Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution below describes expected property losses for the group of 6 buildings. Assume that the property exposures are independent of each other.
Losses $ Probability of Loss
$10,000 0.20
$20,000 0.10
$50,000 0.06
$100,000 0.03
$500,000 0.01
a. Find the average or expected loss of the group of buildings in a given year.
10,000*0.2+20,000*0.1+50,000*0.06+100,000*0.03+500,000*0.01=150,000
b. Calculate the standard deviation of the distribution.
Mean=136,000; Variance=7,604,800,000=; Standard deviation=87,205.5
c. Find the Coefficient of Variation.
CV=SD/Mean=87,205.5/136,000*100%=64.12%
d. What is Terry's actuarially fair premium?
Now suppose Terry joins a risk sharing arrangement with other small business owners and now a total of 18 buildings are in the risk sharing pool. Assume that the property losses for the additional buildings follow the same probability distribution as that given for Terry's buildings and losses are independent.
a. Find the average or expected loss of this larger group of buildings in a given year.
b. Calculate the standard deviation of the distribution.
c. Find the Coefficient of Variation
d. What happens to variance or risk for Terry after the sharing arrangement is in place?
e. What would you expect to happen to variance or risk if the pool was extremely large? Why?
f. What is Terry's actuarially fair premium now? What has happened to his risk premium now?