Prepaid Expenses for UEP
Just wanted to clarify some of the intuition behind the PPE for UEP formula. In the wiki, this is said:
"it's the prepaid expenses in the UEP for the current CY, not the mean. (In other words, the portion of the UEP that goes towards the current CY pre-paid expenses.)"
Formula 2a: PPE for UEP = PPER x m(UEP)
Formula 2b: PPER = net acquisition expense / NWP
The explanation is a little confusing to me -- sure, the PPER looks like it comes from the current year, but how is it the prepaid expenses in UEP for current year, when we're still multiplying the PPER by the mean UEP?
Comments
Actually, I'm not sure if there is good intuition on all of this. The use of the mean in all these formulas is just an approximation anyway. Investment income is being earned continuously throughout the year on whatever funds are in the insurer's control.
Since the loss reserves and unearned premium reserves go up and down every month, a more accurate way to calculate FAIT, for example, is to do an investment income calculation every month and then add everything up at the end of the year.
The formula in the text uses the current year (PPE for UEP) rather than the mean, so I was just trying to come with a way of understanding why that is. But I think they could just as easily have called it m(PPE for UEP) and done the rest of the calculation the same way.
Now that I've looked at it again, maybe a better way to think about it is that PPER is based on current year values, not mean values, so PPER represents a current year value. It's true that you then multiply it by m(UEP) so the formula really is a mixture between a current year value (PPER) and a mean value m(UEP), so what should you call the result: current year or mean. For calculation purposes, it doesn't matter.
You're asking a good question about the meaning of the symbols that are used, but this relies on the symbols being meaningful in the first place (attached to something that is precisely defined) but I'm not sure that's consistently the case here.
Adding on to this
Formula for Net acquisition expenses is given as "calculated as the sum of commissions and brokerage expenses incurred (column 23); taxes, licenses and fees incurred (column 25); other acquisition, field supervisions and collection expenses incurred (column 27); and half of the general expenses incurred (50% of column 29)."
Is there a particular reason that only 1/2 of general expenses incurred is used? Trying to understand so I can remember when and when not to use 1/2 of general expenses (since we don't use 1/2 in the pre-tax profit formula, that is unless given prepaid expenses). Is it just assumed that half of general expenses are prepaid?
I think this relates to something covered in Exam 5 on pricing. For pricing, we assume commissions & brokerage; other expenses; taxes, licenses, and fees are incurred when a policy is written. But general expenses are incurred over the policy term and are (theoretically) expensed as the corresponding premium is earned. Using 50% of general expenses here is a way to account for that and achieve slightly better matching in terms of timing.