An early-retirement-stochastic-PV game

This post takes off from a previous post on stochastic present value(SPV) where I was trying to look at things from the point of view of an early retiree and think about what my future SPVs might look like from today's standpoint (I don't know, maybe I am budgeting for future balance sheets or mindlessly fearful or just messing around with numbers.  I doubt there is a practical usefulness here).  In other words, if I projected/inflated my current spending x% to next year (3% in this example) and then ran a SPV calc as if I was starting from next year's stand point with entirely new longevity assumptions, what would the SPV look like in next year's dollars...and then I inflated today's spending two years to the year after next year with that "platform's" new longevity expectation and so forth.  Is this legit? No idea.


At the time of the last post I used a simulation approach that did not randomize the discount rates in the denominator; just the spending in the numerator was randomized.  I tried to do that denominator randomization today (idea borrowed from a couple papers by D Mindlin on pension liability valuation).  My confidence in my results is maybe 80%.  I made coding mistake after mistake over a much longer time than I wanted.  This was just supposed to be a few minutes of work but two hours later...  I think I fixed them all but my confidence took a hit (by 20% I guess) and like a bad manufacturer I am probably rushing product out the door.  The non-standard amateur math I used to represent today's effort, by the way, looks like this (to me anyway):

where Ct is a custom consumption path (think 100k constant in this case, but here randomized with an random pull from historical inflation data and a spend variance as well).  D is the randomized discount rate. N is a random age based on Gompertz math and L is 120.  spv is the resulting distribution of NPVs for some given start age. Otherwise the assumptions are all the same as in the link above...except that I accidentally shifted the longevity mode assumption in a couple years but I don't think that affects this too much. I call each age below a "platform year" because I treat it as a new starting point with new assumptions for spending and longevity that are tuned to that particular age. 10000 iterations run at each platform age.

With the denominator properly randomized, the analysis in the last post now looks like this.  The main difference here is that I have charted the mean and now also the standard deviation of two different assumption scenarios:
 

Red - mean NPV, uses a discount assumption with mean .03 and var of .04 (arbitrary/illustrative)

Blue - mean NPV, uses a discount assumption with mean .07 and var of .10 (arbitrary/illustrative)

Dotted lines are 1 standard deviation from the mean of the NPV distribution at each platform age

Why did I do all this? Evidently I have too much time on my hands since this is basically the same result as before but now with a visualization of some age-based uncertainty. That and not everyone buys into the spv idea I hear.  I'm not sure if this post adds much but it does show two things, if we believe my code, which is pretty sketchy right now...  

One, this shows that SPV is more or less MC simulation but turned around backwards.  The further away from starting (terminal) assumptions, the more uncertain things are.  In MC sims that project things forward, the uncertainty spreads out when going left to right (further from starting assumptions). In SPV analysis that calculates PVs, the uncertainty expands when going right to left (further from terminal age).  It's the same idea and same processes underneath that make that happen.  

Two, this shows some of the reasons that early retirement is a tougher nut to crack than traditional. The dispersion of uncertainty -- which depends on distance to terminal age and assumptions about returns and volatility -- is relatively high today for an early retiree compared to tomorrow when we'd be a little older and closer to a more certain path.  This is probably why younger retirees tend to be fairly frugal early and keep money in reserve. Beyond that there is not much I can say with any precision.