Gross premium valuation

[ST6_aspirant]

Hi,

Please refer flash card 11 of chapter 21. Question is: discuss how GPV and NPV each allow for future bonuses.

GPV: value an explicit increase to benefits in respect of future reversionary and terminal bonuses.

Take care with overall choice of method and assmpns to allow for the fact that valuation method will capitalise difference between interest and mortality assumptions of valuation and those assumed in calculation of office premium.

Not sure what the last para means. Yes, reserving basis is stronger than that used in pricing basis to calculate office premium. Not sure beyond that. Thanks.

 

[Mark Willder]

Please refer flash card 11 of chapter 21. Question is: discuss how GPV and NPV each allow for future bonuses.

GPV: value an explicit increase to benefits in respect of future reversionary and terminal bonuses.

Take care with overall choice of method and assmpns to allow for the fact that valuation method will capitalise difference between interest and mortality assumptions of valuation and those assumed in calculation of office premium.

Not sure what the last para means. Yes, reserving basis is stronger than that used in pricing basis to calculate office premium. Not sure beyond that.

The problem with GPV is that it capitalises all the loading in the premium basis. This means that if we price the policy with large loadings (for bonuses or expenses) then we have a small reserve at the start of policy, because the present value of the premiums is a deduction in the GPV calculation (it's not a problem for NPV because we don't value the actual premium paid).

This is a big problem for with-profits because it means that all the bonus loadings emerge on day 1, and then there will be no subsequent bonus loadings for future years. (NPV will release a bonus loading each year from the difference between the actual premium and the net premium).

So we need to be careful to use valuation assumptions that add the bonus loadings back in.

Best wishes

Mark

 

[ST6_aspirant]

Got it. Thanks!

 

[Ivanhoe]

This is a big problem for with-profits because it means that all the bonus loadings emerge on day 1, and then there will be no subsequent bonus loadings for future years. (NPV will release a bonus loading each year from the difference between the actual premium and the net premium).

So we need to be careful to use valuation assumptions that add the bonus loadings back in.



Could you please explain? I am unable to see through what you intend to say..especially what does it mean to say " .....loadings emerge on day 1, and then there will be no subsequent bonus loadings for future years......."?

 

[Mark Willder]

"This is a big problem for with-profits because it means that all the bonus loadings emerge on day 1, and then there will be no subsequent bonus loadings for future years. (NPV will release a bonus loading each year from the difference between the actual premium and the net premium).

So we need to be careful to use valuation assumptions that add the bonus loadings back in. "

Could you please explain? I am unable to see through what you intend to say..especially what does it mean to say " .....loadings emerge on day 1, and then there will be no subsequent bonus loadings for future years......."?

When we price conventional with-profits contracts we use a prudent basis in order to make a loading for future bonuses. For example, we could assume a low rate of investment return, 4% say. Then if investment return is actually 7% each year, we have invrestment surplus of 3% each year that we can use to declare bonuses.

We can then think of the premium as having two parts (we'll ignore expenses for simplicity). The first part Pg covers the guaranteed benefits, and the second part Pb covers the future bonuses. The lower the investment return in the pricing basis, the higher the premium and hence the higher the loading Pb.

Now a net premium valuation only allows for the net premium (which includes no bonus loading), so is similar to Pg. The net premium reserve is the value of the benefits less the value of Pg. Each year a surplus is released as the premium P (=Pg + Pb) is received, but only Pg was expected in the reserves. So the surplus is Pb and is used to pay bonuses.

But a gross premium valuation allows for the full premium (which includes a bonus loading), so is Pg + Pb. The gross premium reserve (ignoring expenses) is the value of the benefits less the value of P. So we have deducted the full value of the bonus loadings from the reserve on day 1, ie a gross premium reserve is lower than the net premium reserve by the present value of Pb. Each year there is no surplus as the premium P is received, which is exactly the same as what has been reserved for. So we have no surplus to pay bonuses.

The solution to this is to use a prudent valuation basis for the gross premium method. If the valuation basis assumes interest of say 3% and actual investment returns are 7%, then this will lead to a valuation surplus to declare bonuses.

I hope this helps. Good luck with the exam.

Mark

 

[Ivanhoe]

Thank you for the elaborate response Professor! I just had a question pertaining to the text...

Now a net premium valuation only allows for the net premium (which includes no bonus loading), so is similar to Pg. The net premium reserve is the value of the benefits less the value of Pg. Each year a surplus is released as the premium P (=Pg + Pb) is received, but only Pg was expected in the reserves. So the surplus is Pb and is used to pay bonuses.

But a gross premium valuation allows for the full premium (which includes a bonus loading), so is Pg + Pb. The gross premium reserve (ignoring expenses) is the value of the benefits less the value of P.

Are you using Pb and Pg interchangeably to mean individual premiums received during the year that support the bonus and the guaranteed part and also as the present values of these portions of the premium to be received in the future?..If you are, is it appropriate?

Also, an example of capitalisation of differences in case of gross premium reserves (GPR) could be if I were to assume a certain mortality rate in pricing and a lower mortality rate in GPR, consequently arriving at lower reserves, and thus could increase profits, but I cannot do that for net premium reserving since, by definition the same assumptions are considered for the calculation of net premium and Net premium reserves. Am i correct?

 

[Mark Willder]

Thank you for the elaborate response Professor! I just had a question pertaining to the text...

Now a net premium valuation only allows for the net premium (which includes no bonus loading), so is similar to Pg. The net premium reserve is the value of the benefits less the value of Pg. Each year a surplus is released as the premium P (=Pg + Pb) is received, but only Pg was expected in the reserves. So the surplus is Pb and is used to pay bonuses.

But a gross premium valuation allows for the full premium (which includes a bonus loading), so is Pg + Pb. The gross premium reserve (ignoring expenses) is the value of the benefits less the value of P.

Are you using Pb and Pg interchangeably to mean individual premiums received during the year that support the bonus and the guaranteed part and also as the present values of these portions of the premium to be received in the future?..If you are, is it appropriate?

No, I'm using Pb and Pg to represent premiums received during the year that support the bonus and the guaranteed part (so I am not using this notation to refer to their present value.

I've said that each reserve allows for the appropriate premium. It does this by taking away the expected present value of those premiums.

Also, an example of capitalisation of differences in case of gross premium reserves (GPR) could be if I were to assume a certain mortality rate in pricing and a lower mortality rate in GPR, consequently arriving at lower reserves, and thus could increase profits, but I cannot do that for net premium reserving since, by definition the same assumptions are considered for the calculation of net premium and Net premium reserves. Am i correct?

No, this doesn't sound right I'm afraid. The valuation basis should be stronger than the premium basis, so the valuation basis should have higher mortality for a policy with a death benefit.

The point about capitalisation of the loadings in the premium basis is that we deduct the full value of the premiums from the reserves. So anything that makes the premium bigger (ie a stronger pricing basis) reduces the reserve at outset.

I hope this helps clarify things.

Mark

 

[Ivanhoe]

I get it now! Thanks..