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Statistical Arbitrage
In finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ Mean reversion (finance), mean reversion models involving broadly diversified portfolios of securities (hundreds to thousands) held for short periods of time (generally seconds to days). These strategies are supported by substantial mathematical, computational, and trading platforms. Trading strategy Broadly speaking, StatArb is actually any strategy that is bottom-up, Beta (finance), beta-neutral in approach and uses statistical/econometric techniques in order to provide signals for execution. Signals are often generated through a contrarian mean reversion principle but can also be designed using such factors as lead/lag effects, corporate activity, short-term momentum (finance), momentum, etc. This is usually referred to as a multi-factor approach to StatArb. Because of the large number of stocks involved, the high portfolio turnover and ...
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Finance
Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Administration wich study the planning, organizing, leading, and controlling of an organization's resources to achieve its goals. Based on the scope of financial activities in financial systems, the discipline can be divided into Personal finance, personal, Corporate finance, corporate, and public finance. In these financial systems, assets are bought, sold, or traded as financial instruments, such as Currency, currencies, loans, Bond (finance), bonds, Share (finance), shares, stocks, Option (finance), options, Futures contract, futures, etc. Assets can also be banked, Investment, invested, and Insurance, insured to maximize value and minimize loss. In practice, Financial risk, risks are always present in any financial action and entities. Due ...
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Model Risk
In finance, model risk is the risk of loss resulting from using insufficiently accurate models to make decisions, originally and frequently in the context of valuing financial securities. Here, Rebonato (2002) defines model risk as "the risk of occurrence of a significant difference between the mark-to-model value of a complex and/or illiquid instrument, and the price at which the same instrument is revealed to have traded in the market". However, model risk is increasingly relevant in contexts other than financial securities valuation, including assigning consumer credit scores, real-time prediction of fraudulent credit card transactions, and computing the probability of an air flight passenger being a terrorist. In fact, Burke regards failure to use a model (instead over-relying on expert judgment) as a type of model risk.http://www.siiglobal.org/SII/WEB5/sii_files/Membership/PIFs/Risk/Model%20Risk%2024%2011%2009%20Final.pdf Types Derman describes various types of model ...
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Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''f ...
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Machine Learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ...
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Fourier-related Transforms
This is a list of linear transformations of functions related to Fourier analysis. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum. (These transforms are generally designed to be invertible.) In the case of the Fourier transform, each basis function corresponds to a single frequency component. Continuous transforms Applied to functions of continuous arguments, Fourier-related transforms include: * Two-sided Laplace transform * Mellin transform, another closely related integral transform * Laplace transform: the Fourier transform may be considered a special case of the imaginary axis of the bilateral Laplace transform * Fourier transform, with special cases: ** Fourier series *** When the input function/waveform is periodic, the Fourier transform output is a Dirac comb function, modulated by a discrete sequence of finite-valued coefficients tha ...
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Currency Correlation
A currency pair is the quotation of the relative value of a currency unit against the unit of another currency in the foreign exchange market. The currency that is used as the reference is called the counter currency, quote currency, or currency and the currency that is quoted in relation is called the base currency or transaction currency. Currency pairs are generally written by concatenating the ISO currency codes (ISO 4217) of the base currency and the counter currency, and then separating the two codes with a slash. Alternatively the slash may be omitted, or replaced by either a dot or a dash. A widely traded currency pair is the relation of the euro against the US dollar, designated as EUR/USD. The quotation ''EUR/USD 1.2500'' means that one euro is exchanged for 1.2500 US dollars. Here, EUR is the base currency and USD is the quote currency (counter currency). This means that 1 Euro can be exchangeable to 1.25 US Dollars. The most traded currency pairs in the world are ...
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Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are '' linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However, in g ...
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Cointegration
In econometrics, cointegration is a statistical property describing a long-term, stable relationship between two or more time series variables, even if those variables themselves are individually non-stationary (i.e., they have trends). This means that despite their individual fluctuations, the variables move together in the long run, anchored by an underlying equilibrium relationship. More formally, if several time series are individually integrated of order ''d'' (meaning they require ''d'' differences to become stationary) but a linear combination of them is integrated of a lower order, then those time series are said to be cointegrated. That is, if (''X'',''Y'',''Z'') are each integrated of order ''d'', and there exist coefficients ''a'',''b'',''c'' such that is integrated of order less than d, then ''X'', ''Y'', and ''Z'' are cointegrated. Cointegration is a crucial concept in time series analysis, particularly when dealing with variables that exhibit trends, such as ma ...
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2008 Financial Crisis
The 2008 financial crisis, also known as the global financial crisis (GFC), was a major worldwide financial crisis centered in the United States. The causes of the 2008 crisis included excessive speculation on housing values by both homeowners and financial institutions that led to the 2000s United States housing bubble, exacerbated by predatory lending for subprime mortgages and deficiencies in regulation. Cash out refinancings had fueled an increase in consumption that could no longer be sustained when home prices declined. The first phase of the crisis was the subprime mortgage crisis, which began in early 2007, as mortgage-backed securities (MBS) tied to U.S. real estate, and a vast web of Derivative (finance), derivatives linked to those MBS, collapsed in value. A liquidity crisis spread to global institutions by mid-2007 and climaxed with the bankruptcy of Lehman Brothers in September 2008, which triggered a stock market crash and bank runs in several countries. The crisis ...
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Market Maker
A market maker or liquidity provider is a company or an individual that quotes both a buy and a sell price in a tradable asset held in inventory, hoping to make a profit on the difference, which is called the ''bid–ask spread'' or ''turn.'' This stabilizes the market, reducing price variation (Volatility (finance), volatility) by setting a trading price range for the asset. In U.S. markets, the U.S. Securities and Exchange Commission defines a "market maker" as a firm that stands ready to buy and sell stock on a regular and continuous basis at a publicly quoted price. A Designated Primary Market Maker (DPM) is a specialized market maker approved by an exchange to guarantee a buy or sell position in a particular assigned security, option, or option index. In currency exchange Most foreign exchange trading firms are market makers, as are many banks. The foreign exchange market maker both buys foreign currency from clients and sells it to other clients. They derive income from the ...
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PDT Partners
PDT Partners (Process Driven Trading Partners) is a hedge fund company, led by quantitative trader Peter Muller, that was founded in 1993 as part of Morgan Stanley's trading division and spun off as an independent business in 2012. It has offices in New York City and London. History PDT Partners started out as a proprietary trading division (called the Process Driven Trading Group) of multinational financial services corporation Morgan Stanley in 1993. According to Bloomberg.com, ''Bloomberg'', PDT's investments have returned an estimated annual average of more than 20 percent through 2010. In January 2011, Morgan Stanley announced that it would spin off PDT into a separate hedge fund in order to comply with the Dodd–Frank Wall Street Reform and Consumer Protection Act. The spin-off began in 2012. In October 2012, it was announced that the Blackstone Group had put $500 million into PDT, but without seeking any equity in the hedge fund. Bloomberg.com considered this unusual a ...
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Morgan Stanley
Morgan Stanley is an American multinational investment bank and financial services company headquartered at 1585 Broadway in Midtown Manhattan, New York City. With offices in 42 countries and more than 80,000 employees, the firm's clients include corporations, governments, institutions, and individuals. Morgan Stanley ranked No. 61 in the 2023 Fortune 500 list of the largest United States corporations by total revenue and in the same year ranked #30 in Forbes Global 2000. The original Morgan Stanley, formed by J.P. Morgan & Co. partners Henry Sturgis Morgan (a grandson of J.P. Morgan), Harold Stanley, and others, came into existence on September 16, 1935, in response to the Glass–Steagall Act, which required the splitting of American commercial and investment banking businesses. In its first year, the company operated with a 24% market share (US$1.1 billion) in public offerings and private placements. The current Morgan Stanley is the result of the merger of the origi ...
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