Question

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $360, the probability of a fire is 01%, and in the event of a fire, the insured damages (the payout on the policy) will be $350,000 a. Make a table of the two possible peyouts 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? Standard Deviation Expected Return Variance 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. (Round your "Probablility" answers to 4 decimal places.) Outoome: One Fire Outcome: No Fire Outcome: Two Fires Payout Probeblity d. What are the expected value, variance and standard deviation of your profit?

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Answer 1

a. Probability of fire = 0.1%
Probability of no fire 100% - 0.1% = 99.9%

Payout in case of No Fire = $360
Payout in case of Fire = -$350,000

Probability adjusted payout (No Fire) = 360*99.9% = $359.64
Probability adjusted payout (Fire) = -350000*0.1% = -$350

b. Expected value/return = 359.64 - 350 = $9.64

Variance = (360 - 9.64)²*99.9% + (-350000 - 9.64)²*0.1% = 122,629,377.47

Standard Deviation = 122,629,377.47^1/2 = 11,073.81%

c. P(No Fire) = 99.9%*99.9% = 99.8001%
P(Two Fire) = 0.1%*0.1% = 0.0001%
P(One Fire) = 100 - 0.0001 - 99.8001 = 0.1998%

Payout of No Fire = 360 + 360 = $720
Payout of Two Fire = -350000 - 350000 + 360 + 360 = -$699,280
Payout of One Fire = -350000 + 360 + 360 = -$349,280

d. Expected value/return = (720*99.8001%) + (-699280*0.0001%) + (-349280*0.1998%) = $20

Variance = (720 - 20)²*99.8001% + (-699280 - 20)²*0.0001% + (-349280 - 20)²*0.1998% = 244,755,000

Standard Deviation = 244755000^1/2 = 15,644.65%

e. Risk Pooling Increased the total variance of profit