Use the information for the question(s)below.
Your firm faces an 8% chance of a potential loss of $50 million next year. If your firm implements new safety policies, it can reduce the chance of this loss to 3%, but the new safety policies have an upfront cost of $250,000. Suppose that the beta of the loss is 0 and the risk-free rate of interest is 5%.
-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?

Question

Quizplus · Accepted Answer

To calculate the actuarially fair insurance premium, we use the following formula:

Premium = (probability of loss) x (cost of loss) / (1 - probability of loss) x (risk-free rate + beta x (expected market return - risk-free rate))

For the oil well operator, the premium is:

Premium = 0.005 x 500,000,000 / (1 - 0.005) x (0.02 + (-1.2) x (0.08 - 0.02))
Premium = $2,637,131.10

Therefore, the best choice is option B, which is closest to the calculated actuarially fair insurance premium.

Use the Information for the Question(s)below