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Measure giving the average loss beyond a specified Value-at-Risk level
mathematics, tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated
Tail_value_at_risk
Risk measure estimating the average loss in the worst tail of the distribution
tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), tail value at risk (TVaR)
Expected_shortfall
Estimated potential loss for an investment under a given set of conditions
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)
Value_at_risk
Risk of statistically extreme events
Tail risk, sometimes called "fat tail risk", is the financial risk of an asset or portfolio of assets moving more than three standard deviations from its
Tail_risk
Concept in financial economics
spaces. The entropic value at risk is a coherent risk measure. The tail value at risk (or tail conditional expectation) is a coherent risk measure only when
Coherent_risk_measure
Probability distribution with high skewness or kurtosis
increase in sales due to promotion of the new records that enter the charts. Tail risk Black swan theory Seven states of randomness Taleb distribution Bahat;
Fat-tailed_distribution
Protecting economic value by managing risk exposure
Financial risk management is the practice of protecting economic value in a firm by managing exposure to financial risk - principally credit risk and market
Financial_risk_management
Stock market index measuring tail risk
measure of the perceived tail risk of the distribution of S&P 500 investment returns over a 30-day horizon. The index values are calculated and published
SKEW
Tail risk parity is an extension of the risk parity concept that takes into account the behavior of the portfolio components during tail risk events.
Tail_risk_parity
Possibility of something bad happening
distribution's tail is the loss with a certain probability of exceedance, that is, the value at risk. Risk is often measured as the expected value of the loss
Risk
Overview of finance and finance-related topics
far values spread from their average Expected shortfall (ES; also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss
Outline_of_finance
Concept in financial mathematics
R(X_{1})} Value at risk Expected shortfall Superposed risk measures Entropic value at risk Drawdown Tail conditional expectation Entropic risk measure Superhedging
Risk_measure
distributions. The concept is used in extreme value theory. Random variables that appear to exhibit no correlation can show tail dependence in extreme deviations.
Tail_dependence
by the Expected tail loss (ETL) in the worst q% cases. The ETL is the average loss incurred when losses exceed the Value at Risk at a predefined quantile
Rachev_ratio
Identification, evaluation and control of risks
portfolio value; for an overview see Finance § Risk management. A traditional measure in banking is value at risk (VaR) – the possible loss due to adverse credit
Risk_management
Function of the observed sample results
In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed
P-value
American financial services company
portfolio's value. The market model must be sufficiently specified so that the portfolio can be revalued using information from the market model. The risk measurements
RiskMetrics
Branch of statistics focusing on large deviations
extreme values changes over time, or over another covariate. Extreme risk Extreme weather Fisher–Tippett–Gnedenko theorem Generalized extreme value distribution
Extreme_value_theory
Measure of potential liquidity shortfall in a financial portfolio
liquidity. The concept is closely related to Value at Risk (VaR), but instead of focusing on market value fluctuations, LaR models the probability distribution
Liquidity_at_risk
Feature of some statistical distributions
the primary value of the internet to consumers comes from releasing new sources of value by providing access to products in the long tail. The distribution
Long_tail
Probability distribution
Roughly speaking, “heavy-tailed” means the distribution decreases more slowly than an exponential distribution, so extreme values are more likely. In many
Heavy-tailed_distribution
reinvested Risk measure Distortion risk measure Tail conditional expectation Value at risk Convex risk measure Entropic risk measure Coherent risk measure
List of financial performance measures
List_of_financial_performance_measures
Measure of the asymmetry of random variables
where one tail is long but the other tail is thick, skewness does not obey a simple rule. For example, a zero value in skewness means that the tails on
Skewness
Concept in gambling, insurance, and finance
expected returns, yet paradoxically perceived to be of low investment value) Value at risk Zenios, Ziemba (2006). Handbook of Asset and Liability Management
Risk_of_ruin
Econometric analysis of financial risk
New Tools: Machine learning, extreme value theory, and Bayesian networks are increasingly applied to model tail risk. Regulation: Basel III and Basel IV
Econometrics_of_risk
Risk of collapse of an entire financial system or entire market
In finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to the risk associated with any one individual
Systemic_risk
Process of selecting a portfolio
70% of the true values). Other optimization strategies that focus on minimizing tail-risk (e.g., value at risk, conditional value at risk) in investment
Portfolio_optimization
Risks arising from movements in market variables
covering adverse value changes of a given position. Shape risk Holding period risk Basis risk The capital requirement for market risk is addressed under
Market_risk
purchase tail coverage from the last carrier. Nose coverage is usually less expensive than purchasing tail coverage from the old carrier. Tail coverage
Professional liability insurance
Professional_liability_insurance
Variable in statistics and risk management
used in statistics and risk management, including financial risk. The bPOE is the probability of a tail with known mean value x {\displaystyle x} . The
Buffered probability of exceedance
Buffered_probability_of_exceedance
Risk of disrupting business operations
shareholder value, all while increasing business volatility. Previously, in Basel I, operational risk was negatively defined: namely that operational risk are
Operational_risk
Type of probability distribution in economics
these situations the expected value is very much less than zero, but this fact is camouflaged by the appearance of low risk and steady returns. It is a
Taleb_distribution
2009 book by Ian Bremmer
irregularly high likelihood of catastrophic events. This fat tail represents the risks of an event so unlikely and difficult to predict that many choose
The_Fat_Tail
Type of financial risk
regulators have accepted, a financial risk management technique called value at risk (VaR), which examines the tail end of a distribution of returns for
Foreign_exchange_risk
Insurance that covers legal liability for injury, damage, or loss caused to others
force insureds to become more proactive about risk management and finding ways to control their own long-tail liability. Claims-made policies often include
Liability_insurance
Family of probability distributions
as a means of assessing various financial risks via metrics such as value at risk. However, the resulting shape parameters have been found to lie in the
Generalized extreme value distribution
Generalized_extreme_value_distribution
Financial risk
into actual risk; the underlying latent risk, and perceived risk; what is reported by common risk measurement techniques, such as value at risk and expected
Endogenous_risk
Average value of a random variable
integer-valued random variable X {\displaystyle X} , the expected value can also be expressed in terms of its tail probabilities (sometimes called the tail-sum
Expected_value
Hedge fund established in 2009
L.P. (Saba) is a credit relative value focused hedge fund firm established in 2009. It also has strategies in tail hedge, closed-end funds and SPACs
Saba_Capital_Management
Event that is both extremely large in effect and of unique origins
loss or damage in excess of some value (value at risk), other tail risk measures, and return periods. To provide such risk characterizations, the dynamic
Dragon_king_theory
Type of financial contract
flows that are conditioned stochastically and discounted to present value. The market risk inherent in the underlying asset is attached to the financial derivative
Derivative_(finance)
Mathematical model of financial markets
unexpected risk.[unreliable source?] Among the most significant limitations are: the underestimation of extreme moves, yielding tail risk, which can be
Black–Scholes_model
Assets with no value or available markets
has significantly decreased in value and for which there is no longer a functioning market. These assets cannot be sold at a satisfactory price for the
Toxic_asset
Association of artisans or merchants
revolves around politics within the Guild. In Hiro Mashima's work Fairy Tail, there exists a guild of that name, including many other kinds of guilds
Guild
Theory of response to surprise events
assume normal distributions when using value at risk models, although market returns typically have fat tail distributions. Taleb said: I don't particularly
Black_swan_theory
Mathematical framework for investment risk
MPT by adopting non-normally distributed, asymmetric, and fat-tailed measures of risk. This helps with some of these problems, but not others. Black–Litterman
Modern_portfolio_theory
Theory in actuarial science and applied probability
actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability
Ruin_theory
Academic discipline concerned with the exchange of money
traders, analysts and risk managers frequently modify the "standard models" (see kurtosis risk, skewness risk, long tail, model risk). In fact, Benoit Mandelbrot
Financial_economics
Family of probability distributions
range. The PERT distribution is widely used in risk analysis to represent the uncertainty of the value of some quantity where one is relying on subjective
PERT_distribution
Measure for hazard from asteroid or comet impacts on Earth
increased risk, and potentially an increasing rating. If the real orbit bypasses Earth, with further observations, Earth will only intersect the tail of the
Torino_scale
Insurance purchased by an insurance company
enables them to use less capital to cover any risk, and to make less conservative assumptions when valuing the risk. Reinsurers may operate under a more favourable
Reinsurance
Probability of adverse effects of political decisions
expected value of a given economic action. Political risk can be understood and managed with reasoned foresight and investment. The term political risk has
Political_risk
Approach to investment management focusing on allocation of risk
Risk parity (or risk premia parity) is an approach to investment management which focuses on allocation of risk, usually defined as volatility, rather
Risk_parity
Species of pangolin
moderately common within its limited range, but is at risk due to heavy hunting because of its valued scales and meat. This species is distinguished from
Philippine_pangolin
Removal of a portion of the ears or tail
difficult to near impossible. Veterinarians who presently exercise tail docking risk disciplinary action, and can be removed from the professional register
Docking_(animal)
1960–1969 Catalog of Copyright Entries 1971 Library of Congress [979] Works by or about List of Encyclopædia Britannica Films titles at the Internet Archive
List of Encyclopædia Britannica Films titles
List_of_Encyclopædia_Britannica_Films_titles
Bet sizing formula for long-term growth
Kelly bet) is a formula for risk allocation with the sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth,
Kelly_criterion
Food recall in the United States
Possible Health Risk". www.fda.gov. "Beaver Street Fisheries, LLC Recalls Great Value Frozen Raw Shrimp Because of Possible Health Risk". www.fda.gov.
2025 radioactive shrimp recall
2025_radioactive_shrimp_recall
discretionary investment at r, risk-free rate, before the expected payoff is calculated. The option value is then the expected value of the maximum of the
Datar–Mathews method for real option valuation
Datar–Mathews_method_for_real_option_valuation
Dynamic timeline of 2025 artificial intelligence risks in global finance
risk, and that in a tail-risk event miscalibrated algorithms could amplify and spread shocks faster than human intervention could respond. Other risk
Timeline of artificial intelligence risks in global finance
Timeline_of_artificial_intelligence_risks_in_global_finance
Application of mathematical and statistical methods in finance
Survival analysis Value at risk Volatility ARCH model GARCH model The Brownian model of financial markets Rational pricing assumptions Risk neutral valuation
Mathematical_finance
Estimation of risk associated with exposure to a given set of hazards
predictable. Wild risk follows fat-tailed distributions, e.g., Pareto or power-law distributions, is subject to regression to the tail (infinite mean or
Risk_assessment
Proposals for bank requirements
shortfall instead of value at risk as a measure of risk under stress; thus ensuring that banks capture tail risk events The risk of market illiquidity
Fundamental Review of the Trading Book
Fundamental_Review_of_the_Trading_Book
Set of actions with the intent of earning profit
uses leverage and derivatives to bet that the value of a stock will decline An investor may bear a risk of loss of some or all of their capital invested
Investment
Materials left over from the separation of valuable minerals from ore
Even though the reprocessing of tailings might deliver additional metal value and decreases in some cases the risk for acid mine drainage, the volume
Tailings
Type of dam
A tailings dam is typically an earth-fill embankment dam used to store byproducts of mining operations after separating the ore from the gangue. Tailings
Tailings_dam
kanji radicals The Cabinet of Japan. Jōyō Kanji Table Archived 2011-08-31 at the Wayback Machine. November 30, 2010. "Jōyō Kanji Hyō" 常用漢字表 [List of Joyo
List_of_jōyō_kanji
Species of snake
length, slightly compressed, medium bodied snake with a moderately long tail. Head distinct from narrow neck with a rounded snout. Eyes large in size
Boiga_cyanea
Automotive styling feature
risk of instability or loss of control. The Kammback decreased the area of the lifting surface while creating a low-pressure zone underneath the tail
Kammback
broadcast on Kids' WB on March 15, 2003, as part of a special sneak peek at the upcoming Advanced season. It was later redubbed and rebroadcast for inclusion
List of Pokémon episodes (seasons 1–9)
List_of_Pokémon_episodes_(seasons_1–9)
Breed of cat
on the Isle of Man, with a mutation that shortens the tail. Many Manx have a small stub of a tail, but Manx cats are best known as being entirely tailless;
Manx_cat
Species of bird in Europe and Asia
The long-tailed tit or long-tailed bushtit (Aegithalos caudatus) is a common bird species belonging to the bushtit family found throughout Eurasia. An
Long-tailed_tit
Theory in evolutionary biology
of risk, such as taking drugs. Males and females valued different degrees of heroic risk for mates and same-sex friends. Males valued heroic risk-taking
Signalling_theory
Wagering something of value on a random event
Economic utility Positive expected returns (at least in the long term) Underlying value independent of the risk being undertaken Some speculative investment
Gambling
Use of mathematical and statistical methods in finance
correctly hedged; see FRTB, Tail risk § Role of the 2008 financial crisis. A core technique continues to be value at risk - applying both the parametric
Quantitative analysis (finance)
Quantitative_analysis_(finance)
Concept in economics
guaranteed $50 because they value the certainty of the smaller reward more than the possibility of a larger one, reflecting risk-averse preferences. Standard
Expected_utility_hypothesis
Professional designation in U.S. securities
Hedge Fund Replication The Risk and Performance of Private and Listed Assets Due Diligence & Selecting Managers Cases in Tail Risk Due Diligence of Terms
Chartered Alternative Investment Analyst
Chartered_Alternative_Investment_Analyst
Species of bird
conditions such as ice or by human hunters) are at the greatest risk for eagle predation, white-tailed eagles have preyed upon even healthy adult swans
White-tailed_eagle
NAV Lending: Asset-Based Loans to Private Equity Funds
NAV (Net Asset Value) lending is a form of fund-level financing where loans are secured by the value of a private equity fund’s investments rather than
NAV_lending
American investor and hedge fund manager (born 1971)
Archived April 14, 2010, at the Wayback Machine, CIMS Newsletter, Fall/Winter, 2009 Universa Investments L.P., firm website Tail-Risk Hedge Pioneer Spitznagel
Mark_Spitznagel
Infinite series used to approximate quantiles of probability distributions
Arora, Rohit (2017). "Inefficiency and bias of modified value-at-risk and expected shortfall". Journal of Risk. 19 (6): 59–84. doi:10.21314/JOR.2017.365.
Cornish–Fisher_expansion
Rules to develop an investment portfolio
and long the bottom asset. Value vs Growth: Value investing strategy looks at the intrinsic value of a company and value investors seek stocks of companies
Investment_strategy
Mathematical finance term
"Leveraged Investment Products: Monthly Rebalancing Boosts Performance, but Tail Risk Looms". The Journal of Index Investing. 10 (3): 58–69. doi:10.3905/jii
Volatility_tax
Type of debt security issued by an underwriting bank or special-purpose entity
additional risk compared to an exchange-traded fund (ETF); if the credit rating of the issuer is compromised, the investment might lose value in the same
Exchange-traded_note
Particular case of the generalized extreme value distribution
the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum)
Gumbel_distribution
Simulation of a financial asset or institution under crisis conditions
and Tail Risks: Application to Stress Testing" (PDF). International Monetary Fund, August, 2012. Humphrey, D. (1986). Payments finality and the risks of
Stress_test_(financial)
Copper mine in Romania
used as a settling basin for the ore processing tailings. The basin has continued to fill with tailings, and as of 2015 was 90 meters deep and covered
Roșia_Poieni_copper_mine
Seventeenth letter of the Greek alphabet
Key to Options Risk Management". Investopedia. Retrieved 2026-02-07. Rho (ρ) represents the rate of change between an option's value and a 1% change
Rho
Domesticated species of canid
2024. Diesel G, Pfeiffer D, Crispin S, Brodbelt D (26 June 2010). "Risk factors for tail injuries in dogs in Great Britain" (PDF). Veterinary Record. 166
Dog
Former Orange County, California Treasurer-Tax Collector
high-risk derivatives". Los Angeles Times. December 1, 1995. Retrieved April 7, 2021. "Orange County Case: Using Value-at-Risk to Control Financial Risk"
Robert_Citron
Special case in probability theory; introduces tail events
sense of fat-tailed distributions (or the closely related long tails and tail risks). The events we consider in this article are things like convergence/non-convergence
Kolmogorov's_zero–one_law
Algorithm
the tail; // the head for data values greater the mean // the tail for data values less the mean If (length(head)/length(data) <=40%): Head/tail Breaks(head);
Head/tail_breaks
Statistical test for logistic regression models
Hosmer–Lemeshow test specifically identifies subgroups as the deciles of fitted risk values. Models for which expected and observed event rates in subgroups are
Hosmer–Lemeshow_test
Topics referred to by the same term
object as its temperature changes Tail conditional expectation, a risk measure associated with the more general value at risk Time charter equivalent, a measurement
TCE
Data missing or collected but not analysed
avoided." The continuous storage of dark data can put an organisation at risk, especially if this data is sensitive. In the case of a breach, this can
Dark_data
Limit to value of recommender systems
mathematical characterization of this limit in terms of rating noise and empirical risk minimization, framing it as a lower bound on achievable prediction accuracy
Accuracy_barrier
Functional relationship between two quantities
{\displaystyle a} used above) is greater than 1 (otherwise the tail has infinite area), the minimum value x min {\displaystyle x_{\text{min}}} is needed otherwise
Power_law
Award
or those "deeds aimed at saving other human lives or substantial material values" which put the recipient at significant risk of death. It is unique
Medal of Heroism (Czech Republic)
Medal_of_Heroism_(Czech_Republic)
Breed of herding dog
a natural, long, un-docked tail. There will often be a solid colour spot at the base of the tail and a white tip. The tail should be set moderately low
Australian_Cattle_Dog
2010 EF4 tornado in Minnesota, USA
Otter Tail County. It traveled along a 39.56 mi (63.67 km) long path, and had with a maximum width of 2,288 yd (1.3 mi; 2.1 km) before dissipating at 4:45 p
2010_Wadena_tornado
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