non unit reserve

[i-actuary]

hey,

ibwas wondering if non unit reserve can be negative?
also if so and there is an interest earned on this/will this be capped with 0 or not?
also if only a non unit cash flow is negative will this earn the interest? if yes what does this mean?

 

[Mark Willder]

hey,

ibwas wondering if non unit reserve can be negative?
also if so and there is an interest earned on this/will this be capped with 0 or not?
also if only a non unit cash flow is negative will this earn the interest? if yes what does this mean?

Hello

Yes, non-unit reserves can be negative. These are covered in Section 2.4 of Chapter 19.

Yes, negative non-unit reserves are rolled up with interest. Effectively this is the same as the interest that is charged on a loan.

Best wishes

Mark

 

[omurice]

Hi Mark,

Why do negative non-unit reserves represent a loan from other contracts and need to be repaid from future emerging profits?

If positive reserves mean that assets would need to be set aside for the contract, does negative reserves mean that assets can be taken out from the contract for other purposes first? In this case, shouldn't negative reserves represent a loan to other contracts?

Why does the contract needs a 'loan' from other contracts if it has a negative reserve?

 

[Mark Willder]

This may be easiest to see with an example. We'll ignore mortality, expenses and interest for simplicity.

Policy A is an annuity certain which pays out 50 each year for the next 3 years. This contract needs a reserve of 150. So the insurance company hold assets equal to 150 for this contract.

Policy B is a unit-linked contract with charges of 10 each year for the next 3 years. The insurer is expecting to make a profit on this contract and so holds a reserve of -30.

In total the insurer only holds reserves of 150-30=120. Each year it will pay the annuity of 50, but receive the charges of 10. So each year it loses 40. It covers this loss using the assets in the reserve. The reserve of 120 is exactly right to cover the 3 losses of 40.

So the insurer only has reserves of 120. But Policy A needs assets of 150. These assets are made up of the 120 of reserves held by the insurer (let's say this is invested in cash) and the loan of 30 that Policy A has made to Policy B. Policy B repays the loan each year by using its charges to cover part of the annuity payments of Policy A.

The situation is no different really to your bank balance. If your balance is positive then you are loaning money to the bank. If your balance is negative then the bank is loaning money to you.

I hope this example helps.

Best wishes

Mark

 

[Yash A]

Hi Mark,
In the above solution - you mentioned that each year insurer loses 40 but for Policy A, it must have received premium at the outset. So, how is it losing 40?

 

[Mark Willder]

Hi Mark,
In the above solution - you mentioned that each year insurer loses 40 but for Policy A, it must have received premium at the outset. So, how is it losing 40?

Hi Yash

The reserving calculations above are prospective calculations, so we are looking at cashflows in the future. Yes, there will have been a single premium for the annuity, but this will have been in the past and so doesn't appear in the cashflows discussed above.

Best wishes

Mark

 

[Yash A]

Hi Yash

The reserving calculations above are prospective calculations, so we are looking at cashflows in the future. Yes, there will have been a single premium for the annuity, but this will have been in the past and so doesn't appear in the cashflows discussed above.

Best wishes

Mark

I agree with you, however, I am confused why is insurer "losing" 40. Maybe I am focusing on the word here but I got the point

 

[Mark Willder]

I agree with you, however, I am confused why is insurer "losing" 40. Maybe I am focusing on the word here but I got the point

Hi Yash

I'm sorry if my language wasn't clear. By losing I just mean the insurer is paying out more than they are getting in that year.

Best wishes

Mark