A Reasonableness Check on My Backward Induction Optimization

In my recent post (On Hacking Out a (Really) Rough Asset Allocation Optimizer by Using Backward Induction and Dynamic Stochastic Programming) I showed some results from my attempt at trying to come up with optimal asset allocations by using game theory and backward induction. My "game" was to come to some insight on what allocations, at any given retirement year and portfolio level, might be optimal by working backwards from the end of a planning horizon -- an approach that appears to be a rigorous and mathematically/economically correct way to do it.  In my prior post I concluded that I had done "something" and I guessed that it looked "ok" or was at least correct for my "can I even do it?" objective. This was good enough because this was all more of a lark than a serious effort.  I mainly just wanted to see if I could do it but why do something if it's meaningless or wrong.

Today, on the other hand, I was wondering if it was even remotely reasonable as an outcome.  So to cut to the chase I asked Gordon Irlam, the guy whose article sent me down this path and a guy that takes this stuff many, many orders of magnitude past what I can and want to do, whether I was even in the ball park. His reply is below.



Here was my result for 30 years of decumulation-only portfolio management with a 40k spend inflated at 3% (x= plan year, y=portfolio size in a given x year, z/color=optimal allocation to a risk asset):

When I emailed Gordon, his reply was mostly to point me to AAcalc.com (his site) and this past result of his own more sophisticated backward induction (for a "25 year old in 2013, retiring at age 65 in 2053, and withdrawing an inflation adjusted $50k/year in retirement") which looked like the chart below. Note that the big difference here is that his analysis includes the accumulation part of the life-cycle for a 25 year old (or what would be to the left of my chart since mine is, if I remember, for a 58 year old in retirement with only decumulation). So the right side of his chart should look more or less like my whole chart (with significant emphasis on the "more or less"):

aacalc.com/docs/portfolio_size

So, did I get close? Yeah, I think so but let's quote Gordon (who does not know that I am quoting him here): "Yes, your graph appears quite reasonable for fixed withdrawals...congratulations!"

And with that I can now put this backward induction thing to bed for a while...or at least until I can figure out how I might be able to bridge the several degrees of separation that exist between this kind of thinking and the average retail-investor early retiree who will have no idea what this means or how to apply it to his or her own life.