Risk pooling spreadsheet – solutions for yesterday’s class problem

Here’s a screenshot from a spreadsheet that I coded for the risk pooling class problem (linked below) that we discussed during class yesterday. We found in class yesterday (and now find in this spreadsheet today), that if risks are independent and identically distributed, then by increasing the number of policies in the risk pool, the probability that the average loss exceeds $1,500 declines as we add policies. Without risk pooling, the probability of a “large” loss of $1,500 is 30.85%; with 5 policies, it is 13.18%, and with 10 policies it is 5.69%. However, if risks are positively correlated, then both unique and systematic risks influence this calculation. For example, with 10 policies that have .1 correlation, the probability that the average loss exceeds $1,500 is 12.57% (compared with 5.69% when there is zero correlation):

Risk Pooling Spreadsheet.xlsx

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