Effect on Cumulative Fail Rates by Hedging Longevity Risk With a Deferred Annuity

I wasn't really expecting this chart to look like this but it totally makes sense now that I look at it again.  In this particular case I made my 'theoretical' retirement model invest into a small deferred income annuity (enough to hedge out ~90% of 85+ spending risk).  Then, in order to finance that purchase, I sucked the related capital (the stuff required to make the annuity investment) out of my "starting pile of capital" in order to buy the annuity.  My sorta-kinda-goal in this vague quasi-analysis that I was trying to do was to reduce my overall late-age spending risk by converting some of my general risk-capital from "open and unencumbered" to "closed and dedicated to after 85 spending commitments."  This chart is what it looked like in terms of the changes in fail-rate risk. I guess that one of the basic ideas here is that one can't create something from nothing. In this case, in order to mitigate late life spending risk, the money has to come from somewhere. And in this case it comes from "early" consumption risk and then that is converted here to the risks that are "late."  If I had to characterize the chart, I'd have to say that the early risk-costs might have to be worth the late-age benefits. But then again, Ill have to think about this...  

Black line: my fail rate estimate before annuity hedging
Blue line: my longevity-adjusted fail rate estimate after hedging with a deferred income annuity
Personal Data...


A sharp eye will notice that while I thought at the outset that I was hedging out 90% of my longevity risk I did not nearly achieve that goal. That means that either I have a bug in my simulator, which is always plausible, or I don't really understand how much risk there is. Either way that will be another post.  Most likely, it's an artifact of a low base case fail rate. It's like one of those annoying life lessons I monologue at my kids: you can't, in the end, at the margin, eliminate all risk.


[postscript]

Here is another result that surprised me. I ran this while my kids were eating lunch.  I changed the assumptions to generic (standard stuff: age 65, $1m, 60/40, 4% spend, etc).  I expected the hedge to work but now I remember something from Pfau about how age and capital will affect whether it makes sense to hedge.  In this case here, the 65 year old has to spend 20% of his capital (200k.  This is based on a quote from immediateannuities.com for 8k of monthly income that splits the difference on the age85+ spending.  40k today at age 85 at 3% inflation is 72k/yr and at age 105 it's 130k/yr, so the "split diff" of 100k/12 ~= 8k/month...give or take) to hedge out a major chunk of late age spending.    In this example, the hedge does not look constructive when it comes to the baseline goal of life-cycle risk management...