Aug 8, 2022

Part 4 - Asset Allocation and Portfolio Longevity with (Moderate) Spend Rates

Warning: this is unfinished so TBD...

 This post is an extension of the previous three posts:

where the main explanation of the set-up is in the first link and a revision to some key parameters in the third link. The quick explanation for this post is that I am trying to look at the interaction between: a) an oversimplified and reductive and not all that realistic set of portfolio choices and b) portfolio longevity in years. And I want to take that look without dwelling on planning horizons or human mortality (might here though). 

The major apples-to-oranges shifts I must note here are: 

  • Returns were tempered downward a little bit for realism of a sort, and

  • Spending is now set to 4% not eight. I call that moderate because a constant 4 is pretty high imo for a 50 year old but pretty low for an 85 year old just retiring. It is also the Bengen number except he only looked at one very specific portfolio constrained to one time in history. 

  • I ran 200,000 iterations (not 20k) to smooth out the left tails since many observations are hidden in the right tail at 100 years which was my weak proxy for infinity. i.e., a small numbers problem made the left tail choppy and I had to up the iterations by a bit..
The Portfolios:

- Lower risk - N[1,4]
- Higher risk - N[7,25]
- corr coeff. -   -.20

in MV space are like this, almost as before, just lower returns assumed than in first post

Figure 1

PL in Years, the distributions

As before, if I walk through each black dot in Figure 1, each a portfolio on the EF with a different return and std dev, and then I calculate, using a simulation algo I borrowed from Prof Milevsky and a 4% constant real spend rate, I can create a distribution of the number of years that the portfolio will last. i.e., each time it doesn't last I count 1 to the year it's dead (fail) and accumulate that freq for that year. I later normalize it so that the percentages or mass sums to 1 for convenience and charting. 

Doing that described in paragraph 1 gives me Figure 2: 

Figure 2

Note that most of the observations for the higher risk portfolios get absorbed into the infinite duration category here which is defined helpfully as 100years. Each line is one of the 11 portfolios and the distribution of years survived. The lowest risk portfolio his the high one with a narrow center. The highest risk portfolio is the lowest one and so widely distributed that most of it is hiding in the 100y bin. 

Inspecting the left and right tails in terms of PL years for each portfolio

In Post 1 we looked at the probability, by portfolio, that the portfolio would either 
      A. last less than 10 years, or
      B. last more than 50 years
by integrating the left or right tails as required. I won't dwell on that here but here is the summation in figure 3.  Some of this can also be inferred from a later chart. 

Figure 3


Inside the Distributions

Then as in the 2nd link above, I turned Figure 2 inside out and put portfolios on the X and the PL in years on the Y and the dots and lines are the percentiles of the PLinYears distributions for each portfolio. That's a lot of noise for signal so I hope it works.  

My predictions before I started this post, given the shift down in spending and returns:  
  • All portfolios will last longer in years across the board than with the higher spend, duh!
  • The higher risk portfolios will be hurt more in left tail i.e. bigger penalty vis-a-vis the lower risk
  • Many portfolios will have a higher %  of observations that tip over towards infinity
  • Low risk portfolios will be more viable than not over smaller human horizons
  • To reach for high-horizon-years under these assumptions, higher risk must be necessary
  • Cutting spending (not shown here) is a bigger lever than portfolio design in order to gain years
We'll see. 

Here is, in Figure 4, the inside-outed distributions of Figure 2, now rendered in a related percentile chart. Each line (and dots, say grey) represents a percentile (10-90th, y axis) -- of each portfolio (1-11, X axis) where 11 is the high risk portfolio. 90th percentile is the top line (and dots) and 10th percentile is the bottom one. Best, perhaps, to read this vertically at each portfolio 1-11. The dots (at say 1 on the X) represent the distribution one sees in Figure 2 for a given portfolio 1. The lines just happen to connect the percentiles across portfolios, if that makes sense.  



Figure 4

Misc comments of Figure 4

This is hard for even me to read and I made it. Lot going on...

The weird shapes at the top are either 
   a) simulation artifacts 
   b) because infinity is coerced to 100 
   c) something I don't understand 
   d) coding errors or 
   e) a small numbers thing in left tail since most observations for high risk go to 100+y. 
I vote for b, c, e

Interpretation?

Idk. Let's try a few ideas... 
  1. If the metric were to be at the 50th percentile in terms of Portfolio Longevity   
a) if the plan/policy were to decide to focus on a 30 year horizon (a common human retirement goal), then it looks like most portfolios will get you there. In addition you probably have a legacy mgmt problem at that point except for maybe the 5th percentile of portfolio longevity (PL) outcomes where there is no doubt a bit of a bind. 

b) if the plan/policy were to be to focus on a 50 year horizon then some risk appears to be needed to be taken on in portfolio terms with the proviso that at the 50th percentile, half the portfolios will fall short of the metric by quite a few years, depending on the portfolio up and down the risk spectrum. Hard.  

    2. If the metric were to be at the 10th percentile, or worse outcomes, in terms of portfolio
        longevity (and now that I write this it all sound a bit backwards, but whatever...     
        here we are more or less falling into "fail metric" territory, btw something I won't touch now),
        then:

a) yeah, you are going to probably fall short of that metric for either a 30Y or 50Y policy goal. 

b) You really have no chance of making it to either horizon and the only option in my mind is is to either cut spending or plan for a fail-state some day that is more or less predictable now statistically. I don't discuss the sensitivity to spend changes here. Good luck.


This look-see is objectively a little confusing, even to me. Otoh, this view of things reminds me that the 94 look by Bengen into SWR was really into only one spend rate and one very very particular portfolio over a very very particular interval of the more than lovely mid 20th C. That meant it was a little bit of a head fake on retirement finance. There is no answer to any of this just a range of possible futures depending on assumptions, most of which -- even mine, even Bengen -- are pretty bogus.  The real conclusion from all of this, not explicitly analyzed or stated in anything above, is more than likely that: we need to keep our eye on the ball, save well, spend well and carefully especially early, adapt as wisely as we can when it is warranted and not too late, and seek life income where possible (not addressed here).   

 
Postscript:

On the choice of horizons -- I picked 30 and 50 years in Figure 4 because: a) 30 is a common fixed horizon used in retirement papers and b) when I semi-willingly retired at 50, the longest horizon I was willing to consider -- even though theoretically I could have gone longer -- was 50 years or "to 100."  50 is probably a meaningful working/planning horizon for long dated trusts or endowments but I don't really know those domains well.  Me? If I were to use a chart like #4, which I probably wouldn't do in practice, I might use a number between mean expected longevity up to the 95th percentile using a site like aacalc.com. There, with my age, the horizon would be somewhere between 23 and 36 years. 













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