Liquidity and Skewness Risk in Stock Market: Does Measurement of Liquidity Matter?

Abstract

Purpose: This study aims to explore the relationship between stock liquidity and skewness risk-tail risk (stock price crash risk) in an emerging market, in which problems on liquidity are more severe than in developed markets. Research design, data, and methodology: Based on the Thai market stock exchange over the period of 2000 to 2019, our sample include 13,462 firm-period observations. We employ a panel regression models regarding to five liquidity measures. These five liquidity measures cover three dimensions of liquidity namely the volume-based, price-based, and transaction cost-based measures for the liquidity-tail risk relationship. Results: We find a positively significant relationship between stock liquidity and tail risk in all cases. The finding here shows that the higher the stock liquidity, the larger the tail risk is. Conclusion: As the prior studies show inconclusive effect of stock liquidity on stock price crash risk, we demonstrate that mixed results found in prior studies are probably driven from the type of liquidity measure. The stock liquidity-tail risk association is present in the Stock Exchange of Thailand. The results remain the same regardless of the definition of tail risk and liquidity factors. An endogeneity issue is addressed by employing the two-stage least squares regression.

1. Introduction

Even though the relationship between stock volatility and liquidity are widely documented (Bali et al., 2014; Chung & Chuwonganant, 2018), it is not true for the relationship between stock liquidity and tail risk (hence, stock price crash risk). The results of stock liquidity-tail risk relationship in developed markets remain inconclusive, depending on measurement of stock liquidity. Thus, we question that mixed findings are potentially driven by different liquidity measures. Moreover, studies of the relationship in emerging markets are scant, where stocks are less frequently traded than in developed market. Thus, we scrutinize the role of stock liquidity on crash risk in an emerging market (hence, Thailand) for the following reasons. First, an agency problem between managers and shareholders seems to be worse in emerging markets than advanced markets that allows managers in emerging markets to hoard bad news easier (Bédard et al., 2004; Larcker et al., 2007; Xie et al., 2003). Based on prior study, stock returns in Thailand clearly are skewed (Wattanatorn & Nathaphan, 2022; Wattanatorn & Padungsaksawasdi, 2022). Second, liquidity is found to be an important role in stock returns particularly in the Thai market (Wattanatorn et al., 2020; Wattanatorn & Tansupswatdikul, 2019). To fill the gap in prior literature, the objective of this paper is to investigate the liquidity-tail risk (crash risk) relationship in the Thai equity market by employing several types of liquidity measures.

We contribute to prior literature by examining the relationship between stock liquidity and crash risk based on five illiquidity measures covering three aspects (volume-, price-, and transaction-based) and employing Thailand as the sample setting for a representative of emerging markets. We find consistent results for the positive stock liquidity-crash risk association, which is insensitive to types of liquidity and crash risk measures. Among these five measures, the zero-return liquidity measure shows the strongest, while the Lui’s liquidity measure shows the weakest relationship. Instrumental-variable regressions alleviate endogeneity concern, confirming that our results are robust.

2. Literature Review

2.1. Stock Price Crash Risk Measure

Stock price crash risk is a dramatic decline in stock prices, causing negative return skewness. A plummet decline in stock prices is due to asymmetric information between manager and outside shareholder. Managers have an incentive to delay any bad information of the firm. One important reason is that managers try to withhold this bad news because of their job security (Jin and Myers, 2006; Kothari et al., 2009). Ultimately, an accumulation of bad news has reached to the limit, the firm subsequently makes a public announcement. Thus, a crash in stock prices is inevitable (Chang et al., 2017; Habib et al., 2018). Prior literature in stock price crash risk is widely studied in developed markets (Chen et al., 2001; Jin and Myer, 2006; Hutton et al., 2009; Kim et al., 2011; Francis et al., 2016; Kim et al., 2014; Cohen et al., 2014). Only few studies provide evidence in emerging markets (Vo, 2020; Huang et al., 2021; Wattanatorn and Padungsaksawasdi, 2022). In addition, none deeply focuses on the role of stock liquidity in emerging markets despite an important role of liquidity. Therefore, this study aims to explore the impact of stock liquidity by employing several measurement of stock liquidity. Therefore, this study fills this gap.

3. Research Methods

3.1. Data

All data are from Refinitiv Eikon, excepting for one-month T-bill from the Thai Bond Market Association. The sample period starts from February 2001 to December 2019. After removing insufficient and winsorizing data at the 1% of both tails, the final sample consists of 602 firms, yielding 13,462 firm-period observations.

3.2. Stock Price Crash Risk Measure

We employ two popular measures of stock price crash risk, namely the negative skewness measure (NSKEW_i,t) and the down-to-up volatility (DUVOL_i,t) suggested by Chen et al. (2001).

\(\begin{aligned}\operatorname{NSKEW}_{i, t}=\frac{-\left[n(n-1)^{3 / 2} \sum_{\tau=1}^{T} w_{i, \tau}^{3}\right]}{\left[(n-1)(n-2)\left(\sum_{\tau=1}^{T} w_{i, \tau}^{2}\right)^{3 / 2}\right]}\end{aligned}\)       (1)

\(\begin{aligned}D U V O L_{i, t}=\log \left[\frac{\left(n_{d}-1\right) \sum_{\tau=D O W N}^{T} \sigma_{i, \tau}}{\left(n_{u}-1\right) \sum_{\tau=U P}^{T} \sigma_{i, \tau}}\right]\end{aligned}\)       (2)

w_i,τ is the summation of the third moments of demeaned daily return of firm i. τ is the τth period of six months and n is the number of days in a particular six months period τ. σ_i,τ is the standard deviation of firm i daily return. DOWN (UP) days are daily returns, which is less (more) than the six months average of firm i during a period of six months τ. n_d (n_u) is the number of DOWN (UP) days.

3.3. Illiquidity Measures

In this study, we select five widely well-known illiquidity measures calculated from volume, price, and transaction cost as follows.

3.3.1. Volume-based Measures

3.3.1.1. Adjusted Amihud illiquidity ratio (Kang & Zhang, 2014)

\(\begin{aligned}\operatorname{AdjILLIQ}_{i, t}=\left[\ln \left(\frac{1}{T} \sum_{d=1}^{T} \frac{\left|R_{t, d}^{i}\right|}{V_{t, d}^{i}}\right)\right] \times(1+Zerovol \left._{i, t}\right) \end{aligned}\)       (3)

Zeroval_i,t  \(\begin{aligned}\\=\frac{\text { number of days with zero trading volume in month }}{T}\\\end{aligned}\)       (4)

where R_t,dⁱ and V_t,dⁱ are return and trading volume in million baht of stock i on day d in month t, respectively. T is the total number of trading days in month t. Zerovol_i,t is the number of zero trading volume days in month t divided by the number of total trading days in month t. ln is natural logarithm.

3.3.1.2. Lui (2006)’ s illiquidity measure

\(\begin{aligned}\begin{array}{l}L M 6 \\ =\left[\begin{array}{c}\text { Number ofdays with zero trading volume in prior } \\ \left.- \text { month }+\frac{1 /(6-\text { month turnover })}{11,000}\right]\end{array}\right] \\ * \frac{21 \times 6}{\text { Total number of trading day in prior } x \text { months }}\end{array}\end{aligned}\)      (5)

where 6 - month turnover is the turnover ratio of stock i in prior six months.

3.3.2. Price-based Measure

3.3.2.1 Pastor and Stambaugh (2003)’s gamma

r_i,t+1^e = θ + Φr_i,t + γsign(r_i,t^e) * Vol_i,t + ε_i,t+1       (6)

where r_i,t+1^e and Vol_i,t the value-weighted excess return and trading value in million baht on stock i and on days t+1 and t, respectively. γ represents liquidity of stock.

3.3.3. Transaction Cost Measure

3.3.3.1. Zero return (Lesmond et al., 1999)

zero_i,t\(\begin{aligned}=\frac{\text { number of days with zero return in month } t}{T}\end{aligned}\)       (7)

zero_i,t is the average number of days with zero return for the stock i in month t.

3.3.3.2. Effective spread (Roll, 1984)

\(\begin{aligned}Effective \; spread_{i, t}=2 \sqrt{-\operatorname{cov}_{i, t}}\end{aligned}\)       (8)

coν_i is the first order serial covariance of price changes of stock i between two consecutive months.

3.4. Empirical Model

The baseline regression model is

\(\begin{aligned} \operatorname{CrashRisk}_{i, t}= & \alpha+\beta_{i} L_{m} Q_{i, t-1} \\ & +\sum_{j=1} \beta_{j} \text { Control variable }_{j, t-1} \\ & + \text { Industry }_{\text {Fixed Effect }} \\ & + \text { Year }_{\text {Fixed Effect }}+\varepsilon_{i, t}\end{aligned}\)       (9)

when CrashRisk_i,t is NSKEW_i,t or DUVOL_i,t. LIO is a stock’s illiquidity measure defined in prior section. Control variable are described in Table 1.

Table 1: Variables description

4. Results and Discussion

4.1. Baseline Regression

For interpretation, we follow prior literature by multiplying -1 to all coefficients of illiquidity measures. Thus, when looking at estimated coefficients in the results, for ease, we multiply -1 in order to show the relationship between stock liquidity and tail risk (stock price crash risk). Table 2 clearly demonstrates a negative relationship between stock illiquidity and crash risk in both crash risk measures. However, the effect of liquidity measure on NSKEW is generally greater than that of DUVOL. All coefficients of liquidity measures are also significant. Among different types of liquidity measure, the zero-return illiquidity measure shows the strongest effect with 0.851% increase in crash risk, while the Lui’s liquidity measure shows the least effect (0.0286%). Additionally, control variables are largely significant, which are in line with prior literature.

Table 2: Main results.

Note: we multiply all coefficients of illiquidity measures by -1. *, **, and *** are statistical significance at the 10%, 5%, and 1% levels, respectively.

4.2. Endogeneity

In order to alleviate the endogeneity biases, we apply the two-stage least squares instrumental variable (2SLS). The industry median of liquidity measures is selected as an instrumental variable given two major advantages. First, firm’s liquidity is co-related with industry-wide liquidity, providing similar information (Chordia et al., 2000) . Second, although the management actions could influence crash risk, subsequently affecting stock’s liquidity, it is less likely that they can influence the entire industry. The first stage regression is shown

\(\begin{aligned} L \widehat{I Q_{l, t-1}}=\alpha_{i}+ & L I Q_{\text {median }, t-1} +\gamma_{i} \sum_{i=1}^{k} \operatorname{CONTROL}_{i, t-1}+\vartheta_{t-1}\end{aligned}\)       (10)

Then we repeat the procedure in section 3 for the second stage least square regression and the results are shown in Table 3. The findings are largely similar to Table 2, confirming the negative liquidity-crash risk relationship.

Table 3: Two-stage least squares estimation

Note: we multiply all coefficients of illiquidity measures by -1. *, **, and *** are statistical significance at the 10%, 5%, and 1% levels, respectively.

5. Conclusion

This paper fills the gap in prior literature on mixed findings of the relationship between stock liquidity and tail risk (stock price crash risk simply defined as a negative skewness in return). We perform tests based on the three different dimensions of liquidity measurement namely volume based measures, price based measures, and transaction cost based measures. We show that mixed results found in prior literature are potentially driven from types of liquidity measure. The liquidity-tail risk association is existent in the Stock Exchange of Thailand, in which problem of liquidity is more concerned than in that of advanced economies. The higher the stock liquidity, the larger the tail risk is. The results are robust in terms of measurement of crash risk and liquidity factors. An endogeneity issue is addressed by employing two-stage least squares regression.