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RiskMetrics
The RiskMetrics variance model (also known as exponential smoother) was first established in 1989, when Sir Dennis Weatherstone, the new chairman of J.P. Morgan, asked for a daily report measuring and explaining the risks of his firm. Nearly four years later in 1992, J.P. Morgan launched the RiskMetrics methodology to the marketplace, making the substantive research and analysis that satisfied Sir Dennis Weatherstone's request freely available to all market participants. In 1998, as client demand for the group's risk management expertise exceeded the firm's internal risk management resources, the Corporate Risk Management Department was spun off from J.P. Morgan as RiskMetrics Group with 23 founding employees. The RiskMetrics technical document was revised in 1996. In 2001, it was revised again in ''Return to RiskMetrics''. In 2006, a new method for modeling risk factor returns was introduced (RM2006). On 25 January 2008, RiskMetrics Group listed on the New York Stock Exchange ...
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MSCI
MSCI Inc. (formerly Morgan Stanley Capital International) is an American finance company headquartered in New York City. MSCI is a global provider of equity, fixed income, real estate indices, multi-asset portfolio analysis tools, ESG and climate finance products. It operates the MSCI World, MSCI Emerging Markets, and MSCI All Country World (ACWI) indices, among others. The company is headquartered at 7 World Trade Center in Manhattan. Its business primarily consists of licensing its indices to index funds, such as exchange-traded funds (ETFs), which pay a fee of around 0.02 to 0.04 percent of the invested volume for the use of the index. funds worth over 16.5 trillion US$ were based on MSCI indices. History In 1968, Capital International published indices covering the global stock market for non-U.S. markets. In 1986, Morgan Stanley licensed the rights to the indices from Capital International and branded the indices as the Morgan Stanley Capital International (MSCI) ...
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Value-at-Risk
Value at risk (VaR) is a measure of the risk of loss of investment/capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given Portfolio (finance), portfolio, time horizon, and probability ''p'', the ''p'' VaR can be defined informally as the maximum possible loss during that time after excluding all worse outcomes whose combined probability is at most ''p''. This assumes Mark to market accounting, mark-to-market pricing, and no trading in the portfolio. For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by $1 million or more over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is ex ...
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Coherent Risk Measure
In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance. Properties Consider a random outcome X viewed as an element of a linear space \mathcal of measurable functions, defined on an appropriate probability space. A functional \varrho : \mathcal → \R \cup \ is said to be coherent risk measure for \mathcal if it satisfies the following properties: Normalized : \varrho(0) = 0 That is, the risk when holding no assets is zero. Monotonicity : \mathrm\; Z_1,Z_2 \in \mathcal \;\mathrm\; Z_1 \leq Z_2 \; \mathrm ,\; \mathrm \; \varrho(Z_1) \geq \varrho(Z_2) That is, if portfolio Z_2 always has better values than portfolio Z_1 under almost all scenarios then the risk of ...
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Value At Risk
Value at risk (VaR) is a measure of the risk of loss of investment/capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given portfolio, time horizon, and probability ''p'', the ''p'' VaR can be defined informally as the maximum possible loss during that time after excluding all worse outcomes whose combined probability is at most ''p''. This assumes mark-to-market pricing, and no trading in the portfolio. For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by $1 million or more over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% p ...
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Risk Measure
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the downside risk, risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator (economics), regulator. In recent years attention has turned to coherent risk measure, convex and coherent risk measurement. Mathematically A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns. The common notation for a risk measure associated with a random variable X is \rho(X). A risk measure \rho: \mathcal \to \mathbb \cup \ should have certain properties: ; Normalized : \rho(0) = 0 ; Translative : \mathrm\; a \in \mathbb \; \mathrm \; Z \in \mathcal ,\;\mathrm\; \rho(Z + a) = \rho(Z) - a ; Monotone : \mathrm\; Z_1,Z_2 \in \mathcal \;\mathrm\; Z_1 \leq Z_2 ,\; \mathrm \ ...
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Risk Metric
In the context of risk measurement, a risk metric is the concept quantified by a risk measure. When choosing a risk metric, an agent is picking an aspect of perceived risk to investigate, such as volatility or probability of default. Risk measure and risk metric In a general sense, a measure is a procedure for quantifying something. A metric is that which is being quantified. In other words, the method or formula to calculate a risk metric is called a risk measure. For example, in finance, the volatility of a stock might be calculated in any one of the three following ways: * Calculate the sample standard deviation of the stock's returns over the past 30 trading days. * Calculate the sample standard deviation of the stock's returns over the past 100 trading days. * Calculate the implied volatility of the stock from some specified call option on the stock. These are three distinct risk measures. Each could be used to measure the single risk metric volatility. Examples * ...
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Portfolio Optimization
Portfolio optimization is the process of selecting an optimal portfolio (asset distribution), out of a set of considered portfolios, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk, resulting in a multi-objective optimization problem. Factors being considered may range from tangible (such as assets, liabilities, earnings or other fundamentals) to intangible (such as selective divestment). Modern portfolio theory Modern portfolio theory was introduced in a 1952 doctoral thesis by Harry Markowitz, where the Markowitz model was first defined. The model assumes that an investor aims to maximize a portfolio's expected return contingent on a prescribed amount of risk. Portfolios that meet this criterion, i.e., maximize the expected return given a prescribed amount of risk, are known as efficient portfolios. By definition, any other portfolio yielding a higher amount of expected return must also h ...
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Market Exposure
In finance, market exposure (or exposure) is a measure of the proportion of money invested in the same industry sector. For example, a stock portfolio with a total worth of $500,000, with $100,000 in semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ... industry stocks, would have a 20% exposure in "chip" stocks. References Finance theories Investment {{finance-stub ...
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Black Swan Theory
The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight. The term arose from a Latin expression which was based on the presumption that black swans did not exist. The expression was used in the original manner until around 1697 when Dutch mariners saw black swans living in Australia. After this, the term was reinterpreted to mean an unforeseen and consequential event. The reinterpreted theory was articulated by Nassim Nicholas Taleb, starting in 2001, to explain: # The disproportionate role of high-profile, hard-to-predict, and rare events that are beyond the realm of normal expectations in history, science, finance, and technology. # The non-computability of the probability of consequential rare events using scientific methods (owing to the very nature of small probabilities). # The psychological biases that bl ...
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The Black Swan (Taleb Book)
''The Black Swan: The Impact of the Highly Improbable'' is a 2007 book by Nassim Nicholas Taleb, who is a former options trader. The book focuses on the extreme impact of rare and unpredictable outlier events—and the human tendency to find simplistic explanations for these events, retrospectively. Taleb calls this the Black Swan theory. The book covers subjects relating to knowledge, aesthetics, as well as ways of life, and uses elements of fiction and anecdotes from the author's life to elaborate his theories. It spent 36 weeks on the ''New York Times'' best-seller list. The book is part of Taleb's five-volume series, titled the ''Incerto'', including '' Fooled by Randomness'' (2001), ''The Black Swan'' (2007–2010), '' The Bed of Procrustes'' (2010–2016), '' Antifragile'' (2012), and ''Skin in the Game'' (2018). Coping with Black Swan events A central idea in Taleb's book is not to attempt to predict Black Swan events, but to build robustness to negative events and ...
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Nassim Taleb
Nassim Nicholas Taleb (; alternatively ''Nessim ''or'' Nissim''; born 12 September 1960) is a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist. His work concerns problems of randomness, probability, complexity, and uncertainty. Taleb is the author of the ''Incerto'', a five-volume work on the nature of uncertainty published between 2001 and 2018 (notably, '' The Black Swan'' and '' Antifragile''). He has taught at several universities, serving as a Distinguished Professor of Risk Engineering at the New York University Tandon School of Engineering since September 2008. He has also been a practitioner of mathematical finance and is currently an adviser at Universa Investments. ''The Sunday Times'' described his 2007 book '' The Black Swan'' as one of the 12 most influential books since World War II. Taleb criticized risk management methods used by the finance industry and warned about financial crises, subsequently ...
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Monte Carlo Algorithm
In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are the Karger–Stein algorithm and the Monte Carlo algorithm for minimum feedback arc set. The name refers to the Monte Carlo casino in the Principality of Monaco, which is well-known around the world as an icon of gambling. The term "Monte Carlo" was first introduced in 1947 by Nicholas Metropolis. Las Vegas algorithms are a dual of Monte Carlo algorithms and never return an incorrect answer. However, they may make random choices as part of their work. As a result, the time taken might vary between runs, even with the same input. If there is a procedure for verifying whether the answer given by a Monte Carlo algorithm is correct, and the probability of a correct answer is bounded above zero, then with probability one, running the algorithm repeatedly while testing the answers will eventually give a co ...
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