Jun 1, 2019

Volatility effects on a hypothetical real-wealth-option paid for by spending reductions

This post requires some knowledge of its precursor "Quick and Dirty Experiment with Real Options on Future Wealth vs Spending Choice" and it inherits all the assumptions and analytical models in that post.  The basic concept is to propose the idea of a hypothetical real-wealth-option with a tenure of 30 periods and a strike of initial wealth in real terms -- with all the question marks about those stakes-in-the-ground that were mentioned in the last post.  The underlying is the consumption portfolio with the current "price" being initial wealth at time zero and where the price trajectory is based on a net wealth process that is GBM-like but can go to and through zero. That means that for that underlying we have volatile, randomized returns from which we consume at a constant spend rate. The input arithmetic return assumption is 4% real and spend rates are the thing being varied to see what happens and for which the interval of interest will be 2 to 10%.  Volatility, 12% in the last post, is varied here between 6% 12% and 25%. That's an odd assembly of vol but so be it.  Also, note that the sim iterations were upped to 30k between the 3.5 and 4% spend in order to make sure that I had a good bead on the gap between the output lines in figure 1.

Using the framework from the last post and the new assumptions above, this is what we get:


Figure 1. Real wealth option with changes in vol assumptions


Discussion

It is a bit of a challenge for me to interpret this. It initially looks like that with higher vol we can spend a bunch more but that is probably a flawed interpretation.  The further to the right we go in spending, we know that we will generally impinge on portfolio longevity (if we are working with simulators) or consumption utility (if we were using a life-cycle model).  The further to the left we go, we know we will add to portfolio longevity but also lose, at some point, lifetime consumption utility. We also saw here that volatility all on its own, all else being equal, can suck some life out of portfolio longevity at certain spend rates. That background knowledge breeds caution in my limbic brain when confronted with this chart.

So, if we know intuitively from other analytical perspectives that we shouldn't back up the truck and load up on high-vol-high-spending strategies, what is this telling us (if we believe the model...which I'm telling you to be cautious about)?  The best that I can tell, and I will take reader input, is that if one is going to play the "mess around with higher vol strategies to potentially enhance the period 30 optionality-gained-for-spending-less" game, which we know is potentially destructive to portfolio longevity, then it looks like the biggest bang for your buck, IF [1] you want to do it, is at somewhere around a 4% spend rate (given the fake assumptions...and, oh, by the way: huh? 4%? weird).

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[1] I will say that this whole concept is more or less working at cross-purposes with oneself.  The point in retirement is to decumulate and consume or maybe also create a bequest. It is not typically a time to invest in upside wealth options. That's why I capitalized the IF.  The only reason I was doing this post was to gain some insight into what it looks like when thinking like this.  I realize that there may be some conceptual contradictions at play when messing around with this stuff.

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