Homework SourseAccident frequency probability that an accident will happen
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 |
Solution
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
| Coverage | Loss Ratio |
| Collision | 0.585 |
| Comprehensive | 0.685 |
| Body injury | 0.690 |
| Property Damage | 0.687 |
| Personal injury protection | 0.940 |
