Basic reserving question

[Joseph Barnett]

This question perhaps belongs more in the old CT5 but I don't remember it being addressed there when I studied it.

In CT5, I believe we had three bases:

Realistic/best estimate: what the company expects to happen.
Pricing: more prudent than realistic to generate profit.
Reserving: more prudent still, in order to manage risk and smooth profit emergence.

Now in the absence of interest rates, the reserving basis does not do anything - it just changes when the profit emerges. The amount of profit is determined by the difference between the pricing basis and actual experience (which should be close to the realistic basis if the company has done a good job). So that all makes sense.

In SP2, it is mentioned that reserving is now typically done on a realistic basis, with the risk allowed for in solvency capital requirements; the idea being that the two together will provide enough prudence.

Now, my question is this: if the company is expecting to make a profit, does this not mean that reserves in respect of all policies (or at least the profitable ones) will be negative? Does that then mean that as soon as a profitable policy is written, it will show on the balance sheet as an immediate increase in net assets (ignoring the SCR)?

Assuming I haven't misunderstood anything there, I guess I'm just wondering why this is becoming the preferred approach, instead of just using a prudent reserving basis (which seems more intuitive to me). I guess it's easier to calculate diversification etc. in the SCR than it is for policy level reserves, and maybe it's easier to regulate since it's not so product specific. Are there any other reasons?

Furthermore, if a company is well diversified such that the marginal increase in BE reserves + SCR after writing a policy is much less than the equivalent reserves calculated on the pricing basis, then the company can take an immediate profit on day 1, regardless of the risks for the specific policy?

Hope those questions all make sense.

Joe

 

[Lindsay Smitherman]

Yes, your questions do make sense - and they are good ones! Although possibly we are creeping more into SA2 territory...

Let me take them in turn.

Now, my question is this: if the company is expecting to make a profit, does this not mean that reserves in respect of all policies (or at least the profitable ones) will be negative?

Yes - you are correct: but only if we are talking about regular premium business.

For conventional business, reserves = PV(future benefits + future expenses - future premiums), and this can only be negative if there are future premiums. Reserves for single premium conventional business will always be positive. Also, reserves for conventional regular premium business are likely to become positive at some point in the policy duration, as the PV of future premiums will reduce faster than the PV of future benefits as the policy increases in duration, since premiums tend to be level but the pattern of benefit payments is back-ended to the later years of the contract.

For unit-linked business, the non-unit reserve may be negative (reflecting anticipation of the future profit loadings in the charges, as you indicate), but the total reserve (ie including also the unit reserve) could well be positive - particularly for single premium business.

Does that then mean that as soon as a profitable policy is written, it will show on the balance sheet as an immediate increase in net assets (ignoring the SCR)?

Yes! This is one reason why we say that the more realistic-based reporting approaches such as Solvency II (ignoring capital requirements, as you say) capitalise future profits on the balance sheet.

 

[Lindsay Smitherman]

Assuming I haven't misunderstood anything there, I guess I'm just wondering why this is becoming the preferred approach, instead of just using a prudent reserving basis (which seems more intuitive to me). I guess it's easier to calculate diversification etc. in the SCR than it is for policy level reserves, and maybe it's easier to regulate since it's not so product specific. Are there any other reasons?

The main reason is for transparency and comparability. It is much easier to understand and compare balance sheets if the additional loadings (for risk) are identified explicitly over and above a best estimate liability, rather than being 'hidden' within the liability values through the use of prudential assumptions. In the latter case, different companies are likely to have different levels of prudence in their assumptions, and the presentation makes it harder to be able to compare the balance sheets and understand those differences.

 

[Joseph Barnett]

Great answers both, thank you very much.

 

[Lindsay Smitherman]

Furthermore, if a company is well diversified such that the marginal increase in BE reserves + SCR after writing a policy is much less than the equivalent reserves calculated on the pricing basis, then the company can take an immediate profit on day 1, regardless of the risks for the specific policy?

Yes, however there are a few things to bear in mind:

- This chapter of the SP2 Core Reading is all about the reserves and capital requirements that are held in a supervisory balance sheet. The purpose of this type of reporting is to assess solvency and ensure policyholder protection, not to calculate 'profit'. Profit reporting, through the publication of statutory accounts, would not include explicit solvency capital requirements such as the SCR in Solvency II, which are there to provide policyholder protection.

- If the reserves are determined on a market-consistent basis, as is described in the SP2 Core Reading (see Chapter 20 Section 2.3) the reserves may comprise best estimate liabilities plus an additional amount that reflects risk within the non-economic assumptions (this is equivalent to the Risk Margin in the Solvency II balance sheet, if you are familiar with that). Such a risk adjustment might be added to a best estimate liability within profit reporting in published accounts, and this would defer the recognition of profit - but the risk adjustment would be expected to fall into profit over time, if actual experience is in line with best estimate.

- Accounting standards (which, as suggested above, are what actually drive profit recognition) tend to include the use of other adjustments to reserves which avoid the upfront recognition of future profits and instead cause the profit to be recognised more smoothly through the contract duration. We go into this in more detail in SA2.

Hope that helps too. [Sorry for the gap in the response - lost my wifi signal for a while!]

 

[MindFull]

Yes, however there are a few things to bear in mind:

- This chapter of the SP2 Core Reading is all about the reserves and capital requirements that are held in a supervisory balance sheet. The purpose of this type of reporting is to assess solvency and ensure policyholder protection, not to calculate 'profit'. Profit reporting, through the publication of statutory accounts, would not include explicit solvency capital requirements such as the SCR in Solvency II, which are there to provide policyholder protection.

- If the reserves are determined on a market-consistent basis, as is described in the SP2 Core Reading (see Chapter 20 Section 2.3) the reserves may comprise best estimate liabilities plus an additional amount that reflects risk within the non-economic assumptions (this is equivalent to the Risk Margin in the Solvency II balance sheet, if you are familiar with that). Such a risk adjustment might be added to a best estimate liability within profit reporting in published accounts, and this would defer the recognition of profit - but the risk adjustment would be expected to fall into profit over time, if actual experience is in line with best estimate.

- Accounting standards (which, as suggested above, are what actually drive profit recognition) tend to include the use of other adjustments to reserves which avoid the upfront recognition of future profits and instead cause the profit to be recognised more smoothly through the contract duration. We go into this in more detail in SA2.

Hope that helps too. [Sorry for the gap in the response - lost my wifi signal for a while!]

Good Day Lindsay,

I just wanted to clarify the whole idea of profit emergence. I think that profits can emerge in two ways: explicit profit margin in premium from pricing basis, and the addition of margins for the reserving basis. When we sell a policy, we get the profit margin up front as a source of profit. As for the reserve, if it is set up with margins (and more prudent than the pricing basis), this provides another source of profit - I think. I thought that for example, if we do annual experience studies, and we find that our expenses have gone up, this would cause an increase in reserves which would lower profits for that year but eventually by the end of the policy term, all reserves would be released. Thus, the total profit for the policy is the same but the change in basis only affects the timing or emergence/value of the profit. However, based on what you said, risk adjustment would fall into profit over time only if actual experience is in line with best estimate. So if we have a policy where expenses turned out to be higher than the pricing basis, and as such reserves have been increased to compensate for this, does this mean that the risk margin/adjustment wouldn't fall into profit (even though the reserves are released at the end of the term)?

 

[Mark Willder]

Good Day Lindsay,

I just wanted to clarify the whole idea of profit emergence. I think that profits can emerge in two ways: explicit profit margin in premium from pricing basis, and the addition of margins for the reserving basis. When we sell a policy, we get the profit margin up front as a source of profit. As for the reserve, if it is set up with margins (and more prudent than the pricing basis), this provides another source of profit - I think. I thought that for example, if we do annual experience studies, and we find that our expenses have gone up, this would cause an increase in reserves which would lower profits for that year but eventually by the end of the policy term, all reserves would be released. Thus, the total profit for the policy is the same but the change in basis only affects the timing or emergence/value of the profit. However, based on what you said, risk adjustment would fall into profit over time only if actual experience is in line with best estimate. So if we have a policy where expenses turned out to be higher than the pricing basis, and as such reserves have been increased to compensate for this, does this mean that the risk margin/adjustment wouldn't fall into profit (even though the reserves are released at the end of the term)?

There's a lot going on here and the answer very much depends on what we mean by profit. So it's worth taking a step back to consider what we mean by profit and the factors that affect it.

We can think about the profit emerging at the following times:
The profit emerging on day one of the contract.
The profit emerging each year over the life of the contract.
The total profit (day one, plus the subsequent years).

These profit calculations depend on three things:
the pricing basis
the valuation basis
the actual experience.

The total profit depends only on the pricing basis and the actual experience. If actual experience is better than assumed in the pricing, then we make a profit. Basically the bigger the premium, the bigger the profit. The premium could be big because we made prudent assumptions (for simplicity of explanation we'll assume this is the case), or because we added an explicit profit loading. This is the first type of profit that you mentioned.

In practice, insurers use many different valuation bases. However they have no impact on the total profit (because that only depends on the premium and the actual experience). But, the valuation basis can affect the timing of the profit as follows.

The profit emerging on day one depends on the pricing basis and the valuation basis. If the valuation basis is stronger than the pricing basis, then the initial premium won't be enough to cover the initial reserves and expenses and we record a loss on day 1.

The profit emerging each year then depends on the difference between the valuation basis and the actual experience. If the actual experience is better than assumed in the valuation basis, then we make profits in future years. This is the second type of profit that you mention.

Note that the stronger the valuation basis, the bigger the day one loss, but the higher the year on year profits will be. However, the bigger day one loss is balanced by the higher year on year profits so that the total profitability is unchanged.

Now let's consider what happens if we do an expense analysis and increase our valuation assumption as you suggest. Let's assume that our old expense assumption was 3 for each of the next ten years, and the new assumption has been increased to 4. What happens depends on the actual experience as follows.

Reserves will increase by 10 (ignoring discounting for simplicity), as we have an extra 1 of expenses for 10 years. So we make an immediate loss of 10.

If expenses actually turn out to be 4, then no profit will emerge over the remaining 10 years. The extra reserves will exactly cancel out the higher actual expenses.

However, if the expenses turn out to be 3 after all (so the stronger reserves were unnecessary), then the profit will be 1 in each of the next 10 years, because we had reserves to pay 4 expenses, but only had to pay 3. Note that the profit still emerges year on year, even though the reserves aren't fully released until the end of the contract. So in this case the total profit hasn't changed, but the timing has as you've suggested.

Finally let's take your point on the risk adjustment. Let's say that the pricing expense assumption was 2. You've said that actual expenses are worse than the pricing basis, so let's say the actual expenses are 3. You've split the valuation basis into two parts, let's say our best estimate is 3 and then there's a risk adjustment of 1, giving a total valuation assumption of 4. Let's assume a 10 year policy.

The total profit is -10. The premium expense loading of 2 is not enough to cover the actual expenses of 3. So we lose 1 for each of the ten years.

The day one profit is -20. We need to set up reserves to cover expenses of 4 every year, but only have premium loadings of 2.

Then the year on year profit is 1. The risk adjustment is released each year as profit because we have reserved for 4, but have actual expenses of 3.

So profits are -20 followed by 1 for the next ten years, giving a total of -10 as required.

I hope this numerical example helps to show how the various factors impact the different components of the profit.

Best wishes

Mark

 

[MindFull]

There's a lot going on here and the answer very much depends on what we mean by profit. So it's worth taking a step back to consider what we mean by profit and the factors that affect it.

We can think about the profit emerging at the following times:
The profit emerging on day one of the contract.
The profit emerging each year over the life of the contract.
The total profit (day one, plus the subsequent years).

These profit calculations depend on three things:
the pricing basis
the valuation basis
the actual experience.

The total profit depends only on the pricing basis and the actual experience. If actual experience is better than assumed in the pricing, then we make a profit. Basically the bigger the premium, the bigger the profit. The premium could be big because we made prudent assumptions (for simplicity of explanation we'll assume this is the case), or because we added an explicit profit loading. This is the first type of profit that you mentioned.

In practice, insurers use many different valuation bases. However they have no impact on the total profit (because that only depends on the premium and the actual experience). But, the valuation basis can affect the timing of the profit as follows.

The profit emerging on day one depends on the pricing basis and the valuation basis. If the valuation basis is stronger than the pricing basis, then the initial premium won't be enough to cover the initial reserves and expenses and we record a loss on day 1.

The profit emerging each year then depends on the difference between the valuation basis and the actual experience. If the actual experience is better than assumed in the valuation basis, then we make profits in future years. This is the second type of profit that you mention.

Note that the stronger the valuation basis, the bigger the day one loss, but the higher the year on year profits will be. However, the bigger day one loss is balanced by the higher year on year profits so that the total profitability is unchanged.

Now let's consider what happens if we do an expense analysis and increase our valuation assumption as you suggest. Let's assume that our old expense assumption was 3 for each of the next ten years, and the new assumption has been increased to 4. What happens depends on the actual experience as follows.

Reserves will increase by 10 (ignoring discounting for simplicity), as we have an extra 1 of expenses for 10 years. So we make an immediate loss of 10.

If expenses actually turn out to be 4, then no profit will emerge over the remaining 10 years. The extra reserves will exactly cancel out the higher actual expenses.

However, if the expenses turn out to be 3 after all (so the stronger reserves were unnecessary), then the profit will be 1 in each of the next 10 years, because we had reserves to pay 4 expenses, but only had to pay 3. Note that the profit still emerges year on year, even though the reserves aren't fully released until the end of the contract. So in this case the total profit hasn't changed, but the timing has as you've suggested.

Finally let's take your point on the risk adjustment. Let's say that the pricing expense assumption was 2. You've said that actual expenses are worse than the pricing basis, so let's say the actual expenses are 3. You've split the valuation basis into two parts, let's say our best estimate is 3 and then there's a risk adjustment of 1, giving a total valuation assumption of 4. Let's assume a 10 year policy.

The total profit is -10. The premium expense loading of 2 is not enough to cover the actual expenses of 3. So we lose 1 for each of the ten years.

The day one profit is -20. We need to set up reserves to cover expenses of 4 every year, but only have premium loadings of 2.

Then the year on year profit is 1. The risk adjustment is released each year as profit because we have reserved for 4, but have actual expenses of 3.

So profits are -20 followed by 1 for the next ten years, giving a total of -10 as required.

I hope this numerical example helps to show how the various factors impact the different components of the profit.

Best wishes

Mark

Hi Mark,

The numerical analysis has been very helpful but I think I still am missing something. For example, if our actual experience turns out to be 4 for the rest of the term, isn't the extra reserve of 10 released at the end of the term which would then add 10 to our profit at that time? What am I missing?

Regards.

 

[Mark Willder]

Hi Mark,

The numerical analysis has been very helpful but I think I still am missing something. For example, if our actual experience turns out to be 4 for the rest of the term, isn't the extra reserve of 10 released at the end of the term which would then add 10 to our profit at that time? What am I missing?

Regards.

Reserves aren't all released only at the end of the contract. Instead they build up, or are released, over time.

Taking our example again with a valuation assumption for expenses of 4 each year. We'll add in a maturity benefit of 100 at the end, but still ignore investment. We'll assume it' single premium.

At the start we have reserves of 140. One year later, there's only 9 years of expenses left, so the reserve is only 136. The reserves in subsequent years are then 132, 128, 124, ....., 104.

So every year we release reserves of 4, but expenses are only 3, so we make a profit each year of 1. For example, we started the first year with reserves of 140, but only needed reserves of 136 at the end.

The final year is a bit different. We release reserves of 104 as we don't need reserves once the policy expires. 100 covers the maturity benefit, and again we make a profit of 1 from the expense assumption.

I hope that clarifies the situation.

Best wishes

Mark

 

[MindFull]

Hi Mark,

Thanks again for the explanations. I think I was making reserve releases synonymous with profit increases. So just to be MORE clear, if the policy above had pricing = val. basis, then the premium would be just enough to pay all claims ,expenses, etc. If we were to increase our expense assumption, then that premium would be inadequate and we would have to increase our reserves by the requisite increase in expenses. As the years pass and the actual expense turns out to be the same as our new expense assumption, we would release reserves to pay for that extra expense and no profit would be added to the profit equation for that year. So reserve releases only add to profit if there are no extra outflows for. Is this correct?

Thanks so much for the extra help.
Regards.

 

[Mark Willder]

Hi Mark,

Thanks again for the explanations. I think I was making reserve releases synonymous with profit increases. So just to be MORE clear, if the policy above had pricing = val. basis, then the premium would be just enough to pay all claims ,expenses, etc. If we were to increase our expense assumption, then that premium would be inadequate and we would have to increase our reserves by the requisite increase in expenses. As the years pass and the actual expense turns out to be the same as our new expense assumption, we would release reserves to pay for that extra expense and no profit would be added to the profit equation for that year. So reserve releases only add to profit if there are no extra outflows for. Is this correct?

Thanks so much for the extra help.
Regards.

Yes, that's right.

If actual experience is the same as the valuation basis, then the release in reserves is all used up to pay the cashflows and there's no profit (or loss).

We only get a profit if the release in reserves is bigger than the cashflows. This happens if the actual experience is better than the valuation basis.

Best wishes

Mark