Guaranteed annuity rate and mortality options

[Ivanhoe]

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?

 

[Lynn Birchall]

Hello

I'll just reply about the first question in this post.

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?

I'd say it's because the fixed-interest bonds are a match for the maturity lump sum by term. The bonds are therefore too short to be a match for the annuity guarantee. So, if interest rates are low, then yes the bonds would increase in value, but not by enough.

Best wishes
Lynn

 

[Ivanhoe]

Thank you for the response Professor! I realise that the duration of the bonds would be less and so the increase in bonds won't compensate entirely for the increase in liability. It will still be a hedge to a certain extent though. I feel, the paragraph should have been correctly worded. It is not the risk of lower interest rates but the duration of the bonds not being long enough.

 

[Lynn Birchall]

Thank you for the response Professor! I realise that the duration of the bonds would be less and so the increase in bonds won't compensate entirely for the increase in liability. It will still be a hedge to a certain extent though. I feel, the paragraph should have been correctly worded. It is not the risk of lower interest rates but the duration of the bonds not being long enough.

Fair enough As long as agree that there's a risk to the company that can't avoid because bonds will either be the right duration for the lump sum, or for the annuity, but not both.

 

[Lynn Birchall]

Hello again

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?

Absolutely, the conventional method assumes that 100% exercise and have ultimate mortality.

In making this assumption, we know that it's not true. However, we might be happy to make it because of the cross-subsidies idea, ie we believe that actually the impaired lives who take up the option and the super-healthy lives who take up the option will offset each other.

However, this may not be what happens. In particular the conventional method does leave us vulnerable if the group who don't take up the option (and so who don't contribute their anticipated contribution to the profits) have better than select mortality.

Best wishes
Lynn

 

[Ivanhoe]

In making this assumption, we know that it's not true. However, we might be happy to make it because of the cross-subsidies idea, ie we believe that actually the impaired lives who take up the option and the super-healthy lives who take up the option will offset each other.

However, this may not be what happens. In particular the conventional method does leave us vulnerable if the group who don't take up the option (and so who don't contribute their anticipated contribution to the profits) have better than select mortality.

I agree with this and I have understood the example that acted has quoted. The point that I am trying to make is that the question asks for the difference between the two option loadings calculated using the respective formulae.

The fact that superselect lives might not avail of the option when calculated as per conventional method is not in anyway reflected in the mathematical calculations of the two methods. It is a risk that will materialise only when the actual experience is such (super select lives not exercising). One would then compare this with the option loading that I calculated as per the Conventional method. In fact, you mention this when you say that "it may not be what happens".


The question asks for the reason of the difference in the option cost derived by the two methods. So, at the point of calculation of the option loading, why would the question of cross subsidising arise at all when we are at the point of just comparing the two loadings?

What you are stating is the risk that Conventional method might give rise to Why would this be a reason for the difference in the two loadings?

 

[Lynn Birchall]

Hi again

I'd say this is because our North American calculation is based on 1 particular view of what might happen. In particular, the North American calculation is based on a view that those who do not exercise the option are super-healthy.

So in this question, isn't comparing "conventional vs North American" similar to comparing "conventional vs what happens if experience turns put like the North American assumed"?

Lynn

 

[Ivanhoe]

I'd say this is because our North American calculation is based on 1 particular view of what might happen. In particular, the North American calculation is based on a view that those who do not exercise the option are super-healthy.

So in this question, isn't comparing "conventional vs North American" similar to comparing "conventional vs what happens if experience turns put like the North American assumed"?


Would you have said this had the mortality of those not exercising in North American been "select" or "ultimate"?


Regards,

 

[Lynn Birchall]

Would you have said this had the mortality of those not exercising in North American been "select" or "ultimate"?

Yes, I think so
(Although I'll admit that the fact that you're asking is making me nervous!)

 

[Ivanhoe]

I asked you this because your justification seems to hinge on the fact that the non-exercisers are super select lives in North American and hence the subsidy argument. If they are ultimate of select, I am unsure of its validity. I thank you for your responses anyway. They aid my preparation!

 

[Adam]

It's mentioned that there is "guaranteed lump sum option" for deferred annuity, which converts the annuity income into a lump sum payment at the vesting date. What is the purpose of this option? Or under what circumstance does this option is designed?
My confusion is that if we see deferred annuity as a combination of endowment and immediate annuity then the lump sum at vesting date is simply the maturity benefit from endowment. Hence, does this option means that the endowment maturity benefit is guaranteed?
Thank you.

 

[Mark Willder]

Yes, a without-profits deferred annuity with an option to take a guaranteed lump sum at maturity is effectively the same as a without-profits pure endowment with an option to take a guaranteed annuity rate. Either way, the policyholder can choose between a fixed lump sum and a guaranteed annuity rate.

In some circumstances the policyholder may prefer to take the lump sum option, eg they can spend it now (perhaps if their life expectancy is low) or they can shop around for a better deal from other annuity providers. In other circumstances the policyholder may prefer the guaranteed annuity rate, particularly if annuities have become expensive due to low interest rates or high longevity.

Best wishes

Mark