Sharon, who is risk averse, faces the following probability distribution of loss

Question

Sharon, who is risk averse, faces the following probability distribution of losses:

Probability         Loss amount

              0.8        $0

              0.15      $4,000

              0.05      $400,000

Where the Expected Value of Loss is calculated to be $20,600.

a. If Charles, also risk averse and facing the exact same loss distribution as Sharon, were to “go in with” Sharon on the risk, and share equally with her in their joint probability of loss, what happens to each one’s expected value of loss?

What happens to each person’s standard deviation?

b. What happens to the expected value and standard deviation for each person if Sharon and Charles pool similarly with 10,000 other people who face the same loss distribution?

c. Why is it critical that everyone face the exact same loss distribution for your answers in (c) and (d) to hold?

Explanation / Answer

a)

as both sharon and charles have same loss distribution , it is not going to effect their joint distribution which is going to remain same. But there is change in that they have to share the loss amount making the lost amount half at same probability.

new value of estimated loss also becomes half i.e., 20600/2 = 10300

also the standars reduces by a factor of 2

B)

it is same as the above case but the estimated mean and S.D is distributed among 10,000 people.

So, expected value and standard deviation will become 1/10,000 times the previous value.

C)

It is necessary for all of them to contain same loss distribution because if any one of them possess a different loss distribution probability of each loss amount changes as well which will change the mean and standard deviation.

if all of them have same loss distribution probability of particular loss amount of the whole group remains same irrespective of number of persons joining them. But the final amount has to be shared among everyone.

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