Does time-varying illiquidity matter for the Indian stock market? Evidence from high-frequency data

Abstract

This article examines variations in illiquidity in the Indian stock market, using intraday data. Panel regression reveals prevalent day-of-the-week, month, and holiday effects in illiquidity across industries, especially during exogenous shock periods. Illiquidity fluctuations are higher during the second and third quarters. The ranking of most illiquid stocks varies, depending on whether illiquidity is measured using an adjusted or unadjusted Amihud measure. Using pooled quantile regression, we note that illiquidity plays an important asymmetric role in explaining stock returns under up- and down-market conditions in the presence of open interest and volatility. The impact of illiquidity is more severe during periods of extreme high and low returns.

JEL Classification: G10, G12

Keywords

Asset pricing illiquidity liquidity quantile regression seasonality stock market

1. Introduction

Stock market illiquidity is a complex yet important concept. The market microstructure literature suggests that illiquidity risk is priced (Amihud et al., 2005). Liquidity-based asset pricing models, suggesting an inverse relation between stock illiquidity and price, help explain the low prices of certain hard-to-trade illiquid stocks compared to more liquid stocks with similar cash flows. Knowledge of the variations in stock market illiquidity helps us understand some asset pricing puzzles, such as the insolvency of financial institutions in times of higher stock prices (Allen and Gale, 2004). Asset pricing theories support the presence of an illiquidity premium in expected asset returns. Intuitively, when a risk-averse investor faces the risk of an inventory of stocks potentially not being traded without price distortion, the investor would look for an additional return for bearing this risk (illiquidity premium). Therefore, stock market price movements are often vulnerable to levels of illiquidity.

During the 2008 subprime crisis, the world witnessed how illiquidity variations in various markets, including stock markets, were a precursor to the world economic crisis. While these variations play a crucial role in shaping financial market microstructures in the post-subprime crisis era (Diamond and Rajan, 2011; Hu et al., 2013; Tirole, 2011), the causes of these fluctuations are often debated (Cespa and Foucault, 2014). Illiquidity variations arguably have their root in the technological inventions and strategic innovations initiated after each crisis. To assess the effects of regulations, technological changes, and strategic innovations and to quantify these effects, researchers have used many proxies and indirect measurements, such as excess returns, market volatility, and market illiquidity, on both cross-sectional and time-series data. The choice of liquidity or illiquidity measure and its persistence have a significant impact on the outcome of various studies in this field. The lack of availability of detailed microstructure data in many emerging stock markets poses a challenge in illiquidity studies. The time-series analysis of the illiquidity–return nexus gained momentum with the introduction of Amihud’s (2002: 34) illiquidity measure, ILLIQ, defined as the average ratio of absolute returns to the dollar trading volume. This measure has been persistently used by researchers in liquidity-related studies, since it can be calculated for longer periods with easily available data, facilitating time-series analysis. The time-series analysis of illiquidity explores the explicit order dependence between illiquidity values separated by time, and this time dimension is often a source of information.

This article explains the time-varying nature of illiquidity in the Indian stock market by building an “adjusted illiquidity time series” (A-ILLIQ) on a rolling basis, using Indian firm trading data with a 30-minute frequency. The adjustments are for time trends and exogenous factors that could affect the stock market at the microstructure level. The time variations of ILLIQ and A-ILLIQ, averaged for all stocks, during known domestic and international events are shown in Figure 1. Illiquidity seems to increase during global and local events, as depicted in the figure. The measures capture illiquidity during the aftermath of the dot-com bubble; the September 2011 terror attack in the United States; the stock market crash in 2004, which coincides with the Indian National Congress winning the Indian election; the subprime crisis in the United States and the European debt crisis; the tapering of quantitative easing by the US Federal Reserve; the general election in India in 2014; and the demonetization drive of the Indian government during 2016. The variable A-ILLIQ shows more variations than ILLIQ during this period.

Figure 1.

Time variation in ILLIQ and A-ILLIQ in the Indian stock market.

The study is conducted both at the individual firm level and at the sectoral (industry) level. Using quantile regression (QR), we explore the role of A-ILLIQ in asset pricing in the Indian stock market, while controlling for global liquidity factors. The results validate that the adjusted illiquidity measure not only captures the impact of most of the shocks on liquidity but also shows variation across industries. The measure A-ILLIQ has asymmetric effects on stock returns under up- and down-market conditions.

This study is important for market participants who are concerned about changes in the cost of trading and the risk premium. Given liquidity dry-ups (sudden increases in illiquidity) and consequent flash crashes, the merit of this study lies in its deciphering of illiquidity variations, at both the firm and industry levels, while understanding its role in asset pricing in India.

The remainder of the article is organized as follows. Section 2 reviews the literature. Section 3 describes the data. Section 4 explains the methodology and the models. Section 5 discusses the empirical results. Section 6 concludes the article.

2. Literature review

Two critical facts can explain the presence of the voluminous work on financial market illiquidity. First, adequate liquidity ensures stability in capital markets (Geithner, 2007). Second, a drastic decline of liquidity can trigger illiquidity shock contagion, as evidenced during the subprime crisis of the United States. Asset markets are generally susceptible to periods of illiquidity fluctuations (Acharya and Schnabl, 2010; Anthonisz and Putnins, 2017; Ellington and Milas, 2018). Chen et al. (2018) examine illiquidity measures in the US equity market and argue that these measures have content predictive of real economic activity and stock market returns. The variability of market illiquidity has become a crucial issue, in both the asset pricing and market microstructure literature.

Many early works (Acharya and Pedersen, 2005; Amihud and Mendelson, 1986; Amihud et al., 2005; Brennan et al., 1998; Chordia et al., 2001) on stock market illiquidity premia in asset pricing focus primarily on data from the United States and developed markets. Emerging markets, such as India, are mainly order-driven markets, in contrast to the quote-driven markets of developed countries. In an order-driven market, there are no standby liquidity providers in the form of market makers (Jain, 2005). Emerging markets therefore offer a different setting in which variability in illiquidity can be studied. They also provide an ambiance where the impact of political, regulatory, and economic forces on market illiquidity can vary. Bekaert et al. (2007) argue that, although liquidity-related research focuses more on the US market, the liquidity effect is stronger in emerging markets. Amihud et al. (2015) suggests that evidence supporting an illiquidity premium is biased toward the US market. In our study, we present only the relevant literature related to stock market liquidity. The first section below addresses asset pricing with an illiquidity premium in developed as well as emerging stock markets, while the second section addresses the liquidity and illiquidity proxies used in empirical studies.

2.1. Illiquidity and asset pricing

A plethora of studies investigate the influence of illiquidity on asset pricing in the United States and other developed markets. Their findings are based on diverse illiquidity (liquidity) measures for stock markets. Amihud and Mendelson (1986) use the regression model, and Brennan and Subrahmanyam (1996) use Kyle’s (1985) model on the bid–ask spread for US markets. They find that illiquidity is negatively related to stock returns. Amihud (2002) establishes that expected market illiquidity has a positive impact on observed stock returns. However, the author observes that the higher unanticipated illiquidity leads to lower contemporaneous returns. One possible reason behind this intriguing phenomenon is variability in the time trends of stock market illiquidity, as evident in the work of Chordia et al. (2001). These authors observe that variability in illiquidity has a negative effect on stock returns in the United States over time. Using fluctuations in volume and turnover as proxies for stock market liquidity, Easley et al. (2002) show a negative effect of liquidity on returns in developed stock markets. Empirical studies (Acharya and Pedersen, 2005, and references therein) support the notion that liquidity is priced. Acharya and Pedersen (2005) propose an illiquidity-adjusted capital asset pricing model (CAPM), considering the risk originating from changes in illiquidity over time, as an important factor in asset pricing. Their model shows how illiquidity, if persistent, results in low current returns and high expected future returns. Brunnermeier and Pedersen (2009) suggest variations in liquidity during up and down markets due to shocks and the risk management practices of market participants. Hameed et al. (2010) show that firm-level illiquidity increases with negative returns. Lee (2011) employs zero-return proportion as an indirect measure of illiquidity, supporting Acharya and Pedersen (2005). Hence, an understanding of fluctuations or time trends in illiquidity becomes crucial (Hu et al., 2013).

The literature on stock market illiquidity in the context of emerging markets not only is limited but also presents a different picture in comparison with developed markets. Jun et al. (2003) noted a positive correlation between stock returns and market liquidity in 27 emerging markets, including India, which deviates from findings related to developed markets in a cross-sectional setup. Dey (2005) reports that the relation between turnover and stock returns is significant and positive in emerging markets, but this relation becomes nonsignificant in developed markets. While Bekaert et al. (2007) find evidence that unexpected liquidity fluctuations are positively correlated with concurrent return shocks in emerging markets, Chen et al. (2018) question the validity of their liquidity proxy in influencing stock returns in developed markets. Bekaert et al. (2007) also note that transaction-level data are not widely available in emerging markets and the quality of the data is also questionable. Liang and Wei (2012) suggest that inferences based on data from developed countries are more reliable compared to emerging markets. Using ILLIQ, Amihud et al. (2015) find a positive illiquidity premium in stock returns for both developed and emerging markets. Krishnan and Mishra (2013) study the intraday patterns of 20 stocks listed in India during 2009. They observe that most liquidity measures follow a U-shaped pattern during a day. They provide weak evidence of commonality among liquidity measures and suggest an extended analysis of a larger number of stocks. Kumar and Misra (2019) use ILLIQ in an ordinary least squares (OLS) regression for the period 2012–2015 and note that both systematic risk and firm-specific liquidity risk are priced in India. Bhattacharya et al. (2019) show that liquidity affects stock market returns in both the short and long run.

2.2. Choice of illiquidity measure

The empirical research discussed above is more focused on the quote-driven US stock market, where transactional data are generally available. The bid–ask spread is the most common liquidity proxy considered in these studies, since it can capture various types of transactional costs, including order processing costs, execution costs, and trade-associated taxes. Table 1 summarizes the alternate proxies and corresponding studies.

Table 1.

Key liquidity/illiquidity measures.

Proposed liquidity measure name	Computation	Studies that employ the proposed measure
Zero returns	Lesmond et al. (1999)	Bekaert et al. (2007), Kang and Zhang (2014), Lee (2011), Levine and Schmukler (2006), Marshall et al. (2013)
Amihud (averaged ratio of absolute stock return to its dollar volume)	Amihud (2002)	Amihud et al. (2015), Beber and Pagano (2013), Bortolotti et al. (2007), Lang and Maffett (2011), Marshall et al. (2013)
Pastor and Stambaugh (price changes accompanying order flow)	Pastor and Stambaugh (2003)	Cakici and Tan (2014), Fong et al. (2017), Kang and Zhang (2014), Liang and Wei (2012), Marshall et al. (2013)
Gibbs (based on daily closing prices)	Hasbrouck (2009)	Kang and Zhang (2014), Marshall et al. (2013)
Sadka (firm-level liquidity, decomposed into variable and fixed price effects)	Sadka (2006)	Cakici and Tan (2014)
Liu (standardized turnover-adjusted no. of zero daily trading volumes)	Liu (2006)	Hearn (2010), Kang and Zhang (2014)
LOT Y-split	Goyenko et al. (2009)	Fong et al. (2017)
Effective tick	Goyenko et al. (2009)	Fong et al. (2017)
High–low	Corwin and Schultz (2012)	Fong et al. (2017)
Zero volume	Kang and Zhang (2014)	Kang and Zhang (2014)
FHT measure	Fong et al. (2017)	Fong et al. (2017), Marshall et al. (2013)
Closing percent quoted spread	Chung and Zhang (2014)	Fong et al. (2017)
Turnover	Value of shares traded/ market cap; no. of shares traded/no. of shares outstanding	Dey (2005), Jain (2005), Lecce et al. (2012), Lesmond (2005), Levine and Schmukler (2006)
Value traded ratio	Value of shares traded/GDP	Assefa and Mollick (2014), Levine and Zervos (1998)
Trading value	Value of shares traded	Jun et al. (2003), Lecce et al. (2012), Lin (2008), Sharif et al. (2014)
MEC (market efficiency coefficient)	The ratio of long-period to short-period returns	Bhattacharya et al. (2016), Bhattacharya et al. (2019)
TP (trading probability)	Narayan and Zheng (2011)	Bhattacharya et al. (2016), Narayan and Zheng (2011)

This table outlines key liquidity measures referenced in many seminal research works on stock market microstructure.

Goyenko et al. (2009) test for various illiquidity (liquidity) measures and assess their performance in stock markets. They report that the ILLIQ measure performs quite well in measuring liquidity in stock markets. Fong et al. (2017) use the n-day rolling version of ILLIQ to conclude that it is the best proxy for illiquidity in emerging as well as developed stock markets, where n take values such as 1, 5, 10, or 20 to gauge daily, weekly, biweekly, or monthly aggregations, respectively. This study chooses the rolling version of Amihud’s (2002) ILLIQ measure based on intraday high-frequency (30-minute) trading data.

The empirical studies discussed above indicate that the literature dedicated to order-driven stock markets in emerging countries such as India is relatively scant. In terms of stocks listed, India is among the top five global equity markets, and among the top seven markets in terms of market capitalization as of 2018. We test the following propositions in the Indian stock market.

Propositions 1: The traditional illiquidity measure (ILLIQ) shows time variations.

Propositions 2: The effect of A-ILLIQ on stock returns is significant and asymmetric in up and down markets.

Proposition 1 is tested by estimating the parameters of equation (1). Proposition 2 is tested by the statistical significance of the adjusted illiquidity coefficient across quantiles (equation (2)).

3. Data

This study considers the high-frequency intraday price and volume data at a 30-minute frequency for the firms listed in the NIFTY 500 index of the National Stock Exchange of India (NSE). We consider only those firms that have more than 120 days of data for a specific year. Table 2 shows the numbers of firms available for consideration. The firm-specific data set comprises 14 intervals of 30 minutes each for a day. For missing price and volume data for a few 30-minute windows, we follow Yadav and Roychoudhury (2018) and use the corresponding average value over the day in question. The final data set comprises 1,575,494 data points for firms listed on the NIFTY 500 over the 17 years from 2000 to 2017. The study includes industry-wide time variation in illiquidity, since most of the liquidity-based asset pricing models (Hameed et al., 2010 and references therein) suggest industry-wide contagion of illiquidity. Table 3 presents the Global Industry Classification Standard (GICS) codes and average percentages of stocks for each industry in each year.

Table 2.

Numbers of firms considered each year.

Year	2000	2001	2002	2003	2004	2005	2006	2007	2008
Number of stocks	245	254	262	265	280	296	320	356	384
Year	2009	2010	2011	2012	2013	2014	2013	2016	2017
Number of stocks	396	425	439	447	453	459	474	496	500

Table 3.

Percentage representation of firms in all 11 GICS¹ sectors in each year.

Sector	Percentage in each year
Consumer discretionary (CD)	15–18
Materials (MAT)	15–17
Industrials (IND)	16–17
Financials (FIN)	14–16
Health care (HC)	6–8
Consumer staples (CS)	5–7
Information technology (IT)	5–7
Utilities (UTIL)	3–5
Energy (ENR)	3–4
Real estate (RE)	2–4
Telecommunication services (TEL)	0–1

GICS: Global Industry Classification Standard

4. Methodology

In this article, we use Amihud’s (2002) illiquidity measure, ILLIQ, as the measure of illiquidity. First, we capture seasonal or time variations in illiquidity, using a panel regression with random effects, and use the residuals as the adjusted illiquidity measure (A-ILLIQ). For this, we regress stock i’s illiquidity on day t on a set of variables known to capture time variation in illiquidity (equation 1). Subsequently, we use the residuals from the panel regression along with other factors in a pooled QR analysis to understand the relation between stock returns and illiquidity during up and down markets. The details of these two methods are explained in the sections below.

4.1. Adjusted illiquidity measure: A-ILLIQ

The daily measure of Amihud’s (2002) illiquidity measure, ILLIQ, is built on 30-minute high-frequency trading data on a rolling basis

I L L I Q_{t} = A v e r a g e (\frac{A b s o l u t e R e t u r n_{t}}{V o l u m e_{t}})

where $V o l u m e_{t}$ is the volume, in Indian rupees, for time t. The average is calculated over periods of nonzero volume over the entire day, and t represents a 30-minute interval, where $t \in [1, 14]$ .

We first regress stock i’s ILLIQ for day t on a set of deterministic variables and obtain A-ILLIQ as the residuals. The choice and construction of regressors are based on empirical studies on time variations in illiquidity (Chordia et al., 2005; Hameed et al., 2010). Krishnan and Mishra (2013) highlight the possibility of time-varying patterns in liquidity measures in the Indian stock market.

The day-of-the-week, month-of-the-year, and holiday effects on liquidity are well documented by Chordia et al. (2005) and are included in our model. We include two time trend variables to capture the impact of the subprime crisis $(S U B P R I M E Y E A R)$ and the dot-com bubble $(D O T C O M Y E A R)$ on liquidity. Since algorithmic trading was introduced to the NSE in the middle of the study period and is expected to impact market microstructure (Frijns et al., 2018; Hendershott and Riordan, 2013; Upson and Van Ness, 2017), we need to control for its impact. We follow Hameed et al. (2010) in calculating the two time trend variables and the algorithmic trading dummy variable. The model for A-ILLIQ is illustrated in Figure 2 and is expressed as

\begin{matrix} I L L I Q_{i, t} = \sum_{k = 1}^{4} ϕ_{i, k} D a y_{k, t} + \sum_{k = 1}^{11} θ_{i, k} M o n t h_{k, t} + β_{1, i} H o l i d a y_{t} + \\ β_{2, i} D O T C O M Y E A R_{t} + β_{3, i} S U B P R I M E Y E A R_{t} + β_{4, i} A T R E G I M E_{t} + A - I L L I Q_{i, t} \end{matrix}

(1)

Figure 2.

Model represented by equation (1).

In equation (1), where the dependent variable is the unadjusted illiquidity proxy (ILLIQ), the following variables are used as regressors, respectively:

Day_k,t represents dummy variables, such that Day_k,t=1 if the day is the kth day of the week (Monday through Thursday), and zero otherwise, where φ_i,k denotes the coefficients.

Month_k,t represents dummy variables such that Month_k,t=1 if the day is the kth month of the year (January through November), and zero otherwise, where θi,k denotres the coefficients.

Holiday_t is a dummy variable that captures the impact of holidays on returns. If the tth day is a holiday (t ≠ Monday,Friday), the values of both the (t – 1)st and (t + 1)st days are set to one, and zero otherwise. If the tth day happens to be a Friday or Monday, the preceding Thursday and the following Tuesday, respectively, are set to one.

DOTCOMYEAR_t is a trend variable that is calculated as the difference between the current calendar year and the dot-com year (2000). If a particular stock i is not listed by the year 2000, then the value of DOTCOMYEAR_t is the difference between the current calendar year and the year when stock i was listed.

SUBPRIMEYEAR_t is a trend variable that is calculated as the difference between the current calendar year and the year 2008. If a particular stock is not listed by the year 2008, then the value of SUBPRIMEYEAR_t is the difference between the current calendar year and the year when stock i was listed.

ATREGIME_t is a dummy variable to control for algorithmic trading, and it is set to zero before algorithmic trading was allowed (April 4, 2008), and to one afterward.

A-ILLIQ_i,t is the residual (adjusted illiquidity measure), and A-ILLIQ is interpreted as abnormal or unexpected illiquidity that is present in the stock market.

The residual, A-ILLIQ, is likely to account for factors not in the equation. Brennan et al. (2013) show that Amihud’s (2002) measure could be decomposed into a turnover-based form and firm size (market capitalization). Hence, A-ILLIQ thus obtained is expected to factor in both turnover and firm size.

4.2. Random effect specification

Once the A-ILLIQ time series is obtained at the firm level, as explained in the previous section, we explore the evolution of A-ILLIQ across different industries. We regress ILLIQ on the same set of variables as shown in equation (1) for random effects and obtain A-ILLIQ across different industries/sectors. The error component specification for random effects is $μ_{i} + υ_{i t}, where υ_{i t} ~ I I N (0, σ_{υ}^{2}); μ_{i} ~ I I N (0, σ_{μ}^{2}); C o v (μ_{i}, υ_{i t}) = 0$ . In addition, error terms are not correlated with the predictors of equation (1). This model specification helps in explaining the unobserved heterogeneity (Borenstein et al., 2010). The Hausman test, used here to choose the random effects model over the fixed effects model, hypothesizes that the random effects would be consistent and efficient against the alternative of fixed effects. It tests if the errors are correlated with the regressors, under the null hypothesis that they are not.

4.3. Asset pricing with the adjusted illiquidity factor

Donadelli and Prosperi (2012) argue for the inclusion of open interest and the volatility index as global liquidity factors in asset pricing models. Open interest is the number of options and futures contracts that have not been settled. The volatility index is the stock market’s expectation of volatility over the near term and is published by exchanges. Both measures are highly influenced by international factors. Donadelli and Prosperi find both measures to be statistically significant and positive in most emerging stock markets. We obtain the open interest and volatility index values for the Indian stock market from Bloomberg. For asset pricing, we use QR that models the relation between independent variables and conditional quantiles (τ) of the excess stock returns (dependent variable). We apply the QR model because it provides robust results and a more specific picture of the effect of the independent variables on the dependent variable (ExRET). The τth conditional QR is expressed as follows

E x R E T (τ | x) = \sum_{X} β_{k} (τ) X_{k} = X^{'} β (τ) (0 \leq τ \leq 1)

(2a)

where β(τ) is the vector of QR coefficients associated with τth quantile that determines the dependence relation between the τth conditional quantile of y and $X^{'}$ (where $X^{'}$ is a vector of the independent variables in the model). The dependence is conditional because of the presence of exogenous independent variables.

The dependent variable, $E x R E T_{i t}$ , here is the excess return on the $i th$ stock on day $t$ . Harvey (1995) suggests that the conditional estimation in the CAPM allows researchers to account for the risk-loading time-varying component, whereas Donadelli and Prosperi (2012) argue that emerging market stock returns are impacted by time-varying global liquidity factors and advocate the use of open interest and the volatility index as proxies for global liquidity factors. We estimate a four-factor pooled QR model to understand how illiquidity impacts stock returns. Following Donadelli and Prosperi (2012), we condition the standard CAPM for the first differences of open interest (R_NZI) and the volatility index (R_INVIXN). However, the authors use the OLS method, whereas we consider a pooled QR setup. In addition, the one-period-lagged illiquidity measure (A-ILLIQ_i,t₋₁) is included as a regressor to understand the impact of illiquidity on stock returns. The pooled QR model for asset pricing is

\begin{array}{l} E x R E T_{i t} (τ | x) = α (τ) + β_{1 τ} (M R P_{t}) + β_{2 τ} (M R P_{t} . R I N V I X N_{t}) \\ + β_{3 τ} (M R P_{t} . R N Z I_{t}) + β_{4 τ} (A - I L L I Q_{i, t - 1}) + ε_{i, t} (τ) \end{array}

(2b)

where $τ \in$ [0,1], $β_{k τ}$ is the QR coefficient at the τth quantile (k = 1, 2, 3, 4), and $ε_{i t} (τ)$ is the error term.

The following independent variables are used in the pooled QR model (equation (2b)):

$M R P_{t}$ is the market risk premium $(R_{m t} - R_{f t})$ , calculated as the excess return of the market portfolio on the tth day. It varies over time but, on a given day t, it is same for all stocks.

$M R P_{t} . R I N V I X N_{t}$ or $[(R_{m t} - R_{f t}) . R_{I N V I X N_{t}}]$ , is expected to capture the impact of change in the market volatility over the near term on stock returns, through its interaction with the market risk premium, MRP. The volatility index is a measure of financial options’ implied volatility, and the change in volatility index or the first difference on a given day t is represented by $R I N V I X N_{t}$ . Similar to Donadelli and Prosperi (2012), we use this factor as a proxy for the global liquidity factor.

$M R P_{t} . R N Z I_{t}$ or $[(R_{m t} - R_{f t}) . R_{N Z I_{t}}]$ is intended to capture the impact of change in open interest on stock returns through its interaction with MRP (Donadelli and Prosperi, 2012 noted this to be the global liquidity factor). Open interest represents trading activity in the financial derivatives space and is the number of options and/or futures contracts open on the NIFTY 500 in a particular day. The change in open interest or the first difference on a given day t is $R_{N Z I_{t}}$ .

$A - I L L I Q_{i, t - 1}$ is the unexpected illiquidity for stock i on day t − 1. The A-ILLIQ value for each stock is obtained using equation (1).

We estimate the vector of QR coefficients β(τ) by minimizing the weighted absolute deviations between y and $X^{'}$ for a given τ, as follows

\hat{β} = \min \sum_{t = 1}^{T} (τ - I_{{y_{t} < X'_{t} β (τ)}}) | y_{t} - {X^{'}}_{t} β (τ) |

where $I_{{y_{t} < {X^{'}}_{t} β (τ)}}$ is the indicator function (Mensi et al., 2014).

For the minimization problem, Portnoy and Koenker (1997) show that the use of the interior point method improves computational efficiency relative to simplex-based methods, and they discuss the choice of algorithmic methods to compute the fit in a QR model, depending on the frequency of the data. We use the Frisch–Newton interior point method, since we have more than one million observations, and the mean value of the dependent variable (return) is quite low (for details, see Portnoy and Koenker, 1997). Thus, using the above method, we highlight the kind of dependence structure that exists in the Indian stock market and how it is affected by the selected explanatory variables. To the best of our knowledge, such observations are not available in the microstructure literature in the context of the Indian stock market.

5. Results and discussion

We have run equation (1) individually for all the firms under study. In this section, we present and discuss industry-specific and yearly average results, since the findings for individual firms are too voluminous to be presented here.

5.1. Variation in illiquidity: adjusted illiquidity

Table 4 presents the coefficients of equation (1) for the entire panel data (the column labeled All), as well as for each of the 11 industries.

Table 4.

Results of random effect estimates in equation (1).

Factors	All	CD	CS	ENG	FIN	HC	IND	IT	MAT	RE	TEL	UTIL
February							90.6**
May			286***							2.1**
June							82.9**
July	174***	707**				100***	116***		129**			0.72**
August							80.4**
September	173***	711**					114***		131**
October	206***	830***	182**				77**		258***
November							83.7**		131**
Monday								1.6**		1.7***	0.75**	0.8***
Holiday	196***	631***	149***	38.5***	97.1**	104***	131***	2.6***	185***	0.2***
Dot-Com	−70***	−297***	−35***	−7.9**	−31***	−11***	−24***	−0.6***	−44***	0.4**		−1***
Subprime	20***	124***				−13***	−16***	−1.1***		−0.7***		0.4***
AT-Regime	271***	970***	153**			80.7***	184***	12***	185***	−4***	1.0**	2***
Hausman test: chi-squared and prob.	12.118 (0.881)	7.7362 (0.989)	2.896 (0.998)	2.516 (0.999)	2.120 (0.999)	6.205 (0.997)	7.3697 (0.991)	2.9243 (0.999)	12.685 (0.854)	4.812 (0.999)	31.864** (0.032)	2.5248 (0.999)

This table shows only significant factors. For example, December and January are not listed in the factors column because they are not significant. All numbers (except for Hausman test) have a multiplier of 10E−7. The last row shows the results of the Hausman test (chi-square values), where the figures in parentheses are the probability values. The random effects are consistent in all sectors, except TEL. The table omits figures that are not statistically significant at the 90% confidence level.

**, ***

Significance at 95% and 99%, respectively.

The significant parameters for monthly factors, such as July, August, September, October, and November, as reported in Table 4, indicate a seasonal pattern in unadjusted illiquidity, or ILLIQ, in the Indian stock market. Illiquidity fluctuations appear to have a more substantial presence in the second and third quarters than in the first and fourth quarters, especially for firms belonging to the CD, IND, and MAT industries. However, the month dummies for companies belonging to the ENR, FIN, TEL, and IT sectors capture no such seasonality effects. Illiquidity is usually higher around holidays. The holiday effect is consistent across sectors, except for TEL and UTIL. Illiquidity is slightly higher on Mondays for IT, RE, TEL, and UTIL sectors. However, the evidence does not support any weekend effect on illiquidity.

The regression coefficients of the variables representing event years (Dot-Com, Subprime, and AT-Regime) show industry-wide variations in illiquidity. There is a significant drop in illiquidity around the dot-com bubble. Notably, IT companies saw a lesser decrease in illiquidity relative to other sectors in the dot-com era. The results are consistent with evidence of seasonality in illiquidity, as documented by Chordia et al. (2005). The findings are also in line with those of Hameed et al. (2010) in terms of illiquidity variations around the holidays, but do not support their results for the weekend (Friday) effect.

The subprime crisis increased overall illiquidity in the Indian stock market. However, the impact of the crisis is inconsistent across sectors. CS, ENR, FIN, TEL, and MAT sectors appear neutral during the crises, as far as liquidity dry-ups are concerned. Interestingly, during the crisis, HC, IT, IND, and RE sector stocks became relatively liquid, compared to other sectors. Algorithmic trading appears to increase the overall illiquidity of the Indian stock market, except for RE companies, for which the effect seems to be the opposite. Algorithmic trading seems to have no effect on illiquidity for ENR and FIN sector stocks. The evidence on algorithmic trading–induced illiquidity in the Indian context does not support the results obtained for the US stock market reported by Hendershott et al. (2011).

5.2. Comparison of the most liquid and illiquid firms, based on ILLIQ and A-ILLIQ

In this section, we show, year on year, the most liquid and illiquid stocks, based on both ILLIQ and A-ILLIQ. Panel A of Table 5 presents the year-wise list of the most illiquid (liquid) firms based on the ILLIQ measure, while panel B reports the same results for the A-ILLIQ measure.

Table 5.

Summary of the most illiquid stocks, based on quoted illiquidity (ILLIQ) and adjusted illiquidity (A-ILLIQ).

Panel A: Most illiquid/liquid firms, based on ILLIQ					Panel B: Most illiquid/liquid firms, based on A-ILLIQ
Year	Company	Value(+)	Company	*Value(−)	Company	Value(+)	Company	*Value(−)
2000	Shriram Transport	0.0103	Infosys	1.9	Birla Corp.	0.0334	JBF Industries	−0.6081
2001	Strides Shasun	0.0247	Infosys	1.6	Heidelberg Cement	0.064	IFB Industries	−0.8495
2002	Lakshmi Machine	0.0095	Infosys	0.958	IFB Industries	0.0711	KRBL	−0.038
2003	Videocon	0.0025	Infosys	0.859	Bombay Burmah	0.0097	Videocon	−0.0413
2004	Videocon	0.0018	Infosys	2.36	JK Tyre	0.0257	Greenply	−0.0236
2005	3M India	0.0012	SBI	4.73	Trent	0.0067	3M India	−0.0009
2006	SML ISUZU	0.0016	RIL	6.18	Century Plyboards	0.0021	SML ISUZU	−0.002
2007	AstraZeneca	0.0031	IFCI	6.02	SML ISUZU	0.0149	Somany Ceramics	−0.0028
2008	AstraZeneca	0.0089	ICICI	9.33	Indo Count	0.0075	Cera Sanitaryware	−0.0449
2009	SML ISUZU	0.0046	Unitech	4.95	United Breweries	0.0534	Cera Sanitaryware	−0.0171
2010	3M India	0.0019	SBI	6.28	Whirlpool	0.0002	Avanti Feeds	−0.0072
2011	AstraZeneca	0.0045	SBI	6.65	Igarashi Motors	0.0022	Ramkrishna Forgings	−0.0152
2012	3M India	0.003	SBI	5.11	Igarashi Motors	0.0008	Indo Count Industries	−0.0291
2013	Ramkrishna Forgings	0.0027	SBI	6.43	Indo Count	0.0086	3M India	−0.0023
2014	3M India	0.0018	Unitech	5.21	Rupa & Co	0.0123	3M India	−0.0008
2015	3M India	0.0015	Unitech	5.03	Rupa & Co	0.0026	3M India	−0.0003
2016	3M India	0.0009	ICICI Bank	7.29	Birla Corp.	2.56E−6	Schaeffler India	−0.0003
2017	3M India	0.0007	Suzlon	3.62	Suzlon	3.91E−9	3M India	−0.0002

Panels A and B present the values of ILLIQ and A-ILLIQ, respectively. In both panels, the value(+) column shows the illiquidity values corresponding to the most illiquid stocks, and the value(−) column presents the values corresponding to the most liquid stocks. *All the numbers in the value(−) column of Panel A have a multiplier of 1E−8.

While companies such as Videocon, AstraZeneca Pharmaceuticals, and 3M India could appear to be among firms with the most illiquid stocks (Panel A of Table 5), Rupa & Co, Igarashi Motors, and Birla Corp., for example, are among the most illiquid firms, once we control for seasonality and deterministic time-series variation. The year-wise rankings of the most illiquid stocks look very different, depending on whether we use ILLIQ or A-ILLIQ to measure illiquidity. The percentage difference between fluctuations in A-ILLIQ and ILLIQ can be interpreted as a sudden decline in liquidity or liquidity dry-ups (Madhavan, 2012; Malherbe, 2014). Table 5 highlights that the use of A-ILLIQ over ILLIQ changes the ranking of individual firms in terms of illiquidity and improves our ability to capture illiquidity shocks at specific times for specific causes.

In Figure 3, we plot the two illiquidity time series, for ILLIQ and A-ILLIQ, for each industry. Illiquidity varies across industries, depending on the sensitivity of each industry to seasonality and other factors. Liquidity dry-ups are observed for the majority of sectors; the most significant among these are in 2003 (year of the IT recession), 2004 (Indian election), 2008 (subprime crisis), and 2013, when the US Federal Reserve started tapering quantitative easing. The findings are in line with those of Kyle and Obizhaeva (2016) and Sornette and Huber (2018), supporting liquidity dry-ups for specific stocks. Figure 3 shows that the use of A-ILLIQ improves our ability to capture occasional liquidity dry-ups or illiquidity shocks experienced by certain sectors for specific causes. At the same time, the original ILLIQ averages out the impact of seasonality and other trends in a contemporaneous setting.

Figure 3.

Time trends of quoted illiquidity and adjusted illiquidity.

5.3. Time-varying patterns of the effects of illiquidity on returns

To test the asset pricing model using equation (2b), we consider the 10-year period from 2008 to 2017 as the volatility index (INVIXN) and open interest (NZI) data for the NSE is available from 2008. Table 6 reports the pooled QR estimates with graphical depiction in Figure 4.

Table 6.

Pooled QR estimates using equation (2b).

Quantiles	Intercept (α)	β_MRP	β_INVIXN	β_NZI	β_A-ILLIQ
0.05	−0.0458*** (0.0005)	0.8373*** (0.0075)	0.2799*** (0.0138)	−5.4288*** (0.2622)	−20.0309*** (6.5783)
0.10	−0.0330*** (0.0003)	0.8876*** (0.0046)	0.2303*** (0.0095)	−2.5556*** (0.1645)	−8.5283*** (3.0968)
0.20	−0.02054*** (0.0002)	0.9345*** (0.0031)	0.1714*** (0.0064)	0.3984*** (0.1114)	−4.3006*** (0.9093)
0.30	−0.0133*** (0.0002)	0.9563*** (0.0026)	0.1466*** (0.0055)	2.2281*** (0.0937)	−2.5468** (0.2981)
0.40	−0.0080*** (0.0001)	0.9683*** (0.0023)	0.1243*** (0.0052)	3.4564*** (0.0855)	−0.9813 (1.5063)
0.50	−0.0026*** (0.0001)	0.9855*** (0.0024)	0.1108*** (0.0049)	4.6859*** (0.0846)	−0.1638*** (0.0328)
0.60	0.0033*** (0.0002)	1.0091*** (0.0026)	0.1044*** (0.0048)	5.7232*** (0.0813)	0.8394*** (0.6788)
0.70	0.0109*** (0.0002)	1.0452*** (0.0030)	0.0961*** (0.0052)	6.6931*** (0.0871)	1.7363** (0.7633)
0.80	0.0224*** (0.0003)	1.1094*** (0.0039)	0.1081*** (0.0066)	7.9351*** (0.1098)	3.2411*** (0.3768)
0.90	0.0425*** (0.0004)	1.2194*** (0.0062)	0.1255*** (0.0106)	9.4610*** (0.1715)	4.3884*** (0.1143)
0.95	0.0639*** (0.0007)	1.3331*** (0.0096)	0.1391*** (0.0164)	11.096*** (0.2554)	5.8595 (3.8021)

QR: quantile regression.

The table reports the coefficients of the quantile regression (equation (2b)) where the dependent variable is the excess return on stocks. The standard errors are in parentheses.

***, **

Significance at 99% and 95%, respectively.

Figure 4.

QR coefficients.

The QR estimates obtained from the pooled data show that all the coefficients are significant at all quantiles, except for the illiquidity coefficient being nonsignificant at τ = 0.4 and 0.95. Illiquidity is priced in the Indian stock market. The coefficients of lagged illiquidity, changes in open interest, the market risk premium, and the intercept are monotonically increasing as the quantiles increase. Lagged illiquidity affects contemporaneous returns asymmetrically. At the left tail of the return distribution, it has an adverse impact, but it impacts returns positively at the right tail. This asymmetric impact indicates that investors react differently to illiquidity during higher and lower return periods, and only beyond a certain threshold (when τ = 0.5, i.e. the median) is the illiquidity premium positive. This observation is consistent with that of Altay and Çalgici (2019).

The negative impact of illiquidity on stock returns during periods of negative and lower returns could indicate that investors fear the risk of being stuck with an inventory of illiquid stocks in a falling market. They can then hit the exit button, lowering stock prices and contemporaneous returns. In addition, funding constraints can force levered investors to liquidate in a down market. It is also evident that, at the left tail of the return distribution, both illiquidity and open interest exert a negative influence on stock returns. Short sellers could be similarly fearful of being trapped in illiquid stocks. The influence of illiquidity at the tails is stronger, and it is more impactful in the left tail. This could be because levered investors are more sensitive to liquidity in down markets, since they could be compelled to sell their position.

Figure 4 shows the behavior of all the coefficients across quantiles (horizontal axis), with a convex pattern for the coefficient of change in volatility. The behavior of the open interest coefficient suggests that changes in open interest, which represents a nonprice measure of activity in the derivatives market, have an asymmetric impact on returns across quantiles. The positive impact of the coefficient of change in open interest on stock returns (τ = 0.20 and above) is suggestive of the increased participation of market players and additional buying by investors during most of the return distribution. A negative impact of open interest at the left tail of the return distribution is indicative of a buildup of short positions by traders in down markets. In Figure 4, the horizontal lines represent the OLS regression coefficient, clearly showing that the pooled QR method captures the impact of predictor variables well across the return distribution. The findings lend support to the results of Bhuyan and Chaudhury (2005) and Fodor et al. (2011), where a positive impact of the increase in open interest on returns is emphasized.

The model used is the standard CAPM model, with two additional factors along with A-ILLIQ. It should be noted that trading volume could influence price momentum (Lee and Swaminathan, 2000), and Brennan et al. (2013) show a correlation between ILLIQ and momentum. While A-ILLIQ captures turnover and size jointly (Brennan et al., 2013), the findings do not rule out some role of firm size and momentum affecting stock return through A-ILLIQ. Overall, we have not ruled out a role for the information content of other factors that are not explicitly modeled, such as Fama–French and momentum factors, in influencing returns, given the significant intercept and A-ILLIQ coefficients.

6. Conclusion

We analyze Indian stock market illiquidity and its impact on the Indian stock market. The findings support day-of-the-week, month, and holiday effects on illiquidity. The holiday effect is consistent across all sectors, except for TEL and UTIL. Illiquidity fluctuations are more substantial during the second and third quarters of the financial year, especially for firms belonging to the CD, IND, and MAT sectors. Seasonality effects on ILLIQ are not observed for firms belonging to the ENR, FIN, IT, and TEL sectors, where sectoral reforms initiated by the government are more prominent. The year-wise rankings of most illiquid stocks differ considerably, depending on whether liquidity is captured by adjusted or unadjusted measures. The A-ILLIQ variable captures the illiquidity variations observed during the dot-com bubble, the subprime crisis, the quantitative easing in the United States, the Indian elections, and the demonetization drive of the Indian government. The findings are robust across international and local events.

We use QR to reveal evidence of the asymmetric relation between illiquidity and realized returns. During negative return periods, the impact of illiquidity on realized excess stock returns is negative, possibly because investors holding inventories of illiquid stock hit the panic button in a down market. In their quest to exit from illiquid holdings, they lower contemporaneous stock prices with excess supply. However, when the returns are above the median, illiquidity positively impacts returns. Thus, an illiquidity premium is observed only under up-market conditions. The influence of illiquidity is greater in the distribution tails, more particularly the left tail. At the left tail, both illiquidity and open interest exert a negative influence on stock returns. This finding indicates the possible role of short sellers who fear being stuck in a short position in an illiquid stock. The impact of volatility is relatively higher at the tails of the return distribution, owing to its quadratic nature across quantiles.

Understanding the illiquidity risk of a stock is of paramount importance to market participants, primarily because it impacts the speed at which one can open and close positions. Illiquidity hampers the ability to trade, and thus, intraday traders often lose money when liquidity is low. Even if one is sitting on unrealized gains on illiquid stocks, it might not be possible to reap the profits. A stock’s liquidity is a key factor in determining the spread that a leveraged trading provider can offer. The illiquidity of a stock increases the bid–ask spread, thus increasing the transaction cost. Above all, illiquid stocks can be mispriced, since they do not benefit from the advantage of price discovery through active trading in the market. The lack of transparency and the difficulty of price discovery both make it challenging for traders to see the larger picture for illiquid stocks. Thus, traders need to conduct greater due diligence before taking any position in illiquid stocks. All this calls for additional returns in the form of an illiquidity risk premium. The consequences of holding illiquid assets are stronger during crises, when execution can be difficult, often at less appealing prices.

This article clearly shows that the illiquidity of stocks of different industries increases at varying degrees during crisis periods. To compensate for this risk, estimates of the illiquidity risk premium are important, along with an understanding of other relevant factors that affect stock returns under various market conditions. Traders will find this study useful in this context. The findings are useful for researchers examining the impact of policy- and exchange-level technological innovations on stock market microstructure, especially during times of financial stress, when A-ILLIQ appears to be particularly useful. Although the results are based on daily illiquidity measures built from 30-minute intervals of data, future research could include still lower frequencies of data to obtain more insights.

Footnotes

Acknowledgements

The authors are thankful to the Associate Editor Tim Smith and the anonymous referees for their insightful comments and suggestions.

Final transcript accepted 22 March 2021 by Tom Smith (AE Finance)

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Sharad Nath Bhattacharya

Notes

References

Acharya

Pedersen

(2005) Asset pricing with liquidity risk. Journal of Financial Economics 77: 375–410.

Acharya

Schnabl

(2010) Do global banks spread global imbalances? Asset-backed commercial paper during the financial crisis of 2007–09. IMF Economic Review 58: 37–73.

Allen

Gale

(2004) Financial fragility, liquidity and asset prices. Journal of the European Economic Association 2: 1015–1048.

Altay

Çalgici

(2019) Liquidity adjusted capital asset pricing model in an emerging market: Liquidity risk in Borsa Istanbul. Borsa Istanbul Review 19: 297–309.

Amihud

(2002) Illiquidity and stock returns: Cross-section and time-series effects. Journal of Financial Markets 5: 31–56.

Amihud

Mendelson

(1986) Asset pricing and the bid–ask spread. Journal of Financial Economics 17: 223–249.

Amihud

Hameed

Kang

, et al. (2015) The illiquidity premium: International evidence. Journal of Financial Economics 117: 350–368.

Amihud

Mendelson

Pedersen

(2005) Liquidity and asset prices. Foundations and Trends in Finance 1: 269–364.

Anthonisz

Putnins

(2017) Asset pricing with downside liquidity risks. Management Science 63: 2549–2572.

10.

Assefa

Mollick

(2014) African stock market returns and liquidity premia. Journal of International Financial Markets, Institutions and Money 32: 325–342.

11.

Beber

Pagano

(2013) Short-selling bans around the world: Evidence from the 2007-09 crisis. The Journal of Finance 68: 343–381.

12.

Bekaert

Harvey

Lundblad

(2007) Liquidity and expected returns: Lessons from emerging markets. Review of Financial Studies 20: 1783–1831.

13.

Bhattacharya

Basu

(2019) Stock market and its liquidity: Evidence from ARDL bound testing approach in the Indian context. Cogent Economics & Finance 7 1586297.

14.

Bhattacharya

Sengupta

Bhattacharya

, et al. (2016) Multidimensional liquidity: Evidence from the Indian stock market. Applied Finance Letters 5: 28–44.

15.

Bhuyan

Chaudhury

(2005) Trading on the information content of open interest: Evidence from the US equity options market. Journal of Derivatives & Hedge Funds 11: 16–36.

16.

Borenstein

Hedges

Higgins

JPT

, et al. (2010) A basic introduction to fixed-effect and random-effects models for meta-analysis. Research Synthesis Methods 1: 97–111.

17.

Bortolotti

De Jong

Nicodano

(2007) Privatisation and stock market liquidity. Journal of Banking & Finance 31: 297–316.

18.

Brennan

Subrahmanyam

(1996) Market microstructure and asset pricing: On the compensation for illiquidity in stock returns. Journal of Financial Economics 41: 441–464.

19.

Brennan

Chordia

Subrahmanyam

(1998) Alternative factor specifications, security characteristics, and the cross-section of expected stock returns. Journal of Financial Economics 49: 345–373.

20.

Brennan

Huh

Subrahmanyam

(2013) An Analysis of the Amihud illiquidity premium. Review of Asset Pricing Studies 3: 133–176.

21.

Brunnermeier

Pedersen

(2009) Market liquidity and funding liquidity. Review of Financial Studies 22: 2201–2238.

22.

Cakici

Tan

(2014) Size, value, and momentum in developed country equity returns: Macroeconomic and liquidity exposures. Journal of International Money and Finance 44: 179–209.

23.

Cespa

Foucault

(2014) Illiquidity contagion and liquidity crashes. Review of Financial Studies 27: 1615–1660.

24.

Chen

Eaton

Paye

(2018) Micro(structure) before macro? The predictive power of aggregate illiquidity for stock returns and economic activity. Journal of Financial Economics 130: 48–73.

25.

Chordia

Roll

Subrahmanyam

(2001) Market liquidity and trading activity. The Journal of Finance 56: 501–530.

26.

Chordia

Sarkar

Subrahmanyam

(2005) The joint dynamics of liquidity, returns, and volatility across small and large firms. Report no. 207. New York: Federal Reserve Bank of New York, April.

27.

Chung

Zhang

(2014) A simple approximation of intraday spreads using daily data. Journal of Financial Markets 17: 94–120.

28.

Corwin

Schultz

(2012) A simple way to estimate bid–ask spreads from daily high and low prices. Journal of Finance 67: 719–760.

29.

Dey

(2005) Turnover and return in global stock markets. Emerging Markets Review 6: 45–67.

30.

Diamond

Rajan

(2011) Fear of fire sales, illiquidity seeking, and credit freezes. Quarterly Journal of Economics 126: 557–591.

31.

Donadelli

Prosperi

(2012) On the role of liquidity in emerging markets stock prices. Research in Economics 66: 320–348.

32.

Easley

Hvidkjaer

O’Hara

(2002) Is information risk a determinant of asset returns? Journal of Finance 57: 2185–2221.

33.

Ellington

Milas

(2018) On the economic impact of aggregate liquidity shocks: The case of the UK. Quarterly Review of Economics and Finance. Epub ahead of print 27 October. DOI: 10.1016/j.qref.2018.09.008.

34.

Fodor

Krieger

Doran

(2011) Do option open-interest changes foreshadow future equity returns? Financial Markets and Portfolio Management 25: 265–280.

35.

Fong

KYL

Holden

Trzcinka

(2017) What are the best liquidity proxies for global research? Review of Finance 21: 1355–1401.

36.

Frijns

Indriawan

Tourani-Rad

(2018) The interactions between price discovery, liquidity and algorithmic trading for U.S.-Canadian cross-listed shares. International Review of Financial Analysis 56: 136–152.

37.

Geithner

(2007) Liquidity risk and the global economy. International Finance 10: 183–189.

38.

Goyenko

Holden

Trzcinka

(2009) Do liquidity measures measure liquidity? Journal of Financial Economics 92: 153–181.

39.

Hameed

Kang

Viswanathan

(2010) Stock market declines and liquidity. Journal of Finance 65: 257–293.

40.

Harvey

(1995) Predictable risk and returns in emerging markets. Review of Financial Studies 8: 773–816.

41.

Hasbrouck

(2009) Trading costs and returns for US equities: Estimating effective costs from daily data. Journal of Finance 64: 1445–1477.

42.

Hearn

(2010) Time-varying size and liquidity effects in South Asian equity markets: A study of blue-chip industry stocks. International Review of Financial Analysis 19: 242–257.

43.

Hendershott

Riordan

(2013) Algorithmic trading and the market for liquidity. Journal of Financial and Quantitative Analysis 48: 1001–1024.

44.

Hendershott

Jones

Menkveld

(2011) Does algorithmic trading improve liquidity? Journal of Finance 66: 1–33.

45.

Pan

Wang

(2013) Noise as information for illiquidity. Journal of Finance 68: 2341–2382.

46.

Jain

(2005) Financial market design and the equity premium: Electronic versus floor trading. Journal of Finance 60: 2955–2985.

47.

Jun

Marathe

Shawky

(2003) Liquidity and stock returns in emerging equity markets. Emerging Markets Review 4: 1–24.

48.

Kang

Zhang

(2014) Measuring liquidity in emerging markets. Pacific-Basin Finance Journal 27: 49–71.

49.

Krishnan

Mishra

(2013) Intraday liquidity patterns in Indian stock market. Journal of Asian Economics 28: 99–114.

50.

Kumar

Misra

(2019) Liquidity-adjusted CAPM—An empirical analysis on Indian stock market. Cogent Economics & Finance 7: 1573471.

51.

Kyle

(1985) Continuous auctions and insider trading. Econometrica 53: 1315–1335.

52.

Kyle

Obizhaeva

(2016) Market microstructure invariance: Empirical hypotheses. Econometrica 84: 1345–1404.

53.

Lang

Maffett

(2011) Transparency and liquidity uncertainty in crisis periods. Journal of Accounting and Economics 52: 101–125.

54.

Lecce

Lepone

McKenzie

, et al. (2012) The impact of naked short selling on the securities lending and equity market. Journal of Financial Markets 15: 81–107.

55.

Lee

Swaminathan

(2000) Price momentum and trading volume. Journal of Finance 60: 2017–2069.

56.

Lee

(2011) The world price of liquidity risk. Journal of Financial Economics 99: 136–161.

57.

Lesmond

(2005) Liquidity of emerging markets. Journal of Financial Economics 77: 411–452.

58.

Lesmond

Ogden

Trzcinka

(1999) A new estimate of transaction costs. Review of Financial Studies 12: 1113–1141.

59.

Levine

Schmukler

(2006) Internationalisation and stock market liquidity. Review of Finance 10: 153–187.

60.

Levine

Zervos

(1998) Capital control liberalisation and stock market development. World Development 26: 1169–1183.

61.

Liang

Wei

JKC

(2012) Liquidity risk and stock returns around the world. Journal of Banking & Finance 36: 3274–3288.

62.

Lin

(2008) The impact of lifting the short-sale price restriction on volatility and liquidity in Taiwan. Applied Financial Economics 18: 1657–1665.

63.

Liu

(2006) A liquidity-augmented capital asset pricing model. Journal of Financial Economics 82: 631–671.

64.

Madhavan

(2012) Exchange-traded funds, market structure, and the flash crash. Financial Analysts Journal 68: 20–35.

65.

Malherbe

(2014) Self-fulfilling liquidity dry-ups. Journal of Finance 69: 947–970.

66.

Marshall

Nguyen

Visaltanachoti

(2013) Liquidity measurement in frontier markets. Journal of International Financial Markets, Institutions and Money 27: 1–12.

67.

Mensi

Hammoudeh

Reboredo

, et al. (2014) Do global factors impact BRICS stock markets? A quantile regression approach. Emerging Markets Review 19: 1–17.

68.

Narayan

Zheng

(2011) The relationship between liquidity and returns on the Chinese stock market. Journal of Asian Economics 22: 259–266.

69.

Pastor

Stambaugh

(2003) Liquidity risk and expected stock returns. Journal of Political Economy 111: 642–685.

70.

Portnoy

Koenker

(1997) The Gaussian hare and the Laplacian tortoise: Computability of squared-error vs. absolute error estimators. Statistical Science 12: 279–300.

71.

Sadka

(2006) Momentum and post-earnings-announcement drift anomalies: The role of liquidity risk. Journal of Financial Economics 80: 309–349.

72.

Sharif

Anderson

Marshall

(2014) Against the tide: The commencement of short selling and margin trading in mainland China. Accounting & Finance 54: 1319–1355.

73.

Sornette

Huber

(2018) Stock market crashes: Predictable and unpredictable and what to do about them. Quantitative Finance 18: 897–899.

74.

Tirole

(2011) Illiquidity and all its friends. Journal of Economic Literature 49: 287–325.

75.

Upson

Van Ness

(2017) Multiple markets, algorithmic trading, and market liquidity. Journal of Financial Markets 32: 49–68.

76.

Yadav

Roychoudhury

(2018) Handling missing values: A study of popular imputation packages in R. Knowledge-Based Systems 160: 104–118.