Part 5 - Asset Allocation and Portfolio Longevity with (Lower) Spend Rates

 This post is part 5 of a series on Portfolio Longevity, a series made up of these links:

• Asset Allocation and Portfolio Longevity with High Spend Rates
• Part 2 - Asset Allocation and Portfolio Longevity with High Spend Rates
• Part 3 - Asset Allocation and Portfolio Longevity with High Spend Rates
• Part 4 - Asset Allocation and Portfolio Longevity with (Moderate) Spend Rates

The point of this post is to 

- 1) drop the spending from 4% to 3% (i.e., lower spending). and 

- 2) look at the impact of "asset allocation choice" on portfolio longevity, using the same set-up we started with in the first link but with the following provisos for what I have changed since then. Here is what is different now:

Changes since the last post:

• Spending -- The first link used an 8% constant real spend rate where I called it "high." Then I moved it to 4% which I called "moderate" or at least Bengen-esque.  Now I wanted to go "low" but since I consider 2% vaguely perpetual, I split the difference here and went to 3%. This is mildly felicitous because shortly after I sorta-retired at 50, I had a 50 year horizon and I went from 7% to 3% in a very very hard, aggressive lifestyle change. This means that this post may make more sense to me than to you. 3% is solid for a 50yo, btw, but a little cheap at 90, but that is another post. 
  
  
• Iterations -- I upped the iterations to 300,000. That sounds insane but: a) it didn't take that long, and b) because the 3% spend rate throws so many portfolio longevity (PL) year observations into the infinity range (over 100y in my code) the remainder of the PL distribution on the left, under 100 years, falls into a "small numbers problem" and the distributions are not very smooth and don't take pretty pictures. 
  
  
• Percentile Sequence -- In the prior post, an examination I did was to look at the PL distributions in terms of percentiles for each portfolio (allocation). In the last 4 I looked at increments of .10 from 10th percentile to 90th. That's fine for "high spending" but now that we are approaching a long, sustainable spend (say, 3), more portfolios will last to eternity, so now I want to puff the left tail a bit so I am here examining the lower percentiles: .05, .10, .15, .20, .25. Since good outcomes (portfolio lasts forever) are boring, that means that the left tails (ie we don't survive very long in portfolio terms) are interesting and worthy of a look-see. Hence the focus on the lower percentiles here.
  
  
• Returns are lower -- As in the last post, I tamped down on the real return assumptions amongst the portfolios to reflect my current worries about inflation, which are understated here.  In my case, if, say, the "lower risk" portfolio has a real return of 1 and we expect 3% inflation -- Ha! in the current environment, geezus --  that means what? 4% nominal for the low risk portfolio. Meh but sorta makes sense, I think, but could be even lower or negative or TIPS or annuities or idk. Comment away below. This is my sorta weak, abuse-me assumption, right?
  So: say N[1,4] and N[7,25] which are fake but I needed something.

The PL Distributions

I'm not going to recast all the assumptions and setup here I did before. I mean, I can barely see the screen with my eye crud these days so forgive me. See the first and then subsequent links at the top for all the assumptions and background.  But, taking an "EF" given in the 3rd and 4th post (see 3rd and 4th links at top) and running now a 3% spend rate, I get the following distributions for PL: 

Figure 1.

The Right and Left Tails by Portfolio

Now, if we examine the left and right tails of these distributions in Fig 1, one portfolio at a time, for entirely arbitrary thresholds of: 1) left tail: don't fall below 10 years, or 2) right tail: "let's reach beyond 50 years," and still denominated it in probability terms, the left and right tails might look like this for this particular portfolio and spend setup:

Figure 2

The "Happy" Internal Distributions and the Left Tail

Now, if we render all of this, as we did in the prior posts, in percentiles for each distribution of a portfolio, and here, again, as noted above, we are working the left tails and doing so with .05 to .25 in .05 increments for the cum percentiles, we get more or less the same chart we had in post 3 and 4 of the series but now with the 3% spend rate:

This is a more interesting chart than the last few posts, btw. Idk if it is the lower spend rate or the lower percentile efforts: it is more appealing to me than the last few posts.  Maybe this is because the assumptions are a bit more realistic and it is all a bit closer to my own situation at one point in my life:  1) my horizon is probably still somewhere between 25 and 40 y away, and 2) My spend rate ten years ago went from 7 to 3 (oooof that was hard) and I still kinda know what the spend rate is now but I'm pretty sure it's not 3 but close enough for today. ie I can "see" this chart better than the others. 

Interpretation?

I guess the implicit take away from this, something we can't really see unless we take a close look at the past several posts, is that spending is a big fat goose to portfolio longevity. Whatever, that is another post. Let's look at what we have and interpret that. In general, all I can say is this:

If you want to avoid failing a 30Y metric at a 5% PL level [1] and also have a reasonable attack on 50 years at a 20th+ percentile level then it looks like both low risk and high risk portfolios "suck," something I have harped on here forever.   

• The low risk portfolio won't get you 50 years, if that is a goal,
• The highest risk[2] portfolio will give you infinite PL at the 20th percentile and above, but
• The highest four risk portfolios will FAIL the 30 year horizon at the 5th percentile of PL
• If one were to want, as a policy choice, to avoid failing the 30y hurdle at a lower risk level (5th %tile of PL), and also to push towards 50 years -- or legacy estate problems, too, as it were --  somewhere around the 20th percentile of PL, then there appears to be a sweet-zone between [given this parameterization only!] allocations to risk (this post's portfolios) between 30-70%. This absolutely 100% does not contradict anything I've ever done here (given the 3% spend, yeah). It appears to be a felicitous zone that I can't defend here other than using figure 4 but it is starting to cohere. 

As in prior posts, and contra most finance papers I read, there is no real optimal outcome here or anywhere, really. What there is is: 1) a policy framework that is based on some foreknowledge of how all this works, and 2) an implicit (and un-described here) adaptation and control process to keep the portfolio and spending "in bounds" to achieve the goal assuming stable assumptions. If they are not stable then all bets are off. 

---------------- NOTES -----------------------------------------

[1] This is arbitrary and maybe has nothing to do with optimization. Yaari had a good quip on statistics in his 1965 paper. If your going to use P levels to optimize maybe the P level, usually set to an arbitrary 5, also needs to be optimized as well. Since I don't really know what I'm doing, I'll use a bunch of P levels and let anyone decide. TBD. 

[2] under this post's fake parameterization. You might have to do a custom thing to get closer to reality...