capital market liberalization that has been underway for the past two decades. The primary reason for this lack of research is the paucity of transaction level data on emerging stock markets. To circumvent this problem, some researchers use proxies for liquidity that were obtained from daily return and/or volume data. However, the efficacy of their analysis critically hinges upon the effectiveness of the liquidity proxies that they employ. The most comprehensive study so far regarding the effectiveness of various low-frequency liquidity proxies is by Goyenko et al. (2009).<sup>1</sup>

The study by Goyenko et al. (2009) considers horse races with more than a dozen low-frequency liquidity proxies. It evaluates the correlation between each of the proxies and various benchmark liquidity measures that were retrieved from high-frequency data on the U.S. markets. The study concludes that many low-frequency liquidity measures perform reasonably well, but also adds a caveat by pointing out that the results may not apply to international markets, particularly emerging markets. Goyenko et al. (2009) state, "We do not know whether the measures are effective on international data, especially in relation to those stocks with extremely thin trading" (p. 180).

Our study takes up the analysis of this statement and evaluates whether some popular low-frequency liquidity proxies capture high-frequency liquidity measures effectively in emerging markets, and if they do, which proxy best measures liquidity.

This study is not the first to analyze the effectiveness of low-frequency liquidity proxies in emerging markets. Lesmond (2005) carries out comprehensive stock level comparisons of low-frequency liquidity proxies in 23 emerging markets. Lesmond's (2005) high-frequency liquidity benchmark relies on quarterly recorded quoted spreads. The quoted spread recorded at the end of the day (more specifically, the last day of each quarter) may overstate the average spread in the market because of its well-known U-shaped intraday pattern (McInish and Wood 1992). This problem is exacerbated in the case of small firms and infrequently traded stocks, both of which are common attributes of firms in emerging markets. More importantly, the quoted spread reveals only partial information about liquidity. The quoted spread measures the pre-trade transaction costs (i.e., potential transaction costs) but not the post-trade costs (i.e., actual transaction costs). The actual transaction costs that are borne by investors are measured more accurately by the effective spread, and there is no guarantee that a liquidity proxy that measures the quoted spread best would also measure the effective spread most efficiently. Moreover, extant literature on market microstructure breaks up the spread into post-trade price reversal, and adverse price change—the former being pure immediacy costs and the latter being the loss to the informed, or, simply, price impact.

Understanding these two sources of liquidity costs is of particular importance for emerging markets investors. Since many stocks in emerging markets are traded infrequently, the levels of immediacy costs could be multiple times higher than usually observed in developed markets. Investors in emerging markets could also face substantial information costs because of the lack of transparency in the information environment. Knowledge of the effectiveness of various low-frequency liquidity measures as proxies for different aspects of liquidity costs, such as the effective spread, pure immediacy costs, and price impact, offers invaluable information to emerging market investors.

This paper uses unique and comprehensive tick-by-tick data sets on 1183 stocks from 21 emerging stock markets, spanning four continental regions. The data are electronically fed by the *Bloomberg Terminals* in real time for about three months, and include all quote revisions and transactions at the

<sup>1</sup> 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).

individual stock level. The comprehensiveness of our data allows us to estimate various intraday measures for transaction costs and the price impact for each trade. We then use these estimates as the benchmarks against which we compare various low-frequency liquidity proxies.

We analyze two groups of benchmark liquidity measures that are calculated using the intraday data. Our classification is motivated by the study of Goyenko et al. (2009). The first group includes spread measures such as effective spread (*ES*), quoted spread (*QS*), and realized spread (*RS*). We call this group the "spread benchmarks." The second group consists of trade induced price impacts, the lambda coefficient *LAMBDA* (Hasbrouck 2009), the five-minute price impact *IMP* (Goyenko et al. 2009), and adverse selection costs *ASC* (Huang and Stoll 1996). This group is called the "price impact benchmarks."

The low-frequency liquidity proxies are all calculated using daily data. Specifically, we select three spread proxies, and three price impact proxies that are relatively easy to calculate, and have been widely used in empirical studies.<sup>2</sup> The three spread proxies include *ROLL* (Roll 1984), *HASB* (Hasbrouck 2009), and *LOT* (Lesmond et al. 1999), while the three price impact proxies include *AMIHUD* (Amihud 2002), *AMIVEST* (Cooper et al. 1985), and *PASTOR* (Pástor and Stambaugh 2003).

To assess the effectiveness of spread proxies, we compare low-frequency spread proxies with high-frequency spread benchmarks. Similarly, to assess the effectiveness of price impact proxies, we compare low-frequency price impact measures with high-frequency price impact benchmarks. We partition 21 emerging markets into four groups (G1 to G4) that are based on the cross-sectional average of the daily turnover of all the stocks within each country. We implement the analysis for each group individually and sort the values by average daily turnover. We consider three measures to examine the effectiveness of liquidity proxies. First, we measure the absolute difference between the median of the liquidity benchmark value and of liquidity proxy from each group. We interpret a smaller difference as evidence of a more effective proxy. Furthermore, we measure the absolute difference between the liquidity benchmark and liquidity proxy at the individual stock level, and we carry out a variety of Wilcoxon rank-sum tests. Second, we calculate the average cross-sectional correlation between a benchmark and a proxy across individual stocks within each group. Third, using regression, we compute the proxy-induced improvement in the coefficient of determination *R*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*<sup>2</sup> has improved.

When we compare spread benchmarks and spread proxies, all three measures (absolute difference, correlation, and incremental *R*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*<sup>2</sup> measures carry more weight.

In our study, we analyze 21 emerging markets comprising eight stock markets in the Asia Pacific, four in Eastern Europe, six in Latin America, and three in Africa and the Middle East. While many of these markets show similarities in that they have generally low levels of liquidity, lack of transparency,

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

and poor investor protection, they also display substantial dissimilarities in terms of trading rules and systems, legal systems, the degree of market openness, and investor composition. We run cross-sectional regressions to examine what factors influence the effectiveness of the liquidity proxies.

The remaining paper is organized as follows. Section 2 explains various high-frequency liquidity benchmarks and low-frequency liquidity proxies. Section 3 describes the datasets and sample construction, while Section 4 contains the empirical results. Finally, Section 5 concludes the paper.
