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 95% VaR of 1million,thatmeansthatthereisa0.05probabilitythattheportfoliowillfallinvaluebymorethan1 million over a one-day period if there is no trading. Informally, a loss of 1millionormoreonthisportfolioisexpectedon1dayoutof20days(becauseof5Moreformally,pVaRisdefinedsuchthattheprobabilityofalossgreaterthanVaRis(atmost)(1−p)whiletheprobabilityofalosslessthanVaRis(atleast)p.AlosswhichexceedstheVaRthresholdistermeda"VaRbreach".Itisimportanttonotethat,forafixedp,thepVaRdoesnotassessthemagnitudeoflosswhenaVaRbreachoccursandthereforeisconsideredbysometobeaquestionablemetricforriskmanagement.Forinstance,assumesomeonemakesabetthatflippingacoinseventimeswillnotgivesevenheads.Thetermsarethattheywin100 if this does not happen (with probability 127/128) and lose 12,700ifitdoes(withprobability1/128).Thatis,thepossiblelossamountsare0 or 12,700.The10, because the probability of any loss at all is 1/128 which is less than 1%. They are, however, exposed to a possible loss of $12,700 which can be expressed as the p VaR for any p ≤ 0.78125% (1/128).
VaR has four main uses in finance: risk management, financial control, financial reporting and computing regulatory capital.
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In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environment), often focusing on negative, undesirable consequences. Many different definitions have been proposed. The international standard definition of risk for common understanding in different applications is "effect of uncertainty on objectives".
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility. There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the most commonly used types of market risk are: Equity risk, the risk that stock or stock indices (e.g. Euro Stoxx 50, etc.) prices or their implied volatility will change. Interest rate risk, the risk that interest rates (e.g. Libor, Euribor, etc.) or their implied volatility will change.
Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss (ETL), and superquantile.
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