Equity in UPR
Hi,
I have a bit of the confusion regarding to the definition of Equity in UPR in the source paper:
Page 4:
Equity in the net unearned premium: amount by which the net UPR plus unearned (reinsurance)
commissions **exceeds the **net policy liabilities in connection with unearned premium.
Page 10:
The maximum deferrable policy acquisition expenses are commonly referred to as the equity in
the UPR.............The maximum deferrable policy acquisition expenses (net) is defined as follows:
Net UPR
+ Premium deficiency
+ Unearned (reinsurance) commissions
– Net policy liabilities in connection with unearned premium
My question is, are they referring to the same thing? If so, why does the second definition has an extra term "premium deficiency"?
Thanks!
Comments
Both formulas are correct, but it isn't obvious and I wish the source text had explained it better. The reason the page 10 formula is true is that only 1 of DPAE and PDR can be non-zero at the same time. This is explained below.
As you wrote above, the page 4 formula is:
Now, equity in the UPR can be either positive or negative (or zero, which is the easy case):
If you substitute each of these 2 cases separately into the page 10 formula below, you'll see both cases reduce to the page 4 formula: (I'll let you do that calculation. It's easy.)
My advice is to make sure you understand the concept that only 1 of DPAE and PDR can be non-zero at the same time and make sure you can do the DPAE calculation. (There are 2 practice templates for this.)
I see! A follow up question: When there is a PDR. How does liability on B/S and expense on I/S change? My guess is premium liability will go up, but expense wont change thus income remains the same?Please let me know!
Yes, the PDR would go on the liability side of the balance sheet. The income statement wouldn't change immediately, rather it would change gradually as the premium is earned and the loss flows into U/W income.
What about?
Line 20 (Page 20.30): Premium Deficiency Adjustments
Part of Underwriting Income (Loss)
It's a little convoluted how it's explained in Odomirok and I had to go back and think through it. The subsection "Income Statement" in Odomirok Chapter 28 states:
But what do they mean by "premium adjustments"? A few paragraphs later, Odomirok further states:
In symbols, this inequality is:
So we have to determine when this inequality is true. We know from the premium liability reading that:
Rearranging this gives:
So if PDR>0 (so DPAE=0) then removing PDR from this equation makes the inequality true. The conclusion would that an adjustment to U/W income would then be necessary. It doesn't say explicitly what the adjustment would be however. Presumably it's the amount by which the PDR changed from the last valuation? (But this is never actually stated and the examples don't shed any light.)
Something still doesn't seem quite right to me though because the associated UPR doesn't flow into income until it's earned, so why doesn't it work the same way for the "unearned" future losses. It's reasonable to assume these future losses don't flow into U/W until they are "earned".
And what about if there is DPAE instead of PDR? There's no mention of any DPAE "adjustment" being added to U/W income. It seems that DPAE and PDR should be treated in a similar way.
Unfortunately the examples provided in Odomirok aren't detailed enough to understand exactly how it all works.
There are only about two companies who acquired any significant deficiency in the last 10-years:
Note: Page 20.30 is reported as YTD. Also, line 20 on page 20.30 is deducted from income.
Company codes come from OSFI
https://www.canadianunderwriter.ca/insurance/state-farm-group-reports-3-1-billion-underwriting-loss-in-2010-1000403580/
This represented 1.1% of State Farms assets at the time. And 16% of Great American's assets in 2009Q3
This is not commonly used by companies as you need your loss ratio plus LAE to be effectively greater than 100%. This is a lot like earthquake premium reserve and earthquake reserve components where no one is using it, but for some reason we are tested on it.
Very thorough. Thanks.
Hello @graham , as a follow up to your first response to @yunal911111 above, are you saying that the Maximum DPAE can only take one of the two following values:
1) Premium deficiency (Where Equity in UPR < 0 & Premium Deficiency = -Equity in UPR)
2) Equity in UPR ( Net UPR + UE.Comm - PolLiabs > 0)
Also I am bit confused if DPAE and Max DPAE are calculated in the same way. Because from the example in the WIKI for this paper, we are asked to calculate the MAX DPAE, but it looks like we are using this formula: DPAE = UPR - PolLiab + UE Comm. Or is the calculation just based on my first question above ?
Sorry, I am a bit confused with the part.
Thank you !
Yes to your first question.
About your second question: I suppose I was a little sloppy in my presentation. What we're calculating with the formulas is the max DPAE even though I just called it DPAE. The DPAE is more accurately called the booked DPAE and it doesn't have to be the same as the max DAPE, but it cannot be greater. If the accountants wanted to book a DPAE value less than the max, they are free to do that, but as actuaries we just need to tell them what the maximum allowable is.