Negative liabilities

[Joseph Barnett]

Hi,

As I'm doing more questions leading up to the exam I'm noticing that I'm really not that confident with how a life insurer's balance sheet is put together, and I'm blagging my way through a lot of questions where that's important background knowledge.

I'm probably confused about a lot of things but for the sake of asking one straightforward question, I think I'm mostly hung up on the concept of a negative liability vs. a positive asset. It's mostly embedded value questions that are making me sweat but I think it probably applies to any question where I really have to think about what would happen to the balance sheet. To keep things simple I'll just restrict my question to a market consistent embedded value calculation.

I'm always tempted to treat premiums and charges as assets and benefits and expenses as liabilities, but on reflection I think this is all liabilities. I think what's always stopped me from making that jump is that if a contract is purely profitable it will just look like a negative liability, which takes some getting used to.

Now... for embedded value we have the two components - net shareholder assets plus present value of future profits. If a unit-linked policyholder decided to throw in a big premium, what I think would happen is:

1. The company creates a bunch of units for the policyholder, which sit on the liability side
2. The company buys a bunch of assets to back the units, which sit on the asset side
3. The company expects (hopefully) more from the contract due to a higher fund value (from % charges), and this sits on the liability side as a negative figure

So if I'm right about that, then a big single premium of X is added to a unit-linked policy will increase the assets by X, and the BEL by slightly less than X. And therefore, if we're talking about EV, I guess this would mainly hit the net asset component rather than the PVFP component. Is that right? My poor brain really wants to have a nice simple picture where premiums and charges mean profit and profit means increase in assets, but I think at this point in my actuarial career I should maybe just get used to the idea that insurance profits mostly come from under-performing liabilities...I never would have guessed that accounting would be the hardest part of being an actuary!

I'd appreciate if someone could have a look through my explanation and tell me if I'm getting it or if I'm just talking nonsense.

Thanks,
Joe

 

[Mark Willder]

Hi,

As I'm doing more questions leading up to the exam I'm noticing that I'm really not that confident with how a life insurer's balance sheet is put together, and I'm blagging my way through a lot of questions where that's important background knowledge.

I'm probably confused about a lot of things but for the sake of asking one straightforward question, I think I'm mostly hung up on the concept of a negative liability vs. a positive asset. It's mostly embedded value questions that are making me sweat but I think it probably applies to any question where I really have to think about what would happen to the balance sheet. To keep things simple I'll just restrict my question to a market consistent embedded value calculation.

I'm always tempted to treat premiums and charges as assets and benefits and expenses as liabilities, but on reflection I think this is all liabilities. I think what's always stopped me from making that jump is that if a contract is purely profitable it will just look like a negative liability, which takes some getting used to.

Now... for embedded value we have the two components - net shareholder assets plus present value of future profits. If a unit-linked policyholder decided to throw in a big premium, what I think would happen is:

1. The company creates a bunch of units for the policyholder, which sit on the liability side
2. The company buys a bunch of assets to back the units, which sit on the asset side
3. The company expects (hopefully) more from the contract due to a higher fund value (from % charges), and this sits on the liability side as a negative figure

So if I'm right about that, then a big single premium of X is added to a unit-linked policy will increase the assets by X, and the BEL by slightly less than X. And therefore, if we're talking about EV, I guess this would mainly hit the net asset component rather than the PVFP component. Is that right? My poor brain really wants to have a nice simple picture where premiums and charges mean profit and profit means increase in assets, but I think at this point in my actuarial career I should maybe just get used to the idea that insurance profits mostly come from under-performing liabilities...I never would have guessed that accounting would be the hardest part of being an actuary!

I'd appreciate if someone could have a look through my explanation and tell me if I'm getting it or if I'm just talking nonsense.

Thanks,
Joe

Hi Joe

I think you have this spot on.

Reserves are the expected present value of Premiums/Charges less Claims less Expenses. So yes, premiums and charges are considered on the liability side of the balance sheet and have the opposite sign to the claims and expenses.

We'd hope that the premium/charges would exceed the claims and expenses on a best estimate basis over the life of the contract, so we'd make a profit. So yes, we'd get a negative reserve at outset on a market-consistent basis for a regular premium policy at outset.

So yes you're right about your unit-linked contract. The assets go up by the premium (less some expenses). The unit reserve goes up by the premium (less some initial charges) - these probably largely cancel out. The non-unit reserve should gives a negative impact because we expect to make profits out of future charges on a market-consistent (best estimate) basis.

Best wishes

Mark

 

[ActuarialKropotkin]

Hi Mark

I'm a also bit confused about negative liabilities from an accounting / balance sheet perspective. I am comfortable with the concept of negative liabilities for profitable risk business (or, similarly, negative non-unit reserves for profitable unitised business). Negative liabilities arise simply because of the fact that EPV(Claims + Expenses) < EPV(Premiums) when contracts are priced profitably.

What I struggle with, however, is what this means for the balance sheet. From accounting fundamentals we have Assets = Equity + Liabilities, so generally an increase in Liabilities would be coupled with an increase in Assets. Does this then mean that holding a negative liability is coupled with an equal decrease in Assets? So, for example, if writing a profitable term assurance policy results in a negative liability of -100 at the outset, would that then mean a decrease in assets of 100? How would assets be affected by this (my understanding here is that Equity is not affected)?

I'm struggling to "see" or interpret the impact on the asset side of a negative liability, because, in my mind, a negative liability is basically an asset. Therefore, if the assets do in fact decrease, then zeroising the negative liability would again mean that Assets would increase, resulting in a net zero impact, i.e. there never really was any "change" in assets to begin with?

Please explain the flaws in my reasoning above, because this is creating confusion in my mind about a topic that I thought I understood.

 

[Mark Willder]

Hi

It's probably easiest to see what is going on with a numerical example.

Consider an insurer with assets of 100 and liabilities (reserves for insurance contracts) of 80. It then has free surplus of 100 - 80 = 20.

Now lets see what happens if the company writes a block of profitable term assurance business. The contract has high initial expenses, but the future premiums are more than enough to cover future claims/expenses and to recover these high initial expenses. So cashflows are times 0 to 5 might be: -10, 3, 3, 3, 3, 3. So ignoring discounting to make the calculations easier, we see that this contract would have a negative reserve 5 x -3 = -15 (because as you said, the EPV of the premiums is bigger than the EPV of the claims and expenses) and makes a profit of 5 x 3 -10 = 5

The immediate impact on the balance sheet would be a fall in assets of 10 and a fall in liabilities of 15. So yes, a fall in liabilities is often associated with a fall in assets, but they will not be equal in size (we'd expect assets to fall by less than the liabilities if the contract is profitable). So the company now has assets 100 - 10 = 90, and liabilities 80 - 15 = 65, and free assets 90 - 65 = 25. So the free assets have increased reflecting the expected future profits (this is where your logic had gone wrong as you had assumed that the free assets wouldn't change).

I hope this numerical example helps to explain what is going on.

Best wishes

Mark