Question

Question:

Explain why VaR is not a coherent measure. Which property does VaR not satisfy? Provide an example to show how VaR fails to satisfy this property.

Answer 1

Dear a detailed solution is Given. If you're satisfied with my explanations please THUMBS UP.. Thanks in advance for your support and love...

Coherent risk measure is one which satisfies the following properties:

• cash invariance
• homogeneity
• monotonicity
• subadditivitve

Generally VaR not satisfied sub additive. Correlation of individual risk factors is going into VaR calculation. Correlation only measures linear association not nonlinear. So it is a reason for VaR that become not additive.

Example

Let there are 60 grocery stores. Assuming there are no risk for these stores except robbed. Exactly one store is robbed in each year costing 50000 currency units. Suppose a local store manager calculates 5% VaR is Zero due to the probability of his store being robbed is 0.03 (3%). Now 3 stores managers together forms a cooperative grocery stores. Probability of a store being robbed for any of these 3 is 7% (0.07). Then 95% VaR for cooperative is 50000 currency units.

Non Subadditivitve occurs since 0+0+0 < 50000