{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T06:26:10Z","timestamp":1762064770341,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T00:00:00Z","timestamp":1661385600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"research project \u201cDynamics and Information Research Institute\u2014Quantum Information, Quantum Technologies\u201d within the agreement between UniCredit Bank and Scuola Normale Superiore"},{"name":"UniCredit Bank R&amp;D group for financial support through the \u201cDynamics and Information Theory Research Institute\u201d at the Scuola Normale Superiore"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We developed a simple method for estimating volatility and price staleness in empirical data in order to filter out such regularity patterns from return time series. The resulting financial time series of stock returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback\u2013Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group of 18 stocks. The inefficiency of the Moscow Stock Exchange that we have detected is a signal of the possibility of devising profitable strategies, net of transaction costs. The deviation from the efficient behavior for a stock strongly depends on the industrial sector that it belongs to.<\/jats:p>","DOI":"10.3390\/e24091184","type":"journal-article","created":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T21:28:12Z","timestamp":1661462892000},"page":"1184","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Efficiency of the Moscow Stock Exchange before 2022"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9299-369X","authenticated-orcid":false,"given":"Andrey","family":"Shternshis","sequence":"first","affiliation":[{"name":"Quantitative Finance Research Group, Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7198-513X","authenticated-orcid":false,"given":"Piero","family":"Mazzarisi","sequence":"additional","affiliation":[{"name":"Quantitative Finance Research Group, Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5105-8876","authenticated-orcid":false,"given":"Stefano","family":"Marmi","sequence":"additional","affiliation":[{"name":"Quantitative Finance Research Group, Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,25]]},"reference":[{"key":"ref_1","first-page":"41","article-title":"Proof that properly anticipated prices fluctuate randomly","volume":"6","author":"Samuelson","year":"1965","journal-title":"Ind. 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