# 100% Equities, the final frontier

In our quest to better understand how a portfolio of 100% equities performs during we retirement, we started by looking at how they did in a 1960s/70s retirement and found that they did basically as well as a traditional 60/40 portfolio.

However, when we looked at the crashes of 1929 and 2000 we found some scenarios where they did quite a bit worse.

All of that was a somewhat ad hoc investigation. Just poking around in historical data looking at individual graphs. Now we want to try two things. One, bring a little bit of rigour to the search. Are there other years we’re missing out on? How big is the gap normally? Things like that. Two, try to reconcile the charts we looked at previously with summary statistics we’ve seen before.

What do I mean by that? When we looked at HREFF metrics 100% equities did extremely well.

When we looked an annual income, even in “worst case scenarios”, 100% equities seemed to do pretty well. For instance in my “Income Harvesting shootout” we found that, at the 5th percentile, a 100/0 portfolio generated $32,039 of annual income and a 60/40 portfolio generated $31,956 of annual income.

Those annual income and HREFF numbers suggest that 100/0 is a slam dunk win. But the charts we looked at found a number of disturbing cases where 60/40 is clearly better. That’s what we want to find an explanation for.

# Regret Minimisation & tail risk

Okay, with that prelude out of the way…

We know that when we look at “5th percentile income” we don’t see any real difference between 100/0 and 60/40. 5th percentile income *sounds* like it is pretty conservative. But is it?

When we run a backtest of retirement incomes using US historical data we end up with 3,450 total years. 115 different start dates from 1871 to 1986 and each retirement runs for 30 years. So 5th percentile income means 172 of those years are *lower* than the 5th percentile income. 172 kinda seems like a lot when we’re talking about our one and only shot at retirement.

If we look at 1st percentile — 1 in 100! — the 100/0 portfolio still looks pretty okay. $25,924 for 100/0 and $26,528 for 60/40. But even 1st percentile income means 35 years do worse. Three or four bad years in our own retirement might make things pretty unpleasant…especially if they occur consecutively.

But honestly, even when we look at the worst 2 or 3 years, neither strategy appears to have a compelling lead.

The worst 3 years for 60/40 are

`$21,389`

$22,493

$22,538

And the worst 3 years for 100/0 are

`$20,473`

$21,295

$22,153

It looks like just a few hundred dollars here or there. But in our charts last time we often saw differences of thousands of dollars.

# Apples to Apples

The problem is that we’re not really making an apples to apples comparison. When we look just at incomes like that we’re comparing very different years. One of them might come from 1942 for a 1926-retiree and the other might come from 2003 for a 1981-retiree. Most people benchmark and suffer from regret if they do worse than the benchmark.

What we really want (I think) is to compare “how much money would I have made in 1943 when you compare 60/40 versus 100/0”. That is, for every year of our simulation we want to calculate the difference between the two strategies.

Furthermore, we really care about tail risk here. Due to the prevalence of the 4% rule, I think a lot of people use that as a benchmark in their retirement planning. If we expected to retire on $40,000 a year and 60/40 return $50,000 but 100/0 returns $55,000….we probably aren’t going to care much either way. So we only care when income drops below 4% of the initial portfolio value.

When we combine those two we have a (I think) more useful data set.

- Years when income for one of the strategies was below $40,000
- The difference in income between those two strategies for
*that*year.

Here are the full results as a Google Sheet.

The “Income Date” column tells you the year of initial retirement and the year at which that specific income was received. So if the “Income Date” says “1946/1975” then that row is for someone who retired in 1946 and received the income in 1975.

Overall, out of our 3,450 total years, there are 558 years where one of the strategies gave us less than $40,000. On the one hand, that’s good news because it means 84% of the time we don’t have to worry no matter what asset allocation we pick.

At first glance, things look very similar. When we look at the 5% of cases most in favor of the 60/40 portfolio the difference is $8,702 a year. And the 5% of cases most in favor of the 100/0 portfolio shows $8,303 a year.

But when we include more context differences emerge.

Here are the scenarios where 100/0 outperforms by the most, giving us over $10,000 a year more in income than a 60/40 portfolio would.

We can immediately spot that, while the 60/40 portfolio ** is** under $40,000…it is just barely under $40,000. The average income of the 60/40 portfolio in these scenarios is still $37,689.

Here are the scenarios where the 60/40 portfolio outperforms by the most.

This time we notice that several of the 100/0 portfolio values are quite a bit under $40,000. A few are in the $20,000s. The average income for the 100/0 portfolio in these scenarios is just $31,499.

Incidentally, by looking at the “Income date” in the detailed spreadsheet we can confirms something we weren’t positive about before: the 60/40 portfolio *only* outperforms around the 1929 & 2000 crashes. If count up all the times that 60/40 outperformed by at least $4,000 (i.e. 10%) it looks like

If you didn’t retire in one of those 8 years — associated with only 2 bear markets — then 60/40 didn’t outperform. Another way of looking at the same thing is to sum up the lifetime differences for our dataset (which, remember, only includes “bad” years). We can see the dramatic impact on a 1929-retiree.

We knew that holding bonds was insurance and helping protect against tail risk, so this isn’t exactly a startling discovery. But I think it is still interesting to see the data laid out like that.

Just from eye-balling the charts we know that looking at the differences in income alone isn’t enough. We also need to take into account our shortfall — how fall we below $40,000 in income we are.

We can create a simple metric to combine the two to create a *Retirement Regret Score*, which will just be two numbers multiplied together:

- Absolute Regret: How far under $40,000 our actual withdrawal is.
- Relative Regret: How much better the other portfolio did. Up to a point. Remember that $40,000 is our magic number. Anything above $40,000 doesn’t count.

This is what the formula actually looks like, where s1 is *our* strategy and s2 is the *other* strategy.

When we sort by this *Retirement Regret Score* these are the scenarios where the 100/0 portfolio outperforms the most. (Alternatively said, where the 60/40 portfolio has the most regret.)

And here’s where the 60/40 portfolio outperforms by the most.

The 60/40 portfolio has 156 “regretful” years — when the 100/0 portfolio did noticeably better than it. But the average *Regret Score* across those years was only 15.758. By contrast, the 100/0 portfolio had 130 “regretful” years but the *Regret Score* was 31.821. If we turn those two numbers into a ratio, let’s call it the *Regret Ratio*, we get 2.02. Fewer years of regret but double the regret when the black swan strikes.

Which offers evidence that downside for 100/0 ** is** worse, though we’re talking about 130 years out of 3,450.

After all of this…have we just confirmed the common wisdom? Having 100% equities is high-risk but high-upside. Having some bonds is lower upside but lower risk. Well duh.

To an extent, definitely. Some of our summary statistics seemed to show that there was no real downside to a 100/0 portfolio. But I think we’ve convinced ourselves that isn’t actually the case. We just needed more nuanced numbers to see the true situation.

On the other hand, while we didn’t *disprove* the common wisdom, we saw quite a few things to temper it. When we look at the next-to-last chart — the one with *Retirement Risk Scores* where 100/0 did best — we see quite a few scenarios where 60/40 did legitimately worse.

Admittedly, with the 60/40 portfolio we don’t see the same length or depth of underperformance that we do with the 100/0 portfolio. The 1915-retiree has 4 years of painful underperformance (to go along with 3 years of mild underperformance) with an average underperformance of $4,500 a year with a 60/40 portfolio. But the 1929-retiree with a 100/0 portfolio had 8 years of painful underperformance (and 2 years of mild underperformance) with an average underperformance of $8,400.

A 60/40 portfolio doesn’t always help. But it ** definitely** helped people who retired in 1929, 1930, or 2000 (and to a lesser extent the retirees of 1998, 1999, 1928).

Is there a way to just…*not retire* at those points in time?