Reserve concept

[Arush]

Trying to get my head around the concept of reserving and captial, some questions (let's consider solvency 2):

1. The techinical provisions or reserves = BEL + Risk Margin. Why would a positive BEL (outgo - income) exist under normal circumstances as any business written, on a best estimate basis, would be expected to generate profits i.e. income > outgo? But in normal practice, I see there always exists a positive.

2. If the BEL is negative i.e. income > outgo, why is a risk margin needed? One simplied approach I have observed being used is looking at the PV of claims to arrive at the required capital to estimate the risk margin, why are premiums ignored?

3. If the BEL is negative, would that imply the asset side to reflect a negative amount as well? To simplify, let's consider these are the only 2 items for the B/S.

 

[Arush]

4. One of the IFoA presentations say that tech provisions = claim provisions + premium provisions + risk margin. Is the PV of future cashflows = claims provisions + premium provisions? And what exactly do premium and claim provisions mean? Any example would be really helpful.

Thanks!

 

[Mateusz]

Hi Arush,

see some initial answers below.

1. One example to think of - a single-premium investment policy. Your total BEL could be thought of as the sum of the unit and non-unit liabilities. It is the non-unit liability which could be negative, for reasons you point out, but not the total BEL.

3. Not sure if I understood the question correctly, but if you have a negative BEL, it will sit as a negative liability on the SII balance sheet (gross of reinsurance). On the asset side you would report the reinsurance asset (e.g. PV of reinsurance premiums less PV of reinsurer's share in the benefits and expenses captured in the BEL).

4. I think this split is useful for general insurance, where we normally have material provisions for claims that have already occured (both for those already reported to the insurer and those that have yet to be reported, the latter known as IBNR). This would be the claims provision. The premium provision would refer to unexpired coverage, that is benefits and related expenses from claims that are expected to occur after the valuation date from the current portfolio. If there are any future premiums expected, those would be deducted.

In life insurance, claims provision is not material, because claims are normally settled with small delay. The premium provision would be the standard PV benefits + PV expenses - PV premiums. But technically, yes, you need to account for both in the SII BS.

Regards,
Mateusz

 

[Lindsay Smitherman]

Hi - just to add to the useful comments above, please do bear in mind that the specifics of Solvency II are not in scope for SP2. You won't get into the details until SA level. However, SP2 does describe how a market-consistent approach to reserves would start from a risk-neutral reserve (with non-investment assumptions set at best estimate) plus a separate risk margin, which is equivalent to the Solvency II technical provisions (= BEL + risk margin).

Picking up on each of your questions in turn:

1. As another example, reserve for conventional business = PV { future benefits + future renewal expenses - future premiums }. This will always be positive for any type of single premium business, as there are no future premiums to deduct. It will also likely be positive for regular premium business other than at early durations, as the number of future premiums reduces but the future benefits remains high.

 

[Lindsay Smitherman]

2. If the BEL is negative i.e. income > outgo, why is a risk margin needed?

A negative BEL means that future expected income > future expected outgo, so we are effectively treating that policy as an asset. But that has been done on a best estimate basis. Broadly speaking, there is a 50% chance that this is incorrect in the wrong direction (ie that we have overstated the value of that 'asset').

The risk margin is basically what you would have to add onto the BEL in order to give the total amount at which a third party would trade the liability with you. It reflects the risks inherent in the liability being traded. If the BEL is negative (say -100), that means that the third party would be paying you to take the liability off your hands (because it is expected to generate future profits). However, they would probably want to reduce the amount they are prepared to give you, in order to reflect the risk that the actual profits emerging turn out to be less than the best estimate. So we add the risk margin (say 10) to the BEL which makes it less negative in total (-90 overall in this example). Hence the third party is paying less to take on the liability (90 now rather than 100), reflecting the margin for risk within the transaction.

Where the BEL is negative, the risk margin might even make the total provision positive. And of course if the BEL is positive (as it often will be), the total provision again would be positive once the risk margin has been added. In these cases, you would have to pay the third party an amount in order for them to be prepared to take the liability on.

 

[Lindsay Smitherman]

2. One simplied approach I have observed being used is looking at the PV of claims to arrive at the required capital to estimate the risk margin, why are premiums ignored?

I'm not entirely sure what you mean here, but perhaps this is referring to using PV of claims as the risk driver in order to proxy the run-off of the capital requirements within the RM calculation under the 'cost of capital' approach?

This doesn't mean that the capital requirements themselves are projected as being equal to PV of claims only. It means that the pattern of run-off of the current required capital is assumed to be the same as the pattern of run-off of the PV of claims for that particular portfolio.

Any driver can be used, provided it adequately represents the underlying risk. So, for example, the component of the risk margin relating to mortality risk might be simplified by using the value of death benefits as the driver.

 

[Lindsay Smitherman]

3. If the BEL is negative, would that imply the asset side to reflect a negative amount as well? To simplify, let's consider these are the only 2 items for the B/S.

I'm not sure I've quite understood this either, but FWIW if you have a negative BEL on the liabilities side of the balance sheet, there would also probably have been a negative impact on the asset side to the extent of initial expenses incurred being higher than the initial premium paid (bearing in mind that we would only tend to have negative BELs for regular premium business, at early durations).

 

[Arush]

I'm not sure I've quite understood this either, but FWIW if you have a negative BEL on the liabilities side of the balance sheet, there would also probably have been a negative impact on the asset side to the extent of initial expenses incurred being higher than the initial premium paid (bearing in mind that we would only tend to have negative BELs for regular premium business, at early durations).

Sorry, if my question was not clear. I am trying to say that say, the BEL + Risk Margin i.e. the technical provision is negative, so on the liability side in the B/S, we have a negative amount. How the does the asset side correspond to this?

Conversely, in scenarios where the technical provisions are positive (i.e. future outgo > income), that amount is backed by the assets which results in those assets being locked.

But when the technical provisions are negative, I am thinking if there is even a need to back it with assets as negative assets seems strange to hold or back negative reserves, sorry if this question is a bit strange.

 

[Arush]

I'm not entirely sure what you mean here, but perhaps this is referring to using PV of claims as the risk driver in order to proxy the run-off of the capital requirements within the RM calculation under the 'cost of capital' approach?

This doesn't mean that the capital requirements themselves are projected as being equal to PV of claims only. It means that the pattern of run-off of the current required capital is assumed to be the same as the pattern of run-off of the PV of claims for that particular portfolio.

Any driver can be used, provided it adequately represents the underlying risk. So, for example, the component of the risk margin relating to mortality risk might be simplified by using the value of death benefits as the driver.

Yes, that was my question on the use of claims as a risk driver. So I am just trying to understand the logic here (which you have already explained to some extent). Would it be possible to explain the calculation of risk capital based on the claims run-off using a simplified example? I understand how the CoC gets calculated using the risk capital amount.

 

[Lindsay Smitherman]

Sorry, if my question was not clear. I am trying to say that say, the BEL + Risk Margin i.e. the technical provision is negative, so on the liability side in the B/S, we have a negative amount. How the does the asset side correspond to this?

Conversely, in scenarios where the technical provisions are positive (i.e. future outgo > income), that amount is backed by the assets which results in those assets being locked.

But when the technical provisions are negative, I am thinking if there is even a need to back it with assets as negative assets seems strange to hold or back negative reserves, sorry if this question is a bit strange.

If a reserve is negative, it just means that the total of reserves across all business is lower than would otherwise be the case, and so you have to hold less assets to back them. Hence you have a higher amount of free assets. Does that make a bit more sense?

 

[Lindsay Smitherman]

Yes, that was my question on the use of claims as a risk driver. So I am just trying to understand the logic here (which you have already explained to some extent). Would it be possible to explain the calculation of risk capital based on the claims run-off using a simplified example? I understand how the CoC gets calculated using the risk capital amount.

Here's a very simple example. We can determine the capital requirement for Risk A now (time t=0); let's say it is 100. We need to project what this will be at times t=1, t=2 etc. That might be a tricky projection.

So we find a simpler driver that we think Risk A is going to have a close relationship with. We work out what the value of that driver is now, let's say it's 10 at time t=0. And we project what we expect it to be in the future, let's say 9 at time t=1 and 8 at t=2, etc.

We can see that our driver is currently 10% of the capital requirement for Risk A, and we assume that proportion remains unchanged.

Hence our estimated projection of the capital requirement for Risk A is 90 at time t=1 and 80 at time t=2, etc.

Hope that helps.

 

[Arush]

If a reserve is negative, it just means that the total of reserves across all business is lower than would otherwise be the case, and so you have to hold less assets to back them. Hence you have a higher amount of free assets. Does that make a bit more sense?

I understand. I was coming from a view (probably not very realistic) when an insurance company starts operations and has no business in the past. In that case, assuming profitable business is written, there would be negative reserves. In such a scenario, how would the corresponding asset side on the B/S look like? Again, a simple example is always helpful

 

[CapitalActuary]

I understand. I was coming from a view (probably not very realistic) when an insurance company starts operations and has no business in the past. In that case, assuming profitable business is written, there would be negative reserves. In such a scenario, how would the corresponding asset side on the B/S look like? Again, a simple example is always helpful

Let's say I raise £10m from investors, who have all bought shares, to start an insurance company. Now I have a balance sheet with £10m of cash on the assets side, £0 of liabilities, and £10m of available capital which we can also think of as money owed to the shareholders.

Let's say I write a bunch of business which I'm legally bound to, but the policies haven't started yet, i.e. they've not 'incepted'. If I expect to get £3m in premiums from this business and only pay out £2m, then under Solvency II I can record technical provisions of -£1m (let's ignore the various complexities here). Then I have £10m cash, -£1m liabilities, and £11m available capital.

Solvency II probably says I need something like £4m of regulatory capital to support the business I've written (depending on the sort of business yada yada). So of my £11m available capital, only £7m is free assets. At this point I still have £10m cash.

Does this clarify things for you? I think you're overthinking it. The -£1m technical provisions could just as well be recorded as a £3m 'premium receivable' asset (remember assets are just things we are own or thing we are owed) and a £2m reserve.

 

[CapitalActuary]

I'll paste an answer I've made before about assets, liabilities and capital. This might help clear some things up for you. It's a question that comes up a lot for some reason, perhaps because people have forgotten all of CT2 by the time they come to do the later exams (it's really just about understanding accounting properly).

Assets, liabilities and capital
Assets are things that you own or that you are owed. Liabilities are things that you owe. Available capital is assets minus liabilities.

Reserves are a liability, representing the amounts owed to policyholders. You don't know for certain what these amounts will be, so this is an estimate. The reason you don't know is because some claims won't have happened yet, some will have happened but haven't been reported yet, and some have been reported but take some time to settle.

Capital is one of the broadest words in finance and economics. Generally, where I've met it, it tends to refer to parts of available capital (defined above).

Required capital refers to the part of available capital that you, or the regulator, think is required to carry out business. Alternatively, you can think of this as the excess assets, over and above liabilities, that are required. Reasons you need to have more assets than liabilities include, but are certainly not limited to:

• deviations of actual vs expected claims payments - i.e. your reserves will be wrong because they were just an estimate of claims
• regulatory (e.g. PRA) or market (e.g. Lloyd's) requirements to hold a certain level of capital
• taking advantage of opportunities as they arise, e.g. writing new business
• dealing with unexpected events, e.g. operational events like COVID require money you don't expected to spend

Often though, required capital will just mean something like the 'SCR' (Solvency Capital Requirement) under Solvency II regulations. An internal (to a company) definition of required capital could differ from this, but in reality tends not to.

Free capital is any available capital that isn't required capital. So it's the assets left over once you take off the liabilities and the required capital. If you have more of this, it means you can get away with taking more risk with it, e.g. investing these assets into high yielding bonds or equities, because even if you lose some of that free capital in the short term you'll have enough assets to meet your liabilities and required capital.

Solvency level can mean different things as well. You can simplistically measure how solvent a company is by comparing how much available capital it has to how much premium it writes, for example by calculating solvency level = (assets - liabilities) / written premium. The idea of this is that if a company writes loads of premium it's taking on a lot of risk, and it shouldn't be doing so if it doesn't have much available capital. Usually though, especially in the UK and Europe, solvency level (aka solvency cover) = available capital / SCR. The idea is the same here - the SCR will be high if the company is running lots of risk, and if they are running a lot of risk compared to their available capital their solvency cover should be low.

If solvency cover (talking about the SCR definition now) is below 100% then it means you don't have enough assets to cover your liabilities plus the SCR, so the regulator (e.g. the PRA) will start to intervene and the company will need to take actions to bring their solvency cover above 100%. A lot of companies will have internal solvency targets of 115%, 125% or 150% and try to maintain this level just to be 'extra secure'. This brings other benefits too like potentially receiving a higher credit rating which is attractive to policyholders and reinsurers.

How are reserves and capital 'used'? (People get confused about this, as they hear people referring to reserves / capital being used up by things, but it doesn't make sense to pay for things with liabilities.)

I'll give an example of assets, liabilities, and capital. Then I'll try to give an example about how we can think about reserves vs capital being 'used'. (The below isn't exactly how things work but hopefully gives a simplified idea to help you understand the terms involved.)

Let's say I raise £10m from investors, who have all bought shares, to start an insurance company. Now I have a balance sheet with £10m of cash on the assets side, £0 of liabilities, and £10m of available capital which we can also think of as money owed to the shareholders.

Now I sell £5m of insurance, which means I get £5m of cash from policyholders (if they all pay up front for their insurance). I estimate I'll end up paying out about £4m of this in claims. Let's say I use £7m cash to buy £7m of bonds to get some return from my money instead of letting it all just sit there as cash. So my balance sheet is now £8m of cash in assets, £7m of bonds, £4m liabilities and £11m of available capital.

The regulator tells me I need to calculate my SCR for all the risks involved in writing that £5m of business and other risks like operational risk and the investment risk associated with the bonds I bought. I do the calculation, which in this instance let's say is a complex formula given to me by the regulator, and the SCR turns out to be £8m. So even though I wrote £5m, my required capital to cover the risks associated with this (and other risks like investment risk) is £8m!

Now the balance sheet is £7m bonds and £8m cash on the assets side, £4m of liabilities (the reserves), and I can split my £11m available capital into £8m of required capital and £3m of free capital.

So, when is capital 'used' versus when are reserves 'used'? Things can get a little theoretical at this point. If a £1m is reported to me, and I think this claim was already included in my estimated "reserve for claims that hadn't been reported", then my liabilities don't change. I was expecting to owe £1m to a policyholder, and now I still expect that. My required capital may or may not change from £8m, depending on the results of the calculation the regulator gave me. Once it's time to pay out this claim, I pay out £1m in cash to the policyholder and this extinguishes the £1m liability I have for that claim in my reserves. So I can think about this claim using my reserves.

If a really bad claim for £3m came in, the type of which I never expected and didn't include in my reserve calculations, then we should probably hold the existing £4m reserve the same as we're still expecting all these claims. What will happen as soon as I know about this £3m claim is I'll add a reserve for it to the existing £4m reserve, so my reserves are now £7m. My required capital may or may not change from £8m, depending on how the results of the formula the regulator gave me change. But in this instance I *could* think about my required capital having served it's purpose - and that I've *used* £3m of the £8m required capital. After all, the reason this required capital is required is to make sure we have enough assets to sustain deviations from what we expected when we estimated the reserves. At the end of the day though, this is all theoretical attribution. What will happen is that I'll pay out the £3m claim from my cash and get rid of the £3m liability I added.

As you can see, when we pay out claims we're just using cash (assets) to pay for them. The balance sheet gives us a way to think about some of our assets as 'backing' our reserves and other liabilities, some as 'backing' our required capital, and the rest as 'free capital'. The reserves and required capital are often just estimates of things though, with some modelling and things done in the background to come up with numbers. You can certainly scratch your head and think about which asset movements (such as paying out a claim) correspond with movements in liabilities, which with movements in required capital, which with movements in free capital, or some combination of the three though.

 

[o.menary]

Hi,
So if a reserve were to increase/decrease does that impact profit? or does reserves only impact cash flow?

 

[CapitalActuary]

Reserves are a liability item on the balance sheet. If you increase the value of the reserves on the end of period balance sheet, it will decrease the profit (increase losses) over the corresponding period between balance sheets.

This is something separate from cash flows. The reserve increase will likely be due to an increase in the expected future cash flows paid out, this isn’t to do with paying out claims *now* though.

 

[o.menary]

Reserves are a liability item on the balance sheet. If you increase the value of the reserves on the end of period balance sheet, it will decrease the profit (increase losses) over the corresponding period between balance sheets.

This is something separate from cash flows. The reserve increase will likely be due to an increase in the expected future cash flows paid out, this isn’t to do with paying out claims *now* though.

Thank you! Also, can i clarify your defintion of capital please? I understand it is availble funds, however is it raised from shareholder investment or is it funds available to be distributed to shareholders?

 

[CapitalActuary]

Capital can be used to mean either of those things. It can have a pretty broad array of meanings, some of which are themselves very broad.

In my example above I was talking about available capital, which is a label for the amount on the balance sheet which is “the value of assets less the value of liabilities”.

If your question is “where does this amount come from?”, that’s like asking “why do the assets exceed the liabilities?”. This can be because the company has raised money through equity financing rather than using loans, because the company has been profitable over time and not distributed all of these profits out to shareholders, or some combination of these.

Regarding whether “capital” is available for distribution to shareholders: remember “capital” here is just a name for the amount by which the assets exceed the liabilities. You cannot, in a “physical” sense, pay shareholders with “capital”. You can pay them with cash though, in the form of dividends, which would deplete the assets A on the balance sheet and therefore also deplete the available capital (=A-L). We can’t completely deplete the available capital though, because insurance companies have required capital. Only the “free capital” is available to dividend out to shareholders, which is the excess available capital over and above the required capital.

In practice not all of the free capital might be distributed out though. It can be reinvested in the business, held to maintain some level of credit rating, held to make use of future opportunities that come the company’s way, or many other reasons for making your assets exceed liabilities plus required capital (which is the same thing as holding free capital).

 

[o.menary]

Capital can be used to mean either of those things. It can have a pretty broad array of meanings, some of which are themselves very broad.

In my example above I was talking about available capital, which is a label for the amount on the balance sheet which is “the value of assets less the value of liabilities”.

If your question is “where does this amount come from?”, that’s like asking “why do the assets exceed the liabilities?”. This can be because the company has raised money through equity financing rather than using loans, because the company has been profitable over time and not distributed all of these profits out to shareholders, or some combination of these.

Regarding whether “capital” is available for distribution to shareholders: remember “capital” here is just a name for the amount by which the assets exceed the liabilities. You cannot, in a “physical” sense, pay shareholders with “capital”. You can pay them with cash though, in the form of dividends, which would deplete the assets A on the balance sheet and therefore also deplete the available capital (=A-L). We can’t completely deplete the available capital though, because insurance companies have required capital. Only the “free capital” is available to dividend out to shareholders, which is the excess available capital over and above the required capital.

In practice not all of the free capital might be distributed out though. It can be reinvested in the business, held to maintain some level of credit rating, held to make use of future opportunities that come the company’s way, or many other reasons for making your assets exceed liabilities plus required capital (which is the same thing as holding free capital).

Thank you for your help! So to your previous point, higher claims than expected now won't mean a company will increase reserves. However, high claims now will result in the business using more of the funds in the current reserve? i'm finding the concept a bit diffcult to understanding since in pricing, if claims were higher than previously thought, this would influence future prices

 

[CapitalActuary]

If you’re trying to price something using a costs plus approach, this is quite similar to some parts of reserving. In both you are trying to estimate the expected future claims the company will need to pay out. However, in reserving you are estimating the future claims the company will have to pay out for business it has already written, and in pricing you are estimating the future claims for business it has not yet written.

If there is worse than expected claims experience, and the company believes this means future cash out-flows for policies it has not yet written will be higher, then it would likely increase prices, yes. If they also believe future cash out-flows for policies it has already written will be higher, they would increase their reserves. It all depends on whether they think the claims experience so far should affect future cash flows though.

For example, if a large event like COVID hits and insurers have to pay out lots of claims, they might not think this should affect *future* claims if they assume everything will return to normal. On the other hand if they see that miracle medicine XYZ has been invented, and they see their life policy claims dropping compared to what they expected, they might think both future prices should be lower and their reserves should be lower.

 

[CapitalActuary]

Some more (perhaps contrived but hopefully illustrative) examples of when you might change reserves and/or prices:

If regulation is announced saying that you have to charge non-smokers and smokers the same for their life insurance policies, then you’d probably have to increase prices on average. You might not change your reserves though, as long as the regulation doesn’t disallow you from using smoking status to set reserves.

If you find out that loads of your policyholders are into base jumping and you’re getting loads of claims from them splatting into things, you’d probably increase your reserves for your remaining not-yet-splatted policyholders. Rather than increase prices for base jumpers though, you might add an exclusion to your policies and keep the prices unchanged. (Presumably the only reason lots of your policyholders were extreme sports nuts was anti-selection due to no base jumping exclusion and “standard” life policy prices.)