April 2020 Q6(ii)

[Actuary_140]

Hi,

Would someone be able to help explain the examiner reports answer to this question? In particular, how the 'Top or Drop' layer works in this question?

Any guidance at all would be appreciated. This certainly looks to be one of the hardest RI questions in recent sittings.

Thanks

 

[Darren Michaels]

This question is actually relatively straightforward as the examiners have told you everything you need to know about the top and drop and layer and how it works. There have definitely been more difficult reinsurance calculation questions in the past.

In part (ii) you have been asked to consider a single large loss, so you only need to consider the 'top' option for Programme A as you need a second loss to be able to recover from the 'drop' option.

You then need to compare the cost of each programme in terms of reinsurance premiums (including any reinstatement premiums payable) with the reinsurance recoveries made, for losses of various different sizes from below both programmes all the way up to the beyond the top of both programmes. You will then be able to determine which programme is more beneficial at which points.

There is a detailed solution to this question in the ASET for this paper.

 

[Jammy]

Having read this comment in the examiner report/ASET as well, I will take this opportunity to point out that the workings of this layer were not clear based on the question wording itself - to someone who had never come across the concept of 'top or drop' reinsurance.

However, on doing some searches on the internet about such a reinsurance structure, then the details of the question were sufficient to understand how the layer worked.

Of course, this is just my opinion and if a majority of candidates did have a fair attempt at this question then it is not representative.

 

[Caoimhe Murphy]

Hi all, on this question in part (iii), I am not sure about the reinsurance recoveries on the drop layer?


first loss 600m, recovery = 0 cant recover first claim assume can only recover after first claim
second loss of 75m, recovery = 50, use one free reinstatement
third loss of 60m, recovery = 35, free reinstatements used up - can you pay to reinstate?
last loss of 50m would give a recovery of 25 - but have we used up all our reinstatement now? no more cover here after using our one free reinstatement

solutions say total recovery for drop layer - 110, but my answer is 85 because we have used up our reinstatement?

What do you think?

 

[Darren Michaels]

Remember we have £150m of cover available from the drop layer in total, the original £75m plus the reinstated £75m.

If we don't use up all of the layer on one loss, the remainder can be used on the next loss and so on, provided no more than £75m is recovered in respect of any one loss.

The second loss only uses £50m of cover, the third one a further £35m, so we have up to £65m left after the third loss. Hence, we can recover £25m from the fourth loss, making the total recoveries 50+35+25=£110m.

 

[Hamed shah]

Hi, On Q6 (ii), I don't understand the 'Net benefit to programme' calculation.

In the solution, where the loss between £75m and £100m is considered, where does the -22.25 come from in the equation below?

'(x-75) -22.5 -(x-75)*5% = -22.25 '

I understand that the Insurer needs to pay RI premium of 20 and 22.5 respectively on the programs A and B.

 

[Darren Michaels]

We are equating recoveries less premiums (including reinstatement premiums pro-rata to amount recovered) for programme B and programme A.

So for a loss of size £Xm, between £75m and £100m, the recoveries from B are X-75 and the premiums payable are 5%*450+(X-75)*5%, including the reinstatement premium on the portion of layer that is utilised. This gives the expression on the left-hand side of the equation.

For programme A, as the initial layer attaches at £100m, no recoveries are made in this scenario, but we need to pay the premium for the initial layer =5%*£400m and the top and drop layer =1.5%*£150m, which totals £22.25m, ie the right-hand side of the above equation.

 

[o.menary11]

Hi,

for part (ii), the minimum for both the top and bottom layer is between the recoveries and 150, where has the 150 value come from?

Thanks in advance!

 

[Darren Michaels]

I think you mean part (iii)?

If so, the 150m is the maximum cover available under either the top or the drop layer option.

The top layer is 150m xs 500m so has 150m of available cover and the drop layer is 75m xs 25m with one free reinstatement, so the total cover available is 2x75m=150m.

 

[o.menary11]

I think you mean part (iii)?

If so, the 150m is the maximum cover available under either the top or the drop layer option.

The top layer is 150m xs 500m so has 150m of available cover and the drop layer is 75m xs 25m with one free reinstatement, so the total cover available is 2x75m=150m.

Hi,

Thank you for your help. Is this also why the cost of the reinstatement of A is 1.5% * 150m? (i.e. the cost of programme A is 400m*5%+1.5%*150m= 22.5m)

Thanks

 

[Darren Michaels]

1.5% * 150m is the cost of the first option of the 'Top or Drop' layer (ie the 'Top' option) not the cost of the reinstatements. We are told that the cost of the Top or Drop layer is 1.5% rate on line.

The Top or Drop layer either has no reinstatements (Top option) or one free reinstatement (Drop option).

Only the original layer of 400xs100 has paid reinstatements (two at 100% of cost).

It is very important to make sure that you read the information provided in the question clearly.