# State-Dependent Stock Liquidity Premium: The Case of the Warsaw Stock Exchange

## Abstract

**:**

## 1. Introduction

## 2. Literature Overview

## 3. Methodology and Data

#### 3.1. Empirical Framework and Hypotheses Development

**Hypotheses**

**1**

**(H1).**

**Hypotheses**

**2**

**(H2).**

_{it}denotes the value of liquidity measure for i-th stock in month t, while superscripts E and U are related to expected and unexpected level of liquidity respectively, and

**X**is a vector of control variables.

_{it}_{t}and B

_{t}are dummy variables that equal to 1 if month t is considered to be the bull and bear market period respectively, and 0 otherwise. Thus, estimated ${\widehat{\tilde{b}}}_{1}^{H}$ and ${\widehat{\tilde{b}}}_{1}^{B}$ reflect per unit liquidity premium during bull and bear market respectively, and estimated ${\widehat{b}}_{3}^{H}$ and ${\widehat{b}}_{3}^{B}$ reflect the effect of unexpected liquidity on contemporaneous stock returns during bull and bear market respectively. However, the use of interactive variables requires the identification of bull and bear market periods on the Warsaw Stock Exchange during the analyzed period. For this purpose, Markov-switching models will be utilized.

#### 3.2. Variables

- raw returns: ${r}_{it}-r{f}_{t}$
- excess returns: ${r}_{it}-{r}_{Mt}$
- CAPM-adjusted returns: ${r}_{it}^{}-{r}_{it}^{CAPM}={r}_{it}-r{f}_{t}-{\beta}_{it}\left({r}_{mt}-r{f}_{t}\right)$
- FF3-adjusted returns: ${r}_{it}^{}-{r}_{it}^{FF3}={r}_{it}-r{f}_{t}-{\beta}_{it}^{MKT}\left({r}_{mt}-r{f}_{t}\right)-{\beta}_{it}^{SMB}SM{B}_{t}-{\beta}_{it}^{HML}HM{L}_{t}$
- Carhart-adjusted returns: ${r}_{it}^{}-{r}_{it}^{Carhart}={r}_{it}-r{f}_{t}-{\beta}_{it}^{MKT}\left({r}_{mt}-r{f}_{t}\right)-{\beta}_{it}^{SMB}SM{B}_{t}-{\beta}_{it}^{HML}HM{L}_{t}-{\beta}_{it}^{UMD}UM{D}_{t}$

_{t}) has been utilised the one-month Warsaw Inter-Bank Offered Rate (WIBOR 1M). Values of the Warsaw Stock Exchange Index (WIG) were used as a proxy for the value of market portfolio, so the return on market portfolio (r

_{Mt}) is calculated based on the relative change in the value of WIG. Size and value factors (SMB and HML) are constructed from raw data based on the original methodology of Fama and French (1992, 1993), and momentum factor (UMD) is constructed from raw data with the use of the original methodology of Carhart (1997). Parameters of pricing models for month t are estimated with the use of data from the previous 36 months (from t − 36 to t − 1), therefore β coefficients can take different values in consecutive months.

_{m}denotes the proportion of zero-return days in month m, σ

_{m}is the volatility of daily returns in month m and ϕ is the cumulative standardized normal distribution.

- natural logarithm of the market value of equity (ln(MV))—to take into account the size effect (Fama and French 1992, 1993),
- book-to-market value of equity (BV/MV)—to take into account the effect of company’s value (Fama and French 1992, 1993),
- dividend yield (DY)—to control for the effect of liquidity on dividend policy (Banerjee et al. 2007; Griffin 2010; Igan et al. 2011; Stereńczak 2018b),
- cumulative return from the last twelve months (rt-12-t-1)—reflecting the momentum effect (Jegadeesh and Titman 1993),
- standard deviation of monthly returns from the last 36 months (σ) or the standard error of residuals from estimated pricing model (σ
_{ε})—reflecting stock risk and stock residual risk respectively.

#### 3.3. Data

## 4. Empirical Results

#### 4.1. Liquidity Premium in the Warsaw Stock Exchange

#### 4.2. Liquidity Premium During the Bull and the Bear Market

_{j}is the estimate of the unknown value of the parameter β

_{j}, and S(b

_{j}) is the standard error of this estimate; t

_{0.05;n−k−1}is the critical value of t-Student distribution for 0.05 significance level and n − k − 1 degrees of freedom. Confidence interval for the estimate of the parameter is therefore:

## 5. Robustness Tests

#### 5.1. Accounting for Endogeneity: DiD Approach

#### 5.2. Application of Different Liquidity Measures

^{H}and P

^{L}denote the highest and the lowest observed daily price, respectively, and Vol is a respective trading volume. Second modification involves changing the interval from daily to minute—this modification will be hereafter marked as ILLIQ

^{I}.

^{R}and ILLIQ

^{I}measures, are not presented, but available upon request. The application of different liquidity measures does not change the conclusions presented earlier. The estimates of the parameters for the amortized liquidity measure are positive and statistically significant at the 0.01 significance level in all estimated models, which indicates the existence of liquidity premium. All estimates of the parameters for unexpected level of liquidity are negative and statistically significant at the 0.01 level. The values of the parameter estimates a decrease with an increase in the number of factors explaining normal rates of return, which confirms that liquidity premium is at least partially captured by market risk premium and size and value factors. The exceptions are the estimates in the models where Carhart-adjusted return was a dependent variable—change in the liquidity measure causes that in these models estimates of the parameters for amortized liquidity measure are higher than in models with FF3-adjusted and CAPM-adjusted returns as dependent variables.

^{R}measure equals 8.159. This results in an average total liquidity premium equal to 0.006 percentage point monthly, which is 1.42% of average stock returns in the analyzed period. Similar values are obtained for ILLIQ

^{I}measure: the average total liquidity premium equals a 0.004 percentage point monthly, and the mean value of the parameter estimate is 0.127. These results confirm the small economic relevance of liquidity premium on the Warsaw Stock Exchange.

^{R}and ILLIQ

^{I}measures calculated for the entire market. Correlation coefficients (Pearson’s r, Spearman’s ρ, and Kendall’s τ) between ILLIQ

^{R}(ILLIQ

^{I}) measure and the investment horizon equal to 0.7402 (0.6115), 0.8052 (0.6993), and 0.6159 (0.5098), respectively. Thus, this confirms the previous conclusions that during the period of low market liquidity, investors lengthen the investment horizon in order to reduce the frequency of incurring liquidity costs. Obtained results are thus robust to the choice of liquidity measure.

#### 5.3. Determination of Unexpected Liquidity

#### 5.4. Methods of Estimation

#### 5.5. Determination of Bull and Bear Market Phases

## 6. Concluding Remarks

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Bull and bear market phases on the Warsaw Stock Exchange identified with the use of AR(1) Markov switching model. Abbreviations: WIG, Warsaw Stock Exchange Index.

**Table 1.**The results of the estimation of the models of the relationship between stock liquidity and returns.

Dependent Variable | M1 | M2 | M3 | M4 | M5 |
---|---|---|---|---|---|

${\mathit{r}}_{\mathit{i}\mathit{t}}-\mathit{r}{\mathit{f}}_{\mathit{t}}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{M}\mathit{t}}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{i}\mathit{t}}^{\mathit{C}\mathit{A}\mathit{P}\mathit{M}}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{i}\mathit{t}}^{\mathit{F}\mathit{F}3}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{i}\mathit{t}}^{\mathit{C}\mathit{a}\mathit{r}\mathit{h}\mathit{a}\mathit{r}\mathit{t}}$ | |

Intercept | 0.116 *** | 0.054 *** | 0.058 *** | 0.081 *** | 0.097 *** |

(10.79) | (4.967) | (5.170) | (7.347) | (8.152) | |

lnMV | −0.019 *** | −0.019 *** | −0.017 *** | −0.016 *** | −0.020 *** |

(11.82) | (11.51) | (10.06) | (9.647) | (11.00) | |

BV/MV | 0.001 *** | 0.001 *** | 0.001 *** | 0.001 *** | 0.001 *** |

(3.297) | (3.451) | (3.737) | (3.340) | (2.984) | |

DY | 0.000 | 0.001 | 0.004 | 0.004 | −0.002 |

(0.025) | (0.083) | (0.351) | (0.371) | (0.126) | |

r_{t}_{−12−t−1} | 0.008 *** | 0.009 *** | 0.005 ** | 0.003 | 0.004 * |

(4.021) | (4.350) | (2.369) | (1.499) | (1.867) | |

σ | −0.082 *** | −0.081 *** | |||

(3.747) | (3.772) | ||||

σ_{ε} | −0.069 *** | −0.045 * | −0.053 * | ||

(2.749) | (1.713) | (1.839) | |||

amFHT_{t}_{−1} | 2.636 *** | 2.667 *** | 2.571 *** | 2.460 *** | 2.394 *** |

(4.164) | (4.208) | (4.066) | (4.151) | (4.227) | |

FHT^{U} | −0.010 | −0.001 | −0.028 | 0.086 | 0.076 |

(0.102) | (0.010) | (0.271) | (0.835) | (0.744) | |

Stocks effects | YES | YES | YES | YES | YES |

Months effects | YES | YES | YES | YES | YES |

N | 41,110 | 41,117 | 41,146 | 41,142 | 41,140 |

R^{2} | 0.209 | 0.076 | 0.075 | 0.030 | 0.033 |

F | 25.293 | 24.525 | 18.457 | 17.933 | 20.737 |

D−W | 1.980 | 1.986 | 1.983 | 1.996 | 1.973 |

AIC | −55,844.32 | −55,798.82 | −54,825.37 | −52,419.18 | −50,496.79 |

_{t}

_{−12−t−1}is the cumulated return from the months from t − 12 to t − 1; σ is the standard deviation of monthly returns in last 36 months; σ

_{ε}is the standard error of residuals from the pricing model; amFHT is the value of FHT measure in month t − 1 amortized by the expected holding period, approximated by the reciprocal of the turnover ratio in month t; FHT

^{U}is the residual from AR(1) model of FHT measure. t-statistics are given in the parentheses and asterisks denote the statistical significance at the 0.1 (*), 0.05 (**) and 0.01 (***) level.

**Table 2.**The results of the estimation of the modified models of the relationship between stock liquidity and returns.

Dependent Variable | M1a | M1b | M1c | M1d | M1e |
---|---|---|---|---|---|

${\mathit{r}}_{\mathit{i}\mathit{t}}-\mathit{r}{\mathit{f}}_{\mathit{t}}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-\mathit{r}{\mathit{f}}_{\mathit{t}}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-\mathit{r}{\mathit{f}}_{\mathit{t}}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-\mathit{r}{\mathit{f}}_{\mathit{t}}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-\mathit{r}{\mathit{f}}_{\mathit{t}}\text{}$ | |

Intercept | 0.104 *** | 0.098 *** | 0.098 *** | 0.104 *** | 0.055 *** |

(10.27) | (9.599) | (11.41) | (4.955) | (3.096) | |

lnMV | −0.019 *** | −0.018 *** | −0.018 *** | −0.023 *** | −0.023 *** |

(11.82) | (11.31) | (16.45) | (6.772) | (10.25) | |

BV/MV | 0.001 *** | 0.001 *** | 0.001 *** | 0.001 | 0.001 *** |

(3.297) | (3.297) | (5.291) | (0.969) | (3.577) | |

DY | 0.000 | 0.000 | 0.003 | −0.033 | 0.004 |

(0.025) | (0.025) | (0.274) | (1.400) | (0.379) | |

r_{t}_{−12−t−1} | 0.008 *** | 0.008 *** | 0.008 *** | −0.000 | 0.007 ** |

(4.021) | (4.021) | (5.359) | (0.008) | (2.404) | |

σ | −0.220 *** | −0.071 ** | |||

(4.936) | (2.389) | ||||

σ^{ortog_amFHT} | −0.082 *** | ||||

(3.747) | |||||

σ^{ortog_lnMV} | −0.082 *** | ||||

(3.747) | |||||

amFHT_{t}_{−1} | 2.441 *** | 2.636 *** | 2.579 *** | 4.409 ** | 2.351 *** |

(3.920) | (4.164) | (13.63) | (2.489) | (3.849) | |

FHT^{U} | −0.010 | −0.010 | 0.021 | 0.492 ** | −0.088 |

(0.102) | (0.102) | (0.335) | (2.202) | (0.759) | |

Stocks effects | YES | YES | YES | YES | YES |

Months effects | YES | YES | YES | YES | YES |

N | 41110 | 41110 | 41110 | 10455 | 30655 |

R^{2} | 0.209 | 0.209 | 0.209 | 0.269 | 0.180 |

F | 25.293 | 25.293 | 66.205 | 13.548 | 20.000 |

D−W | 1.980 | 1.980 | 1.982 | 1.901 | 2.010 |

AIC | −55,844.32 | −55,844.32 | −55,819.27 | −12,110.91 | −44,050.55 |

_{t}

_{−12−t−1}is the cumulated return from the months from t − 12 to t − 1; σ is the standard deviation of monthly returns in last 36 months; amFHT is the value of FHT measure in month t − 1 amortized by the expected holding period, approximated by the reciprocal of the turnover ratio in month t; FHT

^{U}is the residual from AR(1) model of FHT measure. In model M1a risk is orthogonalized vs. liquidity; in model M1b risk is orthogonalized vs. size of the company; in model M1c risk variable is omitted; model M1d is estimated using the data from the subperiod 2004–2009; model M1e is estimated using the data from the subperiod 2010–2016. t-statistics are given in the parentheses and asterisks denote the statistical significance at the 0.1 (*), 0.05 (**) and 0.01 (***) level.

**Table 3.**The results of the estimation of the models of the relationship between stock liquidity and returns during the bull and bear market phases.

Dependent Variable | M6 | M7 | M8 | M9 | M10 |
---|---|---|---|---|---|

${\mathit{r}}_{\mathit{i}\mathit{t}}-\mathit{r}{\mathit{f}}_{\mathit{t}}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{M}\mathit{t}}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{i}\mathit{t}}^{\mathit{C}\mathit{A}\mathit{P}\mathit{M}}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{i}\mathit{t}}^{\mathit{F}\mathit{F}3}\text{}$ | ${\mathit{r}}_{\mathit{i}\mathit{t}}-{\mathit{r}}_{\mathit{i}\mathit{t}}^{\mathit{C}\mathit{a}\mathit{r}\mathit{h}\mathit{a}\mathit{r}\mathit{t}}\text{}$ | |

Intercept | 0.115 *** | 0.054 *** | 0.057 *** | 0.081 *** | 0.097 *** |

(10.78) | (4.947) | (5.158) | (7.346) | (8.154) | |

lnMV | −0.019 *** | −0.019 *** | −0.017 *** | −0.016 *** | −0.020 *** |

(11.82) | (11.52) | (10.07) | (9.655) | (11.01) | |

BV/MV | 0.001 *** | 0.001 *** | 0.001 *** | 0.001 *** | 0.0004 *** |

(3.309) | (3.461) | (3.742) | (3.330) | (2.973) | |

DY | 0.000 | 0.001 | 0.004 | 0.004 | −0.002 |

(0.019) | (0.077) | (0.345) | (0.368) | (0.128) | |

r_{t}_{−12−t−1} | 0.008 *** | 0.009 *** | 0.005 ** | 0.003 | 0.004 * |

(3.946) | (4.270) | (2.288) | (1.453) | (1.826) | |

σ | −0.082 *** | −0.081 *** | |||

(3.741) | (3.762) | ||||

σ_{ε} | −0.067 *** | −0.045 * | −0.053 * | ||

(2.750) | (1.718) | (1.844) | |||

amFHT_{t}_{−1*}H | 2.648 *** | 2.660 *** | 2.523 *** | 2.392 *** | 2.349 *** |

(3.816) | (3.855) | (3.678) | (3.723) | (3.804) | |

amFHT_{t−}_{1*}B | 2.501 ** | 2.653 ** | 2.851 ** | 2.919 ** | 2.690 ** |

(2.569) | (2.426) | (2.463) | (2.410) | (2.469) | |

FHT^{U}*H | −0.093 | −0.081 | −0.110 | 0.037 | 0.032 |

(0.860) | (0.733) | (0.990) | (0.340) | (0.291) | |

FHT^{U}*B | 0.575 ** | 0.082 ** | 0.542 ** | 0.414 * | 0.378 |

(2.412) | (2.446) | (2.293) | (1.371) | (1.556) | |

Stocks effects | YES | YES | YES | YES | YES |

Months effects | YES | YES | YES | YES | YES |

N | 41,110 | 41,117 | 41,146 | 41,142 | 41,140 |

R^{2} | 0.209 | 0.076 | 0.075 | 0.030 | 0.033 |

F | 21.107 | 20.177 | 15.852 | 14.590 | 16.516 |

D−W | 1.981 | 1.986 | 1.983 | 1.996 | 1.973 |

AIC | −55,853.02 | −55,807.00 | −54,833.85 | −52,420.07 | −50,496.28 |

_{t}

_{−12−t−1}is the cumulated return from the months from t − 12 to t − 1; σ is the standard deviation of monthly returns in last 36 months; σ

_{ε}is the standard error of residuals from the pricing model; amFHT is the value of FHT measure in month t − 1 amortized by the expected holding period, approximated by the reciprocal of the turnover ratio in month t; FHT

^{U}is the residual from AR(1) model of FHT measure; H is a dummy variable that equals 1 if month t is considered as belonging to the bull market and 0 otherwise; B is a dummy variable that equals 1 if month t is considered as belonging to the bear market and 0 otherwise. t-statistics are given in the parentheses and asterisks denote the statistical significance at the 0.1 (*), 0.05 (**) and 0.01 (***) level.

Panel A: Pre-Match and Post-Match Propensity | ||||

Variable | Pre-Match | Post-Match | ||

Intercept | −1.208 * | 0.215 | ||

(1.837) | (0.800) | |||

lnMV | 0.143 *** | −0.016 | ||

(3.058) | (0.8045) | |||

BV/MV | −0.007 | −0.045 | ||

(0.669) | (0.379) | |||

r_{t}_{−12−t−1} | 0.145 | 0.067 | ||

(0.437) | (0.800) | |||

σ | −2.286 | 0.640 | ||

(0.247) | (0.810) | |||

FHT | −1.040 | −1.812 | ||

(0.628) | (0.667) | |||

N | 222 | 110 | ||

p-value of χ^{2} | 0.000 | 0.967 | ||

pseudo-R^{2} | 0.091 | 0.006 | ||

Panel B: Post-Matching Differences | ||||

Variable | Treatment | Control | Difference | t-Statistic |

lnMV | 11.193 | 11.253 | −0.06 | −0.1532 |

.BV/MV | 1.4175 | 1.7221 | −0.3046 | −0.7701 |

r_{t}_{−12−t−1} | −0.21202 | −0.25052 | 0.0385 | 0.3831 |

σ | 0.13734 | 0.13679 | 0.00055 | 0.0578 |

FHT | 0.022066 | 0.024574 | −0.002508 | −0.4292 |

_{t}

_{−12−t−1}is the cumulated return from the months from t − 12 to t − 1; σ is the standard deviation of monthly returns in last 36 months; FHT is the value of FHT measure in month t − 1; t-statistics are given in the parentheses and asterisks denote the statistical significance at the 0.1 (*) and 0.01 (***) level.

Variable | (1) | (2) | (3) |
---|---|---|---|

Intercept | −0.065 *** (3.142) | −0.096 (1.173) | −0.081 (1.030) |

After_{t} | 0.154 *** (4.577) | 0.148 *** (4.639) | 0.164 *** (5.066) |

Treatment_{i} | 0.050 * (1.690) | 0.052 * (1.751) | 0.051 * (1.698) |

After_{t}*Treatment_{i} | −0.060 (1.176) | −0.053 (1.050) | −0.074 (1.523) |

Control | NO | YES | YES |

FHT | NO | NO | YES |

N | 220 | 220 | 220 |

R^{2} | 0.114 | 0.117 | 0.131 |

_{t}is a dummy variable that equals one if month t is after April 2013 and 0 otherwise; Treatment

_{i}is a dummy variable that equals 1 if firm i belongs to a treatment group and 0 if firm i belongs to a control group; control variables are the same as in Table 1. t-statistics are given in the parentheses and asterisks denote the statistical significance at the 0.1 (*) and 0.01 (***) level.

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Stereńczak, S.
State-Dependent Stock Liquidity Premium: The Case of the Warsaw Stock Exchange. *Int. J. Financial Stud.* **2020**, *8*, 13.
https://doi.org/10.3390/ijfs8010013

**AMA Style**

Stereńczak S.
State-Dependent Stock Liquidity Premium: The Case of the Warsaw Stock Exchange. *International Journal of Financial Studies*. 2020; 8(1):13.
https://doi.org/10.3390/ijfs8010013

**Chicago/Turabian Style**

Stereńczak, Szymon.
2020. "State-Dependent Stock Liquidity Premium: The Case of the Warsaw Stock Exchange" *International Journal of Financial Studies* 8, no. 1: 13.
https://doi.org/10.3390/ijfs8010013