Stock extreme illiquidity and the cost of capital

Accepted Manuscript

Stock extreme illiquidity and the cost of capital Mohamed Belkhir , Mohsen Saad , Anis Samet PII: DOI: Reference:

S0378-4266(18)30012-8 10.1016/j.jbankfin.2018.01.005 JBF 5281

To appear in:

Journal of Banking and Finance

Received date: Revised date: Accepted date:

8 September 2016 25 November 2017 13 January 2018

Please cite this article as: Mohamed Belkhir , Mohsen Saad , Anis Samet , Stock extreme illiquidity and the cost of capital, Journal of Banking and Finance (2018), doi: 10.1016/j.jbankfin.2018.01.005

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Stock extreme illiquidity and the cost of capital

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Mohamed Belkhir International Monetary Fund Center for Economics and Finance, Kuwait [email protected] Tel: + 965 2224 5062

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Mohsen Saad* School of Business Administration American University of Sharjah, United Arab Emirates [email protected] Tel: +971 6 515 2325

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Anis Samet School of Business Administration American University of Sharjah, United Arab Emirates [email protected] Tel: +971 6 515 2316

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*School of Business Administration, The American University of Sharjah, SBA-1112, Airport road, Sharjah, P.O. Box 26666, UAE *Corresponding author. Tel.: +971 6 515 2325

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Abstract We examine the relationship between stock extreme illiquidity and the implied cost of capital for firms from 45 countries. We document robust evidence that firms whose stocks have a greater potential for extreme illiquidity realizations suffer from higher cost of capital. A one standard deviation increase in a stock’s liquidity tail index leads to a rise of 30 basis points in the cost of equity. The reported evidence for stock extreme illiquidity is independent of the systematic extreme liquidity risk and extends to alternative cost-percent liquidity proxies. We further find that this relation is stronger in periods of down markets and high volatility and is weaker in environments with better information quality and stronger investor protection. JEL classification: G11; G12; G14; G15; F36 Keywords: Liquidity; Extreme illiquidity; Cost of capital; Market conditions; Institutions

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1. Introduction The literature on liquidity and asset pricing shows that the level as well as the variability of liquidity may influence stock expected returns.1 Acharya and Pederson (2005) present a

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theoretical equilibrium model with liquidity risk and provide the empirical evidence that different liquidity risks, measured as the covariances between the individual stock liquidity and returns and the market liquidity and returns, are priced in the cross-section of stock expected returns. More recent studies explore an additional dimension of liquidity risk, which reflects the

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asymmetrical nature of such risk, and suggest a role for liquidity tail risk in determining expected returns (e.g., Ruenzi et al., 2013; Anthonisz and Putnins, 2017; Wu, 2016). This paper contributes to this literature by proposing a new empirical measure of liquidity tail risk, which captures the potential for a stock’s liquidity to spiral down below a certain threshold to extremely

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low levels. As we detail throughout the paper, our measure turns out to be a feasible and strong

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empirical proxy for liquidity risk that bears a significant premium for a sample of international stocks that trade in markets where liquidity issues can be especially acute.

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An important feature of stock liquidity is that it varies over time. A stock that is in a normal liquidity state most of the time can occasionally experience episodes when its liquidity

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quickly vanishes and trading costs become prohibitively high for traders to enter or exit

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positions. The potential for extreme declines in stock liquidity wherein trades may fail to occur because of the lack of counterparties on the other side underscores the relevance of focusing on

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Examples of studies that report a premium for illiquidity level include Amihud and Mendelsen (1986), Brennan and Subrahmanyam (1996), Eleswarapu (1997), Brennan et al. (1998), Amihud (2002), Hagströmer et al. (2013), and Amihud et al. (2015). Other empirical work that investigates liquidity risk includes: Pastor and Stambaugh (2003), Liu (2006), Lou and Sadka (2011), and Lee (2011). Extensive reviews of the literature on liquidity in asset pricing are presented in Amihud et al. (2005) and Holden et al. (2013). 1

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the tail of the liquidity distribution. In a recent comment, the Financial Times chief economics commentator, Martin Wolf, states, “The big problem with such analyses of market liquidity is that things tend to look fine until they do not. One has to focus instead on the tail risks…Investors ought to worry, instead, since the risk that nobody will be on the other side of

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their trades is a real one.” (FT, 2015). Despite such calls on the significance of liquidity tails, the existing literature on stock liquidity has not yet explored the impact of extreme realizations of illiquidity on expected returns. We add to this important yet understudied literature by providing evidence that a stock’s potential for a sudden evaporation of its liquidity has a negative influence

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on the price that investors are willing to pay and hence is positively related to firms’ cost of equity capital.

The bulk of research on the pricing of liquidity risk, including studies that advocate

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considerations for extreme illiquidity, focuses on U.S. stock markets.2 Instead, we turn our attention to international markets where investors may be more concerned about liquidity-related

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issues than those investing in U.S. markets. For instance, Bekaert et al. (2007; p.1784) argue that “liquidity effects may be particularly strong” in emerging markets and Lee (2011; p.137)

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suggests that “the importance of liquidity could be more pronounced in markets other than the

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U.S, where liquidity is allegedly high”. Further, stocks may be more prone to severe liquidity dry-ups in international markets than in the U.S, which makes extreme liquidity risk more

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relevant to investors in stock markets outside the U.S. Hence, taking a global approach provides a good setup to exploit the rich variation in the trading environments of equity markets and accounts for markets where stock liquidity may be particularly fragile and investors’ concern for

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Notable exceptions include Bekaert et al. (2007) and Lee (2011) who investigate the pricing of liquidity risk in 19 emerging equity markets and markets from 50 countries, respectively. 2

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such fragility is particularly strong. An international setting offers the advantage of capturing the potentially wide variation in stock extreme liquidity risk across countries and the nature of its relation with firm cost of capital. Yet, one major challenge in a study of liquidity risk and cost of equity at the international level is finding a suitable measure that can capture liquidity risk

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consistently across markets. In many emerging and less developed countries, stock markets suffer from severe weaknesses such that liquidity risk can have different sources and take various forms; it may thus not be fully captured by the traditional liquidity covariances of Acharya and Pederson (2005). Consistent with this idea, our empirical findings suggest that, indeed, extreme

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liquidity risk that measures the potential for extreme illiquidity is a relevant metric of liquidity risk in international markets and particularly for illiquid stocks whose liquidity risk can be notoriously difficult to measure.

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In the existing liquidity literature, little is known about extreme illiquidity at the

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individual stock level and its relation with stock prices. Recent studies investigate the pricing effect of extreme illiquidity but only as a market-wide systematic risk. For instance,

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Brunnermeier (2009) highlights the dramatic consequences of sudden and severe drops in liquidity by stating, “…shocks can get amplified to a full-blown financial crisis when liquidity

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evaporates” (p.91). Cao and Petrasek (2013) further assert the importance of liquidity in extreme market events.3 Wu (2016) provides empirical evidence that the systematic risk of extreme

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market illiquidity is priced in the cross-section of stock expected returns. By combining liquidity with the threshold-based tail risk, Hill’s (1975) estimator, Wu (2016) defines extreme liquidity

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Within an event-study setting, Cao and Petrasek (2013) investigate factors that affect the cross-sectional variations in stock returns during periods of market-wide liquidity crises. The study finds that liquidity risk is strongly related to stock abnormal returns on days with market liquidity crisis; in contrast to market risk, which does not seems to play any significant role.

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risk as the tail of illiquidity of all stocks within a market. Wu (2016) shows that stocks with higher sensitivities to the market extreme liquidity risk (extreme liquidity beta) earn significantly higher returns. We share with Wu (2016) the notion of a threshold-based measure of extreme illiquidity. However, a key difference is that while Wu (2016) studies extreme illiquidity by

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focusing on the tail distribution of liquidity at the market level, we rather focus on the tail distribution of liquidity at the individual stock level. Our study is not centered around a liquidity beta per se, but is concerned with the investigation of whether extreme illiquidity at the stock level is related to the firm’s cost of equity. In this regard, our approach to extreme illiquidity is

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closer to Menkveld and Wang (2012) who study whether liquileaks, defined as the probability that a stock hits an illiquid state and remains in that state for a week or longer, affects expected returns. However, unlike Menkveld and Wang (2012), our measure of extreme illiquidity

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captures the potential for a stock’s illiquidity to exceed a certain threshold rather than the probability to be trapped in an illiquid state for a certain period of time.

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We address a previously unexplored question of whether investors require a

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compensation for holding stocks with the potential for extreme realizations of illiquidity. Empirically, we assess stock extreme illiquidity by focusing on the tail distribution of an

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individual stock’s liquidity. We adopt Extreme Value Theory, which deals with extreme behavior of a probability distribution. Extreme Value Theory models the behavior of heavy tailed

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distributions and provides the best possible estimate of the tail index of the distribution. We apply the parametric Maximum Likelihood Estimation approach on Generalized Pareto Distribution to gauge the liquidity tail index (

hereafter), which captures the potential

exceedances of an individual stock’s illiquidity over a certain threshold. As for our measure of expected returns, we use the cost of equity implied by the stock price and earnings forecasts

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(

). Pastor et al. (2008) empirically show that the implied cost of capital outperforms realized

returns in detecting a risk–return tradeoff. They recommend using

rather than realized

returns because the former is forward-looking with greater capacity to capture the time-varying expected returns. Li et al. (2013) show that

has a greater ability than traditional ratios in

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predicting future stock returns.4

We carry out our investigation in an international setting that encompasses 13,779 stocks from 45 countries over the period spanning 1985 to 2012 (more than 90,000 observations). Our

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regression results indicate that the potential for extreme illiquidity is a significant determinant of the firm cost of equity, while controlling for a host of firm and country variables. We find that a one standard deviation increase in Amihud (2002)-based

raises

by 30 basis points. The

finding of a positive association between a stock’s extreme illiquidity and the cost of capital is

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confirmed for Hill’s (1975) tail index estimator as an alternative measure of extreme illiquidity. Further, we extend our investigation beyond the Amihud measure to three additional percent-cost

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liquidity proxies, namely the Closing Percent Quoted Spread, developed by Chung and Zhang

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(2014), the High-Low liquidity measure proposed by Corwin and Schultz (2012), and the liquidity proxy developed by Fong et al. (2017). The evidence based on the percent-cost liquidity

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proxies complements our results by using tail indices that capture the potential of realizing

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extreme illiquidity costs as measured by the spread dimension of liquidity.

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We recognize, however, that the implied cost of capital is far from being a perfect proxy for stock expected returns. For instance, Hughes et al. (2009) argue that the implied cost of capital contains noises and biases that can potentially contaminate empirical results. More recently, Lyle and Wang (2015) also argued against the use of the implied cost of capital as a proxy for expected returns. They wrote that the implied cost of capital literature “has produced a plethora of proxies that not only are fraught with implementation issues but also have not been found to be reliable” (p.506-507). In robustness tests, we address some of the limitations of . 5

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The empirical analysis addresses the concern that our extreme illiquidity measure may be capturing extreme illiquidity due to market-wide extreme liquidity risk rather than idiosyncratic extreme liquidity risk. In particular, we create the orthogonal variant of

through regressing it

on Wu’s (2016) measure of market extreme liquidity risk. We then collect the residuals that model. These residuals measure the

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result from the regression and use them in the

likelihood of illiquidity costs to exceed the 95th percentile threshold due to severe liquidity shocks that are idiosyncratic in origin and independent of any systematic extreme liquidity risks. Our findings show that the residuals retain the ability to explain changes in cost of equity capital

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even after controlling for the market extreme liquidity risk. The evidence that we present is robust to a wide range of tests that include: revised sample analysis to subsets of countries and to subsets of stocks, limitations in the implied cost of equity measures, and alternative measures of

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extreme illiquidity. Finally, we also find that the adverse effect of extreme illiquidity on the implied cost of capital is more severe during episodes of market downturns and higher market

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investor protection.

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volatility and in institutional environments characterized by high information opacity and weak

Our study contributes to several strands of the literature. First, we add to the scant literature

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on extreme illiquidity. Existing studies are few and typically examine the potential impact of a stock’s sensitivity to market-wide liquidity crashes on realized stock returns (e.g., Ruenzi et al.,

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2013; Anthonisz and Puntins, 2017; Wu, 2016). By focusing on extreme liquidity of individual stocks, we allow for the cost of equity to be determined by a new proxy for liquidity risk – the potential that liquidity spirals down below a certain threshold to extremely low levels. Using a new measure of extreme illiquidity, the implied cost of equity, and an international setting, we provide several new insights on stock extreme illiquidity. We primarily document robust

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evidence that stock extreme illiquidity requires an equity premium globally. We further show that the magnitude of this premium increases in times of market downturns and higher volatility, and varies across countries according to their institutional quality of information and investor protection.

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Second, our work adds to the literature that examines liquidity in international markets. The findings of Lee (2011), Karolyi et al. (2012), and Amihud et al. (2015) suggest that stock liquidity level and risk are priced differently across countries according to geographic, economic,

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and institutional environments. We add to these studies by focusing on another metric of liquidity risk, namely the potential for a stock’s liquidity to dry-up. To the best of our knowledge, this is the first study that addresses this issue in an international setting. We complement the findings of the above literature with evidence that extreme illiquidity

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realizations matter to investors in international financial markets with an impact on the cost of equity that varies by financial market conditions and by the quality of countries’ institutional

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environments.

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Third, our paper contributes to the literature on the determinants of the cost of equity capital. Prior cross-country studies suggest that the implied cost of capital is influenced by the nature of a

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country’s institutions (e.g., Hail and Leuz, 2006) and several firm-level factors, such as voluntary disclosure (Francis et al., 2005) and corporate governance (e.g., Chen et al., 2011). While these

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studies generally underscore the importance of firm-level characteristics for the implied cost of equity, none of them considers the potential association between extreme illiquidity and the implied cost of capital internationally. We thus extend the cost of capital literature by providing novel evidence that a stock’s potential for extreme illiquidity is a significant determinant of the cost of equity.

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Our findings have important implications. The documented evidence suggests that firms can enjoy cheaper cost of capital and higher valuation by putting in place policies that would enhance stocks’ liquidity and reduce its potential to reach extremely low levels. One potential measure is to enhance disclosure, which according to Balakrishnan et al. (2014) improves stock

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liquidity and thereby reduces firm cost of capital. Moreover, the findings that the extreme illiquidity premium is higher in environments with better information quality and investor protection suggest that certain countries with poor records along these two institutional dimensions can contribute to the lowering of their firms’ cost of capital by adopting reforms

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aimed at strengthening investor protection and reducing information opaqueness.

The remainder of the paper is organized as follows. Section 2 describes our data and

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2. Data and variables

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variables. Section 3 presents our empirical results. Finally, section 4 concludes.

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We extract all available equities listed on all stock exchanges around the world from DataStream, for the period spanning January 1985 to October 2012. We follow the standard

Main variables

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2.1.

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sample selection and data filtering as described in Karolyi et al. (2012).

2.1.1. The implied cost of equity capital We follow Hail and Leuz (2006) and Dhaliwal et al. (2006) and calculate the implied cost

of capital,

, as the average estimate obtained from four different models, Claus and Thomas

(2001), Gebhardt et al. (2001), Easton (2004), and Ohlson and Juettner-Nauroth (2005). Using 8

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the average of four estimates has the advantage of reducing the possibility of obtaining biased results due to the reliance on one model rather than the others (Dhaliwal et al., 2006). The individual estimates of the implied cost of capital obtained using the models of Claus and Thomas (2001), Gebhardt et al. (2001), Easton (2004), and Ohlson and Juettner-Nauroth (2005)

solution while

,

, ,

, , and

respectively. We note that

involve numerical techniques wherein the solution is bounded

between 0% and 100%.

, we use I/B/E/S database to get the positive one-, two-, and three- year-

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To calculate

is estimated in a closed form

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are denoted

ahead mean forecasted earnings per share (

) and the long-term growth rate forecast. In

line with Frankel and Lee (1998) and Hail and Leuz (2009), we substitute missing or negative by the historical earnings per share estimated using the beginning year book value per

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share and the three-year median return on equity in the same year, country, and industry. In this

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study, we consider only firms with sufficient I/B/E/S forecasts. We eliminate firm-year observations for which none of the implied cost of equity estimates converges (Easton, 2004;

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Claus and Thomas, 2001; and Gebhardt et al., 2001 models) or is undefined (Ohlson and Juettner-Nauroth, 2005 model).5 We provide detailed descriptions of the four models used to

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estimate the implied cost of equity in Appendix A.

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In a robustness test, we impose the restriction of having a valid cost of equity estimate for each model before taking the average to calculate . The results remain unchanged. 9

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2.1.2. Amihud liquidity proxy and liquidity tail indices Defined as the absolute value of the daily return-to-volume ratio, the Amihud (2002) liquidity measure reflects the price impact of a monetary unit of trade. According to this

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measure, a stock is considered liquid if it can accommodate heavy trading with the least impact on the price. In a paper that identifies high quality liquidity proxies, Goyenko et al. (2009) show that low-frequency liquidity proxies that are built using daily data are highly correlated with intraday transaction costs. Among the numerous low-frequency liquidity proxies evaluated in the

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study, the authors report that Amihud (2002) is capable of capturing the price impact component of liquidity, while other liquidity proxies do a better job measuring liquidity spreads. In a similar fashion to Goyenko et al. (2009), Fong et al. (2017) rank different low-frequency liquidity proxies according to their ability to estimate their respective intraday liquidity benchmarks.

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Examining thirteen different cost-per-dollar-volume liquidity proxies relative to the slope of the

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price function, known as “lambda”, as a benchmark, Fong et al. (2017) find that Amihud is one of five measures that tie as the best liquidity proxy.6 Additionally, Hasbrouck (2009) shows that

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the Amihud measure is more correlated with high-frequency price impact coefficient than any

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other daily liquidity proxy.

In addition to being easy to construct, the strong positive correlation with Kyle’s (1985)

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microstructure estimate of the price impact contributes to the popularity of the Amihud measure. Therefore, the Amihud liquidity proxy is especially suitable to use in liquidity studies that cover

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Fong et al. (2017) group low-frequency liquidity proxies into two major categories, percent-cost and cost-per-dollar-volume. The first category of percent-cost liquidity proxies represents the transaction cost required to execute a small trade. The second category of cost-per-dollar-volume liquidity proxies represents the marginal transaction costs of trading an additional dollar amount of a large trade.

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international samples, which are known to suffer from data limitations (e.g., Karolyi et al., 2012). We follow prior literature and take the natural logarithm of a constant (one) plus the Amihud measure:

Where

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(1)

measures stock illiquidity for stock i on day d. |

of return in local currency,

is the dollar price, and

| is the absolute value

is the trading volume. To reduce the

or the

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impact of outliers, we discard stock-day observations if either the stock daily return, or the price, falls in the top or the bottom 1% of the cross-sectional distribution within a country. We estimate two liquidity tail indices that depict the behavior of the heavy-tailed

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distributions in illiquidity to proxy for the potential for extreme values in the Amihud at the firm level. We deploy the Extreme Value Theory (

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extreme values of a probability distribution.

), which is commonly used in modeling has been applied in various financial markets

around the world for various financial times series data, such as the tails of stock returns, price

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impact, or trading volume (e.g., Quintos, et al., 2001; Wagner, 2003; Werner and Upper, 2004).

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We adopt the Maximum Likelihood Estimation parametric approach to estimate our primary proxy of the liquidity tail index,

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using Generalized Pareto Distributions (

. According to

, tails are typically modeled

), which are right-skewed, parameterized with a

shape parameter , a scale parameter, σ, and threshold parameter, . The threshold parameter, marks the end of the distribution center and the beginning of the tail. It represents a suitably extreme quantile such that any illiquidity measures exceeding that threshold are assumed to obey

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the specified tail distribution. In our framework, the shape parameter, whereby threshold exceedances would occur when

captures

,

> .

Following Balkema and De Haan (1974) and Pickands (1975), the probability density with shape parameter

, can be described as follows. For notational

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function for the

convenience, the subscripts are not shown.

for

<

, when

for

<

<

, when

.

.

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and for

)

(3)

= 0, the

is equivalent to the exponential distribution. If

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and

(

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( )

If

(2)

, the density function becomes:

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For

, or

)

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( )(

, the

is equivalent to the Pareto distribution with a scale parameter equal to

and and a

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shape parameter equal to . For consistency with the annual frequency of

estimations, we estimate the liquidity

tail index at a yearly basis. To ensure a reliable estimation of

and

which requires a large

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number of threshold exceedances, we set measure.7 The

at the 95th percentile of a three-year window of the

is updated by rolling the

window forward on an annual basis.

The estimated tail index, , is therefore interpreted to indicate the potential for exceedances over the liquidity threshold that is determined by the stock’s own

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years.

distribution in the prior three

In addition to

, we estimate a second proxy for the potential for extreme

realizations in the Amihud measure. Castillo and Daoudi (2009) show that the parametric may not exist in small samples. Alternatively, the liquidity tail index

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estimator based on

can be estimated non-parametrically according to the approach originally proposed by Hill (1975), commonly referred to as the Hill estimator.8 As another measure of the liquidity tail index, the Hill estimator,

. An advantage of the Hill estimator over the estimation methods

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extreme observations in

, serves as an alternative proxy for the potential of realizing

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that are based on the generalized extreme value distribution is that it can be estimated without requiring exact asymptotic limit conditions. Its drawback, however, is that it assumes that the

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scale parameter, , is equal to 1. Hence the Hill estimator may under- or over- estimate the tail index for all distributions where

to unity, but rather models its estimation endogenously.

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constrain

is not equal to 1. As such, the parametric approach does not

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The estimation of upper “tail threshold”

is as follows. Conditional upon exceeding some extreme

, we assume that

obeys the tail probability distribution, described

below in Equation (4). As discussed earlier, the threshold parameter

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defines the beginning of

Our results continue to hold when we use a 1-year window. Tsay (2009) provides a comprehensive review of the different empirical estimation methods of the parameters of the extreme value distribution.

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the tail distribution, which we set at the 95th percentile of the stock illiquidity over a 3-year rolling window. For every stock, we estimate the liquidity tail by applying Hill’s (1975) power law estimator, which takes the form: ∑

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Where

(4)

is the Hill estimator for liquidity tails in year y;

liquidity measure that falls above the extreme value threshold

is the

during period t; and

is the

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total number of such exceedances within period t. It is important to note that the extreme value approach constructs Hill’s measure using only those observations that exceed the tail threshold (observations such that

/

, referred to as “ -exceedances”) and discards non-

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exceedances.

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2.1.3. Additional liquidity proxies

As mentioned earlier, the high correlation between Amihud measure and the price impact

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dimension of liquidity is a major reason behind its wide application in liquidity studies. The low-

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frequency Amihud measure that can be calculated from daily data as the absolute percentage returns per dollar volume is often used in international settings. However, the estimation of the

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Amihud measure can be burdened with challenges because it requires positive trading volume data. This problem is more serious for stocks that experience days with no trading activity or days with trading activity but with very low trading volume. Additionally, volume data may suffer from trend issues and outliers, which are likely to be more abundant in some emerging markets that are included in our sample.

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In our set of additional liquidity proxies, we resort to the category of percent-cost liquidity proxies described by Fong et al. (2017), as they do not suffer from the measurement shortcomings of the Amihud (2002) measure. Evaluating ten liquidity proxies, Fong et al. (2017) find that the Closing Percent Quoted Spread is the best monthly percent-cost measure, when

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available. In the event the Closing Percent Quoted Spread is not adequately available, the authors recommend using the second best proxies, either the High-Low or the

measures. Based on

these findings, we investigate the relation between implied cost of equity capital and extreme illiquidity based on the Closing Percent Quoted Spread (

), the High-low (

), and the

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liquidity proxies. By considering these proxies as alternatives to Amihud, we do not only avoid the volume-related issues that are inherent to the measurement of Amihud, but also complement our results by providing evidence on extreme liquidity that is based on spreads

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rather than the price impact dimension of liquidity.

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Chung and Zhang (2014) define the percent-cost liquidity proxy,

, as the difference

between the daily Ask price and the daily Bid price divided by the mean of the Ask and Bid is more closely linked with the intraday-

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prices. The authors report that the low-frequency

based spreads in a cross-sectional setting than any other low-frequency measure. Our second liquidity proxy, proposed by Corwin and Schultz (2012), is a simple bid-ask

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percent-cost

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spread estimator defined from the daily high and low prices. This bid-ask spread estimator is a function of high-low ratios over one-day and two-day intervals. The authors show that the liquidity proxy is highly correlated with intraday-based spreads. Finally, Fong et al. (2017) develop the

liquidity proxy as a simplified version of another percent-cost liquidity proxy,

known as the LOT mixed measure. Originally advanced by Lesmond et al. (1999), the LOT measure is built on the idea that transactions costs cause distortions in stock returns. However,

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one disadvantage that is associated with LOT is that it is difficult to estimate given its level of complexity and non-analytic nature. By making certain assumptions about the LOT model, Fong et al. (2017) are able to construct a simpler liquidity proxy, the

liquidity proxy, while still

retaining the core element of the LOT mixed measure.9 In essence, the

liquidity proxy is

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built on the proportion of zero returns within a timeframe and the standard deviation of daily stock returns.

We estimate the three additional liquidity proxies by following the methodology outlined

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by Fong et al. (2017). Corresponding to every measure, we adopt the same methodology described in the previous section for Amihud and create two proxies of extreme illiquidity by calculating two liquidity tail indices, the parametric Maximum Likelihood estimator and the nonparametric Hill estimator. A total of six new liquidity tail indices are created. We refer to the

,

, and

are referred to as

, and

, respectively. In the same order, the three ,

, and

liquidity proxies as extreme measures

.

Control Variables

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2.2.

,

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measures that are estimated based on the

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three

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2.2.1. Liquidity level and risks

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An extensive body of research documents that liquidity level and risk are components of the firm cost of equity (e.g., Pastor and Stambaugh, 2003; Acharya and Pederson, 2005; Liu, 2006; Watanabe and Watanabe, 2008; and Korajczyk and Sadka, 2008). Motivated by these

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Fong et al. (2017) remark that in comparison to LOT, the analytic nature of the FHT measure makes it 1000 faster to estimate, using one line of the SAS code. 16

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studies we control for both liquidity level and risk in all regressions that investigate the relationship between extreme illiquidity and the cost of equity. We measure stock illiquidity as the innovations in

after we run first-order auto-

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regressive filtering regressions that control for day-of-the-week effects in liquidity (Hameed et al. 2010, Karolyi et al. 2012). For every stock , on a day , in a month following regression:

where

(

denotes day-of-the-week dummies. The error term

innovations in liquidity.

is the

, the vector of control variables includes liquidity risk measures. Acharya

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Besides

(5)

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∑

, we estimate the

and Pederson (2005) develop the Liquidity-Adjusted Capital Asset Pricing Model, (LCAPM)

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that integrates the different channels through which liquidity risks may affect expected returns. The LCAPM provides a theoretical justification for three conditional liquidity covariance risks

, the firm-level returns and the market liquidity,

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liquidity,

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which are determined by the co-movements between: the firm-level liquidity and the market

and the firm-level liquidity and the market returns,

. Moreover, Acharya and , defined as the

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Pedersen (2005) propose an additional liquidity covariance risk,

,

summation of the three liquidity covariances: (6)

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The daily time-series of the firm-level returns and liquidity as well as the time-series of the market-wide returns and liquidity are utilized to estimate the conditional covariances: , and

, and the daily market liquidity, of firm-level returns,

. To obtain the daily market return,

, in a market,

, and firm-level liquidity,

, we take the equally-weighted average , respectively.10 Each market portfolio,

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,

, includes all individual stocks listed in a country. In our calculations of

and

, we

require at least 10 daily observations for the market average to be considered a valid observation.

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To estimate the time-varying liquidity conditional covariances between the stock liquidity and returns with market liquidity and returns, we rely on the dynamic conditional correlation and the generalized autoregressive conditional heteroskedasticity, DCC-GARCH(1,1), model.

and negatively correlated with

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We expect the implied cost of capital to be positively correlated with and

. In other words, the implied

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cost of capital is predicted to increase (i) in the co-movement between firm-level liquidity and market liquidity, and decrease (ii) in the co-movement between firm-level returns and market

PT

liquidity and also decrease (iii) in the co-movement between firm-level liquidity and market returns.11 Intuitively, investors require higher expected returns (cost of equity) for holding stocks

CE

that become illiquid when the market is illiquid (the risk of commonality in liquidity). However,

AC

investors are willing to accept lower expected returns for stocks that have higher returns when the market is illiquid or for stocks that become less illiquid when market returns are down.

10

We rely on equal-weighted average because it is more representative of the market than the value-weighted average that is biased towards large stocks (Acharya and Pederson, 2005). 11 For example, see Brockman et al. (2009); Karolyi et al. (2012) for the commonality, and Pastor and Stambaugh (2003); Liu (2006); Korajczyk and Sadka (2008); Lou and Sadka (2011) for the co-movement between firm-level returns and market liquidity. 18

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2.2.2. Other firm- and country- level control variables Based on prior research on the determinants of firm cost of equity capital (e.g., Fama and French, 1992; Hail and Leuz, 2006; Chen et al., 2011), we control for supplementary firm-level and the three DCC-conditional liquidity risk measures. These factors are

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factors, other than

the market risk (BETA), estimated as the covariance between stock returns and the market return relative to the variance of market returns; financial leverage (LEVERAGE), measured by the ratio of total debt to the market value of equity; Book-to-Market Ratio (BTM), measured as the ratio

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of book value of equity to market value of equity; and firm size (SIZE), measured by the natural logarithm of total assets. We expect the implied cost of capital to be negatively related to SIZE (Fama and French, 1992) and positively related to BETA (Sharpe, 1964; Lintner, 1965),

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LEVERAGE (Fama and French, 1992), and BTM (Fama and French, 1992). In addition to the firm-level determinants of the implied cost of equity capital, we

ED

account for the potential impact of country-level factors. Guided by prior research (e.g., Hail and Leuz, 2006; Wurgler, 2000; Chen et al., 2011), we control for economic development, (LNGDP),

PT

inflation (INFL), and financial development (FD). LNGDP is calculated as the logarithm of a

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country’s GDP per Capita, INFL as the annualized yearly median of a country-specific one-yearahead realized monthly inflation rate, and FD as the sum of market capitalization and private

AC

credit relative to GDP.

We also control for industry affiliation using Campbell (1996) 12-industry classification.

Further, in all our specifications we include year and country dummy variables to account for the potential impact of time (business cycles) and country-fixed effects, respectively, on the cost of equity capital. Appendix B provides a description of all variables used in this study as well as their sources. 19

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2.2.3. Descriptive statistics Table 1 presents country-by-country mean values of for the four measures of liquidity ( and

,

, and

) as well as their tail indices

). The Table shows large variations in the average cost of capital across countries,

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(

,

. It also reports similar statistics

with a minimum

observed in China (5.56%) and a maximum recorded in India (18.64%).

Column (2) of Table 1 reports mean values of a stock’s level of illiquidity based on the Amihud measure. It shows that average stock illiquidity is highest in Singapore and lowest in Japan and

the

,

and the

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South Korea. In the following three columns, we find that the cross-sectional global averages for liquidity measures are equal to 0.0133, 0.0063, and 0.0085,

respectively. Overall, the distributions of the country averages for the different liquidity proxies seem to suggest that regardless of the adopted liquidity measure, there is a great deal of variation

ED

Further, Table 1 shows that

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in average stock illiquidity across countries.

varies from a minimum of -0.007 in the U.S. to a

maximum of 0.005 in Pakistan. This indicates that, on average, stocks that trade in the U.S. are

PT

least likely to experience extreme illiquidity costs, while stocks in Pakistan are the most

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vulnerable to liquidity crises. One can notice that, regardless of the used liquidity measure, most of the countries have average negative values of

, implying that in these countries, the

AC

liquidity of the average stock has a thin-tailed distribution (negative tail index) rather than a heavy-tailed distribution (positive tail index). This result is not surprising as we report the average of

across stocks and over time. We witness similar variations in extreme illiquidity

costs for stocks from different countries when the liquidity tail index is measured by

.

Based on the Amihud measure, we find that stocks from the U.S. have the least likelihood to

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realize extreme illiquidity (minimum at 0.0038), whereas stocks from Pakistan rank at the other end of the spectrum (maximum at 0.0112). Remarkably, the same country ranking was reached based on

.

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The last column reports the number of firm-year observations per country. The total number of observations is 93,396 and varies across countries. The largest number of observations is recorded for the U.S. (20,766), followed by Japan (16,404), corresponding to around 22% and 18% of our sample set. On the other end, some countries have very small data

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coverage. For example, there are only 34 firm-year observations for India.

Panel A of Table 2 reports full-sample summary statistics for the variables used in our regression analyses. A sample firm has mean

of 7.40% (median: 5.32%), and a mean

M

systematic risk measure, BETA of 0.975. The mean debt ratio, LEVERAGE, is 31.04% and the mean Book-to-Market Ratio, BTM, is 1.01.12 The average logarithm of total assets is 13.78. An

ED

average firm has a positive covariance between its liquidity and market liquidity, a negative covariance between its returns and market liquidity, and also a negative covariance between its

PT

liquidity and market returns.

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Panel B of Table 2 presents the correlation coefficients among the variables used in our main analysis. Consistent with our expectations, Panel B shows that

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significantly correlated with

is positively and

. Importantly, the reported low correlation between

and

suggests that these two measures are capturing different aspects of stock liquidity. Further,

most of the control variables are correlated with

12

consistent with theoretical literature and

Note that we scaled BTM by dividing it by 100. The following variables: FD, FBIAS, LTG, and LTICPQS are also scaled in the same way. 21

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prior empirical literature findings. The correlation coefficients among the control variables are generally low, comforting us that multi-collinearity is not a major concern for our empirical analyses.

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3. Empirical Results In this section, we report our empirical results on the relation between extreme illiquidity measures and the implied cost of capital. In subsection 3.1, we present our evidence of the impact of extreme illiquidity on the cost of capital using the Amihud proxy. In subsection 3.2,

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we report our analysis wherein we disentangle idiosyncratic extreme illiquidity from marketwide extreme illiquidity. In subsection 3.3, we report evidence on the extreme illiquidity-cost of capital relation using alternative liquidity proxies. In subsection 3.4, we present robustness tests.

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In subsection 3.5, we report results related to the potential influence of market conditions and the effect of country-level institutional quality. Main evidence

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3.1.

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Our primary conjecture in this paper is that stocks with a greater likelihood for their liquidity to spiral down below a certain level suffer a higher cost of equity capital. We examine

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the relation between stock extreme illiquidity and the implied cost of capital by estimating , is

AC

various specifications of the following regression model where the dependent variable,

regressed on a liquidity tail index that is based on the Amihud measure and various firm- and country-level controls. For notational convenience, the subscripts are not shown. (7)

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In the above model,

stands for liquidity tail index and is the main proxy of the

potential for stock illiquidity to realize extreme values in the Amihud liquidity proxy. refers to the set of firm- (

,

,

,

,

,

SIZE, BETA, LEVERAGE, and BTM) and country-level (LNGDP, INFL, and FD) control

our regressions are estimated with robust standard errors.

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variables described earlier. FE is the set of country, industry, and annual dummy variables. All

The results of our estimations of the impact of the liquidity tail index,

, on the

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implied cost of capital are presented in Table 3, columns (1)-(4). To avoid potential multicolinearity concerns, we test the effect of

on

while separately introducing each

of the three liquidity risk covariances and their aggregate liquidity risk factor in regression models (1)-(4). Column (1) shows that in line with our expectations,

is positive and

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significant at the 1% level, which suggests that stocks with greater potential for extreme

ED

realizations in illiquidity costs bear higher cost of capital.13 Our evidence is in favor of the conjecture that investors require an illiquidity risk premium for a stock’s susceptibility to a on

is not only statistically significant, but also

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liquidity dry-up. The effect of

economically meaningful; our estimation in column (4) shows that a standard deviation (0.0049) translates into a 30 basis points (0.616

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increase in

0.005 = 0.0030184) increase in the

AC

implied cost of capital, ceteris paribus. Interestingly, we find that the impact on the cost of capital is higher for

(30 basis points) than for

(21 basis points).14

13

We test the sensitivity of this finding to the choice of the selection parameter . We reach similar conclusions when is set at the 90th and the 97th percentiles. 14 Estimated as a one standard deviation in AMH (0.0005) multiplied by the estimated coefficient on AMH in column 4 (4.332).

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Our findings across columns (1) to (4) are consistent with prior research (e.g., Acharya and Pedersen, 2005) and indicate that liquidity level and covariance risks are significant determinants of the costs of capital. Our results suggest that a stock’s potential to suffer severe liquidity crashes is a significant determinant of the cost of capital over-and-above the influence

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of the traditional liquidity covariance risks in stock pricing. Moreover, the coefficient estimates on our firm-level control variables are consistent with our predictions. In particular, a firm’s cost of equity capital increases in market risk, the book-to-market ratio, and financial leverage while it decreases in firm size, as BETA, BTM, and LEVERAGE have positive and significant

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coefficient estimates and SIZE has a negative and significant coefficient estimate. In regards to the country-level controls, we find that only INF is positively and significantly associated with .15 Overall, our results show that a stock’s potential to exceed a certain illiquidity threshold

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is a significant liquidity risk for which investors require an additional equity premium.

ED

Columns (5)–(8) show that using

, as an alternative measure of stock extreme

illiquidity, confirms our conclusions regarding the influence of liquidity tail index on the implied has a positive and significant coefficient

PT

cost of capital. Particularly, we find that

estimate at the 1% level across all four specifications. The impact of the Hill estimator on the

CE

cost of capital is also meaningful. Based on the estimated coefficients in column (8), a one (0.0026) results in an increase of around 50 basis points

AC

standard deviation increase in (0.0026

1.920 = 0.004992) in the cost of capital. We note that the sign and statistical

significance of all the control variables, including the liquidity variables, do not change. In

15

Since all control variables are related to local risks, we follow Amihud et al. (2015) and control for a global risk factor, which we define as the Morgan Stanley Capital International (MSCI) global equity index in excess of US one-month Treasury bill rate. The unreported estimated results show that our findings do not change. 24

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summary, our findings indicate that firms with higher potential of realizing extreme illiquidity costs bear more expensive equity costs even after accounting for factors that vary across firms or countries and are known to determine the cost of equity. Idiosyncratic extreme illiquidity

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3.2.

In this subsection, we address the concern that the reported relation between the implied cost of capital and our measures of extreme illiquidity potentially reflect the impact of systematic extreme liquidity risk, which we do not control for. Though the variability in stock liquidity

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could be related to the individual firm-level events such as stock splits (e.g., Lin et al., 2009) or ownership structure and level of information asymmetry (Attig et al., 2006), extreme events of stock illiquidity could also result from liquidity crises at the market level (Brunnermeier and

M

Pedersen, 2009). Hence, a liquidity crisis at the individual stock level (idiosyncratic) can be triggered by a simultaneous liquidity crisis at the market level (systematic). Wu (2016) shows

ED

that rare events of a dry-up in market liquidity significantly influence investors’ expected returns. Therefore, the liquidity tail index,

, which we interpret as the potential for extreme

PT

realizations in liquidity costs due to idiosyncratic reasons could be influenced by market-wide

CE

dry ups in liquidity. Since the empirical methodology employed in equation (7) does not allow for disentangling these two effects, it may not be clear whether the documented

AC

relation in Table 3 is due to a severe shock in individual stock liquidity or in market liquidity. To mitigate this concern, we attempt to discern the idiosyncratic portion of extreme

realizations in stock illiquidity. We start with a careful estimation of the extreme liquidity risk as described in Wu (2016). By including all stocks that trade in a specific market, we construct the yearly extreme liquidity risk from the daily Amihud data. We estimate a unique measure of the

25

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extreme liquidity risk for every market based on the parametric Maximum Likelihood estimator (

) and an alternative measure based on the nonparametric Hill estimator (

). We

then follow a two-step regression model. In the first step, we create the orthogonal variants of by collecting the respective residuals that result from regressing

on

. In

(4), after replacing we introduce

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the second step, we re-estimate the regression models initially presented in Table 3, models (1)by its respective residuals estimated in the first step. We ensure that as an additional variable to control for the extreme systematic changes in

market liquidity. The estimation results reported in Table 4, columns (1)-(4), show that, loads positive and is statistically significant. Moreover, in

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consistent with Wu (2016),

support of our conjecture, we find that investors require a premium for idiosyncratic extreme fluctuations in the illiquidity levels as the estimated coefficients on the residuals are found to be

M

positive and significant. This result suggests that investors account for the idiosyncratic extreme

ED

illiquidity risk beyond the effect of a systematic risk in the market extreme liquidity. We conduct a comparable analysis as in columns (1)-(4) using the Hill estimator of

residuals of

PT

extreme illiquidity and report the results in columns (5)-(8). The estimated coefficients on the are significant with the correct sign, even in the presence of

.

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Overall, our findings indicate that the idiosyncratic portion of extreme illiquidity risk is

AC

significantly associated with the cost of equity capital. 3.3.

Evidence based on alternative liquidity proxies

We are cautious before drawing final conclusions about the relation between extreme illiquidity and the cost of equity. An accurate measurement of the liquidity proxy is essential for the careful detection of extreme illiquidity realizations that lie beyond a certain threshold. Given

26

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the potential shortcomings in measuring Amihud, discussed in subsection 2.1.3, we supplement our analyses with additional evidence that is based on alternative liquidity proxies.16 We repeat the analysis presented in Table 3 for a set of newly estimated liquidity tail

model for each liquidity measure (

,

, and

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indices using additional liquidity proxies. Table 5 reports the results of estimating a regression ) on its respective

(or

)

measure. For the sake of brevity, we show the regression output only using the liquidity aggregate risk factor,

are found to be positive and statistically significant. The potential for

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and

. As evidenced in columns (1) and (3), the estimated coefficients on

extreme realizations in illiquidity costs measured by the

or the

liquidity proxies are

significantly related to the implied cost of equity. However, a change in the constructed by the

that is

liquidity proxy has no material impact on the implied cost of equity

M

(column 5). We further notice that the estimated coefficients on the levels of all liquidity proxies

ED

have the expected sign and significance.

Columns (2), (4), and (6) show the results for the Hill estimator. We report a significant

estimator. This relation is found to be consistent across all alternative liquidity proxies.

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the

PT

relation between the implied cost of equity capital and the liquidity tail indices that are based on

The evidence that the relation between the implied cost of equity capital and tail indices

AC

in the distributions of cost-percent liquidity measures complements our earlier findings using the Amihud measure that are documented in Table 3. The results suggest that under severe liquidity crises, investors worry about the potential for extreme illiquidity costs not only as measured by

16

We thank an anonymous referee for raising this point.

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the price impact but also by the spread dimension of liquidity. Finally, the significant findings in Table 5 for the added liquidity proxies alleviate some of the concerns about the ability of the Amihud measure to accurately estimate illiquidity costs under some circumstances for a broad

3.4.

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range of stocks in international markets. This issue is further addressed in the robustness section. Robustness checks

We subject our main finding that extreme illiquidity determines the cost of equity to a wide range of robustness tests. In subsection 3.4.1, we conduct a subsample analysis by

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reevaluating our finding in revised samples that comprise either subsets of countries or subsets of stocks. In subsection 3.4.2, we check for the limitations in the implied cost of equity measure. In subsection 3.4.3, we test whether the documented relation holds for alternative proxies that

ED

3.4.1. Revised sample

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measure extreme illiquidity. Our main findings survive all these tests.

The measurement of the Amihud proxy may be plagued by issues in the volume data for

PT

some stocks in international markets. These issues are likely to be more critical in the less developed financial markets where many stocks may not trade for extended periods of time. This

CE

may cast doubts on inferences, which are based on our evidence that relies on detecting extreme

AC

realizations in the Amihud measure. Although the results in Table 5 show that the relation between the implied cost of equity capital and extreme realizations in illiquidity largely holds irrespective of how liquidity is measured, we continue to address this concern by conducting a revised sample analysis. Rather than relying on alternative proxies to the Amihud measure, we limit our sample to a subset of countries or stocks for which the Amihud measure can be reliably estimated. 28

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In columns (1)-(4) of Panel A in Table 6, we report the results using four different subsamples that include subsets of countries. First, we take advantage of the fact that stocks that trade in the U.S. financial markets are among the most liquid in the world and therefore the least likely to suffer from any of the shortcomings of the Amihud proxy. Accordingly, we estimate the

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regression models for stocks that trade in the New York Stock Exchange. The reported results in column (1) show that our basic findings do not change. Second, since estimating the Amihud measure is likely to be a bigger concern in emerging markets, we repeat the analysis for stocks in developed markets only. We follow the classification that is recommended by the International

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Financial Corporation (IFC) of the World Bank Group and consider 21 countries in our sample as developed (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Singapore, Spain, Sweden,

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Switzerland, the U.K, and the U.S.). Column (2) shows that the results still hold. Third, we revise the sample by excluding 10 countries with the least active financial markets based on the

ED

yearly average of the total dollar volume of all stocks within a market. The excluded countries are: Argentina, Morocco, New Zealand, Philippines, Egypt, Hungary, Austria, Pakistan, Ireland,

PT

and Israel. We repeat the analysis and report the results in Column (3). Fourth, we exclude from

CE

the sample 10 countries with the smallest financial markets based on the yearly average of the market capitalization in US dollars. The countries that we eliminate are: Sri Lanka, Hungary,

AC

Pakistan, Argentina, Egypt, Morocco, Austria, Portugal, Turkey, and New Zealand. The regression estimation for the revised sample is reported in column (4). The results in columns (3) and (4) show positive and significant associations between

and

and indicate that the

documented relation is not affected.

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One concern with focusing on a subset of countries, as done in columns (1)-(4), is that it indiscriminately eliminates all stocks that trade in the excluded markets, including the group of stocks that are highly traded and whose liquidity can still be accurately assessed. Moreover, limiting the sample to a subset of developed markets does not ensure that every stock in the

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newly formed subsample has a reliable Amihud measure. In the following two tests, we provide a more comprehensive investigation by reporting results for subsamples that are created by selecting individual stocks across the different international markets. Fifth, we conduct a univariate analysis on the dollar volume for individual stock data and we remove firms that fall

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in the bottom 10 percentile of the distribution of volume for the entire sample of stocks. We present the estimation results for the revised subsample that excludes firms with the least traded activity in column (5). Sixth, we follow Amihud et al. (2015) and discard microcap stocks that

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are known to be extremely illiquid. We define microcap stocks as the smallest 10 percent of stocks in terms of market capitalization. We repeat the analysis and show the results in column

ED

(6). The reported evidence in columns (5) and (6) shows that our earlier documented findings

PT

remain intact.

Overall, the results in panel A indicate that the relation between implied cost of capital and

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the potential for stocks to exceed extreme illiquidity costs as measured by Amihud liquidity proxy exists in a wide range of subsamples. This helps attenuate any concerns in regards to the

AC

issues in measuring the Amihud liquidity proxy. 3.4.2. Limitations of the implied cost of equity capital We inspect whether our results are affected by the limitations of the implied cost of equity estimations. First, recall that we calculate

as the arithmetic average of the four

30

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implied of cost of equity measures (

,

,

,

).17 We check if our findings continue to

hold for the individual cost of equity measures by re-estimating the regressions with similar specification to the model presented in column (4) of Table 3, but after replacing the dependent variable

with each of the four alternative measures. Alleviating this issue, the reported

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results in columns (1)-(4) of Panel B in Table 6 show a significant coefficient estimate for across all cost of equity models. Second, we replace the average of the four individual measures of the implied cost of equity with the principal component and we re-estimate the

concern that and

and

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regression. The reported results in column (5) confirm our earlier findings. Third, we address the are sensitive to the choice of the long-term growth. The estimations of

require the assumption of a long-term growth rate, which in this study we calculate

as the yearly one-year-ahead realized inflation rate that we consider at 3%. On the other hand, and

do not rely on any long-term growth rate. We note

M

the models used to calculate

that casual observation of the reported results for and

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consistent results with those for

and

in columns (1) and (2). However, to formally

PT

address this concern, we compute a principal component for principal component for

and

in columns (3) and (4) shows

and

only and another

. We then repeat the regression estimations for each of the

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two principal components and report the results in columns (6) and (7), respectively. In other words, instead of conducting a unique principal component estimation for all cost of equity

AC

measures as we did in column (5), we split the analysis by the identity of the cost of equity model (columns 6 and 7). The reported results lead to the same conclusion.

17

In unreported statistics we find that the means for the cost of equity measures and (13.73%, and 13.28%) are higher than (11.06% and 7.58%) and that the correlations of and with (0.889 and 0.882) are higher than those of and with and 0.822). These statistics are consistent with Dhaliwal et al. (2006).

and (0.509

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Fourth, the implied cost of equity can be criticized for its accuracy in relation to the overoptimism of analyst forecasts that is an input in the computation of the

(e.g., Kothari, 2001).

To account for the noise in analyst forecasts, we introduce four control factors, each in a separate regression. Our first control variable (FBIAS) is defined as the difference between the one-year-

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ahead forecasted and realized earnings. The second variable (LTG) is the firm’s long-term growth that is based on I/B/E/S five-year consensus earnings growth rate. It controls for potential biases in analyst forecasts due to their tendency to be overly optimistic. The third control variable (DISPERSION) measures the degree of disagreement in the analyst forecasts. The fourth

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control variable (ANALYSTCOV) is the number of analysts actively providing forecasts and captures the availability of information and likely its precision. The reported results in columns (8)-(11) show that introducing these control variables does not change the main finding of our remain positive and strongly significant. In summary,

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study; the estimated coefficients for

the reported evidence on the relation between the implied cost of capital and the liquidity tail

PT

ED

index is not affected by the limitations of the implied cost of capital model measures.

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3.4.3. Alternative measures of extreme illiquidity Another measure of extreme illiquidity relates to the concept of liquidity-black holes

AC

according to which, under some circumstances, stock liquidity entirely dissipates and spirals down to a complete dry-up (Morris and Shin, 2004). We construct the liquidity black-hole measure (

) as a third proxy to detect stock extreme illiquidity occurrences relative to the

market liquidity. Illiquidity exceedances are identified over a threshold that is determined by the cross-section of all individual stock liquidity measures in the market. We follow Lang and

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Maffett (2011) and set the threshold at

times the market liquidity average. Specifically, for

every stock , on a specific day, in a market the value of 1 if

is defined as a dummy variable that takes

; and 0 otherwise. It is an indicator of when the stock is

times more expensive to transact than an average stock in the market. When averaged

over a specific time interval,

measures the frequency of extreme illiquidity incidences

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at least

,

within that time period. Since the threshold level, , is not based on theory, we create 4 extra threshold levels that monotonically increase in the degree of detecting extreme observations in

starting at the case for

times to and

to its normal level is amplified by a factor of 10,

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. Specifically, the multiple of

times. Although the

measure is not theoretically justified, as it is

, all three measures share the intuition of a threshold-based extreme

liquidity event. An important distinction however is that while

and

defines the

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exceedances with reference to a stock’s own historical liquidity distribution,

define

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threshold after pooling the cross-sectional average of all stock liquidities within a market.18 Table 7 shows that irrespective of the magnitude of , the relation with the implied cost

PT

of capital is significant for all 5

measures. Examining the coefficients, we find that the

estimated cost of equity impact of the different

measures is greater for higher threshold

CE

levels. Holding all everything else constant, our analysis reveals that the cost of equity increases

AC

with the degree of liquidity extremes. The latter result is consistent with the notion that investors require liquidity premiums for exceptionally high levels of stock illiquidity.

Gabaix et al. (2006), Kelly and Jiang (2014), and Wu (2016) set a relative threshold at the 95th percentile of the pooled distribution of the cross-section of all stocks within a market. 18

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In one last set of unreported results, we use the kurtosis in stock liquidity distribution, which is a fourth moment measure that captures the behavior of fat tails of stock liquidity as our fourth alternate proxy for extreme illiquidity. We find that the coefficient estimate on the

3.5.

Crisis period and institutional quality analysis

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kurtosis variable is positive and significant at the 1% level.

The previous section establishes a consistently positive and significant effect of the likelihood of extreme illiquidity costs on the implied cost of capital. In this section, we assess

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whether the relation between stock extreme illiquidity based on the Amihud measure and the cost of capital, documented in Table 3, varies with market conditions. Our conjecture is that the impact of extreme liquidity events on the cost of equity is more pronounced in crisis periods.

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While investors’ concern about the potential for a stock’s liquidity to dry-up is continuous, it can be even more acute in periods of market turmoil. This is justified by the fact that stock liquidity

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behaves differently in normal periods versus crisis periods when markets are characterized by low returns or high volatility. Early empirical research has documented this asymmetric behavior

PT

of stock liquidity.19 Stocks’ potential to fall into extreme liquidity states can thus increase during

CE

market turmoil, which may affect investors’ expected returns. To distinguish crisis periods in market returns and volatility, we create two dummy variables, (

. The

) takes on one when the country’s stock market returns

AC

dummy variable

and

19

For instance, Pastor and Stambaugh (2003) report a much higher correlation between stock liquidity and market returns (0.5) in negative-return months compared to positive-return months (near zero). Recent theoretical research also suggests that sudden liquidity dry-ups occur more during market downturns and increased volatility. The theoretical model of Brunnermeier and Pederson (2009) predicts that financial market turmoil tightens funding constraints of traders and thereby lowers their ability to provide liquidity. When markets decline, traders suffer losses on securities they use as collateral or face greater margins, which leads them to provide less liquidity and liquidate their positions in many securities. This reduced market liquidity leads to more losses and higher margins, creating an “illiquidity spiral” that further lowers traders’ ability to provide liquidity. The theories in Gromb and Vayanos (2002) and Kyle and Xiong (2001) also suggest that an increased volatility tightens traders’ funding constraints, which restrict their capacity to provide liquidity. A common theme among these studies is that liquidity tends to evaporate in times of high volatility or declines in financial markets. 34

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(volatility) drops below (exceeds) its 3-year historical moving average by more than one standard deviation; and zero otherwise. We also create two interaction variables: , which are the result of the multiplication of

and

, respectively. We estimate the following regression controls. For

notational convenience, the subscripts are not shown.

is either

or

by

(8)

. The results of the estimations

AN US

Whereby

CR IP T

and

are reported in Table 8. Regression models reported in columns (1)-(2) of Table 8 provide consistent evidence that

has a greater effect on the cost of equity when markets are

down. Specifically, in column (1) not only

, appears with a positive and highly

M

but also the interaction variable,

loads positive and significant at the 1% level,

significant coefficient estimate. This finding shows that the concern about the potential for a

ED

stock’s liquidity to dry-up is more pronounced in periods of down markets. Investors require

PT

extreme stock-level illiquidity premium for holding stocks that are vulnerable to sudden liquidity crashes and this premium increases in market downturns. This translates into a greater cost of

CE

capital for firms in periods of market downturns. Turning to market volatility as our second consideration of crisis periods, column (2) lends further support to the market downturn results.

AC

We report a stronger relation between the liquidity tail index and the implied cost of equity during periods of increased volatility, as evidenced by the significant coefficient estimates on the interaction variable,

. In terms of control variables, the signs and significance

are generally the same as previously reported. Overall, our estimations point out that market

35

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conditions shape the way investors consider extreme liquidity events that become a bigger concern during periods of market turmoil. Finally, we study the effect of the varying institutional environments across our sample countries on the strength of the relation between extreme liquidity events and the implied cost of

CR IP T

capital. A country’s institutional quality may have an effect on the strength of the relation between a firm’s extreme illiquidity events and its cost of capital. A growing body of literature links information quality and investor protection, as country-level institutional qualities, to stock liquidity level and risk. Countries that emphasize greater transparency and disclosure by firms

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mitigate information asymmetry and reduce investors’ uncertainty about the intrinsic value of stocks, which potentially leads to higher liquidity level and lower liquidity risk. 20 Legal protection of investors can also affect liquidity through its impact on information quality and

M

investor participation. We focus on two institutional traits, particularly: investor protection and information quality. We expect stronger investor protection and better information quality to

ED

mitigate the impact of the likelihood of stock extreme illiquidity occurrences on the cost of

PT

equity.

To test this proposition, we use a set of three institutional variables (disclosure intensity,

CE

media penetration, and opacity) to capture a country’s information quality and similarly another set of three variables (anti-self dealing, rule of law, and investor protection) for investor

AC

protection. Created by The Center for International Financial Analysis and Research (CIFAR),

20

Consistent with this argument, Eleswarapu and Venkataraman (2006) report evidence that stocks from countries with better accounting standards enjoy lower liquidity costs. As for liquidity risks, Dang et al. (2015) report evidence of higher commonality in liquidity in countries with more information opacity. Likewise, Empirical evidence suggests that stronger investor protection lowers a stock’s cost of liquidity (Eleswarapu and Venkataraman, 2006) and that liquidity commonality is, on average, higher in countries with poor investor protection (Karolyi et al., 2012; Dang et al., 2015). 36

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the disclosure intensity index measures the degree of financial disclosure based on accounting and non-accounting items reported in the annual reports of sample companies (Bushman et al., 2004). Media penetration, on the other hand, is a proxy for dissemination of firm-specific information as measured by the penetration of the media channels in the country (Bushman et al.,

CR IP T

2004). The media index is defined as the average rank of countries’ per capita number of newspapers and television channels reported by World Development Indicators. The third information variable is the opacity index which measures a country’s opacity in the five areas of corruption, legal system, economic policies, accounting standards, and regulatory regime.

AN US

Furthermore, to evaluate the strength of the country’s investor protection environment, we first rely on the anti-self dealing index of Djankov et al. (2008) that measures the legal protection of minority shareholders against expropriation by corporate insiders. The second investor protection

M

variable is the rule of law index. Retrieved from World Governance Indicators of the World Bank, the investor protection index reflects perceptions of the extent to which agents have

ED

confidence in and abide by the rules of society, in particular the quality of contract enforcement, property rights, police, courts, and the likelihood of crime and violence. Our last institutional

PT

variable, the investor protection index, is derived from the Doing Business report and measures

CE

the degree of legal protection a country provides to minority shareholders. With the exception of the opacity index, higher values in the country-level variables represent a better institutional

AC

environment.

For each of the country variables, disclosure intensity, media penetration, opacity, anti-

self dealing, rule of law, and investor protection, we create the following dummies: ,

, and

. With the exception of

,

, all dummy variables take

on one if the country scores above- and a zero if below- the median value. For ease of

37

ACCEPTED MANUSCRIPT

interpretation, the dummy variable

is defined in the opposite direction so that all dummy

variables are equal to one in a country with stronger institutions. The interaction terms: , and

,

,

,

,

are then determined by the multiplication of the liquidity tail index with

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each of the dummy variables.

To assess the impact of the country’s institutional variables on the relation, we regress

, an institutional dummy variable, the interaction variable

and the respective dummy variable, and our set of controls. The results are

AN US

between

on

reported in Table 8 columns (3)-(8). We find that

loads positive and highly significant

across the six columns of Table 8. Moreover, column (3) shows that the coefficient estimate on is negative and significant at the 1% level and the coefficient estimate on the interaction , is negative and significant at the 5% level, implying that a better

M

variable,

ED

reporting environment not only reduces firms’ cost of capital but also lowers the impact of liquidity tail risk on the cost of capital. Likewise, column (4) reports a negative and significant and

. This finding

PT

coefficient estimate on the interaction variable between

suggests that environments of better information dissemination through media channels lower

CE

the influence of liquidity tail index on firms’ cost of capital. Similar results are reported for the

AC

opacity index in column (5). Columns (6)-(8) show the results of estimations where we account for the potential

influence of the legal protection of investors. In column (6), we find that the interaction term between

and

loads negative and significant at the 5% level, revealing that the

positive effect of liquidity tail index on firm cost of capital is mitigated in environments where

38

ACCEPTED MANUSCRIPT

minority shareholders enjoy a stronger protection against insiders’ self-dealing. Further, column (7) suggests that the impact of liquidity tail index on the cost of capital is lower in environments where the rule of law prevails; the coefficient estimate on the interaction term, is negative and significant at the 1% level. Finally, column (8) reports a negative and , which points out that

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significant coefficient estimate on the interaction term,

better investor protection attenuates the effect of liquidity tail index on the implied cost of capital. Taken together, results reported in Table 8 indicate that while liquidity tail index increases a firm’s cost of capital, the magnitude of this increase is lowered by better information

AN US

quality and greater legal protection of investors.

We generally find that our firm- and country-level controls continue to have similar signs and significance as reported in our initial estimations. In unreported results, we find that our

M

results continue to hold when we use any of the three alternative measures of extreme illiquidity

ED

events. In sum, a country’s institutional quality plays a significant role in the extent to which investors are concerned about stock extreme illiquidity events. Collectively, our findings point

PT

out that the relation between extreme liquidity and cost of capital is particularly weakened in

CE

countries where investors are protected and information is less opaque. 4. Conclusion

AC

This paper studies the effect of stock extreme illiquidity on the cost of equity capital. The

main question is whether investors require a compensation for bearing extreme illiquidity costs, which would translate into a higher cost of capital for firms. We focus on extreme illiquidity realizations at the individual stock level and apply Extreme Value Theory to estimate the liquidity tail index that captures the potential for a stock’s illiquidity to exceed a certain

39

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threshold. Using different liquidity measures and the cost of capital, we find that the potential for a stock’s liquidity to dry up has a positive and economically significant impact on the cost of equity capital even after controlling for other aspects of liquidity, level and risk, as well as other firm- and country-level factors. The reported cross-country evidence is robust to revised

CR IP T

subsamples of countries and stocks, different limitations in the estimation of the implied cost of equity capital, and finally to other measures for stock extreme illiquidity.

The international aspect of the study allows us to investigate the documented extreme

AN US

illiquidity impact on the cost of equity in different economic settings. We examine the influence of market conditions and institutional quality on the relation between extreme illiquidity and the cost of capital and find a stronger effect of extreme illiquidity on the cost of capital when financial markets are down and highly volatile and for stocks listed in countries where

M

information quality and investor protection is low.

ED

By shedding light on an aspect of liquidity that has received little attention in prior literature and assessing its impact on the cost of equity capital, our study contributes to several

PT

strands of the literature, such as literatures on extreme liquidity events, liquidity in international

CE

markets, and the cost of equity capital. Our findings have implications on corporate financial decisions and on public policy. The reported results suggest that a firm may enjoy cheaper cost

AC

of equity if it can maintain normal levels of trading costs and prevents liquidity from drying-up. Firm managers’ can reduce the firm’s cost of capital by adopting policies that reduce their stock’s potential to suffer extreme liquidity events. One potential measure is to improve disclosure, which is shown to enhance stock liquidity and thereby lower the cost of capital. At the policy level, countries can also contribute to the lowering of their firms’ cost of capital by upgrading their legal protection of investors and improving the quality of information as we find 40

ACCEPTED MANUSCRIPT

that these two institutional factors affect the extent to which extreme illiquidity costs affect the

AC

CE

PT

ED

M

AN US

CR IP T

cost of capital.

41

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Table 1: Descriptive statistics per country

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This table presents the means for the measure of cost of equity capital ( ), the four measures of the liquidity proxies (AMH, CPQS, HML, and FHT), and the respective parametric liquidity tail index (LTI) and the nonparametric liquidity tail index (HILL) for each liquidity proxy. The statistics are computed for each of the 45 countries in our sample over the 1985-2012 period. is the average of the four cost of equity estimates that result from different estimation models, which are described in Appendix A. AMH is the Amihud (2002) liquidity proxy, CPQS is the Closing Percent Quoted Spread by Chung and Zhang (2014), HML is the High-Low liquidity measure by Corwin and Schultz (2012), and the FHT is the liquidity proxy by Fong et al. (2017). LTI is the liquidity tail index generated by the maximum likelihood estimator of the tail index using Generalized Pareto Distributions, and HILL is the Hill (1975) estimator of liquidity tails. The last column reports the firm-year observations for each country. The definitions and data sources for all the variables used in the study are provided in Appendix B.

47

LTI LTIAMH -0.0021 -0.0023 -0.0030 -0.0039 -0.0018 -0.0024 -0.0003 -0.0065 -0.0036 0.0007 -0.0030 -0.0046 -0.0034 -0.0031 -0.0019 -0.0019 -0.0028 0.0029 0.0004 -0.0059 -0.0046 -0.0057 -0.0005 0.0008 -0.0041 -0.0031 -0.0009 -0.0021 0.0051 0.0020 -0.0033 -0.0014 -0.0011 0.0025 -0.0011 0.0002 -0.0037 -0.0041 -0.0009 -0.0037 -0.0047 -0.0001 -0.0053 -0.0012 -0.0070 -0.0040

LTICPQS -0.0112 -0.0131 -0.0125 -0.0127 -0.0108 -0.0121 -0.0115 -0.0103 -0.0120 -0.0119 -0.0124 -0.0121 -0.0139 -0.0129 -0.0126 -0.0129 -0.0139 -0.0127 -0.0122 -0.0125 -0.0108 -0.0126 -0.0116 -0.0109 -0.0127 -0.0122 -0.0110 -0.0121 -0.0126 -0.0121 -0.0117 -0.0116 -0.0126 -0.0122 -0.0128 -0.0107 -0.0111 -0.0122 -0.0131 -0.0120 -0.0120 -0.0124 -0.0116 -0.0141 -0.0101 -0.0120

LTIHML -1.1490 -1.2212 -1.1797 -1.1551 -1.2834 -1.2172 -0.9718 -1.3234 -1.1721 -1.1881 -1.1981 -1.2074 -1.1949 -1.2542 -1.2143 -1.1980 -1.2161 -1.1531 -1.1597 -1.2798 -1.2514 -1.1985 -1.1267 -1.1281 -1.2431 -1.1238 -1.1672 -1.1036 -1.2384 -1.1337 -1.2192 -1.2004 -1.1677 -1.0877 -1.1772 -1.1013 -1.2672 -1.2282 -0.9696 -1.2084 -1.1948 -1.1483 -1.1904 -1.0740 -1.2506 -1.1953

LTIFHT -1.7285 -1.7113 -1.7281 -1.7139 -1.6737 -1.7069 -1.7094 -1.7154 -1.7309 -1.6696 -1.7240 -1.7318 -1.7119 -1.7305 -1.7127 -1.6502 -1.7968 -1.7196 -1.6511 -1.6464 -1.7042 -1.7072 -1.7068 -1.7013 -1.7311 -1.7400 -1.6958 -1.7239 -1.6633 -1.6916 -1.6388 -1.7164 -1.7287 -1.6437 -1.6935 -1.7232 -1.7531 -1.7166 -1.6673 -1.7026 -1.7042 -1.6978 -1.6985 -1.7180 -1.7250 -1.7150

AN US

FHT 0.0122 0.0053 0.0038 0.0047 0.0027 0.0077 0.0103 0.0013 0.0100 0.0012 0.0074 0.0051 0.0028 0.0046 0.0109 0.0053 0.0036 0.0445 0.0020 0.0013 0.0024 0.0059 0.0122 0.0031 0.0072 0.0065 0.0149 0.0140 0.0070 0.0285 0.0082 0.0060 0.0010 0.0048 0.0129 0.0126 0.0049 0.0051 0.0193 0.0097 0.0067 0.0126 0.0101 0.0212 0.0044 0.0085

M

HML 0.0040 0.0059 0.0050 0.0060 0.0089 0.0065 0.0033 0.0099 0.0056 0.0077 0.0060 0.0068 0.0053 0.0078 0.0074 0.0067 0.0110 0.0087 0.0076 0.0055 0.0075 0.0056 0.0054 0.0053 0.0042 0.0048 0.0029 0.0060 0.0069 0.0052 0.0084 0.0059 0.0093 0.0044 0.0058 0.0050 0.0112 0.0070 0.0038 0.0066 0.0054 0.0064 0.0104 0.0052 0.0070 0.0063

ED

CPQS 0.0067 0.0171 0.0006 0.0103 0.0108 0.0124 0.0138 0.0015 0.0172 0.0318 0.0127 0.0117 0.0133 0.0104 0.0129 0.0339 0.0162 0.0324 0.0111 0.0027 0.0101 0.0071 0.0148 0.0201 0.0139 0.0100 0.0155 0.0190 -0.0753 0.0269 0.0123 0.0095 0.0060 0.0043 0.0157 0.0180 0.0054 0.0082 0.0384 0.0136 0.0130 0.0103 0.0075 0.0284 0.0025 0.0133

PT

Liquidity level AMH*103 0.1159 0.4911 0.0964 0.1338 0.1143 0.4911 0.0009 0.0008 0.0530 0.1544 0.5337 0.3003 0.4507 0.5592 0.0936 0.0014 0.3815 0.0028 0.2885 0.0738 0.1427 0.0003 0.3096 0.0783 0.0216 0.2471 0.3886 0.0655 0.0461 0.0959 0.3602 0.5262 0.0830 0.0006 0.5654 0.1969 0.0003 0.0883 0.0845 0.0595 0.0449 0.2416 0.3450 0.0032 0.0608 0.1285

CE

RICC 0.0952 0.1048 0.0638 0.0689 0.0927 0.0940 0.0806 0.0566 0.0843 0.1043 0.0777 0.0693 0.0723 0.0653 0.0899 0.0935 0.1864 0.1151 0.0744 0.0783 0.0755 0.0608 0.0662 0.0830 0.0782 0.0726 0.0674 0.1204 0.1269 0.0964 0.1183 0.0725 0.1697 0.0941 0.0724 0.0884 0.1203 0.0655 0.1061 0.0911 0.0628 0.0908 0.1003 0.0865 0.0611 0.0740

AC

Country Argentina Australia Austria Belgium Brazil Canada Chile China Denmark Egypt Finland France Germany Greece Hong Kong Hungary India Indonesia Ireland Israel Italy Japan Malaysia Mexico Morocco Netherlands New Zealand Norway Pakistan Philippines Poland Portugal Russian Federation Saudi Arabia Singapore South Africa South Korea Spain Sri Lanka Sweden Switzerland Thailand Turkey United Kingdom United States Full sample

HILL HILLAMH 0.0064 0.0058 0.0054 0.0050 0.0066 0.0059 0.0079 0.0041 0.0060 0.0079 0.0062 0.0050 0.0052 0.0055 0.0065 0.0064 0.0063 0.0108 0.0072 0.0041 0.0048 0.0043 0.0075 0.0076 0.0063 0.0056 0.0067 0.0071 0.0112 0.0094 0.0060 0.0067 0.0075 0.0053 0.0071 0.0079 0.0054 0.0050 0.0092 0.0057 0.0051 0.0079 0.0047 0.0067 0.0038 0.0053

HILLCPQS 0.0729 0.0540 0.0244 0.0301 0.0602 0.0391 0.0927 0.0045 0.0571 0.0947 0.0443 0.0411 0.0276 0.0421 0.0428 0.0840 0.0624 0.0826 0.0334 0.0098 0.0427 0.0168 0.0509 0.0895 0.0577 0.0326 0.0551 0.0619 0.0185 0.1127 0.0435 0.0298 0.0251 0.0119 0.0576 0.0707 0.0218 0.0259 0.0906 0.0315 0.0436 0.0369 0.0131 0.0590 0.0130 0.0350

HILLHML 0.0301 0.0309 0.0293 0.0304 0.0390 0.0334 0.0231 0.0410 0.0300 0.0398 0.0308 0.0337 0.0305 0.0362 0.0386 0.0354 0.0547 0.0534 0.0350 0.0267 0.0334 0.0294 0.0312 0.0310 0.0268 0.0267 0.0185 0.0360 0.0372 0.0352 0.0425 0.0287 0.0483 0.0236 0.0323 0.0304 0.0506 0.0316 0.0298 0.0347 0.0284 0.0350 0.0468 0.0281 0.0319 0.0320

HILLFHT 0.0462 0.0376 0.0166 0.0171 0.0183 0.0279 0.0349 0.0084 0.0365 0.0088 0.0268 0.0196 0.0146 0.0155 0.0360 0.0208 0.0180 0.1479 0.0213 0.0070 0.0103 0.0214 0.0376 0.0199 0.0240 0.0218 0.0405 0.0533 0.0368 0.0776 0.0256 0.0220 0.0143 0.0157 0.0429 0.0425 0.0188 0.0186 0.0692 0.0323 0.0256 0.0421 0.0294 0.0722 0.0156 0.0300

# of firmyear obs. 156 2,175 404 754 309 3,855 430 3,008 1,126 183 966 4,392 942 553 2,552 197 34 964 136 215 2,034 16,404 2,845 616 126 1,788 600 1,280 232 507 183 382 68 126 1,700 1,356 694 1,603 127 2,313 2,055 1,890 560 9,790 20,766 93,396

Table 2: Descriptive statistics and correlation matrix

CR IP T

ACCEPTED MANUSCRIPT

This table reports descriptive statistics and Pearson's correlation coefficients for the main variables used in our analyses. Panel A reports the descriptive statistics for the cost of capital as well as the explanatory variables used in the main analysis. The labels N, Mean, P25, P50, P75, and Std_dev reported in the first row in panel A stand for the number of observations, average, 25th percentile, median, 75th percentile, and the standard deviation, respectively. Panel B reports Pearson's correlation coefficients among the primary liquidity tail index variable (LTIAMH), the Amihud measure (AMH), the aggregate liquidity covariance , the firm-level control variables (BETA, BTM, LEVERAGE, and SIZE), the country-level control variables (LNGPD, FD, INF) and the cost of equity ( ). Note that we scaled the following variables: BTM, FD, FBIAS, LTG, and LTICPQS by dividing each by 100. Bolded numbers indicate significance. The total sample consists of 93,396 firm–year observations from 45 countries between 1985 and 2012. The definitions and data sources for all the variables used in the study are provided in Appendix B.

Panel A: Descriptive Statistics of the cost of equity and the main explanatory variables

) ) )

BETA BTM LEVERAGE SIZE LNGDP FD INF

Mean 0.0740 0.0001 0.0133 0.0063 0.0085 -0.0040 -0.0120 -1.1953 -1.7150 0.0053 0.0350 0.0320 0.0300 0.0001 -0.0005 -0.0001 0.0007 0.9754 0.0101 0.3104 13.7811 10.1000 1.0510 2.4260

P25 0.0402 0.0000 0.0034 0.0039 0.0014 -0.0076 -0.0145 -1.3683 -1.7384 0.0034 0.0100 0.0200 0.0082 0.0000 -0.0003 0.0000 0.0000 0.5904 0.0029 0.0473 12.4344 10.2393 0.6563 1.0822

P50 0.0532 0.0000 0.0080 0.0058 0.0040 -0.0040 -0.0127 -1.2228 -1.5556 0.0047 0.0200 0.0300 0.0162 0.0000 0.0000 0.0000 0.0000 0.9265 0.0053 0.2485 13.6320 10.4311 0.9211 2.1349

P75 0.0806 0.0000 0.0163 0.0082 0.0101 -0.0005 -0.0111 -1.1122 -1.4152 0.0067 0.0400 0.0400 0.0325 0.0000 0.0000 0.0000 0.0006 1.2854 0.0084 0.5075 14.9632 10.5273 1.3137 3.2259

AN US

N 93,396 93,396 63,354 93,339 93,375 93,396 79,530 90,511 87,656 93,396 80,144 88,776 90,895 93,396 93,396 93,396 93,396 93,396 93,396 93,396 93,396 93,396 93,396 93,396

M

Stats RICC AMH CPQS HML FHT LTIAMH LTICPQS LTIHML LTIFHT HILLAMH HILLCPQS HILLHML HILLFHT ( ( (

Std_dev 0.0645 0.0005 0.0193 0.0036 0.0163 0.0049 0.0048 0.5475 0.5781 0.0026 0.0513 0.0214 0.0510 0.0006 0.0013 0.0004 0.0018 0.5734 0.0875 0.2814 1.9250 0.8978 0.6959 3.4166

RICC

AMH

ED

Panel B: Pearson’s correlations for the main variables LTIAMH

BETA

BTM

LEVERAGE

SIZE

LNGDP

FD

RICC

1.000

AMH

0.105

1.000

LTIAMH

0.181

0.145

0.122

0.509

0.149

1.000

BETA

0.093

-0.022

-0.131

-0.022

1.000

BTM

0.095

-0.007

0.038

-0.009

0.004

1.000

LEVERAGE

0.082

-0.057

-0.060

-0.013

0.033

0.116

SIZE

-0.209

-0.231

-0.380

-0.181

0.145

0.013

0.335

LNGDP

-0.056

-0.021

-0.241

-0.075

0.063

-0.085

-0.066

0.139

0.002

0.045

0.048

0.023

-0.023

-0.011

-0.182

-0.027

0.103

1.000

0.095

0.012

0.133

0.121

-0.022

0.058

0.067

-0.039

-0.366

-0.116

48

1.000

PT

CE

INF

AC

FD

INF

1.000 1.000 1.000 1.000

Table 3: Tails in the Amihud (2002) liquidity proxy and the implied cost of equity This table reports pooled OLS regression results of the following implied cost of equity capital model:

CR IP T

ACCEPTED MANUSCRIPT

(1)

(2)

(3)

3.246** (2.258) 0.621*** (5.788)

6.355*** (3.803) 0.618*** (5.773)

4.128** (2.616) 0.618*** (5.713)

Variables AMH LTIAMH HILLAMH

)

(

)

BETA BTM LEVERAGE SIZE LNGDP FD INF Constant

-4.543** (-2.394)

(6)

(7)

(8)

4.332*** (3.087) 0.616*** (5.807)

2.979** (2.086)

5.950*** (3.612)

3.968** (2.561)

4.009*** (2.869)

1.927*** (6.445) 4.300* (1.968)

1.938*** (6.461)

1.923*** (6.343)

1.920*** (6.457)

-1.239* (-1.926) -4.062** (-2.176)

0.015*** (8.820) 0.047*** (5.157) 0.049*** (12.435) -0.009*** (-5.279) -0.013 (-0.622) -0.003 (-1.665) 0.001*** (8.586) 0.261 (1.490)

0.016*** (8.647) 0.047*** (5.156) 0.049*** (12.302) -0.008*** (-5.191) -0.013 (-0.604) -0.003 (-1.650) 0.001*** (9.159) 0.256 (1.456)

1.675** (2.308) 0.015*** (8.856) 0.047*** (5.158) 0.049*** (12.245) -0.008*** (-5.178) -0.013 (-0.604) -0.003* (-1.793) 0.001*** (8.378) 0.256 (1.466)

0.016*** (9.029) 0.048*** (5.222) 0.048*** (12.242) -0.008*** (-4.940) -0.015 (-0.695) -0.003 (-1.606) 0.001*** (9.459) 0.250 (1.453)

0.016*** (9.124) 0.048*** (5.225) 0.048*** (12.437) -0.008*** (-5.030) -0.015 (-0.717) -0.003 (-1.671) 0.001*** (8.784) 0.253 (1.486)

0.016*** (8.944) 0.048*** (5.225) 0.048*** (12.329) -0.008*** (-4.966) -0.015 (-0.700) -0.003 (-1.644) 0.001*** (9.336) 0.249 (1.455)

1.613** (2.267) 0.016*** (9.158) 0.048*** (5.226) 0.048*** (12.273) -0.008*** (-4.949) -0.015 (-0.698) -0.003* (-1.800) 0.001*** (8.592) 0.249 (1.462)

93,396 0.179

93,396 0.179

93,396 0.179

93,396 0.179

93,396 0.181

93,396 0.181

93,396 0.181

93,396 0.181

AC

49

(5)

0.016*** (8.728) 0.047*** (5.153) 0.049*** (12.204) -0.008*** (-5.160) -0.013 (-0.602) -0.003 (-1.600) 0.001*** (9.340) 0.257 (1.457)

CE

Observations Adjusted R-squared

-1.262* (-1.938)

(4)

M

(

4.490* (1.995)

ED

)

PT

(

AN US

For firm i in year t, the dependent variable is the average of the four implied cost of equity capital models described in Appendix A. In columns (1)-(4), is defined as the liquidity tail index generated by the maximum likelihood estimator of the tail index in the Amihud measure using Generalized Pareto Distributions. Columns (5)-(8) report the results of the same model specifications as models (1)-(4) for the , which is defined as the Hill (1975) estimator of liquidity tails in the Amihud (2002) measure. The set of control variables is comprised of: AMH: defined as the stock illiquidity using Amihud (2002) model, : co-movement between firm-level liquidity and market liquidity, : co-movement between firm-level returns and market liquidity, : co-movement between firm-level liquidity and market returns, and , and other determinants at the firm-level and the country-level. FE is the set of fixed effects at the country, industry, and year levels. The firm-level variables are: SIZE, estimated as the natural logarithm of a firm’s total assets; BETA, estimated as the covariance between the firm returns and the market return relative to the variance of the market returns; LEVERAGE, computed as total debt to the market value of equity; and BTM, computed as the book value of equity divided by the market value of equity. The countrylevel variables are: LNGDP, Logarithm of GDP per capita; INFL, measured as the annualized yearly median of a country-specific one-year-ahead realized monthly inflation rate; and FD, calculated as the sum of market capitalization and private credit relative to GDP. The total sample consists of 93,396 firm–year observations from 45 countries between 1985 and 2012. The definitions and data sources for all the variables used in the study are provided in Appendix B. Beneath each coefficient is the robust t-statistic clustered at the country level.

CR IP T

ACCEPTED MANUSCRIPT

Table 4: Idiosyncratic extreme illiquidity and the implied cost of equity This table reports pooled OLS regression results of the following implied cost of equity capital model:

(1)

(2)

(3)

3.728** (2.614) 0.623*** (6.487) 0.873** (2.077)

6.702*** (4.000) 0.621*** (6.476) 0.896** (2.100)

4.476*** (2.813) 0.620*** (6.418) 0.866** (2.038)

Variables AMH RESID_LTIAMH ELRLTI

ELRHILL

(

)

BETA BTM LEVERAGE SIZE LNGDP FD INF Constant

50

-0.924 (-1.609)

(5)

(6)

(7)

(8)

4.999*** (3.671) 0.619*** (6.497) 0.901** (2.138)

3.023** (2.120)

6.167*** (3.802)

4.035** (2.639)

4.158*** (3.031)

1.890*** (6.038) 1.986** (2.247) 4.567** (2.070)

1.904*** (6.066) 1.884** (2.079)

1.887*** (5.927) 1.923** (2.074)

1.884*** (6.059) 1.956** (2.232)

-1.261* (-1.928)

-4.517** (-2.297)

-4.375** (-2.320)

0.015*** (8.722) 0.037** (2.113) 0.045*** (12.187) -0.008*** (-4.912) -0.017 (-0.841) -0.002 (-1.405) 0.001*** (4.361) 0.267 (1.678)

0.015*** (8.757) 0.037** (2.114) 0.045*** (12.443) -0.008*** (-5.027) -0.017 (-0.865) -0.002 (-1.415) 0.001*** (4.476) 0.272* (1.720)

0.015*** (8.644) 0.037** (2.111) 0.045*** (12.275) -0.008*** (-4.936) -0.017 (-0.844) -0.002 (-1.437) 0.001*** (4.455) 0.265 (1.677)

1.401** (2.076) 0.015*** (8.789) 0.037** (2.115) 0.045*** (12.253) -0.008*** (-4.935) -0.017 (-0.848) -0.003 (-1.576) 0.001*** (4.465) 0.269* (1.704)

92,241 0.173

92,241 0.173

92,241 0.173

92,241 0.173

AC

Observations Adjusted R-squared

4.280* (1.961)

ED

)

PT

)

(

CE

(

(4)

M

RESID_HILLAMH

AN US

For firm i in year t, the dependent variable is the average of the four implied cost of equity capital estimates described in Appendix A. In columns (1)-(4), ELRLTI is the extreme liquidity risk as defined by Wu (2016) that is estimated by the maximum likelihood estimator of the tail index in the Amihud measure for the market liquidity using Generalized Pareto Distributions; is defined as the liquidity tail index generated by the maximum likelihood estimator of the tail index in the Amihud measure for the individual stock liquidity using Generalized Pareto Distributions; and RESID_LTIAMH are the orthogonal variants of that are collected as the residuals that result from regressing on . In columns (5)-(8), ELRHILL is defined similarly as ELRLTI but using the HILL (1975) estimator; is defined as the Hill (1975) estimator of liquidity tails in the Amihud (2002) measure for the individual stock liquidity; and RESID_LTIHILL are the orthogonal variants of that are collected as the residuals that result from regressing on . The set of control variables is comprised of: AMH: defined as the stock illiquidity using Amihud (2002) model, : co-movement between firm-level liquidity and market liquidity, : co-movement between firm-level returns and market liquidity, : co-movement between firm-level liquidity and market returns, and , and other determinants at the firm-level and the country-level. FE is the set of fixed effects at the country, industry, and year levels. The firm-level variables are: SIZE, estimated as the natural logarithm of a firm’s total assets; BETA, estimated as the covariance between the firm returns and the market return relative to the variance of the market returns; LEVERAGE, computed as total debt to the market value of equity; and BTM, computed as the book value of equity divided by the market value of equity. The country-level variables are: LNGDP, Logarithm of GDP per capita; INFL, measured as the annualized yearly median of a country-specific one-year-ahead realized monthly inflation rate; and FD, calculated as the sum of market capitalization and private credit relative to GDP. The total sample consists of 93,396 firm–year observations from 45 countries between 1985 and 2012. The definitions and data sources for all the variables used in the study are provided in Appendix B. Beneath each coefficient is the robust t-statistic clustered at the country level.

0.016*** (8.949) 0.048*** (5.211) 0.047*** (12.193) -0.008*** (-4.919) -0.017 (-0.853) -0.002 (-1.258) 0.001*** (10.054) 0.412* (1.955)

0.016*** (9.061) 0.048*** (5.214) 0.048*** (12.413) -0.008*** (-5.015) -0.018 (-0.869) -0.002 (-1.352) 0.001*** (9.223) 0.413* (1.987)

0.016*** (8.869) 0.048*** (5.214) 0.047*** (12.293) -0.008*** (-4.944) -0.017 (-0.853) -0.002 (-1.330) 0.001*** (9.851) 0.409* (1.959)

1.684** (2.355) 0.016*** (9.087) 0.048*** (5.216) 0.047*** (12.234) -0.008*** (-4.930) -0.017 (-0.856) -0.002 (-1.495) 0.001*** (9.002) 0.410* (1.981)

93,396 0.182

93,396 0.181

93,396 0.181

93,396 0.182

Table 5: Alternative liquidity proxies

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ACCEPTED MANUSCRIPT

This table reports pooled OLS regression results of regressing , defined as the average of the four implied cost of equity capital models described in Appendix A, on an alternative liquidity proxy indicated as either one of CPQS, HML, and FHT (described in Section 2) and its respective liquidity tail index (LTI or HILL), while controlling for the same set of firm-level and country-level variables, defined earlier. For brevity, we show the results using the aggregate liquidity covariance risk, . For each liquidity measure, we report two regression specifications. The total sample consists of 93,396 firm–year observations from 45 countries between 1985 and 2012. The definitions and data sources for all the variables used in the study are provided in Appendix B. Beneath each coefficient is the robust t-statistic clustered at the country level. (1)

(2)

(3)

Variables 3.981*** (9.505) 0.003*** (4.715)

LTIHML

2.385*** (3.690)

HILLHML

AN US

HML

0.369* (1.745)

FHT

0.848*** (5.377) 0.003*** (4.535)

LTIFHT HILLFHT

(5)

0.625*** (4.819)

0.098*** (3.243)

CPQS LTICPQS

BTM LEVERAGE SIZE LNGDP

PT

FD INF

AC

Observations Adjusted R-squared

88,726 0.212

CE

Constant

0.744*** (4.934)

2.009** (2.471) 0.008*** (7.067) 0.051*** (7.008) 0.045*** (12.885) -0.008*** (-5.118) -0.010 (-0.637) -0.005*** (-2.852) 0.001*** (3.468) 0.332** (2.033)

2.042*** (3.040) 0.015*** (9.210) 0.054*** (7.043) 0.043*** (15.438) -0.006*** (-5.140) -0.021 (-1.034) -0.003** (-2.023) 0.001*** (7.043) 0.406** (2.027)

2.007*** (3.052) 0.015*** (9.197) 0.055*** (7.004) 0.042*** (14.883) -0.006*** (-4.962) -0.021 (-1.045) -0.003** (-2.071) 0.001*** (6.109) 0.396* (1.999)

1.290* (1.892) 0.018*** (12.601) 0.055*** (4.095) 0.040*** (11.644) -0.007*** (-7.337) -0.054*** (-5.154) -0.002 (-0.845) 0.001*** (5.817) 0.577*** (6.554)

88,776 0.219

87,656 0.210

87,656 0.211

59,905 0.226

59,905 0.229

ED

2.144*** (2.720) 0.009*** (5.903) 0.050*** (6.604) 0.045*** (11.666) -0.008*** (-4.501) -0.010 (-0.617) -0.005*** (-2.903) 0.001*** (3.938) 0.345** (2.060)

BETA

0.905*** (6.278) 0.041 (0.443)

0.101*** (2.802) 1.100* (1.708) 0.019*** (12.490) 0.055*** (4.129) 0.039*** (11.635) -0.006*** (-7.525) -0.054*** (-5.219) -0.002 (-0.823) 0.001*** (5.012) 0.576*** (6.545)

M

HILLCPQS

51

(4)

(6)

CR IP T

ACCEPTED MANUSCRIPT

Table 6: Robustness checks

In Panel A, we repeat the same analysis shown in Table 3 for LTI using AMH but for different subsamples. The subsample for column (1) consists of only the U.S. financial market (New York Stock Exchange); in column (2) of only countries with developed financial markets; in column (3) of only countries whose financial market is not one of the 10 least active in terms of dollar volume, and in column (4) of only countries whose financial market is not one of the 10 smallest in terms of market capitalization. The subsample in column (5) excludes stocks that fall in the bottom 10 percentile of the distribution of the dollar volume of the all the stocks, and in column (6) excludes stocks that fall in the bottom 10 percentile of the distribution of the market capitalization of the all the stocks. For brevity, we show the results using the aggregate liquidity covariance risk, .

AN US

In Panel B, columns (1)-(4) repeat the same analysis as in Table 3 model (4) after replacing with each of , , and that represent the implied cost of equity estimates of Easton (2004), Gebhardt et al. (2001), Ohlson and Juettner-Nauroth (2005), and Claus and Thomas (2001), respectively. Column (5) replaces with the principal component of , , and ; column (6) replaces with the principal component of and ; and column (7) replaces with the principal component of and . All remaining columns use as the dependent variable. Columns (8) –(11) separately introduce an additional control variable at a time: FBIAS, defined as the difference between the one-year-ahead forecasted and realized earnings; LTG: the firm’s long-term earnings growth; DISPERSION: measured as the ratio of the standard deviation of estimated first year earnings per share by the average forecasted first year earnings per share; and ANALYSTCOV: measured as the number of analysts who are covering the firm by providing earnings forecasts. The four cost of equity models are defined in Appendix A. The definitions and data sources for all the variables used in the study are provided in Appendix B. Beneath each coefficient is the robust t-statistic clustered at the country level.

Panel A: Revised sample (1)

(2)

(3)

(4)

BETA BTM LEVERAGE SIZE LNGDP FD INF Constant

20, 766 0.095

77,635 0.180

NYSE

Developed Markets.

4.626*** (3.223) 0.664*** (5.882) 1.547** (2.083) 0.015*** (8.707) 0.047*** (5.183) 0.048*** (11.904) -0.008*** (-5.044) -0.009 (-0.420) -0.003* (-1.793) 0.001*** (8.277) 0.389 (1.514) 90,640 0.179

Exclude 10 countries with the least active markets in terms of dollar volume.

52

AC

CE

Observations Adjusted Rsquared Sub-sample

5.252*** (3.304) 0.677*** (5.359) 2.180** (2.487) 0.016*** (7.971) 0.074*** (7.227) 0.047*** (11.053) -0.009*** (-4.675) 0.035 (1.636) -0.003 (-1.490) 0.001* (1.795) -0.209 (-0.937)

ED

LTIAMH

-0.941 (-0.898) 0.721*** (9.749) 4.292*** (5.401) 0.013*** (24.199) 0.061*** (4.320) 0.037*** (31.517) -0.003*** (-16.469) 0.061*** (18.576) -0.014*** (-12.403) 0.000* (1.884) -0.547*** (-16.167)

PT

AMH

(5)

(6)

4.383*** (2.992) 0.663*** (5.867) 1.863** (2.575) 0.015*** (8.689) 0.047*** (5.103) 0.049*** (11.769) -0.008*** (-5.019) -0.012 (-0.519) -0.003* (-1.767) 0.001*** (5.390) 0.410 (1.588)

3.259* (1.843) 0.626*** (6.996) 1.787** (2.458) 0.016*** (8.858) 0.048*** (5.235) 0.048*** (13.597) -0.008*** (-5.353) -0.020 (-1.048) -0.003 (-1.549) 0.001*** (7.908) 0.429** (2.131)

4.243** (2.454) 0.613*** (6.046) 1.630** (2.245) 0.016*** (8.759) 0.048*** (5.138) 0.048*** (13.449) -0.008*** (-5.454) -0.017 (-0.843) -0.003 (-1.637) 0.001*** (7.962) 0.406* (1.970)

90,429 0.178

88,906 0.176

91,117 0.176

M

Variables

Exclude 10 countries with the smallest markets in terms of market capitalization.

Exclude the least actively traded stocks, defined as stocks in the bottom 10 percentile of the distribution in the dollar volume.

Exclude the smallest stocks, defined as stocks in the bottom 10 percentile of the distribution in the market capitalization.

Panel B: Limitations in the estimation of the cost of equity capital (1)

(2)

(3)

(4)

(5)

(6)

Variables

(7) (

AMH

6.046** (2.556) 0.713*** (4.856)

LTIAMH

3.438*** (2.860) 0.285*** (2.793)

5.590*** (3.558) 0.316** (2.325)

4.158** (2.099) 0.427*** (3.120)

175.724*** (3.107) 15.652*** (4.405)

102.383*** (3.112) 12.510*** (3.915)

FBIAS LTG

)

(

,

(8)

(9)

(10)

(11)

4.452*** (3.085) 0.599*** (5.662) 0.0328 (1.486)

2.221* (1.897) 0.344*** (5.251)

4.915*** (4.050) 0.453*** (5.447)

4.170*** (3.112) 0.562*** (5.278)

)

130.548*** (3.248) 11.494*** (4.582)

0.0030*** (2.911)

DISPERSION

0.216*** (3.799)

BTM LEVERAGE SIZE LNGDP FD INF Constant

1.185** (2.509) 0.010*** (7.952) 0.003 (0.487) 0.056*** (17.805) -0.007*** (-12.728)

0.153 (0.419) 0.002* (1.913) 0.294 (1.415) 0.027*** (7.417) -0.005*** (-6.805)

25.101* (1.885) 0.270*** (15.016) 83.850*** (8.481) 1.183*** (9.211) -0.165*** (-5.736)

19.662* (1.776) 0.171*** (10.660) 7.153** (2.713) 1.205*** (23.226) -0.115*** (-7.623)

19.218** (2.272) 0.180*** (7.047) 29.841*** (6.486) 0.797*** (7.351) -0.112*** (-5.317)

1.602** (2.245) 0.015*** (8.859) 0.050*** (6.402) 0.048*** (12.577) -0.008*** (-5.162)

0.955* (1.932) 0.011*** (11.313) 0.052*** (5.413) 0.041*** (19.406) -0.004*** (-6.299)

1.379** (2.108) 0.014*** (8.564) 0.049*** (4.476) 0.038*** (14.830) -0.006*** (-5.713)

-0.001*** (-3.197) 1.645** (2.173) 0.016*** (8.669) 0.047*** (5.274) 0.045*** (11.866) -0.007*** (-4.400)

-0.048** (-2.300) -0.010*** (-4.017) 0.002*** (11.568) 0.679*** (3.595)

-0.029 (-1.131) 0.001 (0.639) 0.002*** (4.224) 0.316 (1.543)

-0.052** (-2.024) -0.008*** (-3.355) 0.002*** (7.264) 0.589*** (2.905)

-0.026 (-0.963) -0.001 (-0.849) 0.002*** (3.315) 0.312 (1.417)

-1.904 (-1.039) -0.013 (-0.343) 0.015 (0.798) 19.107 (1.026)

-1.305 (-1.011) -0.036 (-0.904) 0.015 (0.879) 13.707 (1.049)

-1.200 (-0.994) -0.020 (-0.740) 0.013 (1.222) 11.723 (0.952)

-0.013 (-0.649) -0.003* (-1.761) 0.001*** (9.018) 0.379* (1.839)

-0.022** (-2.194) -0.003** (-2.372) 0.001*** (10.065) 0.261*** (3.308)

-0.011 (-0.717) -0.003** (-2.557) 0.001*** (3.467) 0.321* (1.780)

-0.018 (-0.970) -0.004** (-2.123) 0.001*** (8.856) 0.403** (2.083)

66,616 0.191

58,985 0.322

60,565 0.233

49,375 0.117

59,644 0.243

47,669 0.198

91,471 0.178

83,445 0.172

80,430 0.226

93,385 0.182

44,206 0.268

AC

CE

PT

ED

Observations Adjusted R-squared

-0.379 (-1.159) -0.000 (-0.024) 0.368*** (12.580) 0.035*** (6.638) -0.003*** (-4.220)

AN US

BETA

1.412** (2.421) 0.018*** (11.513) -0.006 (-1.070) 0.079*** (19.803) -0.009*** (-8.342)

M

ANALYSTCOV

53

,

CR IP T

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Table 7: Liquidity black holes and the implied cost of equity This table reports pooled OLS regression results of the following implied cost of equity capital model:

CR IP T

ACCEPTED MANUSCRIPT

For firm i in year t, the dependent variable is the average of the four implied cost of equity capital estimates described in Appendix A. LBH stands for liquidity black holes which measure the frequency of extreme liquidity events defined when the firm AMH exceeds a predefined multiple (50 times) of the market AMH. In the table below, LBH10, LBH20, LBH30, and LBH40 respectively record an extreme liquidity event when the firm illiquidity is more than 10, 20, 30, and 40 times the market average illiquidity. The set of variables in is defined in the descriptions of Tables 3 and 4. The total sample consists of 93,396 firm–year observations from 45 countries between 1985 and 2012. The definitions and data sources for all the variables used in the study are provided in Appendix B. Beneath each coefficient is the robust t-statistic clustered at the country level. (1)

(2)

(3)

4.737*** (3.579) 0.822*** (4.465)

4.263*** (3.034)

4.467*** (3.259)

AMH LBH LBH10

0.408*** (4.138)

LBH20

(4)

(5)

4.598*** (3.411)

4.684*** (3.513)

0.541*** (4.211)

LBH30 LBH40

LEVERAGE SIZE LNGDP FD INF Constant

93,396 0.188

AC

CE

PT

Observations Adjusted R-squared

M

BTM

1.590** (2.173) 0.017*** (8.685) 0.048*** (5.362) 0.044*** (12.713) -0.007*** (-5.019) -0.015 (-0.749) -0.004* (-1.740) 0.001*** (8.286) 0.369* (1.815)

ED

1.617** (2.252) 0.016*** (9.583) 0.048*** (5.401) 0.045*** (15.421) -0.007*** (-6.418) -0.014 (-0.670) -0.004* (-1.749) 0.001*** (8.079) 0.368* (1.770)

BETA

54

AN US

VARIABLES

93,396 0.186

0.646*** (4.278)

1.593** (2.193) 0.017*** (9.104) 0.048*** (5.395) 0.044*** (14.201) -0.007*** (-5.746) -0.015 (-0.732) -0.004* (-1.739) 0.001*** (8.262) 0.370* (1.811)

1.600** (2.214) 0.017*** (9.318) 0.048*** (5.392) 0.044*** (14.807) -0.007*** (-6.085) -0.014 (-0.707) -0.004* (-1.743) 0.001*** (8.188) 0.370* (1.795)

0.739*** (4.350) 1.608** (2.233) 0.017*** (9.460) 0.048*** (5.390) 0.045*** (15.184) -0.007*** (-6.299) -0.014 (-0.686) -0.004* (-1.748) 0.001*** (8.130) 0.369* (1.781)

93,396 0.187

93,396 0.188

93,396 0.188

ACCEPTED MANUSCRIPT

Table 8: Crisis periods and country institutional quality analyses In columns (1) and (2) we regress on , a market condition dummy variable, an interaction variable between and the market condition dummy variable, and the same set of controls, as defined in earlier tables. The market condition variable is either or . The dummy variable ( ) takes on one when the country’s stock market returns (volatility) drops below (exceeds) its 3-year historical moving average by more than one standard deviation; and zero otherwise. In columns (3)-(8), we regress on , an institutional dummy variable, an interaction variable between and the respective institutional dummy variable, and the same set of controls, as defined in earlier tables. The institutional dummies: , are defined to capture a stronger institutional quality measured by country’s disclosure intensity, media penetration, information opacity, anti-self dealing, rule of law, and investor protection. The definitions and data sources for all the variables used in the study are provided in Appendix B. Beneath each coefficient is the robust t-statistic clustered at the country level. The total sample consists of 93,396 firm–year observations from 45 countries between 1985 and 2012. The definitions and data sources for all the variables used in the study are provided in Appendix B. Beneath each coefficient is the robust t-statistic clustered at the country level. (2)

(3)

(4)

(5)

4.355*** (3.124) 0.594*** (5.685) 2.044** (2.305) 2.044** (2.305)

4.424*** (3.118) 0.576*** (5.325)

4.200*** (3.315) 0.688** (2.436)

3.884*** (2.790) 0.949*** (4.438)

4.108*** (3.206) 0.463** (2.541)

LTIAMH Mktdown LTIAMH*Mktdown MktVol

0.030*** (2.703) 2.842** (2.411)

LTIAMH*MktVol CIFAR

-0.025*** (-3.501) -0.558** (-2.036)

LTIAMH*CIFAR MEDIA

(7)

(8)

4.356*** (3.447) 0.565** (2.437)

3.678*** (2.911) 1.002*** (4.458)

4.095*** (3.381) 0.505** (2.489)

AN US

AMH

(6)

CR IP T

(1) Variables

-0.046 (-0.947) -0.870** (-2.717)

LTIAMH*MEDIA OPA

M

LTIAMH*OPA ASDI LTIAMH*ASDI

0.016 (0.368) -0.433** (-2.071)

-0.032 (-1.178) -0.580** (-2.566)

LTIAMH*RLAW INVP

PT

LTIAMH*INVP

LEVERAGE SIZE

AC

LNGDP FD

INF

Constant

Observations Adjusted R-squared

55

1.671** (2.300) 0.015*** (8.860) 0.047*** (5.161) 0.049*** (12.374) -0.008*** (-5.202) -0.013 (-0.624) -0.003* (-1.801) 0.001*** (8.348) 0.383* (1.807) 93,396 0.179

CE

BETA BTM

-0.043 (-1.190) -0.928*** (-2.798)

ED

RLAW

1.683** (2.301) 0.015*** (8.920) 0.047*** (5.311) 0.048*** (12.248) -0.008*** (-5.176) -0.015 (-0.679) -0.002 (-1.122) 0.001*** (7.297) 0.397* (1.843) 93,396 0.181

1.563** (2.167) 0.015*** (8.806) 0.067*** (7.263) 0.046*** (14.244) -0.008*** (-5.703) 0.008 (0.407) -0.003 (-1.646) 0.001*** (7.273) 0.220 (1.055) 87,839 0.176

1.555** (2.166) 0.016*** (9.169) 0.065*** (6.639) 0.047*** (12.498) -0.009*** (-5.209) 0.013 (0.610) -0.003* (-1.914) 0.001*** (7.106) 0.178 (0.780) 88,236 0.176

1.653** (2.273) 0.015*** (8.646) 0.045*** (5.277) 0.048*** (14.138) -0.008*** (-5.881) -0.013 (-0.682) -0.004** (-2.203) 0.001*** (8.333) 0.377* (1.873) 90,224 0.169

1.585** (2.235) 0.015*** (9.184) 0.046*** (4.335) 0.047*** (14.753) -0.008*** (-5.871) -0.013 (-0.683) -0.003* (-1.966) 0.001*** (7.372) 0.386* (1.935) 92,120 0.172

1.519** (2.200) 0.015*** (9.214) 0.048*** (5.020) 0.048*** (12.263) -0.009*** (-5.232) 0.010 (0.436) -0.003* (-1.867) 0.001*** (7.907) 0.207 (0.909) 89,294 0.176

0.010 (0.340) -0.452** (-2.104) 1.528** (2.114) 0.015*** (9.014) 0.047*** (5.241) 0.047*** (14.147) -0.008*** (-5.884) 0.003 (0.138) -0.004** (-2.236) 0.001*** (8.561) 0.259 (1.260) 88,791 0.173

ACCEPTED MANUSCRIPT

Appendix A: Implied cost of equity models We first define the following variables that are common to the four models: Variable

Description

Model 1:

CR IP T

Stock price in June of year t. Book value per share at the beginning of year t. Mean forecasted earnings per share from I/B/E/S or implied EPS forecasts for year t + j recorded in June of year t. Long-term growth forecast in June of year t. The forecasted payout ratio. To estimate the dividend per share for year t + j, we use the firm’s dividend payout ratio at time t if available and 50% if not, as in Claus and Thomas (2001). The implied cost of equity derived from each of the four different models.

Ohlson and Juettner-Nauroth (2005)

Model 2:

AN US

This model is derived from the abnormal earnings valuation model developed by Ohlson and Juettner-Nauroth (2005). It uses one-year-ahead and two-years-ahead earnings per share, the future dividend per share, and a proxy of the long-term growth rate. The future dividend, , is estimated as multiplied by . The asymptotic long-term growth rate, glt, is calculated using the annualized yearly median of country specific one-year-ahead realized monthly inflation rates. glt constitutes a lower bound for the cost of equity estimates.

: Claus and Thomas (2001) ∑

: Gebhardt, Lee, and Swaminathan (2001) ∑

PT

Model 3:

ED

M

In this model, the price is a function of the future forecasted earnings per share, the book value per share and the asymptotic longterm growth rate. Claus and Thomas (2001) implement the model using the I/B/E/S forecasted earnings per share for the next five years. If the forecasts for earnings per share, , are not available in I/B/E/S for the years t + 3, t + 4, and t + 5, = (1 + LTG). The long-term abnormal earnings growth rate, glt, is calculated using the annualized yearly median of a country specific one-year-ahead realized monthly inflation rates. Future book values are estimated by assuming the clean surplus relation, that is, = + . The future dividend, , is estimated by multiplying by POUT. glt constitutes a lower bound for the cost of equity estimates.

AC

CE

For the years t +1 to t +3, is equal to / . After the forecast period of three years, is derived by linear interpolation to the industry-median ROE. Average ROEs are computed in a given year and country for each of the 12 industry classifications of Campbell (1996). Negative industry median ROEs are replaced by country-year medians. The abnormal earnings at year t + 12 are then assumed to remain constant afterwards. Future book values are estimated by assuming clean surplus. The future dividend, , is estimated as multiplied by . We assume that T = 12.

Model 4:

: Easton (2004)

To implement the model, Easton (2004) uses the one-year-ahead and two-years-ahead forecasted earnings per share reported in I/B/E/S. The future dividend, , is estimated as multiplied by . This model requires a positive change in forecasted earnings per share to yield a numerical solution.

56

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Appendix B: Variables, definitions, and sources Variable Definition Panel A. Implied Cost of Equity

Source

Implied cost of equity estimated using the Claus and Thomas (2001) model.

As above As above As above Authors’ calculation based on DataStream.

CR IP T

Implied cost of equity estimated using the Gebhardt et al. (2001) model. Implied cost of equity estimated using the Ohlson and Juttner-Nauroth (2005) model. Implied cost of equity estimated using the Easton (2004) model. Equally weighted average of , , , and Panel B. Liquidity control variables

Authors’ calculation based on I/B/E/S and DataStream. As above

The main proxy for stock illiquidity using Amihud (2002) model.

AC

CE

PT

ED

M

AN US

The Closing Percent Quoted Spread by Chung and Zhang (2014), an additional proxy for stock illiquidity. The High-Low measure by Corwin and Schultz (2012), an additional proxy for stock illiquidity. The FHT measure by Fong et al. (2017), an additional proxy for stock illiquidity. Co-movements between the firm-level liquidity and the market liquidity, multiplied by 103, where, is the innovation in stock illiquidity using Amihud (2002) model and is the innovation in market liquidity using Amihud (2002) model. Co-movements between firm-level returns and the market liquidity, multiplied ( ) by 103, where is the daily stock return in local currency and is the innovation in market liquidity using Amihud (2002) model. Co-movements between firm-level liquidity and the market returns, multiplied by 103, where, is the innovation in stock illiquidity using Amihud (2002) model and the market return in local currency. ( ) ( ) Panel C. Extreme liquidity risks Liquidity tail index obtained using the maximum likelihood estimator based on Generalized Pareto Distribution of the measure of stock liquidity. Liquidity tail index obtained using the maximum likelihood estimator based on Generalized Pareto Distribution of the measure of stock liquidity. Liquidity tail index obtained using the maximum likelihood estimator based on Generalized Pareto Distribution of the measure of stock liquidity. Liquidity tail index obtained using the maximum likelihood estimator based on Generalized Pareto Distribution of the measure of stock liquidity. Liquidity tail index obtained using the non-parametric approach of Hill (1975) based on the measure of stock liquidity. Liquidity tail index obtained using the non-parametric approach of Hill (1975) based on the measure of stock liquidity. Liquidity tail index obtained using the non-parametric approach of Hill (1975) based on the measure of stock liquidity. Liquidity tail index obtained using the non-parametric approach of Hill (1975) based on the measure of stock liquidity. Extreme liquidity risk obtained using the maximum likelihood estimator based on Generalized Pareto Distribution of the measure of market liquidity. Extreme liquidity risk obtained using the non-parametric approach of Hill (1975) based on the measure of market liquidity. LBH Liquidity black hole is a dummy that equals 1 when stock exceeds 50 times the market ; and zero otherwise. LBH10 Liquidity black hole is a dummy that equals 1 when stock exceeds 10 times the market ; and zero otherwise. LBH20 Liquidity black hole is a dummy that equals 1 when stock exceeds 20 times the market ; and zero otherwise. LBH30 Liquidity black hole is a dummy that equals 1 when stock exceeds 30 times the market ; and zero otherwise. LBH40 Liquidity black hole is a dummy that equals 1 when stock exceeds 40 times the market ; and zero otherwise. 57

As above

As above As above

As above

As above

As above As above Authors’ calculation As above As above As above As above As above As above As above As above

As above As above As above As above As above

ACCEPTED MANUSCRIPT

Panel D. Main control variables BETA Estimated as the covariance between the firm returns and the market return relative to the variance of the market returns. BTM Computed as book value of equity divided by the market value of equity. We divide this variable by 100. LEVERAGE Computed as total debt to the market value of equity. SIZE Estimated as the natural logarithm of the firm’s total assets. LNGDP

Logarithm of GDP per capita.

Calculated as the sum of market capitalization and private credit relative to GDP. We divide this variable by 100. INFL Measured as the annualized yearly median of a country-specific one-yearahead realized monthly inflation rate. Panel E. Market Condition Variables Mktdown The dummy variable takes on one when the country’s stock market return drops below its 3-year historical moving average by more than one standard deviation; and zero otherwise. MktVol The dummy variable takes on one when the country’s stock market volatility exceeds its 3-year historical moving average by more than one standard deviation; and zero otherwise. Panel F. Institutional Variables CIFAR A dummy variable that takes on one if the country score is above the median disclosure intensity index; zero otherwise. The index was created by the Center for International Financial Analysis and Research (CIFAR) to measure disclosure intensity in a given country. The index that varies between 0 and 90, with greater values indicating an environment of greater transparency. MEDIA A dummy variable that takes on one if the country score is above the median media penetration index; zero otherwise. The media index is a country-level proxy for firm-specific information dissemination measured by the penetration of the media channels in the country. It is defined as the average rank of countries’ per capita number of newspapers and television channels. OPA A dummy variable that takes on one if the country score is below the median opacity index (OPACITY); zero otherwise. OPACITY is an index that measures a country’s opacity in five areas that affect capital markets: corruption, legal system, economic and fiscal policies, accounting standards and practices, and regulatory regime. ASDI A dummy variable that takes on one if the country score is above the median anti-self dealing index; zero otherwise. The anti-self-dealing index measures the extent to which minority shareholders are legally protected against expropriation by corporate insiders. Greater values of the ASDI indicate a better legal protection of minority shareholders. RLAW A dummy variable that takes on one if the country score is above the median rule of law index; zero otherwise. The index reflects perceptions of the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence. Greater values of the rule of law index indicate better protection of economic agents. INVP A dummy variable that takes on one if the country score is above the median investor protection index; zero otherwise. The investor protection index measures the extent to which a country provides legal protection to minority shareholders. It varies between 0 and 10, with greater values indicating better protection of investors. Panel G. Robustness check variables FBIAS Defined as the difference between the one-year-ahead forecasted and realized earnings. We divide this variable by 100. LTG Five-year consensus earnings growth rate. We divide this variable by100. DISPERSION Measured as the ratio of the standard deviation of estimated first year earnings per share by the average forecasted first year earnings per share. ANALYSTCOV Measured as the number of analysts who are covering the firm by providing earnings’ forecasts.

As above As above As above International Financial Statistics and World Development Indicators As above As above

AC

CE

PT

ED

M

AN US

CR IP T

FD

Authors’ calculation based on DataStream.

58

Authors’ calculation

As above

Bushman et al. (2004) and authors’ calculation

Bushman et al. (2004) and authors’ calculation

Bushman et al. (2004) and authors’ calculation

Djankov et al. (2008) and authors’ calculation World Governance Indicators of the World Bank and authors’ calculation

Doing Business reports and authors’ calculation

Authors’ calculation based on I/B/E/S As above As above As above