A coherent risk measure has four properties. Briefly explain each property.

 

The 4 properties of coherent risk measure are:

1. sub-additivity

2.monotonicity

3. homogeneity

4. translational invariance.

Step-by-step explanation

The 4 properties of coherent risk measure are:

1. sub-additivity

If the risks of the two portfolio are added together, they cannot increase the measure of risk. This implies the effect of adding two risk portfolio together will not get worse since there may be economies of scale that will make the risk better. Mathematically this means, P(X + Y) < P(X) + P(Y)

2.monotonicity

The property of monotonicity says that if one portfolio has better values than the other under all situations, then its risk will be better. This implies that if X < Y in every situation then P(X) > P(Y)

3. homogeneity

The property of homegenity denotes that if you double your portfolio, then the risk will be double.This implies that for all X > 0 then P(XX) = XP(X)

4. translational invariance.

The property of translational various says that addition of capital or cash to the portfolio, then you will cut off the risk. This means if capital is added to a portfolio, then the risk will be reduced. This implies that for all constant C, then P(X + C) = P(X) — C