An operator of an oil well has a 0.5% chance of experiencing a catastrophic failure.This failure will cost the operator $500 million.If the risk-free rate is 2%,the expected return on the market is 8%,and the beta of the risk is -1.2,what is the actuarially fair insurance premium?
A)$2,500,000
B)$2,637,131
C)$2,550,000
D)$2,753,304
E)$2,145,000

Question

Quizplus · Accepted Answer

The actuarially fair insurance premium is equal to the expected loss, which is the probability of the catastrophic failure multiplied by the cost of the failure:
0.005 x $500 million = $2.5 million
Then, the premium is adjusted for the risk of the investment:
risk premium = beta x market risk premium
risk premium = -1.2 x (8% - 2%) = -9.6%
Actuarially fair insurance premium = expected loss + risk premium
Actuarially fair insurance premium = $2.5 million - 9.6% x $2.5 million
Actuarially fair insurance premium = $2,637,131 (rounded to nearest dollar)
Therefore, the best choice is B.

An Operator of an Oil Well Has a 0