Reserves

[Benjamin]

Hi,

CMP question 18.3 asks about the mortality risk faced on two books:
- RP NP WoL contracts taken out 30yrs ago by men aged 30
- RP NP WoL contracts taken out in the last year by men aged 60

The answer says that the impact is much greater in the second case as in the first case, reserves are large so impact of deaths on net assets is smaller.

I realised I'm not clear on the concept of raising reserves as I thought the reserves would be the same either way, due to the reserve having to reflect the ultimate liability (being that a man now aged 60 dies whenever). I get that relative to policy inception, the asset share will be positive in the first case and probably negative in the second case...

My understanding of what happens at policy inception is that the capital requirement is the difference between the expected liability and the asset share, which is fronted from surplus assets but not clear on how the amount of reserve released each year is determined and ultimately, in the year of death, the company still needs the value of the benefit on hand to pay out the policy so is this not the reserve, which must always be the full amount?

 

[Mark Willder]

Hi,

CMP question 18.3 asks about the mortality risk faced on two books:
- RP NP WoL contracts taken out 30yrs ago by men aged 30
- RP NP WoL contracts taken out in the last year by men aged 60

The answer says that the impact is much greater in the second case as in the first case, reserves are large so impact of deaths on net assets is smaller.

I realised I'm not clear on the concept of raising reserves as I thought the reserves would be the same either way, due to the reserve having to reflect the ultimate liability (being that a man now aged 60 dies whenever). I get that relative to policy inception, the asset share will be positive in the first case and probably negative in the second case...

My understanding of what happens at policy inception is that the capital requirement is the difference between the expected liability and the asset share, which is fronted from surplus assets but not clear on how the amount of reserve released each year is determined and ultimately, in the year of death, the company still needs the value of the benefit on hand to pay out the policy so is this not the reserve, which must always be the full amount?

I think the key thing to note is that the premium will be much larger for a whole life contract sold at age 60 than for a whole life contract sold at age 30 (assuming the same sum assured).

So the policy sold at age 60 will start with a small reserve (and also a small asset share) but this will grow rapidly due to the high premiums.

The policy sold at age 30 will have a smaller premium, so reserves (and asset shares) grow more slowly. However, by the time the policyholder has reached age 60, the reserve will have grown very large due to premiums and investment.

Hopefully this helps the solution to make more sense.

Mark

 

[Benjamin]

Hi Mark,

That's helpful thank you - didn't think about premium size. Still a bit confused about the whole nature of reserves thing though.

Reserves are basically funds put aside to cover the expected liability so early in the policy, mortality rate is low, expected payout is low so reserves are low on a per policy basis.
In the solution to question 17.8 in the CMP (Ch17, page 39), for the fourth policy in the question, the solution states that for a SP NP TA, the reserve decreases towards the end of the policy. I realise that as there are fewer available years to die in, the time in which a claim to be made shrinks. But does this always necessarily outweigh the increasing mortality as the person gets older? And if so, is there a standard point at which reserves peak for a term assurance policy?


And also, if the SP way exceeds the reserve required, does the excess go to free assets?

 

[Mark Willder]

Hi Mark,

That's helpful thank you - didn't think about premium size. Still a bit confused about the whole nature of reserves thing though.

Reserves are basically funds put aside to cover the expected liability so early in the policy, mortality rate is low, expected payout is low so reserves are low on a per policy basis.
In the solution to question 17.8 in the CMP (Ch17, page 39), for the fourth policy in the question, the solution states that for a SP NP TA, the reserve decreases towards the end of the policy. I realise that as there are fewer available years to die in, the time in which a claim to be made shrinks. But does this always necessarily outweigh the increasing mortality as the person gets older? And if so, is there a standard point at which reserves peak for a term assurance policy?


And also, if the SP way exceeds the reserve required, does the excess go to free assets?

We need to be careful here, because we need to consider the cashflows in all future years, and not only the cashflows next year.

So yes, mortality rates do increase over time and this will lead to bigger claim costs in the later years. But this does not mean that reserves will necessarily increase.

A numerical example might help. Consider a six year term assurance. Ignore expenses for simplicity. The premium each year is 10. The claims increase each year as the number of claims increases with age, say 3, 7, 9, 11, 13, 15. So our net cashflows are +7, +3, +1, -1, -3, -5. So as you said, we see things getting worse with age.

Now to calculate the reserves we need to calculate the present value of all future years, and set up a reserve that is equal and opposite to offset the value of the cashflows. Using an interest rate of zero for simplicity, we get reserve at the start of the first year of -(7, +3, +1, -1, -3, -5) = -2. Some countries do allow negative reserves, but others would set this to zero. Note that this suggests that we have made a profit and we get 2 to add to our free assets as you suggested.

we get reserve at the start of the second year of -(3, +1, -1, -3, -5) = 5

we get reserve at the start of the third year of -(1, -1, -3, -5) = 8

we get reserve at the start of the fourth year of -(-1, -3, -5) = 9

we get reserve at the start of the fifth year of -(-3, -5) = 8

we get reserve at the start of the sixth year of -(-5) = 5

So actually the highest reserves occur at the start of year four because this is the point at which we have the most negative cashflows still to come.

The above pattern would change a little if we used more realistic assumptions (eg if we included expenses and interest), but the basic idea that reserves grow to a peak in the middle years and then fall doesn't change.

Best wishes

Mark

 

[Benjamin]

That pattern actually clarifies a lot - thank you! For some reason I had it in my head that it increases continually and was throwing me off.

One final question on reserves (I hope!) - flashcard Ch19, card 3 mentions that a contributor to negative reserves on non-linked business is initial expenses - could you clarify why please? If initial expenses are an outflow, would this not (at time zero before anything has actually happened) require raising the reserve?

 

[Mark Willder]

That pattern actually clarifies a lot - thank you! For some reason I had it in my head that it increases continually and was throwing me off.

One final question on reserves (I hope!) - flashcard Ch19, card 3 mentions that a contributor to negative reserves on non-linked business is initial expenses - could you clarify why please? If initial expenses are an outflow, would this not (at time zero before anything has actually happened) require raising the reserve?

We calculate reserves for in-force policies. So the initial expenses have already happened and don't need to be reserved for.

However, the initial expenses may be recouped from charges throughout the contract. So these charges will be included in the reserves. So big initial expenses will lead to big future charges and hence bigger negative reserves.

I hope this helps.

Mark