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The 5% Value at Risk of a hypothetical profit-and-loss probability density function. 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.
In financial mathematics, tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the more general value at risk. It quantifies the expected value of the loss given that an event outside a given probability level has occurred.
Expected shortfall is considered a more useful risk measure than VaR because it is a coherent spectral measure of financial portfolio risk. It is calculated for a given quantile -level q {\displaystyle q} and is defined to be the mean loss of portfolio value given that a loss is occurring at or below the q {\displaystyle q} -quantile.
Value at risk is, however, coherent, under the assumption of elliptically distributed losses (e.g. normally distributed) when the portfolio value is a linear function of the asset prices. However, in this case the value at risk becomes equivalent to a mean-variance approach where the risk of a portfolio is measured by the variance of the ...
Many risk measures have hitherto been proposed, each having certain characteristics. The entropic value at risk (EVaR) is a coherent risk measure introduced by Ahmadi-Javid, [1] [2] which is an upper bound for the value at risk (VaR) and the conditional value at risk (CVaR), obtained from the Chernoff inequality.
Market risk and other financial risks are measured by simulating adverse movements of the risk factors affecting the value of an entity's financial instruments during the holding period, implicitly assuming that the pricing models used by the entity correctly reflect the instrument value and that capacity is maintained along all the holding period.
Earnings at risk (EaR) and the related cash flow at risk (CFaR) [1] [2] [3] are measures reflecting the potential impact of market risk on the income statement and cash flow statement respectively, and hence the risk to the institution's return on assets and, ultimately, return on equity.
Calculating the value at risk of the portfolio Calculating the multiperiod cash flow or financial accrual income and expense for N periods forward in a deterministic set of future yield curves Doing step 4 with random yield curve movements and measuring the probability distribution of cash flows and financial accrual income over time.