ASET Sept 2014 Q1 i

[Viki2010]

The solution to the question discusses the Bonus Earning Capacity and states the following:

"The bonus earning capacity can be calculated by equating the Asset Share to a realistic bonus reserve valuation....allowing for some target level of terminal bonus....using the regular bonus as the variable."

The idea here is to solve for RB value. How would the RBR be calculated? Would that be based on BEL for guaranteed bonus? How and where is the target TB allowed i.e. in the RBR or AS or both?

There is a possibility that the RBR is based on SI methods, which is what the Core reading mentions and it might be what is being used here?

 

[Mark Willder]

The solution to the question discusses the Bonus Earning Capacity and states the following:

"The bonus earning capacity can be calculated by equating the Asset Share to a realistic bonus reserve valuation....allowing for some target level of terminal bonus....using the regular bonus as the variable."

The idea here is to solve for RB value. How would the RBR be calculated? Would that be based on BEL for guaranteed bonus? How and where is the target TB allowed i.e. in the RBR or AS or both?

There is a possibility that the RBR is based on SI methods, which is what the Core reading mentions and it might be what is being used here?

A bonus earning capacity calculation is performed for management decision making purposes, so we wouldn't have to use the regulatory solvency basis (although we could choose to). We're more likely to use best estimate assumptions.

A simplified formula for the calculation (assuming everyone survives to maturity) for CWP would be:

Projected asset share = (sum assured plus declared reversionary bonuses) x [(1 + RB) ^ t] x (1 + TB)

We can then solve for the sustainable bonus rate RB, that can be declared up to maturity time t, given that we intend to declare a terminal bonus TB.

In the equation above I have rolled everything up to maturity. An alternative would be to discount everything back to now. The present value of the right hand side would then be a bonus reserve valuation, and the left hand side would be the current asset share.

Best wishes

Mark

 

[Studystuff]

A bonus earning capacity calculation is performed for management decision making purposes, so we wouldn't have to use the regulatory solvency basis (although we could choose to). We're more likely to use best estimate assumptions.

A simplified formula for the calculation (assuming everyone survives to maturity) for CWP would be:

Projected asset share = (sum assured plus declared reversionary bonuses) x [(1 + RB) ^ t] x (1 + TB)

We can then solve for the sustainable bonus rate RB, that can be declared up to maturity time t, given that we intend to declare a terminal bonus TB.

In the equation above I have rolled everything up to maturity. An alternative would be to discount everything back to now. The present value of the right hand side would then be a bonus reserve valuation, and the left hand side would be the current asset share.

Best wishes

Mark

Hi Mark,

can I ask you what the relevance of “assuming everyone survives to maturity” is in the above” ? I’m starting to get confused thinking about where we should potentially have a survival function

 

[Studystuff]

Is it that our projected asset share needs to cover cover maturity payments on those surviving, so we should multiply the right hand side by (1-qx) ?

my idea of an asset share was that it took probabilities into account so I wouldn’t have thought we would need any on the right hand side of the equation. I could well be wrong though!

 

[Studystuff]

Or by “simplifying” do you mean in the case of the gross premium valuation method (so the second part of your answer) because we do need to account for survival probabilities in that case ?

 

[Mark Willder]

Or by “simplifying” do you mean in the case of the gross premium valuation method (so the second part of your answer) because we do need to account for survival probabilities in that case ?

Hi

I was just trying to give a nice simple example that made the key principles of bonus earning capacity clear without worrying about complicating factors. In practice we could allow for mortality as part of the asset share on the left hand side as the cost of benefits is a deduction of the asset share. We'd then have the additional difficulty of deciding what the bonuses would be to calculate the death benefits.

Best wishes

Mark