Non-Unit Reserves: zeroise negative cashflows

[Logarithm n Blues]

I'm a little bit uncomfortable with the way that the methodology is described for calculating non-unit reserves and I think I might be missing something simple.

For a prudent regime the method is described as:
-Start with the last period in which the net cashflow is negative
-Set up an amount at the start of the period that "zeroises" the negative cashflow (Allowing for investment return)
-Ad the cost of setting up this reserve to the end of the previous period
-"zeroise" the previous period similarly
-Recursively work backwards like this to the valuation date

But I don't see what's different between this and:
-Consider all cashflows up to and including the last period where the net cashflow is negative
-Discount all cashflows back to the valuation date.

Is there a difference? is there a reason to describe it in this convoluted way? Any advice around this would be appreciated.

 

[Mark Willder]

I'm a little bit uncomfortable with the way that the methodology is described for calculating non-unit reserves and I think I might be missing something simple.

For a prudent regime the method is described as:
-Start with the last period in which the net cashflow is negative
-Set up an amount at the start of the period that "zeroises" the negative cashflow (Allowing for investment return)
-Ad the cost of setting up this reserve to the end of the previous period
-"zeroise" the previous period similarly
-Recursively work backwards like this to the valuation date

But I don't see what's different between this and:
-Consider all cashflows up to and including the last period where the net cashflow is negative
-Discount all cashflows back to the valuation date.

Is there a difference? is there a reason to describe it in this convoluted way? Any advice around this would be appreciated.

Yes there's an important difference between the two when we have both negative and positive net cashflows in the future. It won't matter if all the future cashflows are negative.

A numerical example will help. We'll ignore discounting and survival probabilities for simplicity.

Consider an insurer with the following end of year cashflows: 3, 2, -2, -2, -2, 3.

Using your second approach we would just discount all these cashflows back to the beginning and get the answer 2. This is positive so we wouldn't hold any reserves (unless negative reserves were allowed).

However, by using your first approach and starting from the last negative, we see we need a reserve of 2 at the start of the fifth year, a reserve of 4 at the start of the fourth year, a reserve of 6 at the start of the third year, a reserve of 4 at the start of the second year, a reserve of 1 at the start of the first year.

So, to be prudent we should hold a reserve of 1. Looking at all six of the cashflows, we see the cashflows are positive in total, but the last positive cashflow comes too late to make the payments in time five. So we must hold a reserve of 1 at the start to make sure we always have enough reserves to pay the claims in time.

I hope this helps.

Best wishes

Mark

 

[Logarithm n Blues]

Thanks for the reply.

I don't think I expressed my method clearly. Step 1 would remove that cash flow of +3 at the end.
Leaving 3, 2, - 2, - 2, - 2
Discounting back (at rate 0%)would give a total of - 1 so required reserve of 1.

Would you say that this step by step approach is just a way of making it clear where we cut off?

 

[Mark Willder]

Thanks for the reply.

I don't think I expressed my method clearly. Step 1 would remove that cash flow of +3 at the end.
Leaving 3, 2, - 2, - 2, - 2
Discounting back (at rate 0%)would give a total of - 1 so required reserve of 1.

Would you say that this step by step approach is just a way of making it clear where we cut off?

Yes, that's right. Step 1 would effectively remove the last cashflow at the end.

However, we could end up with even more complex examples.

Consider 3, 2, - 2, - 2, - 2, 3, -4, 2. The initial reserve for this is 2 as we have to consider year 7.

However for 3, 2, - 2, - 2, - 2, 3, -2, -1 the initial reserve is 1. Years 7 and 8 are covered by year 6.

Further 3, 2, - 2, - 2, 0, 3, -2, -1 needs no initial reserve at all, but will need a reserve later on.

It could get a lot more complicated if we had several switches between positives and negatives. The above examples are reasonably easy to see as we have no discounting or survival probabilities. The only safe way to do it as to start at the end and work our way to the beginning one year at a time - this also has the added advantage that we know the reserves for every future year as well as just time zero.

Best wishes

Mark

 

[Logarithm n Blues]

Brilliant. Got it. Thanks very much.

It might be unlikely that a question would come up that would test this distinction, but I feel a lot better for understanding what's going on and I would answer a more usual question with more confidence!