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Your firm faces a 6% chance of a potential loss of $45 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 $350 000. Suppose that the beta of the loss is 0 and the risk-free rate of interest is 5%.
-An operator of an oil rig 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 need to use the formula:

Actuarially fair insurance premium = expected loss + risk premium

Expected loss = probability of loss * magnitude of loss

Risk premium = beta * (expected return on market - risk-free rate)

For the oil rig operator:

Expected loss = 0.5% * $500 million = $2.5 million

Risk premium = -1.2 * (8% - 2%) = -7.2%

Actuarially fair insurance premium = $2.5 million - 7.2% * $2.5 million = $2,637,131.

For the firm with the potential loss:

Without new safety policies:
Expected loss = 6% * $45 million = $2.7 million
Risk premium = 0 * (expected return on market - risk-free rate) = 0
Actuarially fair insurance premium = $2.7 million + 0 = $2.7 million

With new safety policies:
Expected loss = 3% * $45 million = $1.35 million
Risk premium = 0 * (expected return on market - risk-free rate) = 0
Total cost = $350,000 + $1.35 million = $1.7 million

Therefore, the best choice is to implement the new safety policies to reduce the potential loss and pay the upfront cost of $350,000.

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