Question

A property insurer has 100,000 houses insured over a long period and, on average, 2 percent, burn each year. There is a variation of 250 houses from the expected number of losses. What is the objective risk? (4 points) 1b. A property insurer has 10,000,000 houses insured over a long period and, on average, 2 percent, burn each year. There is a variation of 2500 houses from the expected number of losses. What is the objective risk? (4 points) 1c. Why did objective risk decline?

Answer 1

objective risk = expected variation/average loss = expected variation/(percentage loss expected*number of houses insured)

1a). Objective risk = 250/(2%*100,000) = 12.50%

1b). Objective risk = 2,500/(2%*1,000,000) = 1.25%

1c). Objective risk declines because as the number of exposures increases, the variation in loss decreases (as sample size is more) so risk goes down compared to a case where number of exposures is less. This can be understood as a loss of 10 out of 100 insured is bigger compared to a loss of 10 out of 1,000 insured.