Perfect withdrawal rates, trend following, and stochastic longevity

In the post right before this one I linked a paper from the cfa inst. by Andrew Clare and his collaborators on sequence risk and trend following.  I have to admit I haven't read it yet but I have printed it off so I can read it later on a plane flight because I think it'll be interesting.  But before I read it -- since I know he uses the perfect withdrawal rate method (PWR: what withdrawal rate given a particular sequence of returns would work out perfectly to result in a FV of zero, I think is the right way to put it. I'll check on that later) -- I wanted to run a little test with my own PWR tool and my own strategy's trend-informed return distribution to make sure I understand what is going on before I actually start reading.  I figure it'll help me get what he is saying more efficiently.  In addition I want to add an embellishment that I have not seen him or anyone else use: I make the periods over which PWR is calculated stochastic in a way that matches actuarial longevity similar to what is in the SOA annuitant table for me at age 59.  This is not a rigorous analysis by the way, just a quick-hit to see what happens.




A. The Baseline 

First we'll run PWR three ways:

1. [black] a normally distributed 8% return 10% sd. Periods used are a fixed 30 years.
2. [blue] same as #1 but here I let the periods vary using Gompertz math with a Mode of 90
3. [red] use a return distribution from a Vanguard 60/40 fund, let periods vary as in #2

which looks like this. x-axis is the distribution of "perfect withdrawal rates" when simulated/iterated 10k times.  This is maybe a little busy but I didn't want to do too many charts:

If you look closely you can see the effect of variable longevity when going from black to blue.  The PWR's on the left side don't change much because the difference between 30 years fixed and the variable periods that go long isn't that big but when there are variable periods that are short (die early) obviously in retrospect one could have spent more freely (right side).  The red density shows the effect of a less than normal distribution (and a little higher vol). In that world there are scenarios where spending a little less (than in the blue or black worlds) might have been a constructive thing to do.


B. Adding a little trend to the mix.

Now, we'll keep the red Vanguard 60/40 PWR density line and in addition we'll calculate another new one using the return profile of a strategy I use that while it is not 100% trend following it is heavily influenced by trend following.  The net effect is something around 7% return with 4% sd and not normally distributed.  The downside is very slightly attenuated but I have not proved or illustrated that (and the returns only cover 2011-2017, so untested by hard markets). Without making a very good case for it I'll propose that for the moment this can stand in as a proxy for a trend following method. There are other ways to do this I guess but this was on short notice and I had the data handy.  As before I let longevity/periods vary.  When charted it looks like this with the new distribution in grey:

It's hard to make broad conclusions since I was just winging it with one (probably unrealistic) return distribution I had on hand -- and I have not been a very disciplined data scientist -- but in that one very narrow case, it looks like there is a pretty decent effect on withdrawal rates when looking at the left side of the curve.  I tried to make the case before in other posts that this effect isn't necessarily unique to trend following alone but is probably true for any gain in portfolio efficiency but we'll give Clare the thumbs up on trend following today because I like that methodology. I look forward to reading his paper.