Actuarial Outpost
 
Go Back   Actuarial Outpost > Actuarial Discussion Forum > Life
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions



Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 03-16-2018, 08:05 PM
umich umich is offline
Member
SOA AAA
 
Join Date: Mar 2016
Location: Detroit, MI
College: University of Michigan Alum
Posts: 144
Default 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!
__________________
P FM MLC C MFE FAP APC ILA-LP
Reply With Quote
  #2  
Old 03-16-2018, 09:16 PM
PrinceNReserve PrinceNReserve is offline
Member
CAS SOA
 
Join Date: Aug 2012
Posts: 131
Default

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).
Reply With Quote
  #3  
Old 03-17-2018, 01:31 PM
umich umich is offline
Member
SOA AAA
 
Join Date: Mar 2016
Location: Detroit, MI
College: University of Michigan Alum
Posts: 144
Default

Quote:
Originally Posted by PrinceNReserve View Post
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!
__________________
P FM MLC C MFE FAP APC ILA-LP
Reply With Quote
  #4  
Old 03-19-2018, 08:16 AM
urysohn's Avatar
urysohn urysohn is offline
Member
 
Join Date: Feb 2010
Posts: 16,856
Default

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.
Reply With Quote
  #5  
Old 03-19-2018, 11:11 AM
Colymbosathon ecplecticos's Avatar
Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
Member
 
Join Date: Dec 2003
Posts: 5,911
Default

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.
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"


"I think that probably clarifies things pretty good by itself."
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 12:28 PM.


Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.30556 seconds with 11 queries