A quick, dirty, amateur look at DIAs

A reader asked me recently why, if I had (sorta) proven to myself that by hedging out age 85+ lifestyle with a deferred income annuity (DIA) I could probably increase current spending by up to 15%, I didn't pull the trigger and do so immediately.  No idea, really. I am guessing it is some combo of behavioral reasons and ignorance of the product/concept.  I thought I'd start working on the latter first.  This is my new project: understanding the pros and cons of pooled risk as well as what the annuity paradox means to my own personal planning.



The following is rough.  No inflation is involved here to keep it simple for now.  The following chart is related to 100k in DIA income (don't forget, no inflation adjustments) starting at age 86 and with a purchase option from age 60 through 85:

- the blue lines are my attempt at pricing a DIA premium using survival weighting of cash flows using Gompertz Makeham math and Milevsky's (Halley) equation for annuity pricing at each future age level.  The upper blue is using a 2.5% discount, the lower 3%. No load is applied.

- The red line is a price for a DIA using immediateannuities.com for a dude from FL except I am using monthly income of 8333 rather than annual. One would assume there is a load in there somewhere.

- the dotted line is the AAcalc.com estimate for non-inflation adjusted DIA except that it is using the Society of Actuaries 2012 Individual Annuity Mortality Basic Table with Projection Scale G2. Money's worth ratio is 100% so: no load.

- the green lines are what, ignoring vol and inflation, the premium at each age for my "upper blue line" would grow to by age 86 if I instead invested it and got 5% (lower) or 7% (upper) constant growth.

Can I learn anything from this? Probably not yet.  I was just winging it here while I start reading up on the topic.  Some thoughts, though:

1. I guess my rudimentary pricing math looks like it is at least playing the right game. So far so good.

2. Anomaly 1 (the bump in the red line at age 75) is unknown.  I'd have to ask an actuary.  If pressed I'd guess that it has something to do with the fact that age 75 is an "optimal age" for annutizing so maybe there is a a premium bump for selection hazards or it's maybe surge pricing like Uber.  Maybe it has something to do with the fact that the number of years to earn a return are not great (see the green lines).  Maybe it's just random. Readers? Anyone?

3. Anomaly 2 (the bend up in the AAcalc price at late ages).  I'd have to ask Mr. Irlam at aacalc.  My guess, and I think I read something on this somewhere, is that the SOA projection scale G2 anticipates future gains in longevity.  I could probably duplicate the curve then if I tried to adjust the mode of the Gompertz math in the out years which is more or less the same principle.  Net: I am probably under-pricing late age annuities.  Any actuaries out there??

4. Looking only at the green lines, it looks like at my current age of 59 I might possibly be better off investing what I would alternatively use to insure (ignoring vol and geometric returns over time, etc).  I have future articles to read on optimal timing for annuities and I suspect this kind of thing is part of the game.  Part of me wants to obliterate my superannuation risk right now. Another part says wait. We'll see but I'm thinking it is wait for now.