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46-535: Elwyn Berlekamp invented an algorithm for decoding Bose–Chaudhuri–Hocquenghem (BCH) codes . James Massey recognized its application to linear feedback shift registers and simplified the algorithm. Massey termed the algorithm the LFSR Synthesis Algorithm (Berlekamp Iterative Algorithm), but it is now known as the Berlekamp–Massey algorithm. The Berlekamp–Massey algorithm is an alternative to

92-421: A 30-year span from 1988 to 2018. Renaissance offers two portfolios to outside investors—Renaissance Institutional Equities Fund (RIEF) and Renaissance Institutional Diversified Alpha (RIDA). Because of the success of Renaissance in general and Medallion in particular, Simons has been described as the "best money manager on earth". Simons ran Renaissance until his retirement in late 2009. He continued to play

138-623: A Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society . Along with Tom M. Rodgers he was one of the founders of Gathering 4 Gardner and was on its board for many years. In the mid-1980s, he was president of Cyclotomics, Inc. , a corporation that developed error-correcting code technology. He studied various games, including dots and boxes , fox and geese , and, especially, Go . Berlekamp and co-author David Wolfe describe methods for analyzing certain classes of Go endgames in

184-810: A decade as the Chair of the Department of Mathematics at Stony Brook University . Simons in 1976 was a recipient of the Oswald Veblen Prize of the American Mathematical Society , which is geometry's highest honor. He is known in the scientific community for co-developing the Chern–Simons theory , which is used in modern theoretical physics. The firm uses quantitative trading , where staff tap data in its petabyte -scale data warehouse to assess statistical probabilities for

230-553: A loss: 1989. During 2020 the Medallion fund surged 76%. "[Renaissance] won the [Labor Department]'s permission to put pieces of Medallion inside Roth IRAs. That means no taxes – ever – on the future earnings of a fund that averaged a 71.8 percent annual return, before fees, from 1994 through mid-2014." Renaissance Technologies terminated its 401(k) retirement plan in 2010 and employees' account balances were put into Individual Retirement Accounts . Contributions could be made to

276-598: A new 401(k) plan, and in November 2014 the Labor Department allowed that plan to be invested in Medallion as well. In 2005, Renaissance Institutional Equities Fund (RIEF) was created. RIEF has historically trailed the firm's better-known Medallion fund, a separate fund that only contains the personal money of the firm's executives. In April 2020, Institutional Investor reported that the disparity between Renaissance's Medallion fund and other funds, including RIEF,

322-559: A piece in The New York Times, " Wall Street experience is frowned on and a flair for science is prized." One former employee speculated that the herdlike mentality among business school graduates is to blame for poor investor returns. Renaissance engages roughly 150 researchers and computer programmers, half of whom have PhDs in scientific disciplines, at its 50-acre East Setauket campus in Long Island, New York , which

368-556: A role at the firm as non-executive chairman, which he stepped down from in 2021, and remained invested in its funds, particularly the Medallion fund until his death in 2024. The company is now run by Peter Brown (after Robert Mercer resigned). Both of them were computer scientists specializing in computational linguistics who joined Renaissance in 1993 from IBM Research . The fund has $ 165 billion in discretionary assets under management (including leverage) as of April 2021. James Simons founded Renaissance Technologies following

414-600: A son with his wife Jennifer. He lived in Piedmont, California and died in April 2019 at the age of 78 from complications of pulmonary fibrosis . Berlekamp was a professor of electrical engineering at the University of California, Berkeley from 1964 until 1966, when he became a mathematics researcher at Bell Labs . In 1971, Berlekamp returned to Berkeley as professor of mathematics and computer science, where he served as

460-596: A standard Individual Retirement Accounts and then converted to a Roth IRA regardless of income. By 2012, Renaissance was granted a special exemption by the United States Labor Department allowing employees to invest their retirement money in Medallion arguing that Medallion had consistently outperformed their old 401(k) plan. In 2013, Renaissance's IRA plans had 259 participants whose $ 86.6 million contribution grew to $ 153 million that year without fees or annual taxes. Renaissance set up

506-420: Is a copy of the last discrepancy d (explained below) since L was updated and initialized to 1. m is the number of iterations since L , B ( x ), and b were updated and initialized to 1. Each iteration of the algorithm calculates a discrepancy d . At iteration k this would be: If d is zero, the algorithm assumes that C ( x ) and L are correct for the moment, increments m , and continues. If d

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552-464: Is a ruse and that the fund investors owe taxes at the higher rate. Because Medallion could claim that it owned just one asset – the option – and held it for more than a year, investors could declare their gains to be long-term investments. In September 2021, Simons, Mercer, and other Renaissance executives agreed to pay up to $ 7 billion in taxes and penalties to settle the dispute with the IRS. The settlement

598-837: Is considered to be one of the most successful hedge funds ever. From 1994 through mid-2014, it averaged a 71.8% annual return, before fees. The fund has been closed to outside investors since 1993 and is available only to current and past employees and their families. The firm bought out the last investor in the Medallion fund in 2005 and the investor community has not seen its returns since then. About 100 of Renaissance's some 275 employees are "qualified purchasers", meaning they generally have at least $ 5 million in assets to invest. The remaining are "accredited investors", generally worth at least $ 1 million. "Since 1988, his flagship Medallion fund has generated average annual returns of 66% before charging hefty investor fees—39% after fees—racking up trading gains of more than $ 100 billion. No one in

644-572: Is famed for the best record in investing history. Renaissance was founded in 1982 by James Simons , a mathematician who formerly worked as a code breaker during the Cold War . In 1988, the firm established its most profitable portfolio , the Medallion Fund, which used an improved and expanded form of Leonard Baum 's mathematical models , improved by algebraist James Ax , to explore correlations from which it could profit. Elwyn Berlekamp

690-503: Is known for low personnel turnover and for requiring its researchers to agree to intellectual property obligations by signing non-compete and non-disclosure agreements. In 1978, Simons left academia and started a hedge fund management firm called Monemetrics in a Long Island strip mall. The firm primarily traded currencies at the start. It did not occur to Simons at first to apply mathematics to his business, but he gradually realized that it should be possible to make mathematical models of

736-545: Is near the State University of New York at Stony Brook . Mathematician Isadore Singer referred to Renaissance's East Setauket office as the best physics and mathematics department in the world. The firm's administrative and back-office functions are handled from its Manhattan office in New York City . The firm is secretive about the workings of its business and very little is known about them. The firm

782-406: Is not surprising that our funds, which depend on models that are trained on historical data, should perform abnormally (either for the better or for the worse) in a year that is anything but normal by historical standards,” Renaissance told clients in a September letter seen by Bloomberg. From December 1, 2020 to February 1, 2021, according to Bloomberg , clients (LPs) had withdrawn $ 5 billion from

828-426: Is not zero, the algorithm adjusts C ( x ) so that a recalculation of d would be zero: The x term shifts B(x) so it follows the syndromes corresponding to b . If the previous update of L occurred on iteration j , then m = k − j , and a recalculated discrepancy would be: This would change a recalculated discrepancy to: The algorithm also needs to increase L (number of errors) as needed. If L equals

874-563: Is the Renaissance Institutional Equities Fund (RIEF). RIEF has historically trailed the firm's better-known Medallion fund, a separate fund that contains only the personal money of the firm's executives. Renaissance is a firm run by and for scientists, employing those with non-financial backgrounds for quantitative finance research like mathematicians, statisticians, theoretical and experimental physicists, astronomers, and computer scientists. According to

920-899: The Renaissance Technologies ' Medallion Fund. Berlekamp was born in Dover, Ohio . His family moved to Northern Kentucky, where Berlekamp graduated from Ft. Thomas Highlands high school in Ft. Thomas, Campbell county, Kentucky. While an undergraduate at the Massachusetts Institute of Technology (MIT), he was a Putnam Fellow in 1961. He completed his bachelor's and master's degrees in electrical engineering in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were Robert G. Gallager , Peter Elias , Claude Shannon , and John Wozencraft . Berlekamp had two daughters and

966-699: The Berlekamp switching game , and was one of the inventors of the Berlekamp–Welch algorithm and the Berlekamp–Massey algorithms , which are used to implement Reed–Solomon error correction . He also co-invented the Berlekamp–Rabin algorithm , Berlekamp–Zassenhaus algorithm , and the Berlekamp–Van Lint–Seidel graph . Berlekamp had also been active in investing , and ran Axcom, which became

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1012-477: The Reed–Solomon Peterson decoder for solving the set of linear equations. It can be summarized as finding the coefficients Λ j of a polynomial Λ( x ) so that for all positions i in an input stream S : In the code examples below, C ( x ) is a potential instance of Λ ( x ). The error locator polynomial C ( x ) for L errors is defined as: or reversed: The goal of the algorithm is to determine

1058-433: The #1 individual federal donor, largely to Republicans, and Simons ranked #5, largely to Democrats. They were top donors to the presidential campaigns of Hillary Clinton and Donald Trump. During the 2016 campaign cycle, Simons contributed $ 26,277,450, ranking as the 5th largest individual contributor. Simons directed all but $ 25,000 of his funds towards liberal candidates. Robert Mercer contributed $ 25,059,300, ranking as

1104-577: The Gardner legacy. Berlekamp was one of the founders of G4G and was on its board of directors for many years. Renaissance Technologies Renaissance Technologies LLC , also known as RenTech or RenTec , is an American hedge fund based in East Setauket, New York , on Long Island , which specializes in systematic trading using quantitative models derived from mathematical and statistical analysis . Their signature Medallion fund

1150-773: The IDA, Berlekamp had acquired most of Ax's stake in Axcom and became its CEO. He worked with Sandor Straus, Jim Simons and another consultant, Henry Laufer , to overhaul Medallion's trading system over the course of six months. In 1990, Berlekamp led Medallion to a 55.9% gain, net of fees, and then returned to his duties as a Berkeley professor after selling out to Simons at six times the price for which he had bought his Axcom interests sixteen months earlier. Straus then took Berlekamp's place, running Medallion's revamped trading system, which returned 39.4% in 1991, 34% in 1992 and 39.1% in 1993, according to Medallion annual reports. The Medallion fund

1196-503: The actual number of errors, then during the iteration process, the discrepancies will become zero before n becomes greater than or equal to 2 L . Otherwise L is updated and algorithm will update B ( x ), b , increase L , and reset m = 1. The formula L = ( n + 1 − L ) limits L to the number of available syndromes used to calculate discrepancies, and also handles the case where L increases by more than 1. The algorithm from Massey (1969 , p. 124) for an arbitrary field: In

1242-683: The advisor for over twenty doctoral students. He was a member of the National Academy of Engineering (1977) and the National Academy of Sciences (1999). He was elected a Fellow of the American Academy of Arts and Sciences in 1996, and became a fellow of the American Mathematical Society in 2012. In 1991, he received the IEEE Richard W. Hamming Medal , and in 1993, the Claude E. Shannon Award . In 1998, he received

1288-451: The book Winning Ways for your Mathematical Plays , leading to his recognition as one of the founders of combinatorial game theory . The dedication of their book says, "To Martin Gardner, who has brought more mathematics to more millions than anyone else." Berlekamp and Gardner both had great love for and were strong advocates of recreational mathematics. Conferences called Gathering 4 Gardner (G4G) are held every two years to celebrate

1334-419: The book Mathematical Go. Berlekamp was a close friend of Scientific American columnist Martin Gardner and was an important member of the gifted and diverse group of people that Gardner nurtured and acted as a conduit for; people who inspired Gardner and who were in turn inspired by him. Berlekamp teamed up with John Horton Conway and Richard K. Guy , two other close associates of Gardner, to co-author

1380-495: The case of binary GF(2) BCH code, the discrepancy d will be zero on all odd steps, so a check can be added to avoid calculating it. Elwyn Berlekamp Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley . Berlekamp was widely known for his work in computer science, coding theory and combinatorial game theory . Berlekamp invented an algorithm to factor polynomials and

1426-477: The company's models led Simons to base the fund's trades entirely on the models. By April 1989, however, peak-to-trough losses had mounted to about 30%. Ax claimed to have accounted for such a decline in his models and insisted on continuing to trade. Simons wanted to pause and reevaluate; Simons, as majority owner, prevailed, and Ax departed. Simons then asked Berkeley professor Elwyn Berlekamp to run Medallion. A consultant for Axcom whom Simons had first met at

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1472-514: The data he was collecting. Monemetrics' name was changed to Renaissance Technologies in 1982. Simons started recruiting some of the mathematicians and data-modeling types from his days at the Institute for Defense Analysis (IDA) and Stony Brook University. His first recruit was Leonard Baum , a cryptanalyst from IDA who was also the co-author of the Baum–Welch algorithm . When Baum abandoned

1518-707: The direction of securities prices in any given market. Staff attribute the breadth of data on events peripheral to financial and economic phenomena that Renaissance takes into account, and the firm's ability to manipulate large amounts of data by deploying scalable technological architectures for computation and execution. Renaissance Technologies' hedge fund has employed mathematical models to analyze and execute trades, many of them automated. The firm uses computer-based models to predict price changes in easily traded financial instruments. These models are based on analyzing as much data as can be gathered, then looking for non-random movements to make predictions. Some also attribute

1564-445: The firm's performance to employing financial signal processing techniques such as pattern recognition. The book The Quants describes the hiring of speech recognition experts, many from IBM , including the current leaders of the firm. Renaissance employs specialists with non-financial backgrounds, including computer scientists , mathematicians , physicists , signal processing experts and statisticians . The firm's latest fund

1610-584: The fund. On 25 September 2008, Renaissance wrote a comment letter to the Securities and Exchange Commission , discouraging them from implementing a rule change that would have permitted the public to access information regarding institutional investors' short positions, as they can currently do with long positions. The company cited a number of reasons for this, including the fact that "institutional investors may alter their trading activity to avoid public disclosure". In July 2014, Renaissance Technologies

1656-726: The fund’s worst year was a 21 percent gain, after subtracting fees. Medallion reaped a 98.2 percent gain in 2008, the year the Standard & Poor’s 500 Index lost 38.5 percent." In 1988, Renaissance established its most profitable fund, the Medallion fund (previously the Limroy Colombian fund), which used an expanded form of Leonard Baum 's mathematical models improved by algebraist James Ax to explore correlations from which they could profit. Simons and Ax, who were classmates at UC Berkeley , started Medallion, which they named after their awards in mathematics. The initial success of

1702-525: The idea of trading with mathematical models and took to fundamental trading, Simons brought in algebraist James Ax from Cornell University. Ax expanded Baum's models for trading currencies to cover any commodity future and subsequently Simons set up Ax with his own trading account, Axcom Ltd., which eventually gave birth to the profitable fund — Medallion. During the 1980s, Ax and his researchers improved on Baum's models and used them to explore correlations from which they could profit. "From 2001 through 2013,

1748-511: The investment world comes close. Warren Buffett, George Soros, Peter Lynch, Steve Cohen, and Ray Dalio all fall short." By 2000, the computer-driven Medallion fund had an average annual return of 34% after fees from its 1988 inception. Simons ran Renaissance until his retirement in late 2009. Between January 1993 and April 2005, Medallion only had 17 losing months and out of 49 quarters over the same period, Medallion had only three losing quarters. Between 1989-2005 Medallion had only one year showing

1794-403: The matter. The $ 75 billion firm’s market-neutral fund dropped about 27% and its global-equities fund lost about 25%... The firm, founded by former codebreaker Jim Simons, told investors that its losses are due to being under-hedged during March’s collapse and then over-hedged in the rebound from April through June. That happened because models that had “overcompensated” for the original trouble. “It

1840-403: The minimal degree L and C ( x ) which results in all syndromes being equal to 0: Algorithm: C ( x ) is initialized to 1, L is the current number of assumed errors, and initialized to zero. N is the total number of syndromes. n is used as the main iterator and to index the syndromes from 0 to N −1. B ( x ) is a copy of the last C ( x ) since L was updated and initialized to 1. b

1886-460: The year. Simons said other hedge funds have been forced to sell positions, short-circuiting statistical models based on the relationships among securities." RIEF once again struggled in the high volatility environment of 2020. According to an article in Bloomberg in November 2020, Renaissance saw a decline of about 20% through October in its long-biased fund, according to a person familiar with

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1932-502: Was also questioned by the Internal Revenue Service (IRS). The higher rates for the five years under investigation would have been 44.4 percent, as compared to 35 percent, whereas the lower rate was 15 percent, as compared to 23.8 percent. The IRS contend[ed] that the arrangement Renaissance’s Medallion fund had with the banks, in which the fund owned option contracts rather than the underlying financial instruments,

1978-426: Was among the largest in history. According to OpenSecrets , Renaissance was the top financial firm contributing to federal campaigns in the 2016 election cycle, donating $ 33,108,000 by July. By comparison, over that same period sixth ranked Soros Fund Management has contributed $ 13,238,551. Renaissance's managers were also active in the 2016 cycle, contributing nearly $ 30 million by June, with Mercer ranking as

2024-725: Was approximately 17-19%. Renaissance also offers two Renaissance Institutional Diversified Alpha (RIDA) to outsiders. Simons ran Renaissance until his retirement in late 2009. Renaissance Institutional Equities Fund had difficulty with the higher volatility environment that persisted throughout the end of the summer of 2007. According to an article in Bloomberg in August 2007, "James Simons's $ 29 billion Renaissance Institutional Equities Fund fell 8.7% in August 2007 when his computer models used to buy and sell stocks were overwhelmed by securities' price swings. The two-year-old quantitative, or 'quant', hedge fund now has declined 7.4 percent for

2070-524: Was included in a larger investigation undertaken by Carl Levin and the Permanent Subcommittee on Investigations on tax evasion by wealthy individuals. The focus of the tax avoidance investigation was Renaissance's trading strategy — which involved transactions with banks such as Barclays Plc and Deutsche Bank AG — through which profits converted from rapid trading were converted into lower-taxed, long-term capital gains. The strategy

2116-404: Was instrumental in evolving trading to shorter-dated, pure systems driven decision-making. The hedge fund was named Medallion in honor of the math awards that Simons and Ax had won. Renaissance's flagship Medallion fund, which is run mostly for fund employees, is famous for the best track record on Wall Street, returning more than 66 percent annualized before fees and 39 percent after fees over

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