View Full Version : All10 Confusion with UW ER, OER and Combined Ratio

victorandjenny

02-17-2012, 02:16 AM

In the 2011 version of All10 material on Exam 5, on pages 6 and 7 I read the following:

UW ER=(total UW expenses/Total Premium)

OER=UW ER+(LAE)/(Total EP)

Combined Ratio=LR + (LAE)/(Total EP) + (UW expenses/WP)

It is obvious for me that UW ER is not equal to (UW expenses/WP), because some parts of UW expenses should be divided by EP and other parts should be divided by WP to get accurate UW ER.

However, in the All10 solution of Question 12 in Exam 2010 on page 11, I read that Combined Ratio= LR + OER, which means that UW ER was simplified to (UW expenses/WP). Is this acceptable in the exam?

Bobby

02-17-2012, 03:14 AM

In the problem, you were just given the UW ratio. This doesn't mean that it was simplified to UW Exp / WP.

If calculated in accordance with the exam, it would have been (UW Expenses Incurred throughout policy) / EP + (UW expenses incurred at onset of policy) / WP. This is what you should do on the exam. Always be as precise as possible on the exam because no one really has any idea how they grade these things.

BTW, you can have a ratio that uses both EP and WP as bases for different variables. Maybe that is what is tripping you up?

MightySchoop

02-17-2012, 07:55 AM

In the problem, you were just given the UW ratio. This doesn't mean that it was simplified to UW Exp / WP.

If calculated in accordance with the exam, it would have been (UW Expenses Incurred throughout policy) / EP + (UW expenses incurred at onset of policy) / WP. This is what you should do on the exam. Always be as precise as possible on the exam because no one really has any idea how they grade these things.

BTW, you can have a ratio that uses both EP and WP as bases for different variables. Maybe that is what is tripping you up?

Alternately, you can use all underwriting expenses / WP, and state the assumption that all UW expenses are incurred at policy inception!

Vorian Atreides

02-17-2012, 10:35 AM

When in doubt, check the source material for the current syllabus:

Combined Ratio

The combined ratio is the combination of the loss and expense ratios, and historically has been calculated as:

\text{Combined Ratio} = \text{Loss Ratio} + \frac{\text{LAE}}{\text{Earned Premium}} + \frac{\text{Underwriting Expenses}}{\text{Written Premium}}.

In calculating the combined ratio, the loss ratio should not include LAE or it will be double counted.

As mentioned in the section on underwriting expense ratio, some companies may compare underwriting expenses incurred throughout the policy to earned premium rather than to written premium. In this case, the companies may choose to define combined ratio as:

Combined Ratio = Loss Ratio + OER.

The combined ratio is a primary measure of the profitability of the book of business.

(emphasis added)

Note that one formula was the historical calculation, and it tracks with the assumption of "all expenses are variable expense".

It is also clear that W&M are not equating the two formulas (regardless of what All10 may say/imply). Rather, if one calculates the Expense Ratio using the split between those incurred at policy on-set vs. incurred throughout the policy period, then the Combined Ratio simplifies to the sum of the LR (excluding LAE) and OER.

victorandjenny

02-17-2012, 01:22 PM

I am not sure I understand this part of your answer.

I think it is reasonable to divide commission by WP (but not EP) and divide GE with EP (but not WP). Do you mean that it is also meaningful to divide commission by EP as some commision is based on EP?

BTW, you can have a ratio that uses both EP and WP as bases for different variables. Maybe that is what is tripping you up?

Vorian Atreides

02-17-2012, 01:28 PM

"As mentioned in the section on underwriting expense ratio, some companies may compare underwriting expenses incurred throughout the policy to earned premium rather than to written premium. In this case, the companies may choose to define combined ratio as:

Combined Ratio = Loss Ratio + OER."

In fact, this is the part which confuses me the most. I think only the companies which compare ALL underwriting expenses to written premium can use the formula of "Combined Ratio = Loss Ratio + OER", because Combined ratio is using WP instead of EP. Am I right?

No.

Combined Ratio is a measure of whether or not the company has an underwriting profit.

OER is a measure of how much of the premium is used for expenses--and this is why some underwriting departments will use the "Total U/W Expenses / Written Prem" formula for calculating their expense ratio (primarily, because it's easier to do). And this is the point I believe that W&M are trying to make--be aware that there are different ways a particular value is calculated within an organization.

As actuaries, you want to include expenses appropriately. As an illustration, consider the case that an insurance company goes insolvent, and any unearned premium is then refunded to the policyholder.

Since commissions and taxes are paid at the time premium is collected, and they're not "returned" if the policy is later cancelled (regardless of the reason); they're associated with Written Premium.

General and Other Acquisition Expenses will cease to be incurred (more or less) once the company stops operation. So it's better to associate these with earned premium (since written premium will include unearned premium amounts) to ensure that you're collecting enough for the time period that you are in operation; hence they're associated with Earned Premium.

Vorian Atreides

02-17-2012, 01:30 PM

I am not sure I understand this part of your answer.

I think it is reasonable to divide commission by WP (but not EP) and divide GE with EP (but not WP). Do you mean that it is also meaningful to divide commission by EP as some commision is based on EP?

Bobby is pointing out how are you developing your provision (as a ratio to prospective premium). It sounds like you're fine with this concept--it appears to me what's tripping you up is thinking that for any one concept (like OER), that there's only one way that a company should calculate it for all situations.

This is not the case.

victorandjenny

02-19-2012, 12:49 PM

Got it. Thanks.

herr blau

02-19-2012, 02:42 PM

IMO, 2011 #8 would be a good practice question for this topic.

Vorian Atreides

02-19-2012, 07:47 PM

IMO, 2011 #8 would be a good practice question for this topic.

ITA.

And one might also note that they accepted solutions that involved taking all U/W expenses to WP.

victorandjenny

02-20-2012, 04:59 AM

Thank you for all participants of this series.

ITA.

And one might also note that they accepted solutions that involved taking all U/W expenses to WP.

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