Question

OP You are an insurance agent who must write a policy for a new client named Sam. His company, Society for Creative Alternatives to Mayonnaise (SCAM), is working on a low-fat, low-cholesterol mayonnaise substitute for the sandwich-condiment industry. The sandwich industry will pay top dollar to the first inventor to patent such a mayonnaise substitute. Sam's SCAM seems like a very risky proposition to you. You have calculated his possible returns table as follows: Probability Return Outcome 0.999 $ - 1,000,000 (he fails) 0.001 $1,000,000,000 (he succeeds and sells his formula) The expected value of the uncertain investment is $ 1000. (Round your answer to the nearest dollar) The standard deviation of the uncertain investment is $ 31638568. (Round your answer to the nearest dollar.) Assuming Sam to be risk neutral, the most he is willing to pay for insurance is $ 0. (Round your answer to the nearest dollar.) Suppose you found out that the Japanese are on the verge of introducing their own mayonnaise substitute next month. Sam does not know this and has just turned down your final offer for the insurance. Assume that Sam tells you SCAM is only six months away from perfecting its mayonnaise substitute and that you know what you know about the Japanese. Would you raise or lower your policy premium on any subsequent proposal to Sam? Based on his information, would Sam accept?

Answer 1

Part A

The expected return is,

$\small ER=(0.999)(-1,000,000)+(0.001)(1,000,000,000)$

= —999,000 +1.000,000

= $1,000

So, the expected value of the uncertain investment is $1000

Part B

Here we need to find the variance. Standared deviation is the square root of variance. So,

$\small \sigma ^{2}=(0.999)(1,000,000-1,000)^{2}(0.001)(1,000,000,000-1,000)^{2}$

  $\small =(0.999)(999,000)^{2}(0.001)(999,999,000)^{2}$

  $\small =1,000,998,999,000,000$

So the Standared deviation is,

$\small =\sqrt{1,000,998,999,000,000}$

$\small =\$31,638,568$

So, the stadared deviation of the uncertain investment is $31638568

Part C

if Sam is risk neutral, then he is unwilling to buy insurance.

Part D

The entry of the new firm will reduce the high payoff of Sam. Suppose that the probability of billion dollar payoff is lowered to zero, then,

$\small =1.0(-1,000,000)(0.0)(1,000,000,000)$

$\small =-\$1,000,000$

That means the policy premium raise tremendously. But here, Sam does't know the entry of the Japanese firm and he is continue to refuse the insurance.