Coherent Risk Measures

What are Coherent Risk Measures?

Cohere Risk Measures are the measures that fulfil several properties that make them coherent and reliable. These properties include

  1. Monotonicity: If (regardless of what happens) a portfolio always produces a worse result than another portfolio, it should have a higher risk measure.
  2. Translation Invariance: If an amount of cash K is added to a portfolio, its risk measure should decrease by K.
  3. Homogeneity: Changing the portfolio size by multiplying the amounts of all the components by A results in the risk measure being multiplied by A.
  4. Sub additivity: For any two portfolios, A and B, the risk measure for the portfolio formed by merging A and B should be no greater than the sum of the risk measures for portfolios A and B.
Examples of Coherent Risk Measures:

Value at Risk is a widely used measure for risk measurement. While it fulfils all but does not fulfil the property of subadditivity. Similarly, Expected Shortfall is another measure that meets this fourth property and is a coherent risk measure.