Actuary Certification Risk Assessment 2

Question 1

Which risk measure satisfies the property of subadditivity, ensuring that combining two portfolios never increases total risk beyond the sum of individual risks?

Accepted Answer

Conditional Value at Risk (CVaR)

Answer

CVaR (also called Expected Shortfall) is a coherent risk measure that satisfies subadditivity, unlike VaR which can violate it.

Question 2

In the context of insurance risk, what does the 'law of large numbers' imply for an insurer with a growing portfolio?

Accepted Answer

The average claim experience converges toward the expected value

Answer

The law of large numbers states that as the number of independent, identically distributed trials increases, the sample mean converges to the true expected value.

Question 3

A risk analyst models losses using a Pareto distribution with shape parameter α = 1.5. What does this indicate about the distribution's tail?

Accepted Answer

The tail is heavy with infinite variance

Answer

For a Pareto distribution with α ≤ 2, the variance is infinite, indicating an extremely heavy tail with high probability of large losses.

Question 4

What is the primary purpose of a deductible in property and casualty insurance from a risk management perspective?

Accepted Answer

To eliminate moral hazard and reduce small claim frequency

Answer

Deductibles reduce moral hazard by giving policyholders financial incentive to prevent losses and eliminate costly processing of small, high-frequency claims.

Question 5

In reserve development analysis, a 'reserve deficiency' occurs when:

Accepted Answer

Actual losses develop higher than initially estimated reserves

Answer

A reserve deficiency means actual developed losses exceeded initial reserve estimates, requiring the company to strengthen reserves and reduce surplus.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification Risk Assessment 2