{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:00:12Z","timestamp":1760238012930,"version":"build-2065373602"},"reference-count":61,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,17]],"date-time":"2020-07-17T00:00:00Z","timestamp":1594944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004442","name":"National Science Centre","doi-asserted-by":"publisher","award":["UMO-2017\/25\/B\/HS4\/01546"],"award-info":[{"award-number":["UMO-2017\/25\/B\/HS4\/01546"]}],"id":[{"id":"10.13039\/501100004442","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper examines whether liquidity proxies based on different daily prices and quotes approximate latent liquidity. We compare percent-cost daily liquidity proxies with liquidity benchmarks as well as with realized variance estimates. Both benchmarks and volatility measures are obtained from high-frequency data. Our results show that liquidity proxies based on high-low-open-close prices are more correlated and display higher mutual information with volatility estimates than with liquidity benchmarks. The only percent-cost proxy that indicates higher dependency with liquidity benchmarks than with volatility estimates is the Closing Quoted Spread based on the last bid and ask quotes within a day. We consider different sampling frequencies for calculating realized variance and liquidity benchmarks, and find that our results are robust to it.<\/jats:p>","DOI":"10.3390\/e22070783","type":"journal-article","created":{"date-parts":[[2020,7,17]],"date-time":"2020-07-17T10:22:02Z","timestamp":1594981322000},"page":"783","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Do Liquidity Proxies Based on Daily Prices and Quotes Really Measure Liquidity?"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5193-8304","authenticated-orcid":false,"given":"Barbara","family":"B\u0119dowska-S\u00f3jka","sequence":"first","affiliation":[{"name":"Department of Econometrics, Pozna\u0144 University of Economics and Business, al. Niepodleg\u0142o\u015bci 10, 61-875 Pozna\u0144, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3855-256X","authenticated-orcid":false,"given":"Krzysztof","family":"Echaust","sequence":"additional","affiliation":[{"name":"Department of Operations Research, Pozna\u0144 University of Economics and Business, al. Niepodleg\u0142o\u015bci 10, 61-875 Pozna\u0144, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.2307\/1913210","article-title":"Continuous auctions and insider trading","volume":"53","author":"Kyle","year":"1985","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.jfineco.2008.06.002","article-title":"Do liquidity measures measure liquidity?","volume":"92","author":"Goyenko","year":"2009","journal-title":"J. Financ. Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/S1386-4181(01)00024-6","article-title":"Illiquidity and stock returns: Cross-section and time-series effects","volume":"5","author":"Amihud","year":"2002","journal-title":"J. Financ. Mark."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hautsch, N. (2012). Econometrics of Financial High-Frequency Data, Springer.","DOI":"10.1007\/978-3-642-21925-2"},{"key":"ref_5","unstructured":"Hautsch, N., and Jeleskovic, V. (2020, July 15). Modelling High-Frequency Volatility and Liquidity Using Multiplicative Error Models. Available online: https:\/\/ssrn.com\/abstract=1292493."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1086\/374184","article-title":"Liquidity risk and expected stock returns","volume":"111","author":"Pastor","year":"2003","journal-title":"J. Political Econ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1093\/rof\/rfx003","article-title":"What Are the Best Liquidity Proxies for Global Research?","volume":"21","author":"Fong","year":"2017","journal-title":"Rev. Financ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1111\/j.1540-6261.2012.01729.x","article-title":"A simple way to estimate bid-ask spreads from daily high and low prices","volume":"67","author":"Corwin","year":"2012","journal-title":"J. Financ."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ahn, H.J., Cai, J., and Yang, C.W. (2018). Which Liquidity Proxy Measures Liquidity Best in Emerging Markets?. Economies, 6.","DOI":"10.3390\/economies6040067"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.jfineco.2003.05.006","article-title":"Common market makers and commonality in liquidity","volume":"73","author":"Coughenour","year":"2004","journal-title":"J. Financ. Econ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5","DOI":"10.2753\/REE1540-496X500101","article-title":"Liquidity and Return Relationships in an Emerging Market","volume":"50","author":"Batten","year":"2014","journal-title":"Emerg. Mark. Financ. Trade"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.finmar.2013.02.004","article-title":"A simple approximation of intraday spreads using daily data","volume":"17","author":"Chung","year":"2014","journal-title":"J. Financ. Mark."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4437","DOI":"10.1093\/rfs\/hhx084","article-title":"A Simple Estimation of Bid-Ask Spreads from Daily Close, High, and Low Prices","volume":"30","author":"Abdi","year":"2017","journal-title":"Rev. Financ. Stud."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.frl.2018.02.014","article-title":"The coherence of liquidity measures. The evidence from the emerging market","volume":"27","year":"2018","journal-title":"Financ. Res. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1086\/296072","article-title":"On the Estimation of Security Price Volatilities from Historical Data","volume":"53","author":"Garman","year":"1980","journal-title":"J. Bus."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.jfineco.2011.12.008","article-title":"Understanding Commonality in Liquidity around the World","volume":"105","author":"Karolyi","year":"2012","journal-title":"J. Financ. Econ."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"B\u0229dowska-S\u00f3jka, B., and Echaust, K. (2020). What is the best proxy for liquidity in the presence of extreme illiquidity?. Emerg. Mark. Rev.","DOI":"10.1016\/j.ememar.2020.100695"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1162\/rest.89.4.701","article-title":"Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility","volume":"89","author":"Andersen","year":"2007","journal-title":"Rev. Econ. Stat."},{"key":"ref_19","unstructured":"Bollerslev, T.R.J., and Watson, M. (2010). Measuring downside risk? Realised semivariance. Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle, Oxford University Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1080\/14697688.2014.946660","article-title":"Partial correlation analysis: Applications for financial markets","volume":"15","author":"Kenett","year":"2015","journal-title":"Quant. Financ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.physa.2004.06.144","article-title":"Mutual information: A measure of dependency for nonlinear time series","volume":"344","author":"Dionisio","year":"2004","journal-title":"Physica A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"305","DOI":"10.2307\/1912726","article-title":"The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis","volume":"44","author":"Epps","year":"1976","journal-title":"Econometrica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1111\/j.1540-6261.1976.tb01917.x","article-title":"The determinants of common stock returns volatility: An international comparison","volume":"31","author":"Cohen","year":"1976","journal-title":"J. Financ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"109","DOI":"10.2307\/2330874","article-title":"The relation between price changes and trading volume: A survey","volume":"22","author":"Karpoff","year":"1987","journal-title":"J. Financ. Quant. Anal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0304-405X(86)90065-6","article-title":"Asset pricing and the bid-ask spread","volume":"17","author":"Amihud","year":"1986","journal-title":"J. Financ. Econ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1149","DOI":"10.2307\/2326280","article-title":"A model of asset trading under the assumption of sequential information arrival","volume":"31","author":"Copeland","year":"1976","journal-title":"J. Financ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1561\/0500000003","article-title":"Liquidity and asset prices","volume":"1","author":"Amihud","year":"2005","journal-title":"Found. Trends Financ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.pacfin.2018.04.008","article-title":"Market Volatility, Liquidity Shocks, and Stock Returns: Worldwide Evidence","volume":"49","author":"Ma","year":"2018","journal-title":"Pac.-Basin Financ. J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1111\/j.1540-6288.2007.00178.x","article-title":"Trading Volume and Market Volatility: Developed vs. Emerging Stock Markets","volume":"42","author":"Girard","year":"2007","journal-title":"Financ. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1111\/1468-2362.00072","article-title":"Liquidity, volatility and equity trading costs across countries and over time","volume":"4","author":"Domowitz","year":"2001","journal-title":"Int. Financ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.jfs.2019.05.006","article-title":"The dynamics of low-frequency liquidity measures: The developed versus the emerging market","volume":"42","year":"2019","journal-title":"J. Financ. Stab."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"B\u0229dowska-S\u00f3jka, B., and Echaust, K. (2019). Commonality in Liquidity Indices: The Emerging European Stock Markets. Systems, 7.","DOI":"10.3390\/systems7020024"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1111\/0022-1082.00335","article-title":"Market Liquidity and Trading Activity","volume":"56","author":"Chordia","year":"2001","journal-title":"J. Financ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.irfa.2017.12.010","article-title":"Stock market liquidity and trading activity: Is China different?","volume":"56","author":"Ma","year":"2018","journal-title":"Int. Rev. Financ. Anal."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.finmar.2018.09.003","article-title":"The maximum bid-ask spread","volume":"41","author":"Blau","year":"2018","journal-title":"J. Financ. Mark."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1093\/rfs\/12.5.1113","article-title":"A new estimate of transaction costs","volume":"12","author":"Lesmond","year":"1999","journal-title":"Rev. Financ. Stud."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.jfineco.2004.01.005","article-title":"Liquidity of emerging markets","volume":"77","author":"Lesmond","year":"2005","journal-title":"J. Financ. Econ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.irfa.2016.07.002","article-title":"The impact of the French securities transaction tax on market liquidity and volatility","volume":"47","author":"Havrylchyk","year":"2016","journal-title":"Int. Rev. Financ. Anal."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.irfa.2016.09.013","article-title":"Herd behavior and equity market liquidity: Evidence from major markets","volume":"48","author":"Galariotis","year":"2016","journal-title":"Int. Rev. Financ. Anal."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.physa.2006.07.035","article-title":"Nonextensive statistical features of the Polish stock market fluctuations","volume":"374","author":"Rak","year":"2007","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.5506\/APhysPolB.44.2035","article-title":"Stock Returns Versus Trading Volume: Is the Correspondence More General?","volume":"44","author":"Rak","year":"2013","journal-title":"Acta Phys. Pol. B"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.chaos.2016.03.005","article-title":"Dynamic bifurcations on financial markets","volume":"88","author":"Denys","year":"2016","journal-title":"Chaos Solitons Fractals"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"B\u0229dowska-S\u00f3jka, B. (2019). Commonality in liquidity measures. The evidence from the Polish stock market. Proceedings of the International Scientific Conference Hradec Economic Days 2019, Hradec Kralove, Czech Republic, 25\u201326 March 2019, University of Hradec Kralove.","DOI":"10.36689\/uhk\/hed\/2019-01-003"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"C1","DOI":"10.1111\/j.1368-423X.2008.00275.x","article-title":"Realized kernels in practice: Trades and quotes","volume":"12","author":"Hansen","year":"2009","journal-title":"Econom. J."},{"key":"ref_45","first-page":"1009","article-title":"Market integration and price execution for NYSE-listed securities","volume":"48","author":"Lee","year":"1993","journal-title":"J. Financ."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.finmar.2013.05.004","article-title":"Intraday liquidity dynamics and news releases around price jumps: Evidence from the DJIA stocks","volume":"17","author":"Boudt","year":"2014","journal-title":"J. Financ. Mark."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"885","DOI":"10.2307\/2527343","article-title":"Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts","volume":"39","author":"Andersen","year":"1998","journal-title":"Int. Econ. Rev."},{"key":"ref_48","unstructured":"Boudt, K., Cornelissen, J., Payseur, S., Nguyen, G., and Schermer, M. (2020, July 15). Highfrequency: Tools for Highfrequency Data Analysis. Available online: https:\/\/cran.r-project.org\/web\/packages\/highfrequency\/highfrequency.pdf."},{"key":"ref_49","unstructured":"Doornik, J., and Hendry, D. (2005). Empirical Econometric Modelling, Timberlake Consultants. PcGiveTM11."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/S1386-4181(02)00064-2","article-title":"Issues in assessing trade execution costs","volume":"6","author":"Bessembinder","year":"2003","journal-title":"J. Financ. Mark."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"703","DOI":"10.2307\/1913610","article-title":"A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix","volume":"55","author":"Newey","year":"1987","journal-title":"Econometrica"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1037\/1082-989X.12.4.399","article-title":"Toward using confidence intervals to compare correlations","volume":"12","author":"Zou","year":"2007","journal-title":"Psychol. Methods"},{"key":"ref_53","first-page":"87","article-title":"A partial correlation coefficient and coefficient of determination for multivariate normal repeated measures data","volume":"50","author":"Lipsitz","year":"2001","journal-title":"J. R. Stat. Soc. Ser. Stat."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/1351847032000143396","article-title":"Market risk models for intraday data","volume":"11","author":"Giot","year":"2005","journal-title":"Eur. J. Financ."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1057\/s41283-018-0038-z","article-title":"Is intraday data useful for forecasting VaR? The evidence from EUR\/PLN exchange rate","volume":"20","year":"2018","journal-title":"Risk Manag."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1896","DOI":"10.1016\/j.eneco.2012.08.024","article-title":"On the volatility-volume relationship in energy futures markets using intraday data","volume":"34","author":"Chevallier","year":"2012","journal-title":"Energy Econ."},{"key":"ref_57","unstructured":"Zhang, D. (2020, July 15). Package rsq: R-Squared and Related Measures. Available online: https:\/\/cran.r-project.org\/web\/packages\/rsq\/rsq.pdf."},{"key":"ref_58","unstructured":"Cover, T., and Thomas, J. (1991). Elements of Information Theory, Wiley."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Yue, P., Fan, Y., Batten, J.A., and Zhou, W.X. (2020). Information Transfer between Stock Market Sectors: A Comparison between the USA and China. Entropy, 22.","DOI":"10.3390\/e22020194"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Hu, S., Zhong, M., and Cai, Y. (2019). Impact of Investor Behavior and Stock Market Liquidity: Evidence from China. Entropy, 21.","DOI":"10.3390\/e21111111"},{"key":"ref_61","unstructured":"Meyer, P.E. (2020, July 15). infotheo: Information-Theoretic Measures. Available online: https:\/\/cran.r-project.org\/web\/packages\/infotheo\/infotheo.pdf."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/7\/783\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:49:23Z","timestamp":1760176163000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/7\/783"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,17]]},"references-count":61,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["e22070783"],"URL":"https:\/\/doi.org\/10.3390\/e22070783","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,7,17]]}}}