Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $200, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $190,000. a. Make a table of the two possible payouts on each policy with the probability of each. Outcome A: No Fire Outcome B: Fire!

Payout

b. Suppose you own the entire firm, and the company issues only one policy. What are the expected value, variance and standard deviation of your profit? 1.Expected Return :

2. Variance :

3. Standard deviation:

c. Now suppose your company issues two policies. The risk of fire is independent across the two policies. Make a table of the three possible payouts along with their associated probabilities.

Outcome: No Fire Outcome:One Fire Outcome: Two Fires

Payout :

Probability: % % %

d. What are the expected value, variance and standard deviation of your profit? 1.Expected Return :

2. Variance :

3. Standard deviation:

e. Compare your answers to (b) and (d). Did risk pooling increase or decrease the variance of your profit? Risking pooling ___________ the total variance profit.

f. Continue to assume the company has issued two policies, but now assume you take on a partner, so that you each own one-half of the firm. Make a table of your share of the possible payouts the company may have to make on the two policies, along with their associated probabilities. Outcome: No Fire Outcome:One Fire Outcome: Two Fires

Payout :

Probability: % % %

g. What are the expected value and variance of your profit? 1.Expected Return :

2. Variance :

3. Standard deviation: