Recently I came across a Reddit conversation where someone proposed an “income harvesting” strategy (though he didn’t use that phrase) that he felt was an improvement over simple annual rebalancing.
I’ve written several things about different income harvesting strategies (most of which are linked from):
Income Harvesting shootout
When you’re retired and need to withdraw money from your portfolio you have to make a decision about how exactly you…
I’ve never really formed a concrete opinion on these things one way or another. Intuitively they seem they ought to make a difference. But the differences often seem surprisingly small. And there’s always the nagging feeling that we’ve built an over-fitted model that could explode if the future doesn’t look a lot like the past.
The strategy that the Redditor posted about is the same as the OmegaNot strategy that McClung tests in his book. There is one difference, though: OmegaNot says “sell bonds if your portfolio is under 100% of its inflation-adjusted original value; otherwise sell stocks” whereas the Redditor said “sell bonds if your portfolio is under 90% of its inflation-adjusted original value; otherwise sell stocks”.
That made me curious: does the threshold chosen make a difference? And does exploring different thresholds give us more insight into the behaviour of OmegaNot and other income harvesting strategies?
Warning. There will be a lot of charts. This first part is also very exploratory. We’re just looking at lots of things and seeing what comes out in the wash.
Note. Unless otherwise specified, all portfolios begin with a 60/40 asset allocation. All returns are based on the US.
We’ll consider 3.25%, 3.5%, 4%, 4.5%, and 5% constant dollar withdrawals. We’ll look at variants of OmegaNot with thresholds from 70% to 130% (i.e. “sell bonds if your portfolio is under 70% of its original value” up to “sell bonds if your portfolio is under 130% of its original value”). We’ll also compare against some static allocations 20/80 up to 100/0 in 10% increments. And we’ll look at 3 glidepaths: a traditional one where the amount of bonds increases, a popular variant of the traditional one called “Age in Bonds”, and a rising equity glidepath (aka “inverse glidepath”).
First let’s look at failure rates for a 40-year retirement. We don’t see a big difference in failure rates across OmegaNot thresholds. Using 70% as a threshold seems the same as using 130% as a threshold. There are some slight differences once we get up to 4.5% constant withdrawals but they don’t seem substantial enough to care about.
For annual rebalancing: we see what we already knew. Low bond holdings have a higher tendency to fail, especially with higher withdrawal rates. The break point seems to be around 80% equities.
The “Age in Bonds” glidepath seems to be terrible. The other glidepath is better but still not good. At 3.5% withdrawals it fails as often as the 30/70 portfolio — over 10% of the time. The rising equity glidepath does well but not as well as any OmegaNot variant.
Mostly, though, this just tells us that failures rates don’t tell us much. Whether something succeeds or failures is primarily dependent on the withdrawal rate, not whatever micro-optimisations we do with our asset allocation.
So looking at failure rates isn’t particularly enlightening. Before we move on, let’s zoom in. The chart above has lots of data points so it is a bit tricky to distinguish everything. Let’s look at just one slice: a 40-year retirement using 4.5% withdrawals. Yes, this is higher than most people would actually risk. But it tells us a little bit about how the different strategies handle pressure.
Maximum Safe Withdrawal Rate (MSWR)
Next let’s calculate the MSWR for each strategy.
We can see that most of them are clumped together, with a small number of strategies that are clearly terrible. But there’s so much visual noise it is hard to make any judgments just by looking at the chart.
Here’s a different view of that same data. (The black line indicates how the MSWR varies over 30-, 40-, and 50-year lengths.)
Here we see the same pattern as in the failure rates: the low-equity portfolios all do poorly but everything else seems pretty good. The 120% and 130% thresholds have a tiny bit smaller MSWR but it doesn’t look like a compelling difference.
Maximum Perpetual Withdrawal Rate
The MSWR is based on the portfolio ending with 0% of its original value. Some people prefer to look at the “perpetual rate”: the withdrawal rate that leaves the portfolio with 100% of its original value. (I don’t think this is an especially useful number, particularly for longer retirements.)
Meh, lower absolute numbers but the relative performances seem the same as before. Notice that the perpetual rate is higher for longer retirements. That’s one reason why I’m not a big fan of this metric.
Okay, finally moving on to something a bit more interesting: shortfall years. A common criticism of failure rates is that they don’t convey much information. Failing after 12 years is very different than failing after 29.9 years but they are treated the same.
Here we calculate the average number of years we fell short in our failure states. A lower number is better.
Once we get to 4% and higher withdrawals we start to see a bit of separation finally. But there’s so much visual cruft it is hard to make sense of it. Let’s focus on the 4%+ withdrawals and strip away some of the variants.
A 4% the inverse glidepath does very well but it does a bit worse at 4.5%. The 3 fixed allocations all do worse than OmegaNot.
We wanted to see if thresholds made a difference for OmegaNot, so let’s look at all the variants.
Hard to say anything concretely; there doesn’t appear to be an obvious linear trend between threshold and shortfall years. 130% certainly does worse than average. But the 70% threshold goes from absolute worst at 4% to among the best at 4.5%. The 100% threshold goes from best at 4% to middle of the pack at 4.5%.
Downside Risk-Adjusted Success (D-RAS)
D-RAS is a more complicated measure. It is the ratio between the expected length of the portfolio and the standard deviation of years sustained. A higher number means either the portfolio lasted longer or the length it sustained was less volatile. (A high volatility here means “sometimes it lasted 15 years, sometimes 29” whereas a low volatility means “sometimes it lasted 28 years, sometimes 29”.)
It also only cares about the downside. If doesn’t care if you expected the portfolio to last 34 years and it actually lasted 49 years.
We only look at higher withdrawal rates because with 3.5% and 3.25% there’s no real “downside” to be measuring. Things almost always work out.
A higher number is better.
Here the OmegaNot variants generally do quite well. Though some of the high-equity static allocations also do well.
Let’s see if there are any differences between OmegaNot variants:
Again, no relationship that I’d call obvious & stable. At 5% withdrawals the best performed is the 70% threshold…and the 2nd best performer is 130% threshold.
Let’s look at a smaller sample of strategies and see what we see.
The inverse glidepath generally does worse. But that’s about the only conclusion I can see. The Omegas do better at 4% but worse at 5%. And are mixed at 4.5%.
The Coverage Ratio is the ratio of the number of years the portfolio lasted relative to your goal. That is, if the portfolio lasted 28 out of 30 years then the ratio is 28/30 = 0.933. If the portfolio lasted 42 out 30 years then the ratio is 1.4.
Then we apply a utility formula so that shortfalls are penalised heavily and large excesses are discounted. We care more about failing by 1 year than we do about having 1 year extra. And the difference between 5 years extra and 6 years extra is minimal.
I keep repeating this big chart so you can see that low-equity strategies always do poorly. We see a clump of “decent strategies” that we need to zoom in on and then there’s all the “bad strategies”. Glide paths, “Age in Bonds”, 50/50 portfolios, etc.
Inverse glidepath is consistently the worst.
Interestingly, the static allocations always beat out the OmegaNot strategies. This is one of the few clear & consistent result we’ve seen so far!
We can also look at all the OmegaNot variants:
No real consistency. 130% does best. But 70% is second best.
The Ulcer Index
The Ulcer Index is way of measuring the pain of drawdowns of a portfolio. Long drawdowns hurt. Deep drawdowns hurt. Long, deep drawdowns are just the worst.
A higher number is worse.
The low-equity strategies (somewhat unintuitively) result in “more ulcer”. That’s because drawdowns can be caused by two things: the market going down and your portfolio not keeping up with your withdrawals. A low-equity portfolio is more likely to get drawn down.
Here we notice that the OmegaNot variants do well compared to the static allocations. Also notice that the inverse glidepath does well at 3.25% but increasingly poorly as the withdrawal rate goes up.
Looking at just a handful of strategies makes it even clearer that the OmegaNot variants always beats out the static allocations.
Different thresholds don’t seem to make much of a difference on the Ulcer Index. That’s a bit of a surprise, to be honest.
Average Bond Holdings
One thing we’ve learned is that sometimes a strategy is only better because it results in your holding more stocks and, generally, stocks have higher returns than bonds.
Scroll back up to the MSWR charts and notice that, among the static allocations, there’s a linear relationship between your MSWR and your equity percentage.
We wonder: is OmegaNot actually doing something smart? Or is it just a backdoor way to trick you into holding more stocks?
Obviously, it will result in you holding more stocks on average than you start out with. With OmegaNot you never rebalance. You never buy more bonds. And sometimes you sell bonds. But how big is this effect, really?
Remember we start out every portfolio at 60/40. But we can see that most variants have an average allocation of around 75/25. That’s an average across all retirement cohorts. It’ll change, depending on when you exactly you retire and what the market does during your retirement. We can look at the average bond allocation for each retirement cohort.
We can see that a handful of retirees had an average bond allocation over 30%…but most were under that. You could have a low bond allocation either because the market crashed (and you started selling bonds) or because the market did really well (and stocks appreciated faster than you can sell them off, making bonds a smaller percentage of your portfolio).
Testing Equivalent Bond Allocations
If OmegaNot with a 100% threshold ended up having a 78/22 allocation (on average), then we have to ask ourselves: instead of messing around with a fancy pants income harvesting strategy…maybe we should have just retired with a 78/22 allocation (instead of 60/40) and maintained that static allocation?
We can calculate the MSWR for each retirement cohort using both OmegaNot_100 and a 78/22 portfolio. If OmegaNot is “smart” we would hope to see it consistently beating the static allocation. This would provide some evidence that it is smartly managing our allocation.
But that’s not what we see. The 78/22 static allocation actually has a higher MSWR than OmegaNot most of the time.
If we zoom in on the handful of cases where OmegaNot has the higher MSWR:
We can see how few they are…and how small the outperformance is. When OmegaNot outperforms, it only outperforms by, on average, 0.16 (i.e. an MSWR or 4.16 instead of 4.0). When it underperforms it does so by -0.45 (i.e. 3.55 instead of 4.0).
We see this graphically, too.
This chart shows the difference between the OmegaNot MSWR and 78/22 MSWR. Most points fall below the 0-line, meaning OmegaNot under-performed. And the points below the 0-line are further below it than the ones above it are above.
Single Year Highest Withdrawal Rate
One thing that MSWR and Constant Dollar strategies overlook is the stress real retirees feel when they have to withdraw 5% or 6% or 7% of their current portfolio in order to maintain those constant dollar withdrawals. So we can also look at the single highest withdrawal of each strategy. Maybe one strategy is successful because it puts your through more stress?
All of the OmegaNot variants look to be about the same. The low-equity strategies, again, do poorly. The inverse glide path is somewhere in between.
Certainty Equivalent Withdrawals (CEW)
So far everything we’ve looked at is based on constant dollar withdrawals. In the real world, retirees don’t do that, at least not robotically. Let’s also look at a variable withdrawal strategy and put it through the lens of certainty-equivalency.
Higher numbers are better.
It is getting repetitive but: no difference between the OmegaNot variants. Low equity does poorly. Invest glidepath falls in between.
Of note, the 80%, 90%, and 100% equity static allocations each outperformed all of the OmegaNot strategies.
The previous chart was for average CEW. But averages can sometimes be misleading, especially in retirement where we usually care a lot about downside risk and worst case scenarios. This chart shows us the single worst CEW experienced.
The 80%, 90%, and 100% static allocations fall below the OmegaNot strategies, though the difference isn’t large. If you check the y-axis labels you’ll see it less than $1,000 a year for most OmegaNot variants.
However, we also see some differentiation between OmegaNot variants. Finally. The 100% threshold performs the worst, somewhat surprisingly. But the 110% to 130% variants perform noticeably better.
Harvesting Rate Efficiency (HREFF)
Finally we can look at HREFF. This is similar to CEW but has an explicit floor. If withdrawals fall below 4% then an extra penalty is applied. This tells us how well a strategy can support a spending floor.
In general the OmegaNot strategies do well, especially with a higher threshold.
Okay. So where does all of that leave us?
We didn’t see much compelling evidence for or against the different thresholds for OmegaNot. The CEW and HREFF suggest 130% might be better. But there’s enough conflicting, or simply confusing, results that we’re not exactly confident in that. Ideally we’d consistently see a linear relationship where lower thresholds do better/worse. Instead we see, for instance, that in some tests at least, the 100% threshold does worse than the 90% and the 110% threshold.
We also saw limited evidence in favor of the OmegaNot strategy overall. We suspect that much of its performance is simply due to the higher average bond holdings, rather than anything particularly clever or lucky about how it manages the asset allocation.
(As an aside: this isn’t necessarily a bad thing. If you’re afraid of high equity holdings and a adopting a strategy like OmegaNot helps you gradually move towards higher equity holdings, then it can still be a useful tool.)
For the next step, we still have some unanswered questions. We saw a few weird things above that we might want to figure out.
- Why does the inverse glidepath do poorly on just about everything?
- Why does OmegaNot not exhibit that linear performance we just mentioned?
- If we focus more on individual worse case ever type scenarios, are there any circumstances where OmegaNot is a compelling outperformer?
- OmegaNot never buys more bonds. Does changing that, having triggers to buy more bonds (as Prime Harvesting does) change our results? And if it does, why?