Explain the commonsense criteria that of a measure of risk

Question

Explain the commonsense criteria that of a measure of risk.

Answer 1

An ordinary criticism of traditional VaR has been that this does not satisfy all of specific commonsense criteria. Artzner et al. (1997) explained the following set of sensible criteria as a measure of risk, ρ(X) here X is a set of outcomes, must satisfy. These are as follows:

1. Sub-additivity: ρ(X + Y) ≤ ρ(X) + ρ(Y). This just says that when you add two portfolios together the total risk cannot get any worse than adding the two risks independently. Indeed, there may be cancellation outcomes or economies of scale which will make the risk better.

2. Monotonicity: If X ≤ Y for each scenario then ρ(X) ≥ ρ(Y).
Portfolio’ risk will be better; if one it has better values than other under all scenarios.

3. Positive homogeneity: For all λ>0, ρ(λX) = λρ(X). Double your portfolio after that you doubles your risk.

4. Translation invariance: For all constant c, ρ(X + c) = ρ(X) − c. Imagine of just adding cash to a portfolio; it would come off your risk.

Risks measure which satisfies all of these termed as coherent.