Question

a) When Jennifer goes on holiday she likes to take her camera, valued at £1000. Other than that, she doesn’t take much of value. Even if she is careful with the camera, there is still a 15% chance her camera either gets broken beyond repair or stolen. What does it mean to say that Jennifer is risk natural? If Jennifer is risk neutral, what is the expected value to her of owning the camera?

b) Explain risk aversion, using Jennifer’s ownership of the camera as an example.

c) If Jennifer buys a camera insurance policy for £200 that will reimburse her for the value of the camera if broken or stolen, she eliminates the risk of owning the camera. Then the expected value of the insured camera is 0.85*(£1000-£200) + 0.15*(£1000-£200) = £800. Under what circumstances would Jennifer be prepared to buy the insurance policy?

d) Calculate the expected profit of offering insurance on the camera given the values stated above. e) Now assume that Jennifer is part of a ‘low risk group’ of travelling photographers, each of whose probability of having their camera broken or stolen is 0.15. Assume that there is also a high risk group of professional travelling photographers whose probability of having their camera broken or stolen is 0.35. Assume that while the low risk group are prepared to buy an insurance contract for £200 or less, the high risk group are just prepared to buy the contract for £400 or less. What happens if the firm tries to sell insurance at a price of £300? Who buys the contract and what is the profit on the contract? What problem does this outcome illustrate?

Answer 1

a) The expected value is determined by multiplying the values/payoffs with their respective probabilities,

so Expected value or E(value of owning camera) :

= 0.85 * 1000 + 0.15 * (-1000)

ie. 1000 is the payoff i.e. the value of camera if it stays with her,

-1000 is the payoff if the camera is lost,

also 0.15 = 15% = probability of camera gettng lost/stolen/broken

85% = 0.85= probability of otherwise.

So, Expected value = 0.85 * 1000 + 0.15 * (-1000) = 850 - 150 = 700 pounds

b) Risk aversion is that behaviour of individuals who behave in such a way that they tend to lower the uncertainty when in uncertain situations, they agree to a situation with a lower but more predictable/certain payoff rather than a situation which may have a higher payoff but comes with some degree of uncertainty. So, basically a risk averse individual prefers lower returns with known risks as compared to higher returns that come with unknown risks. So, in this example, Jennifer would be termed as risk-averse if she decides to not take her camera with her on holiday, this implies that though there is a higher return if she takes her camera with her on holiday, as she likes doing that as well as she can bring home pictures she clicked on the trip, she will still prefer to leave her camera at home, as there is even 15% chance or uncertainty that her camera may get broken or stolen.

c) So,expected value of insured camera = 800,

Now, as the expected value of insured camera is more than the expected value of uninsured camera = 800 >700, Jennifer would be prepared to buy the insurance policy. But she will buy the insurance policy only if the premium she pays maintains that expected value of insured camera is more. If the premium becomes a greater amount, and reduces her expected value of insured camera than the uninsured camera, she wont be prepared to buy the insurance policy. So, if premium = x,

So, E(insured camera) = 0.85*(1000-x) + 0.15(1000-x)

0.85 * 100 - 0.85x + 0.15 * 1000 - 0.15x = 1000 - x ,

So, as long as 1000 - x > 700,

300> x i.e. as long as insurance premium is less than 300 pounds, Jennifer will buy the insurance policy. Otherwise she will not.

d) Now, the expected profit of insurance for the insurer :

E(P) = 0.85 * (200) + 0.15(-1000+200), ie. he will get a payoff of premium 200 if insurance is not claimed, and there will be a payoff of -800, if insurance is claimed.

E(P) = 170 - 120 = 50 pounds,

This is the expected profit of offering the insurance.

As per rules, have answered the first four sub parts. Thank you!