Prime Harvesting: Sleep Well At Night (2 of 3)

[You can read the first and third in the series as well.]

Last time we set the stage. Now we’re going to try to decide whether Prime Harvesting — in any sense — provides better outcomes.

From McClung’s book

McClung compared Prime Harvesting to Annual Rebalancing but he used “constant dollar” withdrawals. He then compared “the best possible constant dollar withdrawal” of Prime Harvesting versus that of Annual Rebalancing. He’s essentially saying, “Well if you retired in 1946, with Annual Rebalancing you could have taken out 5.2% to start with and then inflation-adjust that every year afterwards. But with Prime Harvesting you could have taken out 6.9% that first year and then inflation-adjusted the amount afterwards.”

But you can’t know that in advance.

Instead of using constant dollars we can use a variable withdrawal strategy, which doesn’t require us to have knowledge of the future. But if we use variable withdrawals how do we do any kind of easy comparison between the two?

The first thing we can do is take a series of variable withdrawals and turn them into a single “certainty equivalent withdrawal” by using a utility function. Now we can chart Prime Harvesting against Annual Rebalancing again.

Let’s try it with two different variable withdrawal strategies (just to make sure we aren’t inadvertently stumbling on any weirdness caused by a specific withdrawal strategy).

Using longinvest’s VPW for variable withdrawals
Using McClung’s EM for variable withdrawals

The results certainly look less dramatic than in McClung’s original chart. Though, just looking at the charts, I’d still give the nod to Prime Harvesting. The worst scenario — 1921 — has Annual Rebalancing with a $3,806 a year edge. The best scenario — 1939 — has Prime Harvesting with a $5,793 a year edge.

Another way of looking at things is to calculate the “certainty equivalent withdrawal” of every single withdrawal (i.e. every year of every retiree). This gives us a single number to compare:

Annual Rebalancing $40,466
Prime Harvesting $41,205

That suggests that Prime Harvesting has a consistent advantage but it is quite a bit smaller than we initially thought.

Let’s look in a bit more detail at what a retiree would see under Prime Harvesting and Annual Rebalancing.

1966 was the worst year to retire in US history, so this is a useful “worst case scenario” to always check against.

Earlier I said that Annual Rebalancing did (relative to Prime Harvesting) best in 1921 and worst in 1939. Here are those years.

The reason for the big performance differential is that Prime Harvesting kept harvesting and harvesting and harvesting and ended up with a ton of bonds. You could argue that it became too conservative here. This is a scenario where AltPrime does better (though still not as good as sticking to 60% equities.)

And when Prime Harvesting did best — 1939.

$1,000 a year isn’t much when we’re talking about withdrawals that average $47,000. But it is still an improvement.

When we zoom in on individual years, it looks like Prime Harvesting performs best in the worst times. Its best (relative) performance comes in the 1930s and 1960s.

And a lot of the Annual Rebalancing outperformance comes in the 1800s, which you might not consider relevant anymore.

If we only look at post-1900 numbers then Prime Harvesting’s “margin of victory” increases by a fair amount, but then we’re starting to massage the data with arbitrary cut off points. When that makes things look better for Prime Harvesting, we should be suspicious about our motives.

Based on what we’ve seen so far, I’m tentatively willing to consider Prime Harvesting a (slightly) superior strategy.

However…have we really done an apples to apples comparison? We’re looking at a 60/40 fixed allocation and comparing it to one which will vary over time. Are we really just seeing Prime Harvesting do better because it ends up with more stocks, which are riskier but (generally) lead to better performance?

It doesn’t look like that’s what’s happening. Prime Harvesting (in my scenarios) starts out with a 50/50 portfolio and then adjusts over time. These are the stats for the overall bond levels under Prime Harvesting. (And I’ll include Alt Prime because why not.)

Bond levels

The mean bond level is 46%; the median bond level is 48%. There is a lot of variation but it doesn’t, at a quick look, appear that Prime Harvesting is outperforming due to a pervasive tilt towards stocks.

Turning towards overall metrics: Prime Harvesting appears to have slight edge in median withdrawal, 5th percentile withdrawal, 10th percentile withdrawal, lowest withdrawal seen, mean of lowest 25% of withdrawals, and standard deviation. (It also has a significantly lower kurtosis which is a measure of “fat tails” and skew which is a measure of symmetry; high kurtosis means you have more outliers, high skew means the left and right sides of the distribution don’t look similar.)

All of that seems to support what we saw above: the Annually Rebalanced portfolio has some bigger victories (notice the maximum withdrawal seen under Annual Rebalancing is $35,000 a year more than that seen under Prime Harvesting) but Prime Harvesting seems to handle bad situations better.

Graphing this makes it a little easier to see.

All of the above was done with a 40-year retirement length. That stress tests things for longevity but could paint a slightly skewed picture. If most people die in the first 20 years of retirement then those people aren’t going to be very interested in what things are like for years 20–40. “Certainty equivalent withdrawals” help correct for this but let’s take another look at it just to be sure.

Let’s try to mortality-weight our results. This means that results that happen earlier in retirement count more than things that happen later. If, for instance, Prime Harvesting was having some amazing results in years 35–40 (i.e. the retiree was aged 100–105) that pushed up the mean/median/etc we’d probably feel any declaration of victory was somewhat misleading; most retirees would die before seeing any Prime Harvesting outperformance.

Mortality-weighted withdrawals

Notice that Annual Rebalacing’s maximum has gone from $152,000 to $135,000. Some of those excess returns very late in life are now being discounted.

Even with mortality-weighting, Prime Harvesting seems to retain the edge.

Finally, let’s take a look at portfolio values. We want to make sure that Prime Harvesting isn’t giving us better withdrawals at the expense of dramatically lower portfolio values.

Portfolio stats

(Note: these are not just “terminal portfolio values”; we’re looking at every year of data for every retiree.)

Here we don’t see any major differences, which is what we wanted.

Prime Harvesting doesn’t smash the competition but it does seem to offer slightly better withdrawals. It does best in the worst periods (the 1930s; the 1960s). Given our risk-aversion about retirement income, that’s probably a nice characteristic.

So now that I’ve convinced myself Prime Harvesting has better returns than Annual Rebalancing, let’s see if it does that by taking on extra risk.

Continue on to the third part…

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