Unearned premium reserve UPR & retrospective reserve

[Trevor]

Hi, I need some help understanding Unearned Premium Reserve (UPR) in chapter 21, page 8.

By reading the Acted text below it, I understand it as portion of the premium received to cover risk exposure for the following year, though the policy hasn’t claimed.

But why do we need to set up reserve for money coming in?
Even if it is saying we need to consider future cash inflow to not overestimate reserves, shouldn’t this be considered already in the standard reserve calculation formula? (Prospective formula: SA_x+t -Pa_x+t)

In the Acted text too, it mentions it is similar to the retrospective approach (Pa_x - SA_x)
I think I might need help to understand the logic of the retrospective reserving approach too (although this should be cleared in CT5 itself)
The prospective formula is pretty intuitive: from the current time point, we assess how much do we need to pay in the future, offset with how much money we are getting, that tells us how much money we need now.

However I think I don’t quite understand the logic for the retrospective formula:
It looks at how much money have we received up till today, and how much have we actually paid out(based on actual experience, ie: asset share)
How does this imply how much money should we hold for future liabilities?

Can someone help me out?

 

[Mark Willder]

Hi, I need some help understanding Unearned Premium Reserve (UPR) in chapter 21, page 8.

By reading the Acted text below it, I understand it as portion of the premium received to cover risk exposure for the following year, though the policy hasn’t claimed.

But why do we need to set up reserve for money coming in?
Even if it is saying we need to consider future cash inflow to not overestimate reserves, shouldn’t this be considered already in the standard reserve calculation formula? (Prospective formula: SA_x+t -Pa_x+t)

In the Acted text too, it mentions it is similar to the retrospective approach (Pa_x - SA_x)
I think I might need help to understand the logic of the retrospective reserving approach too (although this should be cleared in CT5 itself)
The prospective formula is pretty intuitive: from the current time point, we assess how much do we need to pay in the future, offset with how much money we are getting, that tells us how much money we need now.

However I think I don’t quite understand the logic for the retrospective formula:
It looks at how much money have we received up till today, and how much have we actually paid out(based on actual experience, ie: asset share)
How does this imply how much money should we hold for future liabilities?

Can someone help me out?

Hi Trevor

We use a different approach for long term and short term policies.

For long-term policies, such as a 10-year critical illness plan, we use the formula approach that you suggest, ie something like SA_x+t - Pa_x+t. Note that the big A and little a functions are discounting over many years.

For short-term policies, such as a one-year group pmi, we use the UPR. The long-term formula approach doesn't make much sense here as we don't need to discount over many years. The premium has just been paid, so it's a pretty good estimate of how much the claims will cost.

So to answer your question regarding double counting. We'll be using one approach or the other. We won't be using both.

A UPR example may help. A single premium is paid at the start of contract of 120 for 12 months cover. So we think that claims will be about 10 per month. If the policy is now two months old, we have 10 months left, so our initial estimate of the future costs is 100 and that is what we hold as a UPR. (I guess we get the same answer retrospectively, although I'm not sure that thinking this way helps much, but here goes. The policyholder has paid 120, and so far we've had two months costing 10 for each, so the retrospective reserve is 120 - 20 =100.)

All of the above calculations work if we think the premium is a good enough approximation to the actual costs. If we think the premium charged wasn't enough then we calculate the unexpired risk reserve instead, ie we go back to first principles and estimate how much we think the claims are going to cost for the remainder of the policy.

I hope this helps.

Best wishes

Mark

 

[Trevor]

Hi Mark,

Thanks for the explanation. This is clearer now, but I am thinking how this will work in general case:

1. Regular premium
Lets re-use your example, but with regular premium of 10 per month over 12 months instead.
In this case, thinking of the UPR approach (assuming premium ~= costs) makes sense.
However if I look at the retrospective formula instead, we have only received two 10s by month 2, and also paid two 10s. If we apply the general formula: past premium - past claims, we would end up 0. Which makes intuitive sense because we would have received 10, and pay out 10 in each of the future month.
But does this fit the definition of reserves, to set money aside? We made a promise to payout, so we have liabilities. However our formula implies we do not need to set aside any money now for that.

More generally, does the idea of unearned premium reserve works for regular premiums, where we haven't got any unearned premium?

2. Unexpired risk reserve (URR)
My understanding of the URR is an addition on top of the UPR. So if we think the UPR is insufficient, we top it up with the URR. Is this the correct understanding, or the UPR will be replaced entirely by the URR instead?

Regards,
Trevor

 

[Mark Willder]

Hi Mark,

Thanks for the explanation. This is clearer now, but I am thinking how this will work in general case:

1. Regular premium
Lets re-use your example, but with regular premium of 10 per month over 12 months instead.
In this case, thinking of the UPR approach (assuming premium ~= costs) makes sense.
However if I look at the retrospective formula instead, we have only received two 10s by month 2, and also paid two 10s. If we apply the general formula: past premium - past claims, we would end up 0. Which makes intuitive sense because we would have received 10, and pay out 10 in each of the future month.
But does this fit the definition of reserves, to set money aside? We made a promise to payout, so we have liabilities. However our formula implies we do not need to set aside any money now for that.

More generally, does the idea of unearned premium reserve works for regular premiums, where we haven't got any unearned premium?

2. Unexpired risk reserve (URR)
My understanding of the URR is an addition on top of the UPR. So if we think the UPR is insufficient, we top it up with the URR. Is this the correct understanding, or the UPR will be replaced entirely by the URR instead?

Regards,
Trevor

Hi Trevor

If we have a monthly premium of 10 then there is no need to hold a UPR if the premium is about to be paid - the premium covers the costs. If the premium has just been paid then the UPR is 10. If we are half way through the month then the UPR is 5. It's the same principle as the annual case.

The URR replaces the UPR. The course used to include a reserve called the AURR (additional URR), which is what you are thinking about. So URR = UPR + AURR. The insurer holds the higher of UPR and URR.

Best wishes

Mark

 

[Meher]

Hi Trevor

We use a different approach for long term and short term policies.

For long-term policies, such as a 10-year critical illness plan, we use the formula approach that you suggest, ie something like SA_x+t - Pa_x+t. Note that the big A and little a functions are discounting over many years.

For short-term policies, such as a one-year group pmi, we use the UPR. The long-term formula approach doesn't make much sense here as we don't need to discount over many years. The premium has just been paid, so it's a pretty good estimate of how much the claims will cost.

So to answer your question regarding double counting. We'll be using one approach or the other. We won't be using both.

A UPR example may help. A single premium is paid at the start of contract of 120 for 12 months cover. So we think that claims will be about 10 per month. If the policy is now two months old, we have 10 months left, so our initial estimate of the future costs is 100 and that is what we hold as a UPR. (I guess we get the same answer retrospectively, although I'm not sure that thinking this way helps much, but here goes. The policyholder has paid 120, and so far we've had two months costing 10 for each, so the retrospective reserve is 120 - 20 =100.)

All of the above calculations work if we think the premium is a good enough approximation to the actual costs. If we think the premium charged wasn't enough then we calculate the unexpired risk reserve instead, ie we go back to first principles and estimate how much we think the claims are going to cost for the remainder of the policy.

I hope this helps.

Best wishes

Mark

Hi Mark,
I must say your simple examples add great value to our understanding.
Could you expand on your example here to illustrate URR?
1.would we; based on experience in the prior 2 months; revise cost assumptions for the remaining 10months only?
2.what if we had a better experience in the prior 2months and costs were lower than premiums charged at start?
Regards,
Meher

 

[Mark Willder]

Hi Mark,
I must say your simple examples add great value to our understanding.
Could you expand on your example here to illustrate URR?
1.would we; based on experience in the prior 2 months; revise cost assumptions for the remaining 10months only?
2.what if we had a better experience in the prior 2months and costs were lower than premiums charged at start?
Regards,
Meher

Hi Meher

Yes, we would look at the last two months experience and only revise the expected cost for the remaining 10 months.

We take the larger of the UPR and URR. So if experience is better than the premiums the insurer still has to hold the larger UPR.

Best wishes

Mark

 

[Meher]

Hi Meher

Yes, we would look at the last two months experience and only revise the expected cost for the remaining 10 months.

We take the larger of the UPR and URR. So if experience is better than the premiums the insurer still has to hold the larger UPR.

Best wishes

Mark

Thank you Mark.

Can you also help me understand why in the solutions on the types of reserves to be held for IP (Notes 2019;Chp 21;Pg 6) and PMI (Notes 2019;Chp 21;Pg 10); the solution starts off points b, c and d with in addition to a?

Surely there is a n overlap if the PH for instance is known to be on claim, and we are going to consider a policy reserve (such as he was healthy) and also a reserve for the current claim annuity.
Similarly, in practise wouldn't we assume based on recent experience the expected rate/ratio of policies on IBNR and separate that out from the policy reserve (where PHs are health)?

Is the solution trying to address the policy reserve to cover the liabilities for when the currently sick (or assumed sick) will recover?

 

[Mark Willder]

Thank you Mark.

Can you also help me understand why in the solutions on the types of reserves to be held for IP (Notes 2019;Chp 21;Pg 6) and PMI (Notes 2019;Chp 21;Pg 10); the solution starts off points b, c and d with in addition to a?

Surely there is a n overlap if the PH for instance is known to be on claim, and we are going to consider a policy reserve (such as he was healthy) and also a reserve for the current claim annuity.
Similarly, in practise wouldn't we assume based on recent experience the expected rate/ratio of policies on IBNR and separate that out from the policy reserve (where PHs are health)?

Is the solution trying to address the policy reserve to cover the liabilities for when the currently sick (or assumed sick) will recover?

Hi Meher

Yes, there will be some overlap between the reserves, but disentangling this is likely to be more trouble than it's worth, particularly as the number of claimants in b, c and d will be small compared to the healthy lives in a. We still need to reserve for potential future claims after the claimants recover too, so we still need a reserve similar to (a) for these claimants anyway.

So following the approach in the question is slightly prudent, but is practical and saves a lot of costs.

Best wishes

Mark