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  2. Value at risk - Wikipedia

    en.wikipedia.org/wiki/Value_at_risk

    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.

  3. Coherent risk measure - Wikipedia

    en.wikipedia.org/wiki/Coherent_risk_measure

    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 portfolio's return. The Wang transform function (distortion function) for the Value at Risk is g ( x ) = 1 x ≥ 1 − α {\displaystyle g(x)=\mathbf {1} _{x\geq 1-\alpha }} .

  4. Tail value at risk - Wikipedia

    en.wikipedia.org/wiki/Tail_value_at_risk

    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.

  5. Risk measure - Wikipedia

    en.wikipedia.org/wiki/Risk_measure

    The standard deviation is a deviation risk measure. To avoid any confusion, note that deviation risk measures, such as variance and standard deviation are sometimes called risk measures in different fields.

  6. Modern portfolio theory - Wikipedia

    en.wikipedia.org/wiki/Modern_portfolio_theory

    The risk-free asset has zero variance in returns if held to maturity (hence is risk-free); it is also uncorrelated with any other asset (by definition, since its variance is zero). As a result, when it is combined with any other asset or portfolio of assets, the change in return is linearly related to the change in risk as the proportions in ...

  7. Market risk - Wikipedia

    en.wikipedia.org/wiki/Market_risk

    Market risk is the risk of losses in positions arising from ... The variance covariance and historical simulation approach to calculating VaR assumes that historical ...

  8. Markowitz model - Wikipedia

    en.wikipedia.org/wiki/Markowitz_model

    Risk premium is the product of the market price of risk and the quantity of risk, and the risk is the standard deviation of the portfolio. The CML equation is : R P = I RF + (R M – I RF)σ P /σ M. where, R P = expected return of portfolio I RF = risk-free rate of interest R M = return on the market portfolio σ M = standard deviation of the ...

  9. Expected shortfall - Wikipedia

    en.wikipedia.org/wiki/Expected_shortfall

    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.