Question

An individual owns a car that is worth $20,000, and is considering buying insurance. However, the only insurance which is available has a maximum coverage of $15,000, i.e. the policy will pay only $15,000 if the car suffers a total loss in an accident. The price of the policy is $1,800. There is a 10% chance of having an accident in which the car is a total loss. The focus here is to calculate the expected values with and without insurance. It is not necessary to calculate the variance and standard deviation, as it is obvious that there is less risk with insurance.

(a) Will a risk-averse individual buy the insurance? Show your work and explain.

(b) Will a risk-neutral individual buy the insurance? Show your work and explain.

(c) Will a risk-loving individual buy the insurance? Show your work and explain.

(d) How would your answer to (a)-(c) change if the policy paid $20,000 if the car was a total loss? Explain.

Answer 1

Cost of Insurance = $ 1,800 Cost of Car = $ 20,000 Value of Car Insured = $ 15,000 Probability of loss = 10%

Expected Value = 15000 * 10% = 1,500.

a) Will a risk-averse individual buy the insurance? Yes, the risk averse investor would always try to avoid the risk even if cost him. Thus despite having the expected value of $ 1,500 only he would buy the insurance at $ 1,800.

(b) Will a risk-neutral individual buy the insurance? No, a risk neutral investor would not buy the insurance as the cost of insurance is higher than the expected vale.

(c) Will a risk-loving individual buy the insurance? No, he would not buy the insurance cover because expected value is less than cost of insurance.

(d) How would your answer change if the policy paid $20,000 if the car was a total loss?

In this case, the expected value = 20,000*10% = $ 2,000. So all the three investors would buy it as cost of Insurance ($1,800) is less than expected value. ($2,000)