Mortality charge for Unit linked

[Ivanhoe]

I am unclear about the exact nature of cash flows of Unit linked policies. Some basic issues that I am unfamiliar with. I will be glad if you could respond


1. For a minimum guaranteed sum assured for Unit linked policies, when they charge the unit account by deducting the number of units equal to qx(guaranteed sum assured-Bid value), aren't they actually reducing the unit fund further?


2.If this is anyway followed, this charge will be an inflow to the Non unit account and there will also be an outflow to the same extent, isn't it?

So, what is the risk here? Is it that they underestimate qx? Do we do all the reserving and cash flow forecasting right at the outset or do we determine qx at the end of every year and then smooth it?

Will some one please shed some light on the timing of calculation of cash flows and on the mortality charge?

 

[Lynn Birchall]

I am unclear about the exact nature of cash flows of Unit linked policies. Some basic issues that I am unfamiliar with. I will be glad if you could respond


1. For a minimum guaranteed sum assured for Unit linked policies, when they charge the unit account by deducting the number of units equal to qx(guaranteed sum assured-Bid value), aren't they actually reducing the unit fund further?

Yes

2.If this is anyway followed, this charge will be an inflow to the Non unit account and there will also be an outflow to the same extent, isn't it?

So, what is the risk here? Is it that they underestimate qx? Do we do all the reserving and cash flow forecasting right at the outset or do we determine qx at the end of every year and then smooth it?

Maybe it helps to look at the inflows and outflows of the non-unit fund on an individual policy level first.
For each policy there will be a charge inflow to the non-unit fund of qx(guaranteed sum assured-Bid value) as you say.
The full outflow "guaranteed sum assured bid value" will be paid out only in respect of those policies that actually die.

So the risk to the company is that the actual mortality experience is different from the qx factors that underlie the charges. So yes, basically that they underestimate the qx.

Whether the qx are guaranteed or can be varied by the company during the life of the policy will vary from product to product.

Best wishes
Lynn

 

[morrisja]

Hey, maybe I'm reading into this too much.. but is the first question more about the fact that by deducting a unit charge based on the S@R (SA-UF) we actually increase the S@R (as SA constant but UF drops)?

If so, I think the idea is that while unit reserves have decreased, the charge is allowed for in the non-unit reserve calculation so total reserves will not have changed and should a death occur the situation is no different.


second question - qx is determined from a standard mortality table appropriate to the lives assured (so with adjustments). For reserving purposes qx can be altered as and when you like through a strengthening/weakening of reserves (usually done following experience investigations if required - no arbitrary changes and all that...)

For charging purposes the rates may be reviewable but I don't believe variable mortality rates (so determined at the end of each year) are ever used (this would make setting premiums complicated and be difficult to explain to policyholders).

As far as an "outflow to the same extent" goes - it's likely that mortality charging rates are loaded for some profit (possibly some prudence depending on competitive factors and past experience) so if experience is exactly in line with best estimate mortality rates charges into the non-unit account will exceed outflow due to mortality.


Possibly this isn't what was asked.. but maybe it'll be useful

 

[Ivanhoe]

The full outflow "guaranteed sum assured bid value" will be paid out only in respect of those policies that actually die.

So the risk to the company is that the actual mortality experience is different from the qx factors that underlie the charges. So yes, basically that they underestimate the qx.

Thank you! I am trying to visualise the cash flows in the event of the mortality charges deducted as qx(guaranteed sum assured-Bid value before charge. I understand that this charge would reduce the bid value further..

Now when I am setting up reserves, qx lives are going to die. So there should be an outflow from the non unit fund equal to qx(guaranteed sum assured-bid value after charge) along with the bid value of units that will be paid. So you see that the outflow will always be more than the inflow. I am unable to reconcile this.

 

[morrisja]

Simple hypothetical example time..

100 IID Policies
100k SA
10k UF
qx = 0.01

Charge PH (100k-10k)*0.01 = 900 or 90k total pooled charge
UF now (10k - 900) - 9.1k per policy

1 Policyholder dies as expected given qx

Payout of SA - Mortality Charge - PH UF:

100k - 90k - 9.1k = 900 outflow (the unreconciled amount you're referring to..)

Non unit reserve at this time relating for mortality in this period would be 900 (at least, given prudence will be required) to cover outflow.

I think that is accurate above - though maybe someone else has a different opinion..

I would suggest that mortality rates would be loaded for profit which will offset this. Say use a charging rate of qx = 0.011 for 10% profit. This doesn't answer the question though..

I'd imagine there's an obvious answer to this.. hopefully I've helped to clarify the question for someone who can answer it.

 

[Ivanhoe]

Thank you for your response, Morrisja! Hope some Professor responds

 

[Mark Willder]

Simple hypothetical example time..

100 IID Policies
100k SA
10k UF
qx = 0.01

Charge PH (100k-10k)*0.01 = 900 or 90k total pooled charge
UF now (10k - 900) - 9.1k per policy

1 Policyholder dies as expected given qx

Payout of SA - Mortality Charge - PH UF:

100k - 90k - 9.1k = 900 outflow (the unreconciled amount you're referring to..)

Non unit reserve at this time relating for mortality in this period would be 900 (at least, given prudence will be required) to cover outflow.

I think that is accurate above - though maybe someone else has a different opinion..

I would suggest that mortality rates would be loaded for profit which will offset this. Say use a charging rate of qx = 0.011 for 10% profit. This doesn't answer the question though..

I'd imagine there's an obvious answer to this.. hopefully I've helped to clarify the question for someone who can answer it.

Yes, you're right, there's a flaw in the methodology (but as we'll see later, it doesn't really matter), so the approach given in the notes would be ok in practice.

Strictly (although its beyond the syllabus), we should charge
qx (SA - UF) / (1 - qx). Dividing by 1-qx solves all our problems as we see.

Using your example Charge = (100k - 10k) * 0.01 / (1-0.01) = 909.0909

So the unit fund after the charge is 10,000 - 909.0909 = 9,090.9091

Then if 1% of the people actually do die then we have:
charges of 909.0909 *100 = 90,909.09, which is exactly enough to pay the sum at risk of 100,000 - 9,090.9091 = 90,909,09.

However, this doesn't really matter. Deaths will happen at a later date, by which time the unit fund will have changed anyway. We'd hope that the unit fund has grown, so the sum at risk has fallen, so if we charge slightly too little using qx (SA - UF), then we more than make up the difference after allowing for the investment effect. In practice, mortality charges are monthly, so all the adjustments described here are small anyway (so not material).

In terms of setting reserves. A simple approach should be sufficient, eg set the reserve equal to the charges deducted in the last month.

Interestingly (and again, totally off syllabus) the Americans have solved this. The problem we have in the UK is that the mortality charge is deducted at the start of the period, but the benefits are paid out at the end. The Americans deduct charges in arrears, so they then know exactly what the unit fund and mortality rates are.

I hope this satisfies your curiosity, but as I say, don't worry about it in the exam (its all off syllabus).

Best wishes

Mark

 

[Ivanhoe]

Strictly (although its beyond the syllabus), we should charge
qx (SA - UF) / (1 - qx). Dividing by 1-qx solves all our problems as we see.

Using your example Charge = (100k - 10k) * 0.01 / (1-0.01) = 909.0909

So the unit fund after the charge is 10,000 - 909.0909 = 9,090.9091

Then if 1% of the people actually do die then we have:
charges of 909.0909 *100 = 90,909.09, which is exactly enough to pay the sum at risk of 100,000 - 9,090.9091 = 90,909,09.


Well explained! Thanks

.......so if we charge slightly too little using qx (SA - UF), then we more than make up the difference after allowing for the investment effect....

How so? Do you mean that the error will be less? It will not be eliminated, I suppose

In terms of setting reserves. A simple approach should be sufficient, eg set the reserve equal to the charges deducted in the last month. Interestingly (and again, totally off syllabus) the Americans have solved this. The problem we have in the UK is that the mortality charge is deducted at the start of the period, but the benefits are paid out at the end. The Americans deduct charges in arrears, so they then know exactly what the unit fund and mortality rates are.


This reserve setting should ideally happen at the beginning of every month, is it not? If it is at the end, how does it fit with the definition of a reserve? It will just be a payment for the deaths in that month.