3. Risk Measures

Question 1

Define a risk measure

Answer 1

Quantitative tool or measure used to assess the level of a risk. It allows us to understand the potential loss from a risk and compare risks together.

Question 2

Define regulatory capital

Answer 2

Required capital to comply with regulations

Question 3

Define economic capital

Answer 3

Required capital to comply with the risk appetite of the firm

Question 4

Define VaR

Answer 4

This risk measure is equivalent to the  quantile.

Question 5

Define expected Shortfall

Answer 5

This risk measure is equivalent to the expected value of the loss knowing that the loss is higher than the  quantile.

Question 6

What are the 4 criterias for a risk measure to be coherent?

Answer 6

1. Translation invariance
2. Positive homogeneity
3. Subadditivity
4. Monotonicity

Question 7

Are the VaR and Expected Shortfall coherent?

Answer 7

ES is coherent, but VaR is not.

Question 8

How does subbaditivity interacts with the way diversification works in insurance?

Answer 8

When insuring multiple risks, there is generally a benefit called diversification. This is based on the fact that we believe not every bad scenario would occur at the same time; a bad year for home insurance might be a good year for car insurance. By adding risks, we therefore expect that the total is at most each risk seperately, and that most times it is lower.