Trend Following Can Enhance Withdrawal Rates [part1], and
Those posts describe the original article about trend following and withdrawal rates as well as the math that the original authors and others use. Since we determined that trend following is not necessarily the game that is really afoot but rather portfolio efficiency and since early retirees play a different game than traditional retirees, we are going to look at retirement duration effects on PWRs here. That means that this post can be better titled: "Duration effects on PWRs" where PWR means: "the maximum withdrawal rate possible over a fixed period of time if one had
perfect foresight of investment returns." And by duration effects I mean what happens to the distribution of PWRs if we change the duration of periods from 20 to 50 in 3 (10 year) increments (and what happens if, as an extra test, we nudge volatility of returns down by 1 point in each of those scenarios). I had used an arbitrary 30 periods in the last post.
For (stochastic) returns I'll assume 7% linear returns (compounding/geo effects occur within the sim) with 10% standard deviation. For comparison a 60/40 vanguard fund (1994-today) has had, depending on how you measure it, about 8% arithmetic returns and 10% standard deviation. [1] Since we are in a return-suppressed-expectation era I knocked a percent of the 8% figure which might not be enough but who knows. An academic or practitioner or serious amateur might want to be careful here but I am none of those.
For scenarios[2], I had the following:
| dur | |||
| (yrs) | return | sd(a) | sd(b) |
| 10 | 0.07 | 0.10 | 0.09 |
| 20 | 0.07 | 0.10 | 0.09 |
| 30 | 0.07 | 0.10 | 0.09 |
| 40 | 0.07 | 0.10 | 0.09 |
I have no real hypothesis or goal for making conclusions, I just wanted to see what it looked like. So this is what it looks like based on the above:
Figure 1. PDF
Figure 2. CDF
Figure 3. Duration effects on PWRs at conservative percentiles
Table 1. Data used in Figure 3
| PWRs | ||||||
| duration | 5th percentile | 2.5 percentile | ||||
| .10sd | .09sd | diff | .10sd | .09sd | diff | |
| 20 | 6.016% | 6.261% | 0.244% | 5.592% | 5.865% | 0.274% |
| 30 | 4.752% | 5.116% | 0.364% | 4.349% | 4.752% | 0.403% |
| 40 | 4.276% | 4.597% | 0.321% | 3.902% | 4.228% | 0.326% |
| 50 | 4.024% | 4.303% | 0.279% | 3.691% | 3.972% | 0.281% |
Conclusions
I usually like to say a little something but since I just wanted to see what it looked like I will, for the most part, leave the data to its own conclusions. I guess if pressed I'd say that since returns and longevity are always and forever unknown, then in the absence of annuitization: maybe spend less for a while and try to tamp down on vol a little bit if you can for the same level of return. Not sure how helpful that is...
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[1] Using an approximation of G ≈ m - s^2/2 where m is the linear return, the estimated geo return might be closer to 7.5% and in fact the CAGR for 94-2017 is ≈ 7.56% . Note that G ≈ m - s^2/2 is, if I recall, an approximator for an infinite horizon; 20 years is not really all that infinite. There are other ways to get at geo approximations for non-infinite durations that are not addressed here. In any case it does not really matter since I am looking at bigger duration effects primarily and not splitting hairs on compound return estimation over intermediate time frames.
[2] Also, fwiw, note that the script runs this thing 10,000 times in this post; it was 5k in the last.
[2] Also, fwiw, note that the script runs this thing 10,000 times in this post; it was 5k in the last.
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