Trend Following Can Enhance Withdrawal Rates - Part 2

I finally had the chance to read Can Sustainable Withdrawal Rates Be Enhanced by Trend Following? Clare et. al 2017 (though a little quickly; I'll go back).  I was surprised by how familiar it looked. Well, it was familiar because I had run into the math before.  Earlyretirementnow.com (PhD econ) did a cover of it here and I had covered him on the same topic here and here and maybe a couple other places. I have not applied any rigor to make sure it's exactly the same but it's the same in principle even if I'm off.

The Clare paper does the same thing that ERN math does: solve for a withdrawal rate using the following formula (this means that in a simulated and stochastic return environment a withdrawal rate -- "PWR" in this case, over a given period, solved for a fixed end wealth (say zero in my case) -- will be a distribution).

Since the denominator, as Clare et al point out, is a sum of a series of backwards products [1] that looks like this

the result will be sensitive to the sequence of returns "because the later rates appear more often in the expression." Since expression 4 is in the denominator, there will be an inverse relationship: if the "bad" returns are near the end of n periods, expression 3 will be generally bigger (because there are more low returns in expression 4) and vice versa (hope I got that right).  This is insightful to me because I had done the math but not really thought of it like this. I now get how sequence risk works in both theory and practice; I can see it.

The other thing I realized is that I had not only already seen this stuff before, I had also already instantiated this in an R script.  That meant I could check it out with out too much sweat and tears.  So I did this: I started with a fake return distribution of 7% with stdev of 15% [5,000 cycles, n=30]. That stands in for some baseline fake portfolio that seems reasonable to me as more or less equity-like.  Then in two steps I stepped down vol in stdev terms to 10% and then 5%.  7% return with 5% stdev is about what I am running over the last 40 months in a trend following strategy, by the way (actually closer to 4% stdev). The 5% stdev might also be considered a proxy (in this post anyway) for bond-like volatility (what's AGG running these days? 4%?). So three steps: from generalized equity-like behavior to equity-like returns with bond like vol.  If charted in PDF and CDF form it should more or less look like the original paper.  Let's see:

Yes, in fact it looks kinda like the paper and it also looks like the bad PWRs come in a little more than the good PWRs surrender.  I'm not sure how, this morning, to quantify it but I'm thinking that an Omega ratio (ratio of areas under CDF with respect to a threshold) might do the trick.  I'm not up to it today and this is fake data anyway.  We'll call "looks like" a victory for now. [2]

I'll confess here than my speed-read has not made it all the way to the end...yet.  That means they may have made the same conclusion I'll make...It's just that I have been lazy in my reading and so I'll be lazy in my conclusion here (updates promised when I finish) which is that the result above and in the paper is not so much about trend following as such but is rather a more general outcome of all-else-equal volatility reduction (volatility in which the sequence risk is embedded) in the presence of a spending requirement (but we knew that, right?).  Trend following just happens to be easy to backtest and is known to be effective at vol reduction.  The real general conclusion I'd make as an amateur is that anything that serves portfolio efficiency [3] also well serves the multi-period-spending retiree. This is not, I suppose, a very bold or brilliant conclusion.


Part 1 - Trend Following Can Enhance Withdrawal Rates


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[1] You know, this looks pretty straightforward now that I have coded it but for some reason I had a hard time getting my head around how this worked when I first looked at the ERN math.  The sum is pretty simple in retrospect and even the coding wasn't that hard. It just took me a while. Maybe it's an age thing.

[2] I am not confident in my confidence interval expertise (approaches zero most days) so I'll limit my comments to what I see. In the 5000 cycles I ran for the 15% vol scenario, the point where the cumulative empirical % hits 2.5% is around a 2.9% withdrawal rate and is around 5.9% for the (5k runs) 5% vol scenario. However it's analysed or interpreted that would be a positive outcome for a retiree in real life.

[3] I feel like I want to qualify this with something like "...above and beyond two-asset (or more) asset allocation."