The "stylized" comment merely means the following: trend, following, by it's nature has a convex payoff so that when added as an overlay or as an allocation it has the potential to take the worst and best returns off the tails of the distribution. This creates the possibility of efficiency with a portfolio that can then have roughly the same return for less volatility and less of a fat left tail. I've stylized it here because I don't want to prove it and I need some differences to be more extreme than one might see in the field (I did an attempt to illustrate the idea here). So, in this post I merely "assert" that there are two regimes in question: 4% real return with a 25% standard deviation (my base case) and a 4% return with an 8% standard deviation (an extreme, jacked up, unrealistic trend-following-like scenario). That's pretty far out in left field and not really a proper expectation but I need the distance between the vol assumptions to create the visual. Maybe we can just look at the difference and infer a "tendency" when trying to reduce vol with alternative assets.
Here are some assumptions:
- Case A: returns are randomized normally with a real return of .04 and a standard dev of .25 (red)
- Case B: returns are randomized normally with a real return of .04 and a standard dev of .08 (blue)
- We will call Case B the "trend following on methamphetamine" allocation
- Withdrawal rates are spread out uniformly between 2 and 12 % for each iteration
- A mini sim of the number of years a portfolio lasts is run 100,000 times- "150 years" stands in here for infinity for the portfolios that last forever
- The scatter points are made invisible so that the contour lines can be better seen
- The number of contour levels is set to 20 which might be a little "busy"
- towards the center of the contours are the higher relative frequencies
Note that I will be less interested in summary statistics, significance, and regression than I am in the general shape and movement of things. Besides, I'm not that great at stats. Note also that the contours can be deceiving. In the R function I use, the contour lines are not strictly apples to apples over the two scenarios. Pay more attention to the topography here. Also, at infinity the contours would technically be at the right horizon of 150 years but splay out for visibility.
When I run the sim for case A and case B and do an overlay of one on the other, it looks like this.
Conclusions
As always I am reluctant to over-conclude when using fake, simplified models. But if I was to say anything, I'd say:
1. A 2% withdrawal would effectively be perpetual and is not dissected here. 8-12% I don't recommend to anyone under around 90 though I'll have to check that comment at some point,
2. Over a more plausible (plausible not defined here) range of retirement spend rates, say 3-6 or 7%, I see a fair amount of movement in the mass of portfolio longevity outward. It looks like vol matters in retirement...sequence risk and all that, ya know...
3. For high spend rates, the higher vol strategy, not surprisingly, still offers a type of lottery ticket effect. Without any analysis to prove it, I personally avoid lottery tickets. And high spend rates, too.
4. For early retirees or someone with a very long life expectation, or an endowment, I'd say that the expected horizon might influence the strategy selection but that person would probably be interested in return-neutral vol reduction either way. Hopefully that can be achieved with trend following.
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