I understand most parts of the solution in the Examiners Report given on page 8. Question. A life insurance compnay sells only conventional with-profit life insurance contracts. It uses a net premium method for its statutory valuation. (ii) The value of the assets backing with profits liabilities has fallen by 25% since the last valuation. Explain why the satatutory values of the liabilities is unlikely to have fallen by the same percentage? Examiners Solution The impact of a decrease in the value of assets on the valuation basis depends on the mix of assets and how much fall in assets is absorbed by the free estate. Does the free estate means free assets? If the decrease in value of assets is primarily in the value of equities investments then this would be absorbed by a reduction in the investment reserve and would have little impact on the liabilities. Can you please explain this? If the decrease were accompanied by an increase in interest rates this would decrease the value of liabilities because the valuation interest would also rise. Would for example the value of equities and bonds fall because its cashflows are discounted at a higher interest rate? Thus the value of equities and bonds would fall because of an increase in interest rates However, this would not necessarily mean that the value of liabilities would decrease by the same amount as assets because: the assets and liabilties are unlikely to be matched the valuation interest rate change also changes the amount of net premium meaning that the liabilities are less sensitive than assets of a similiar term/ any changes to the implicit allowance for future bonuses will have an impact Can you explain the above bullet point? the increase in the valuation rate may be limited by any restrictions in the maximum reinvestment rate allowed Can you explain the above bullet point? Many Thanks
Hello These 2 points are related I think. I'd look at this as the "assets backing the with-profits liabilities" being equal to the mathematical reserves + some more assets. The types of asset in each part might be different - eg more bonds to back the mathematical reserves, more equities in the other part. A fall in the value of assets only affects the valuation rate of interest if the assets are in the "mathematical reserves" part of these backing assets. More generally free assets and free estate are terms I would always define if I was going to use them myself in an exam. Free assets normally measured on a statutory basis, free estate normally measured on a realistic basis - see the Glossary for the official version of these definitions Higher interest rates are often associated with falls in equity and bond markets. Saying it's because the future cashflows are discounted at a higher rate is one explanation, but there are other (economic) ways of making this link too (eg as in CA1). Can't be sure value of liabilities will go down as much as the value of the assets because you need to consider if and how the future bonus allowance should be changed if asset values/interest rates change. (For example, you might make this allowance by valuing at "i-b" where b is a bonus rate assumption - you need to consider if/how b will change as well as i.) You might not be allowed to use a higher valuation rate of interest because valuation regulations often restrict (ie put an upper limit on) the valuation rate of interest. A distinction might be made between current interest rates (which are known) and future interest rates (which are unknown). These future interest rates (known as the reinvestment rate) might be more restricted because future is uncertain. Hope these help Lynn
