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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 {\displaystyle X} is ρ ( X ) {\displaystyle \rho (X)} .
A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance. Properties.
VaR is a static measure of risk. By definition, VaR is a particular characteristic of the probability distribution of the underlying (namely, VaR is essentially a quantile). For a dynamic measure of risk, see Novak, [27] ch. 10. There are common abuses of VaR: [7] [10] Assuming that plausible losses will be less than some multiple (often three ...
In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation .
That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. [1] [2] Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk
Example of risk assessment: A NASA model showing areas at high risk from impact for the International Space Station. Risk management is the identification, evaluation, and prioritization of risks, [1] followed by the minimization, monitoring, and control of the impact or probability of those risks occurring. [2]
The coefficient of variation fulfills the requirements for a measure of economic inequality. [ 20 ] [ 21 ] [ 22 ] If x (with entries x i ) is a list of the values of an economic indicator (e.g. wealth), with x i being the wealth of agent i , then the following requirements are met:
A coherent risk measure satisfies the following four properties: 1. Subadditivity. A risk measure is subadditive if for any portfolios A and B, the risk of A+B is never greater than the risk of A plus the risk of B. In other words, the risk of the sum of subportfolios is smaller than or equal to the sum of their individual risks.