How often should we rebalance our portfolio? – SWR Series Part 39

August 5, 2020 – In the 3+ years while working on the Safe Withdrawal Rate Series, I regularly get this question:

What’s my assumption for rebalancing the portfolio?

In the simulations throughout the entire series, I’ve always assumed that the investor rebalances the portfolio every month back to the target weights. And those target weights can be fixed, for example, 60% stocks and 40% bonds, or they can be moving targets like in a glidepath scenario (see Part 19 and Part 20).

In fact, assuming monthly rebalancing is the numerically most convenient assumption. I would never have to keep track of the various individual portfolio positions (stocks, bonds, cash, gold, etc.) over time, but only the aggregate portfolio value. If the portfolio is rebalanced back to the target weights every month I can simply track the portfolio value over time by applying the weighted asset return every month.

But there are some obstacles to rebalancing every single month:

1. It’s might be too much work. Maybe not necessarily the trading itself but keeping track of the different accounts and calculating the aggregate stock and bond weights, potentially making adjustments for taxable accounts, tax-free and tax-deferred accounts, etc.
2. It might involve transaction costs. Even in today’s world with zero commission trades for ETFs, you’d still have to bear the cost of the bid-ask spreads every time you trade.
3. Even if you hold your assets in mutual funds (no explicit trading costs) there might be short-term trading restrictions prohibited you from selling and then buying (or vice versa) too frequently.
4. It might be tax-inefficient. If an asset has appreciated too much you might have to sell more of it than your current retirement budget to bring the asset weight back to target. But that would mean you’ll have an unnecessarily high tax bill that year. Of course, this tax issue could be avoided by doing the rebalancing trades in the tax-advantaged accounts, not in the taxable brokerage accounts.

And finally and maybe most importantly, there might be a rationale for less-than-monthly rebalancing: it might have an impact on your Sequence of Return Risk. So, especially that last point piqued my interest because anything that might impact the safety of my withdrawal strategy is worth studying.

So, on the menu today are the following questions:

• Under what conditions will less-frequent rebalancing do better or worse than monthly rebalancing and why?
• How much of a difference would it make if we were to rebalance our portfolio less frequently?
• Could the “right” rebalance strategy solve or at least alleviate the Sequence Risk problem?

Let’s take a look…

Some preliminary calculations

Before we even look at actual historical stock and bond returns and I show a lot of fancy charts and tables with historical simulations, let’s first take a step back and try to understand the mechanics of how the rebalancing frequency will interact with our withdrawal strategy and under what circumstances it might help or hurt you to rebalance less frequently.

So, I built a tool to calculate and simulate portfolios with different rebalancing frequencies. So, I introduce to you…

… the Big ERN rebalance simulation Google Sheet

As always, when I post a Google Sheet, I cannot grant access for anyone to edit that clean spreadsheet online. Otherwise, people might mess with my formulas and ruin the sheet for everyone else. So, if you like to enter your own numbers, please save your own copy first! See below:

Each tab is for one simulation case study. The user inputs are in the top left corner of each tab. Here’s an example:

• The initial portfolio: $1,000,000
• The annual withdrawal percentage (but the actual withdrawals are monthly): 4%
• The stock allocation: 60%. This implies 40% bonds
• The rebalancing frequency: every 12 months.
• The first rebalancing event: after 12 months. Notice that separating these two parameters allows me to simulate a scenario where someone retires on September 30 but then does the rebalancing every year on December 31. In that case you’d set the frequency to 12 and the first rebalance at month 3.
• The retirement start date (month and year). In this case September 1929, right before the stock market peak. (not applicable in the case studies/ thought experiments involving “made up” return data)
• As always, all returns are in real, CPI-adjusted dollars and all withdrawals are adjusted for inflation as well!

Before we even jump into simulations with actual stock and bond market returns, let’s try to understand some of the rebalance mechanics at work and work through a sequence of scenarios with just some artificial return data.

I cooked up 5 different scenarios to distill the effects of the rebalance strategy:

Scenario 1: Constant Stock and Bond Returns

Let’s assume stock and bond returns are constant at 0.5% and 0.1%, respectively, every month (adjusted for inflation). So, there’s zero volatility and the average returns are roughly in line with historical long-term averages. Also, assume that the portfolio is not rebalanced at all (rebalance frequency = every 10,000 months = essentially never).

It turns out that there’s no impact on the portfolio, see below:

How is that possible? Without actively shifting around assets you can still bring the portfolio weights back through your monthly withdrawals, see the simulation results below. After applying the asset returns for one month, the stock portfolio weight has drifted to 60.10% in month 1. But if you withdraw mostly equities, around just under $3,000 and the remaining $377 in bonds you can bring the equity weight back to exactly 60%. So, you never have to reshuffle the portfolio beyond the monthly asset sales. You’d just have to make sure that the asset sales are not 60/40 but more tilted toward equities to adjust for the drift in the portfolio weights. More like 89/11 in this scenario.

Summary so far:

Lesson 1: The rebalance frequency is likely irrelevant with constant returns assuming that the Stock/Bond return difference is small enough relative to the withdrawal percentage. 

Let’s look at another scenario…

Scenario 2: Return volatility with fast mean reversion

Since we need some return volatility to notice a difference across various rebalance strategies, let’s start with a simple volatile pattern: Stock/Bond returns are +5.0%, -0.5% in odd months, and -4%,+0.7% in even months.

Without actively rebalancing the portfolio, you’d do significantly worse than someone who rebalances monthly. About 0.34% after one year, growing to about 4% underperformance after 10 years, see the main results below:

Let’s look at how the portfolio positions look over time, see below. After the first +5% equity return, the equity portfolio weight goes up to 61.28%. Even if the entire withdrawal of $3,333 comes from the equity portfolio, you only manage to bring the equity share back to 61.16%. Indeed, if you wanted to rebalance this portfolio back to 60/40 you’d actually have to withdraw about $15,000 from equities, shift close to $12,000 back into bonds and withdraw the remaining $3,333. In any case, you now have a higher than target equity weight right before the -5% equity return strikes and this unlucky market timing explains why you underperform.

So, the retiree who rebalances less frequently (or not at all) is effectively a market timer now. But in the worst possible way; a high stock weight right before the next stock market decline and a relatively low stock portfolio weight right before the next big market rally, which explains the underperformance relative to a constant 60% equity weight, achieved through adjusting the weights at a monthly frequency.

Lesson 2: Rebalancing frequently helps you when returns “mean-revert” very quickly. 

Let’s look at the next scenario…

Scenario 3: Positive equity momentum for the first 6 months

Let’s look at the opposite of fast mean-reversion: Momentum. Now imagine that the stock market outperforms for 6 months with 5% monthly returns and then jumps back to 0.5% again as in scenario 1. Wow, now you outperform when you don’t rebalance. Quite substantially:

What’s the reason for this result? Well, let’s look at the account balances over time, see below. After the first 5% return in month 1, the stock share has swelled to 61% again. As in scenario 2, even after withdrawing the entire $3,333 monthly retirement budget from equities, you’re still left with more than 60% post-withdrawal. So, if the good equity returns keep coming in the subsequent months, you’d be crazy if you took money out of equities and put into the low-return bond portfolio. If you face this positive momentum, why change the winning team? Let the strong returns run for as long as possible!

Thus the next main result:

Lesson 3: In light of positive momentum in equity returns, it’s best to balance less frequently

How about negative momentum? That’s the next scenario…

Scenario 4: Negative equity momentum for the first 6 months

Quite intriguingly, you also outperform when you face negative momentum. Assume that the equity market drops 5% every month for 6 months. Not rebalancing adds about 0.73% extra to your portfolio after one year, 0.96% after ten years.

And the reason is the same as before. Don’t try to go against the momentum. After the first month of bad, negative equity returns, don’t move money back into stocks when more bad news is in store for the market in subsequent months. Ride out the bear market and withdraw from the bond portfolio in the meantime.

Thus, the next result:

Lesson 4: The direction of the momentum doesn’t matter. In light of negative momentum, it’s still optimal to rebalance less frequently!

And onto one more scenario, combining the positive and negative momentum scenarios:

Scenario 5: A 6-month equity bear market followed by a 6-month bull market

Let’s combine scenarios 3 and 4 and build a bear market (6 months of -5% returns) followed by a recovery (6 months of +5% equity returns) and then back to scenario 1.

Uhm, well you actually do slightly worse. Without rebalancing, you’d lag behind about 0.1% after 1 year. How’s that possible? Well, you perfectly time the downtrend during the bear market and you have lower than 60% equity weight when the market goes down (about 52%). But the opposite effect is in place on the way up. When the market recovers, you still have less than 60% in stocks. So, you miss the bear market – that’s good! – but you also miss the bull market, which is too bad! The combined effect of the two is just about a wash.

The only way you could have “grabbed” the positive momentum in months 7-12 would have been to rebalance right at the bottom of the market after the last equity market drop.

Lesson 5: The market timing alpha from less-frequent rebalancing goes out of the window if you miss the turning point when the momentum direction changes!

In other words, the less frequent rebalancing works really well within one single updraft or one single downdraft of the market. Ideally, you want to rebalance once at the turning points (market peak and market bottom) to reset the portfolio and then benefit from the momentum in the opposite direction. Doing that at the right times will create a large outperformance relative to monthly rebalancing. But getting the timing wrong might also hurt you.

So: less frequent rebalancing is no free lunch. It relies quite a bit on skill (or luck) when timing the rebalance trades around the market turning points!

Simulations with actual stock and bond return data

What I’ve learned so far is that rebalancing at a frequency less than monthly could help you with Sequence Risk. That’s because the historical retirement cohorts negatively impacted by Sequence Risk started withdrawing funds right at the peak of the stock market and thus right at the beginning of a negative momentum phase for stocks (also known as a Bear Market!). You can ride out the negative momentum during the bear market! Thus, you avoid some of the “catching a falling knife” problem that you’d create with the monthly rebalancing.

The disadvantage of less frequent rebalancing is that if the market recovers quickly and you miss the rebalance at or around the bottom, then some or all of your rebalance alpha will go out of the window again.

So, could we save our butt with the “right” rebalancing strategy? Well, it wouldn’t be the first “solution” to the Sequence Risk problem that turned out to be a bit of a dud. But let’s take a closer look.

First, some case studies…

Case studies of a few prominent market peaks

For the simulations here I’m not relying on the Google Sheet I mentioned above. I built my own little simulation tool in Octave (the free version of Matlab) where I can quickly run simulations for thousands, even millions of cohorts really quickly all in one batch. (But if you like feel free to replicate some of the results with the Google Sheet.)

In any case, as a warm-up, let’s look at some of the retirement cohorts badly impacted by Sequence Risk:

• September 1929 (right before the Great Depression)
• December 1968 (the mid-to-late 60s were some of the worst impacted retirement cohorts on record)
• January 1973 (right before the 1970s economic malaise)
• September 2000 (around the dot-com market peak)
• October 2007 (global financial crisis)

Also, let’s assume we have a 60/40 portfolio and the following rebalancing frequencies: obviously the monthly baseline and the less frequent than monthly between every 2 months and 24 months, and finally also the scenario where we never rebalance (every 10,000 months).

So, I calculate the final portfolio value after 10 years under the different rebalancing assumptions and then compute the percentage advantage over the monthly rebalancing. I plot the results in the chart below. Uhm, that looks like a bit of a mixed bag! While the average is probably positive, there doesn’t seem to be a single rebalance frequency that helped you during every single event. This result shouldn’t come as a surprise given what we know about the rebalance mechanics: some or even all of the rebalance alpha might be lost due to missing the market bottom.

I also wanted to highlight one other issue. Remember from the setup of the Google Sheet above, there are actually two rebalance parameters: 1) the frequency and 2) the date of the first rebalance. For example, if retire in October and you like to do an annual rebalance, you don’t necessarily want to do the rebalance every year in October exactly on the anniversary of your retirement. Maybe you do it in December or around tax season in April. What kind of difference would that make in the five cohorts?

Let’s start with the quarterly rebalancing. Depending on whether the first rebalance occurs in month 1, 2 or 3 you get significantly different outcomes, see the chart below.

Let’s take the example of September 1929. The convention I follow in all of my simulations is that if you retire on September 1, 1929 then your first withdrawal occurs on August 31, 1929. If you pick the first rebalance month in month 1 (Mar/Jun/Sep/Dec rebalancing schedule) you generate a roughly 8% outperformance vis-a-vis the monthly rebalance. If you start rebalancing in month 2 (Jan/Apr/Jul/Oct rebalance schedule) then you lose about 7%. And if you rebalance in month 3 (Feb/May/Aug/Nov rebalancing) you gain 12% over the monthly rebalancing. This was actually the rebalance with the perfect timing because the market bottom occurs in month 33 during this bear market and thus rebalancing in months 3, 6, 9, and so on will perfectly grab that market bottom. Also, notice that the other 4 case study cohorts also have some great and some not so great outcomes depending on when you perform the first rebalance.

And we can do the same for the annual rebalancing. Now I plot the same chart as a function of the first rebalance (x=1,2, and all the way to 12), please see the chart below. Not surprisingly, due to the less frequent rebalancing, you have even more variation in results because there’s more room for messing up the rebalancing timing around the market bottom! In 1929 you’d have anything between a 7% underperformance (first rebalance in month 2) to an 18% outperformance (first rebalance in month 10). Market can be a blessing. Or a bi**h!

Simulation results using all cohorts

Let’s look again at the various rebalance frequencies between 2 and 24 months (plus “never” rebalance) and apply those to every single retirement cohort between 1871 and 2010. 2010 because the last cohort will need 10 years of return data to July 2020. All returns are in real, inflation-adjusted dollars and all withdrawals are adjusted for inflation as well. Then I simulate the first 10 years of withdrawals and compare the results and I compute the IRR of the first 10 years worth of portfolio values and cash flows, i.e., $1m initial investment and then 120 months of $3,333 and a final portfolio value in the last month. The stats for this exercise are below. Some results:

• Less frequent rebalancing will raise the average IRR. Quite intriguingly, the highest IRR prevails for the longest horizon (24 months), but there’s some deterioration when you go from every 24 months to no rebalances at all.
• You gain anywhere between 0.04% to 0.10% annualized. It doesn’t sound like much but keep in mind that this is purely free and lazy alpha. Considering that people make a fuss over 0.01% in the equity index fund expense ratios it’s nothing to sneeze at. For the average retiree with a $2m portfolio, we’re talking about $800-$2,000 p.a.
• Also quite intriguing: the share of cohorts benefiting from less frequent rebalances is above 70% for most of the frequencies. There’s clearly a benefit to letting the momentum run. Rebalancing too frequently would mess with your investment results!

As always, of course, looking only at the unconditional results might not be that informative. It could be that the rebalance strategy helps you mostly when the portfolio is going through the roof anyway. To be a hedge against Sequence Risk, we’d need to see good performance in light of low returns. So, I computed the same results again, but only for the 10% worst performing retirement cohorts (i.e., the lowest decile IRR for the baseline monthly rebalancing). The results are in the table below.

• Well, the average outperformance is now down to essentially zero. For the 24-month and “never” rebalancing strategies you even underperform pretty consistently, both when expressed as the mean but also the distribution; only 28.57% and 6.55% probability, respectively, of outperforming the baseline.
• But I’m positively surprised about how well the 3-month all the way to 6-month frequencies held up. They all still display a slight average advantage over the baseline and outperformed with 50+ and even 60+% probability over the simulations. Not bad!

What’s the net-net? If you have to pin down a desired rebalance frequency, I’d probably advise against an annual frequency due to the 60%+ probability of underperformance in the lowest decile. Instead, I’d probably go with a 3-month rebalance frequency. That seems to give you some outperformance during all market environments but, crucially, also performs well for all the unlucky cohorts during 10% worst market environments during the first 10 years of retirement. But again, always keep in mind that this is not a guaranteed alpha. There have been cases where the less than monthly rebalancing will backfire.

Conclusions

Ideally, you’d want to rebalance only exactly twice during the course of a full market cycle: once at the top of the bull market and once at the bottom of the bear market. And in between simply ride the momentum up and down. But market timing is not something that the average retiree wants to worry about.

Not rebalancing monthly might deliver some slight advantages over my monthly rebalancing assumption. That’s actually really good news for my Safe Withdrawal Rate Series because it means that the monthly rebalance assumption is a bit on the conservative side and actual retirees in the field don’t have to worry that maintaining their portfolio weights less frequently will blow up their retirement safety. Quite the opposite, by being a bit sloppy and lazy and adjusting the weights maybe only every quarter you might do just a little bit better on average.

Would I call this a “solution” to sequence risk, though? Absolutely not. The “timing alpha” inherent in the less-frequent rebalancing is not that consistent. It’s more of a hit-or-miss with a slightly positive mean over time but also some downside risk. By getting the timing of the rebalancing around the turning points wrong just by a month or two you could do worse than with the monthly rebalancing.

Thanks for stopping by today! Please leave your comments and suggestions below! Also, make sure you check out the other parts of the series, see here for a guide to the different parts so far!

Picture Credit: pixabay.com