Q1i) and v) April 2006

[Frances]

Hi there,

Could someone please explain to me the second paragraph under the "Fund 2 : Value of Free Estate" section, i.e.:

"Under option A, for with profits business the liabilities would be equal to
the total earned asset shares. For without profits business, if the asset shares
do not include the value of without profits business surpluses (i.e. option 2)
then the liabilities should equal a realistic valuation, which could be
determined as the statutory valuation less the realistic present value of future
profits. If the asset shares do include the value of without profits business
surpluses (i.e. option 1) then the liabilities for without profits business
should be the statutory valuation reserves (consistent with those that are
assumed in the calculation of future surpluses arising)."

I don't really understand why the without profits liabilities are being valued realistically under option 2, and why they would be valued on statutory basis under option 1.

Also, paragraphs 3&4 under the 'Valuation rate of interest' of part v).

Thanks,
Fran

 

[Lindsay Smitherman]

Hi Fran

It might help to start from the following broad equation for the without-profits business, in a situation where the statutory valuation basis includes prudential margins - as would have been the case in the UK when this question was set (under Solvency I):

Statutory valuation liabilities = Realistic liabilities + present value of future profits (PVFP)

This is because the present value of future profits (PVFP) is basically the release of the prudential margins in the statutory reserves.

Under Option 1, the PVFP has been included in the asset shares that are being used to determine bonuses in the Fund 2: VIF section of the solution. In other words, the PVFP on the without-profits business has been included in the embedded value as part of the Fund 2 VIF. Hence we don't want this PVFP to end up being included in the Fund 2: Value of Free Estate, as then we would be double-counting it in the EV. So we need to define free estate = {assets - statutory liabilities}. If we used realistic liabilities instead, then we would be calculating free estate = {assets - realistic liabilities} = {assets - statutory liabilities + PVFP} and therefore taking credit for the PVPF in both the free estate and the VIF parts of the EV, which would be double-counting.

Under Option 2, the PVFP has NOT been included in the VIF part of the calculation because it has not been added into the asset shares there. Hence we need to value this PVFP within the Fund 2 Free Estate part of the EV calculation. We can do this by using realistic liabilities in the free estate definition which, as we have seen above, gives credit for PVFP in the Fund 2: Value of Free Estate part of the EV calculation as it gives us free estate = {assets - statutory liabilities + PVFP}.

Is that enough to help you unravel this and also to help with what is going on in part (v)? Do come back if not!

 

[Frances]

Thanks Lindsay, that's really helpful!