403 - 1999 paper 1 Qtn 4 (v) Fixed expenese

[Flinty]

Hi

Does anyone know why you would load the fixed expenses up for brokerage, variable expenses and profit in an office premium calculation ? Also I have no idea why the fixed expenses of £5000 have been divided by .5.

many thanks

Flinty

 

[Coralie Clarke]

The brokerage, variable expenses and profit are percentages of the Gross Premium (GP) and this includes the fixed expenses, so we're loading up the GP rather than the fixed expenses.

To give a simplified example, you could have:

GP = £Risk Prem (RP) + £fixed expenses (FE) + brokerage% x GP

which becomes:

GP (1-brokerage%) = £RP + £FE
ie
GP = (£RP + £FE) / (1-brokerage%)

which is the same structure as the forumula in this question.

It looks like the fixed expenses of £5,000 only relate to 50% of the business here (since the reinsurer writes 50% of the layer),

I hope that helps...

 

[amused942]

It looks like the fixed expenses of £5,000 only relate to 50% of the business here (since the reinsurer writes 50% of the layer),

So we load up the fixed expenses back to "100% line" level... but then doesn't that mean the office premium calculated is the 100% line premium, and the office premium that the reinsurer charged should be half of the answer given in the exam solutions (ie. half of £1.819m)?

In other words, I am questioning why the examiner's answer isn't then divided by 2 to get the reinsurer's office premium.

 

[Coralie Clarke]

Yes, you're right. The 1,400,000 pure loss cost relates to the whole layer (see the calculations to part (iii) for confirmation of this). The reinsurer's internal expenses of 5,000 will only relate to the bit they are writing (50%) so we need to multiply by 2 to get the amount for the whole layer.

So the answer of 1,819,000 will be the office premium for the whole layer.

However, the question asks for "the office premium that should be charged". I would interpret this to be the total premium that should be charged to the insurer (policyholder), which is the premium for the whole layer.
You have interpreted this as "the office premium that this reinsurer would need to charge", which isn't quite what was asked for.

In an exam, I'm sure that if you got the rest of this right and explained why you were dividing your final answer by 2, you would pick up full marks.

Coralie