Chapter 7 - Contribution Method

[ActuaryBen]

Dear All,

I have a minor question on the contribution method in with-profit contracts. It is crystal clear that the purpose of this method is to ensure proportion of surplus (or dividend) distributed to each policy equivalent to the proportion of their contribution to the surplus.

We have the dividend formulae in contribution method as: Dividend = Investment surplus + Mortality surplus + Expense surplus

My questions are question A, B and C.

A) Is this the correct step/approach in the process?
1) Insurer identify the surplus made by the company in the portfolio
2) Insurer identify the total surplus distributable to policyholder after smoothing process and contingency needs for future adverse experience
3) Insurer identify the surplus for each homogeneous group
4) Insurer identify the surplus for each policy in each homogeneous group

My question arise with respect to how does the dividend formulae is applied to ensure the objective of distributing surplus equally according to their contribution to the surplus.

Assuming:
1) Insurer has made total surplus of 120 in current valuation year
2) Insurer has identified the total distributable surplus of 100 for current valuation year, after smoothing process
3) Policies are grouped into 2 homogeneous group with significantly different average experience.
4) Two policies remain in book in each group in end of current valuation year, after other policies claimed or lapsed.

I believe we can identify the dividend for each group using the dividend formulae above and average experience in each group. For example, if we arive at the following.
Dividend for group 1 = 30 (where actual experience in the formulae is substituted by average experience in the group)
Dividend for group 2 = 70 (where actual experience in the formulae is substituted by average experience in the group)

Question:
B) In fact, are we really able to arrive total dividend for 2 group equal to 100, which equal to the total surplus distributable identified by insurer?

C) How are we going to distribute the 30 to the 2 policies in group 1 and 70 to the 2 policies in group 2 to ensure achieving the objective such that proportion of surplus distributed to each policy equivalent to the proportion of their contribution to surplus?

 

[Mark Willder]

Dear All,

I have a minor question on the contribution method in with-profit contracts. It is crystal clear that the purpose of this method is to ensure proportion of surplus (or dividend) distributed to each policy equivalent to the proportion of their contribution to the surplus.

We have the dividend formulae in contribution method as: Dividend = Investment surplus + Mortality surplus + Expense surplus

My questions are question A, B and C.

A) Is this the correct step/approach in the process?
1) Insurer identify the surplus made by the company in the portfolio
2) Insurer identify the total surplus distributable to policyholder after smoothing process and contingency needs for future adverse experience
3) Insurer identify the surplus for each homogeneous group
4) Insurer identify the surplus for each policy in each homogeneous group

My question arise with respect to how does the dividend formulae is applied to ensure the objective of distributing surplus equally according to their contribution to the surplus.

Assuming:
1) Insurer has made total surplus of 120 in current valuation year
2) Insurer has identified the total distributable surplus of 100 for current valuation year, after smoothing process
3) Policies are grouped into 2 homogeneous group with significantly different average experience.
4) Two policies remain in book in each group in end of current valuation year, after other policies claimed or lapsed.

I believe we can identify the dividend for each group using the dividend formulae above and average experience in each group. For example, if we arive at the following.
Dividend for group 1 = 30 (where actual experience in the formulae is substituted by average experience in the group)
Dividend for group 2 = 70 (where actual experience in the formulae is substituted by average experience in the group)

Question:
B) In fact, are we really able to arrive total dividend for 2 group equal to 100, which equal to the total surplus distributable identified by insurer?

C) How are we going to distribute the 30 to the 2 policies in group 1 and 70 to the 2 policies in group 2 to ensure achieving the objective such that proportion of surplus distributed to each policy equivalent to the proportion of their contribution to surplus?

Hi Ben

I think the process you have suggested is much more complex than the course notes are suggesting.

There is really just one step, rather than the four you suggest. The insurer applies the formula for each policy individually using the average experience of the group that the policy is in. The insurer then might calculate that a particular policy has a surplus of 30. It might choose to pay out only 80% say of this surplus (for smoothing and to hold back some surplus for a terminal dividend). It then pays out a cash dividend of 80% of 30 = 24. Or is could apply the 24 as a single premium to buy more benefits.

So the company does not need to calculate the surplus of the entire company in the way you suggest. The calculations can be done on a policy by policy basis. This ensures that each contract really does get the surplus that it generates.

Best wishes

Mark

 

[ActuaryBen]

Hi Mark,

Thanks for you clarification! In fact, the approach clarified by you is much more direct and simpler! i think i got the concept now. Thanks so much!!