Immediate Annuity Mortality & Interest Broken Down

gm-bioBecause insurance companies use an actuarial “averaging” method when they price mortality based immediate annuity contracts, it’s hard to distinguish the mortality gains from the interest gains being credited to the contract. This lack of transparency causes consumers and agents a like confusion regarding the deal they are really getting. This lack of transparency can be one of the biggest hurdles of explaining just how mortality based immediate annuity contracts work. If carriers were compelled to produce/illustrate a ledger showing the annual guaranteed interest rates and mortality gains they were using to price their immediate annuity payments for survivors of course, it would make things easier.

Theoretically, because immediate annuity payments can span decades, for interest rates; in a normal interest rate market, they would show a bell shaped curve with gradually rising interest rates moving from left (current time) to right (future time). For mortality credits, they might show the percentage attributable to the next years’ gain, assuming the annuitant/insured survived the previous year.  Of course this would serendipitously reveal much about a carrier’s pricing assumptions to competitors. After working in several home offices this suggestion has always been DOA.

Mortality Gains

Beginning with mortality gains, five individuals gather at the start of the year and each contribute $1,000 to a white paper envelope to be opened at the end of the year by any survivors who will equally divide the contents. At the end of the year there happens to be four survivors. Each of the four survivors receives a return of their $1,000 contribution then receives an equal portion the deceased’s $1,000 share or $250. The four survivors walk away with $1,250 each. So, how much interest did they earn? They earned $0 interest because envelopes don’t pay interest. What they each earned was the mortality gain of $250 just because they survived.

Interest and Mortality Gains

Instead of using a white paper envelope, the group leader goes to the community bank around the corner because the bank is offering to credit an outstanding annual interest rate of 2.00% on their $5,000 deposit. So, at the end of the year, they have an additional $100 ($5,000 x 2.00%) to divide. Each of the four survivor receives their capital sum $1,000 plus their mortality gain of $250. The $100 interest gain is likewise shared. Each survivor receives an additional $25 ($100/4 survivors). Therefore, the total survivor gain, mortality and interest, is $1,275. This kind of survivor mortality gain arrangement with interest has played out over hundreds of years since the times of medieval Europe and ancient Rome.

Modern Insurance Company Annuity Contract

Now the group leader gets smart. Instead of using a white paper envelope or a bank savings account, he goes to the opposite corner and walks into an insurance company office to see what it might offer. The insurance company says; ‘purchase one of our annuity contracts today and if you all survive a year from now, we will pay $1,275.00 to each of you’. This doesn’t sound too bad, after all; if they all survive (longevity), the most each can collect from the bank deposit is $1,020.00 ($5,100/5 survivors)! With the insurance company it’s different. If there is only $5,100 and the contact says each survivor get $1,275 for a total of $6,375 ($1,275 x 5 survivors), where does the extra $1,275 ($6,375 – $5,100) come from? It comes from the insurance company that’s where! This why insurance companies have to post reserves. If they underestimate the rate of death, they have to pay up. This is one reason why consumers consider hedging longevity risk just in case you live to very old ages.

What if the annuity contract is purchased and the expected one person dies, how does the insurance company make out? They make out because they were only crediting 2.00% to the contract when in actuality they were earning 4.00% or $200 ($5,000 x 4.00%). So, if one person dies and the insurance company distributes the promised total payment $5,100/4 survivors or $1,275 each, the insurance company actually earned $100 ($5,200 – $5,100).

Ok, but what if two die and there are only three survivors, then what?  The insurance company only distributes $3,825 ($1,275 x 3 survivors).  But they have $5,200 ($5,000 x 4.00% interest) in their bank account.  What happens to the $1,375 ($5,200 – $3,825) balance?  This is retained by the carrier.  But they don’t go out and have a party. These are only five individuals and the insurance company has thousands of contract holders.  What if they incorrectly estimated the rate of death regarding the remaining bunch?  Because of this, most of the $1,375 finds its way back into additional reserves; just in case the company is wrong the next time.

 

Leave a Reply

Your email address will not be published. Required fields are marked *