Question

AICUS (Auto Insurance Company of the United States) paid out $62,750,000 in car insurance claims last year. During that year, the company had 100,000 clients and charged each client $600 for insurance. Nine hundred and ninety-nine thousand, five hundred of its clients did not get into any accidents. We will call this the low-risk group. Two-hundred-and-fifty clients had minor accidents that cost $1,000 each. Call this the moderate-risk group. An additional 250 clients had major accidents involving lawsuits that cost $250,000 each. Consider this to be the high-risk group. Did AICUS charge all of its clients an actuarially fair insurance rate last year? Ο Νο O Yes O There is not enough information to tell. Next year, AICUS will charge its clients different premiums based on past accidents and risk groups. Which of these options is the most likely one for the insurance company to select? The high-risk group should pay a high premium, whereas the moderate- and low-risk groups should pay no premium. O The high-risk and moderate-risk groups should pay the same high premium, whereas the low-risk group should pay no premium. O The high-risk group should pay the highest premium, the moderate-risk group should pay a moderate premium, and the low-risk group should pay the lowest premium. The low-risk group should pay the highest premium, the moderate-risk group should pay a moderate premium, and the high-risk group should pay the lowest premium. O

Answer 1

First question

Assuming that there was a way to determine who falls in which risk group, the company did not charge fair premium to each group as we can see with a simple metric, i.e., claim to premium ratio for these groups:

High risk: 250000 / 600 = 416.7

Medium risk: 1000 / 600 = 1.67

No risk: 0 / 600 = 0

Second question

The right answer is the third one, as it will bring the likely claim to premium ratios closer.