I
Ivanhoe
Member
April 2013 Q4. Part i (First 2 paras of the solution) Risk of a guaranteed annuity from the proceeds of a without profits endowment lumpsum
The main risk to the company is that at the point of exercise the value of the backing assets will be insufficient to meet the guarantee. The main investment risk is interest rate risk. The precise nature of the underlying investment risk depends on how the company decides to invest to meet the guarantee.
The company might decide to hold fixed interest investments which match the maturity lump sum benefits by term. In this case, the risk is from interest rates at the guarantee date being lower than those used within pricing
The fixed interest bonds are in fact a hedge for the guarantee as they would increase if the interest rates fall, isn't it? How are they mentioned as a risk? I can understand that if unit fund were to back a guaranteed annuity, then an increased unit fund would imply a greater cost of the guarantee. This is a without profit contract though and the guarantee is only in respect of the sum assured at maturity. So, any incremental value above this is for the company to keep. Why is this stated as a risk here?
April 2010 Q6 Part iii.. Difference between the option cost derived by North American and Conventional methods
Part of the solution
The key reasons that the cost for the conventional method is lower is because there is the assumption that 100% of policyholders take the option and the assumed mortality is different. Those with healthier lives have mortality rates which are lower than those assumed in the new policy pricing basis, even allowing for the selection allowance in the pricing.
These policyholders are paying more than the cost of their benefits and so are subsidising the policyholders in ill health.
All lives have "ultimate" mortality at the point of option exercise as per the solution for conventional i.e their mortality is higher and not lower, I believe.
Moreover, I fail to understand the subsidising argument. In Conventional, it is assumed that everyone exercises and everyone has an "ultimate" mortality. So, it is like everyone pays their respective share of the option cost due to them being charged "select" rates. Where does the question of superselect lives cross subsidising those having "worse-than-select" mortality arise? There are no superselect rates in the calculation. Am I missing something here?
I believe that the difference is due to the fact that in the North American method, there is a certain proportion of lives who has a worse than ultimate mortality. They are paying far lesser than what they should have paid. This difference is borne solely by those who exercise and not by everyone.
This does not mean that there is cross subsidy in Conventional and not in North American, because the assumption in Conventional is that everyone has ultimate mortality, everyone opts, and everyone pays. Is my understanding correct?
Would this then mean that if mortality in North american is "ultimate", then the cost of the option should be the same as that in conventional, despite only 30% of the policyholders exercising (since the policyholders assumed to exercise are paying, which is 30% in North american and 100% in Conventional)?
Will you please respond?
The main risk to the company is that at the point of exercise the value of the backing assets will be insufficient to meet the guarantee. The main investment risk is interest rate risk. The precise nature of the underlying investment risk depends on how the company decides to invest to meet the guarantee.
The company might decide to hold fixed interest investments which match the maturity lump sum benefits by term. In this case, the risk is from interest rates at the guarantee date being lower than those used within pricing
The fixed interest bonds are in fact a hedge for the guarantee as they would increase if the interest rates fall, isn't it? How are they mentioned as a risk? I can understand that if unit fund were to back a guaranteed annuity, then an increased unit fund would imply a greater cost of the guarantee. This is a without profit contract though and the guarantee is only in respect of the sum assured at maturity. So, any incremental value above this is for the company to keep. Why is this stated as a risk here?
April 2010 Q6 Part iii.. Difference between the option cost derived by North American and Conventional methods
Part of the solution
The key reasons that the cost for the conventional method is lower is because there is the assumption that 100% of policyholders take the option and the assumed mortality is different. Those with healthier lives have mortality rates which are lower than those assumed in the new policy pricing basis, even allowing for the selection allowance in the pricing.
These policyholders are paying more than the cost of their benefits and so are subsidising the policyholders in ill health.
All lives have "ultimate" mortality at the point of option exercise as per the solution for conventional i.e their mortality is higher and not lower, I believe.
Moreover, I fail to understand the subsidising argument. In Conventional, it is assumed that everyone exercises and everyone has an "ultimate" mortality. So, it is like everyone pays their respective share of the option cost due to them being charged "select" rates. Where does the question of superselect lives cross subsidising those having "worse-than-select" mortality arise? There are no superselect rates in the calculation. Am I missing something here?
I believe that the difference is due to the fact that in the North American method, there is a certain proportion of lives who has a worse than ultimate mortality. They are paying far lesser than what they should have paid. This difference is borne solely by those who exercise and not by everyone.
This does not mean that there is cross subsidy in Conventional and not in North American, because the assumption in Conventional is that everyone has ultimate mortality, everyone opts, and everyone pays. Is my understanding correct?
Would this then mean that if mortality in North american is "ultimate", then the cost of the option should be the same as that in conventional, despite only 30% of the policyholders exercising (since the policyholders assumed to exercise are paying, which is 30% in North american and 100% in Conventional)?
Will you please respond?