Axioms that make a risk measure coherent

What qualifies a risk measure as coherent? List the defining properties.

A risk measure $\rho$ is coherent if it is monotone, subadditive, positively homogeneous and translation invariant. Monotone: a portfolio that is always worse has higher risk. Subadditive: $\rho(X+Y)\le\rho(X)+\rho(Y)$, so diversification never increases risk. Homogeneous: $\rho(\lambda X)=\lambda\rho(X)$ for $\lambda\ge0$. Translation invariant: adding cash $c$ lowers risk by $c$. Expected shortfall is coherent; VaR fails subadditivity.