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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)} .
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 average value at risk (sometimes called expected shortfall or conditional value-at-risk or ) is a coherent risk measure, even though it is derived from Value at Risk which is not. The domain can be extended for more general Orlitz Hearts from the more typical Lp spaces .
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 ...
The methods (or approaches) increase in sophistication and risk sensitivity with AMA being the most advanced of the three. Under AMA the banks are allowed to develop their own empirical model to quantify required capital for operational risk. Banks can use this approach only subject to approval from their local regulators.
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
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.
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.