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(Continued) Example of Pooling: Two business owners own identical buildings valued at $50,000 There is a 10 percent chance each building will be destroyed by a peril in any year Loss to either building is an independent event Expected value and standard deviation of the loss for each owner is: Expected loss = 0.90* $0 +0.10 *$50,000 = $5,000 Standard deviation = 10.90(0 - $5,000) + 0.10($50,000 - $5,000) $15,000 = Basic Characteristics of Insurance (Continued) Example, continued: If the owners instead pool (combine) their loss exposures, and each agrees to pay an equal share of any loss that might occur: = = Expected loss = 0.81* $0+0.09* $25,000+ 0.09*$25,000+ 0.01*$50,000 = $5,000 Standard deviation - 70.81(0-$5,000)+(2)(0.09)($25,000 - $5,000) +0.01($50,000 - $5,000) $10,607 As additional individuals are added to the pool, the standard deviation continues to decline while the expected value of the loss remains unchanged