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==Historical background== [[Benoit Mandelbrot]] claimed the efficient markets theory was first proposed by the French mathematician [[Louis Bachelier]] in 1900 in his PhD thesis "The Theory of Speculation" describing how prices of commodities and stocks varied in markets.<ref>{{cite web|title=Benoit mandelbrot on efficient markets (interview - 30 September 2009)|url=https://www.ft.com/video/c4955fb1-810f-3070-b750-e8726e7566c2 |archive-url=https://ghostarchive.org/archive/20221210/https://www.ft.com/video/c4955fb1-810f-3070-b750-e8726e7566c2 |archive-date=10 December 2022 |url-access=subscription |url-status=live|website=www.ft.com|date=18 October 2010 |publisher=Financial times|access-date=21 November 2017}}</ref> It has been speculated that Bachelier drew ideas from the [[Random walk hypothesis|random walk model]] of [[Jules Regnault]], but Bachelier did not cite him,<ref name="Jovanovic2012">{{cite journal|last1=Jovanovic|first1=Franck|title=Bachelier: Not the forgotten forerunner he has been depicted as. An analysis of the dissemination of Louis Bachelier's work in economics|journal=The European Journal of the History of Economic Thought|volume=19|issue=3|year=2012|pages=431β451|issn=0967-2567|doi=10.1080/09672567.2010.540343|s2cid=154003579|url=http://r-libre.teluq.ca/1168/1/dissemination%20of%20Louis%20Bachelier_EJHET_R2.pdf}}</ref> and Bachelier's thesis is now considered pioneering in the field of financial mathematics.<ref name="CourtaultKabanov2000">{{cite journal |last1=Courtault |first1=Jean-Michel |last2=Kabanov |first2=Yuri |last3=Bru |first3=Bernard |last4=Crepel |first4=Pierre |last5=Lebon |first5=Isabelle |last6=Le Marchand |first6=Arnaud |title=Louis Bachelier on the Centenary of Theorie de la Speculation |journal=Mathematical Finance |volume=10 |issue=3 |year=2000 |pages=339β353 |issn=0960-1627 |doi=10.1111/1467-9965.00098|s2cid=14422885 |url=https://halshs.archives-ouvertes.fr/halshs-00447592/file/BACHEL2.PDF }}</ref><ref name="Jovanovic2012"/> It is commonly thought that Bachelier's work gained little attention and was forgotten for decades until it was rediscovered in the 1950s by [[Leonard Savage]], and then become more popular after Bachelier's thesis was translated into English in 1964. But the work was never forgotten in the mathematical community, as Bachelier published a book in 1912 detailing his ideas,<ref name="Jovanovic2012"/> which was cited by mathematicians including [[Joseph L. Doob]], [[William Feller]]<ref name="Jovanovic2012"/> and [[Andrey Kolmogorov]].<ref name="JarrowProtter2004">{{cite book|last1=Jarrow|first1=Robert|title=A Festschrift for Herman Rubin|last2=Protter|first2=Philip|year=2004|pages=75β80|issn=0749-2170|doi=10.1214/lnms/1196285381|chapter=A short history of stochastic integration and mathematical finance: the early years, 1880β1970|series=Institute of Mathematical Statistics Lecture Notes - Monograph Series|isbn=978-0-940600-61-4}}</ref> The book continued to be cited, but then starting in the 1960s the original thesis by Bachelier began to be cited more than his book when economists started citing Bachelier's work.<ref name="Jovanovic2012"/> The concept of market efficiency had been anticipated at the beginning of the century in the dissertation submitted by Bachelier (1900) to the Sorbonne for his PhD in mathematics. In his opening paragraph, Bachelier recognizes that "past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes".<ref>{{Cite journal|last=DIMSON|first=ELROY|title=MARKET EFFICIENCY|journal=The Current State of Business Disciplines}}</ref> The efficient markets theory was not popular until the 1960s when the advent of computers made it possible to compare calculations and prices of hundreds of stocks more quickly and effortlessly. In 1945, [[Friedrich Hayek|F.A. Hayek]] argued in his article [[The Use of Knowledge in Society]] that markets were the most effective way of aggregating the pieces of information dispersed among individuals within a society. Given the ability to profit from private information, self-interested traders are motivated to acquire and act on their private information. In doing so, traders contribute to more and more efficient market prices. In the competitive limit, market prices reflect all available information and prices can only move in response to news. Thus there is a very close link between EMH and the [[random walk hypothesis]].<ref>Kirman, Alan. "[http://www.voxeu.org/index.php?q=node/4208 Economic theory and the crisis]." ''Voxeu''. 14 November 2009.</ref> Early theories posited that predicting stock prices is unfeasible, as they depend on fresh information or news rather than existing or historical prices. Therefore, stock prices are thought to fluctuate randomly, and their predictability is believed to be no better than a 50% accuracy rate.<ref>{{Cite journal |last1=Sahu |first1=Santosh Kumar |last2=Mokhade |first2=Anil |last3=Bokde |first3=Neeraj Dhanraj |date=January 2023 |title=An Overview of Machine Learning, Deep Learning, and Reinforcement Learning-Based Techniques in Quantitative Finance: Recent Progress and Challenges |journal=Applied Sciences |language=en |volume=13 |issue=3 |pages=1956 |doi=10.3390/app13031956 |issn=2076-3417|doi-access=free }}</ref> The efficient-market hypothesis emerged as a prominent theory in the mid-1960s. [[Paul Samuelson]] had begun to circulate Bachelier's work among economists. In 1964 Bachelier's dissertation along with the empirical studies mentioned above were published in an anthology edited by Paul Cootner.<ref>{{cite book| editor-last = Cootner| editor-first = Paul| title = The Random Character of StockMarket Prices| publisher = MIT Press| year = 1964}}</ref> In 1965, Eugene Fama published his dissertation arguing for the [[random walk hypothesis]].<ref>{{cite journal | last = Fama | first = Eugene | title = The Behavior of Stock Market Prices | journal = Journal of Business | volume = 38 | pages =34β105 | year = 1965 | doi=10.1086/294743}}</ref> Also, Samuelson published a proof showing that if the market is efficient, prices will exhibit random-walk behavior.<ref>{{cite journal | last = Samuelson | first = Paul | title = Proof That Properly Anticipated Prices Fluctuate Randomly | journal = Industrial Management Review | volume = 6 | pages =41β49 | year=1965 }}</ref> This is often cited in support of the efficient-market theory, by the method of affirming the consequent,<ref>{{cite book|url=https://books.google.com/books?id=1Lb3Z96mhCsC&pg=PT25|title=Market Sense and Nonsense: How the Markets Really Work (and How They Don't)|first=Jack D.|last=Schwager|date=19 October 2012|publisher=John Wiley & Sons|via=Google Books|isbn=9781118523162}}</ref><ref>{{cite book|author=Collin Read|title=The Efficient Market Hypothesists: Bachelier, Samuelson, Fama, Ross, Tobin, and Shiller|url=https://books.google.com/books?id=mbpUKryi9vcC&pg=PA85 |isbn=9781137292216|date=2012-12-15|publisher=Springer }}</ref> however in that same paper, Samuelson warns against such backward reasoning, saying "From a nonempirical base of axioms you never get empirical results."<ref>{{cite web|url=http://hrcak.srce.hr/file/116381|title=The efficient market hypothesis: problems with interpretations of empirical tests}}</ref> In 1970, Fama published a review of both the theory and the evidence for the hypothesis. The paper extended and refined the theory, included the definitions for three forms of [[financial market efficiency]]: weak, semi-strong and strong (see above).<ref>{{cite journal | last = Fama | first = Eugene | title = Efficient Capital Markets: A Review of Theory and Empirical Work | journal = Journal of Finance | volume = 25| pages = 383β417| year = 1970 | doi = 10.2307/2325486 | jstor = 2325486 | issue = 2}}</ref>
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