Accident frequency (probability that an accident will happen) and severity (aver

ID: 409631 • Letter: A

Question

Accident frequency (probability that an accident will happen) and severity (average cost per accident) are very important metrics when predicting losses. Using the table below, which coverage would have the highest Loss Ratio? Show your work

Loss Ratio = Losses / Premium

Coverages Collected Customers Accident Probability Accident Collision $4,000 300 1.3% $600 Comprehensive $3,500 250 1.6% $600 Bodily injury $10,000 1,000 2.3% $300 Property Damage $9,600 1,000 5.5% $120 Personal Inj Protection $8,600 870 1.2% $775

Explanation / Answer

Cumulative Loss for each coverage can be defined as

= Number of Customers ( ‘Customers’ x Accident probability in fraction ( ‘Accident probability’/100) x Cost per Accident ( ‘Accident’)

Thus Loss Ratio

= Cumulative loss for each coverage ( as defined above) / Premium Collected ( ‘Collected’)

Following table presents Loss ratios for various types of coverages calculated as per above formula :

Coverage

Loss Ratio

Collision

0.585

Comprehensive

0.685

Body injury

0.690

Property Damage

0.687

Personal injury protection

0.940

From above Table, it is evident that “Personal Injury Protection ” has the highest Loss Ratio

PERSONAL INJURY PROTECTION COVERAGE HAS THE HIGHEST LOSS RATIO