Mildenhall Ch 9: Classical Portfolio Pricing Practice

Question 1

Given A and B have same size, discuss difference in gross premiums and gross LRs between units if B is riskier than A

Answer 1

Given same size, the riskier unit will have a higher gross premium and lower gross LR.

Question 2

Suppose A represents non-cat and B represents cat, briefly describe the expected difference in implied LR between the 2 units.

Answer 2

Since cat is riskier, we would expect lower implied LR for unit B

Question 3

Describe the diff in diversification between a portfolio comprised of 2 thin-tailed LOBs vs one with 1 thin-tailed and 1 thick-tailed

Answer 3

Thinner tailed distributions diversify more effectively.

Hence, we expect a much stronger diversification benefit for the 2 thin-tailed lines portfolio.

The reduction in capital between sum of stand-alone capital figures and total capital figure is expected to be greater for first portfolio.

Question 4

Explain why diversification benefit for premium is expected to be less than diversification benefit from capital.

Answer 4

Since premiums include expected losses, diversification benefit is expected to be smaller than diversification benefit from capital.

Question 5

Briefly describe the takeaway common to both Tame and Cat/Non-Cat case studies

Answer 5

If VaR threshold is below reinsurance attachment point, gross and net VaR PCPs will be identical resulting in lower net LR

Question 6

Briefly describe the takeaways from Hu/SCS case study

Answer 6

VaR fails to capture extremely large losses.

The net LR for Hu is considerably higher than gross LR since net VaR PCP sets premium too low.