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#1
03-16-2018, 08:05 PM
 umich Member SOA AAA Join Date: Mar 2016 Location: Detroit, MI College: University of Michigan Alum Posts: 144
Mortality Gain/Loss Calculation

Hi everyone, I'm trying to understand the mechanics behind the mortality G/L calculation. I am reconstructing my company's payout annuity rollforward analysis and one of the most important lines people always look at is mortality gain/loss. The workbook already has a formula, which I am trying to understand. Mortality G/L is calculated as (Actual Reserve Released - Expected Reserve Released) - (Actual Death Benefit - Expected Death Benefit)

The way I understand the first part is that a release in reserve decreases our liabilities, so if the actual res released is greater than the expected, it indicates a gain. But the second part seems counterintuitive, why is it carving out the delta of actual and expected DB when the formula is intended to calculate mortality G/L?

Thank you!
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#2
03-16-2018, 09:16 PM
 PrinceNReserve Member CAS SOA Join Date: Aug 2012 Posts: 131

I had a fun time at work once figuring out why that formula works

What you are seeing is that the reserve gain = mortality gain (act. res release - exp. res release) + payment gain (exp. payment - act. payment).
#3
03-17-2018, 01:31 PM
 umich Member SOA AAA Join Date: Mar 2016 Location: Detroit, MI College: University of Michigan Alum Posts: 144

Quote:
 Originally Posted by PrinceNReserve I had a fun time at work once figuring out why that formula works What you are seeing is that the reserve gain = mortality gain (act. res release - exp. res release) + payment gain (exp. payment - act. payment).
That makes sense! Thank you!
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#4
03-19-2018, 08:16 AM
 urysohn Member Join Date: Feb 2010 Posts: 16,856

The death benefit component is there because you are looking at a payout annuity. A plain vanilla payout annuity would have no death benefits, so that both parts of that second component would be zero.
However, some payout annuities would be classified as a "refund annuity". This would be like a Return of Premium feature -- if the annuitant dies before the sum of annuity payments equals the initial premium, then there is a lump sum payment at time of death to make up the difference. Once the total annuity payments exceeds the initial premium, no death payment would be made.

It makes more sense to lump this special payment in with "mortality gain" than it would to include it with a "payment gain" (expected annuity payment - actual annuity payment; there's a good chance this is simply suppressed in your rollforward calc as it should almost always be zero) since it is triggered by the death of the annuitant.
#5
03-19-2018, 11:11 AM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,911

I have a somewhat related question.

Suppose that the annuities are on retired workers and that they continue to pay, say 75% of the benefit after the worker dies provided that the spouse is still alive.

If the insured dies, the insurance company gets notified somehow, probably by the bank where the payments are made. But how does the insurance company know about spouse deaths that precede the worker's? Presumably these would free some reserves.
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