Trial run: effects on "Perfect Withdrawal Rates" from allocations to trend following

I think I've done this before and I know that others have done something like this in some papers I found on SSRN[1] but I'm trying to think through some things for some future posts. That makes this post a trial run or an early shake out of some R-script just for the hellovit.  Doesn't hurt to think this through again.

The goal

See what happens to the stats and visuals in a PWR (perfect withdrawal rate) distribution by knocking the fat tail off of an input return distribution. This is based on zero real data and is merely a modeling hypothetical that knows nothing outside the model.


The hypothesis and some modeling constraints

With no proof or justification offered for any of this, let's first, for fun, stipulate that:

- Trend following has a convex payoff (see work at thinknewfound.com)
- An allocation to that convexity can help mitigate left-tail events in some (limited) worlds
- A Gaussian mix can represent a plausible return distribution with a fat left tail
- A normal distribution can perhaps represent a return distribution with a trend following allocation in our "fake-world"
- We can ignore the effects of whipsaw and quickly-unfolding discontinuities in the trend strategy
- We can ignore any implications of returns and variance being "only illustrative" in this run
- Trend following will always have a positive return over the long run (no strategy/behavior decay)
- Moment-matching on the first two moments of returns is good enough to look at "the goal"
- Time-dynamics of returns are implicit in the PWR distrb but can't be seen in the input return distrb.
- 30 periods is "just so:" neither too long nor too short and is ok-enough for our run
- We have no knowledge here of the degree of allocation that achieves a tail reduction, it just is
- We don't care about other parameterizations yet

Those sketchy assumptions might mean that:

- We'll see that there is a higher likelihood of higher portfolio-consumption capacity on the margin, using a tail-risk mitigation strategy, all else being equal (i.e., just ex the fat tail); let's call "on the margin" the 5th percentile of the PWR distribution.

The assumptions

Horizon = 30 periods
Iterations = 50k
Normal return input = .05
Normal std dev imput = .14
Fat return is 83% .065/.10 and 17% -.02/.25 ≈ .05/.14 when combined
Terminal wealth at the end of the horizon = 0

The Return Distributions

The PWR distributions

Provisional Conclusions

Since we are in an entirely fabricated world there is not yet much to say about applying this to real people. If this were real and the full tail-clip could be achieved we'd gain about 17% in spend capacity at the 5th percentile but then vanishingly less the higher in the distribution we go.  That just tells me that high risk aversion would probably favor trend following (in this reduced world) if the "premium" for that kind of strategy is real, consistently positive, and persistent over time.  There are probably other alt-risk strategies that might achieve the same thing. Whether options represent a good net deal in this context has, I believe, been extensively explored by others with mixed-to-slightly-negative conclusions but I can't point to anything specific right now.


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[1] Clare, Seaton, Smith and Thomas (2017a), Can Sustainable Withdrawal rates be Enhanced by Trend Following?