The Elusive Rebalancing Bonus – Part 1

Passive investors typically rebalance their accounts every now and then to get the various positions back in sync with their target asset allocation. This multi-part article studies various rebalancing methods and analyzes if some of those methods provide(d) a significant rebalancing bonus. Part 1 will focus on basics, describing typical rebalancing methods and illustrating them with some historical trajectories. The next parts of the study will explore rebalancing in more quantitative details.

What is rebalancing?

A passive investor articulating an investment plan will typically come up with a target asset allocation (AA), say something like 50% US equities, 20% international equities and 30% US bonds. Such target AA might stay fixed year over year or possibly follow some sort of glide path (say 1% more bonds every year), but the fact is, every year, there is a target to aim at.

In the mean time, the stock market tends to follow a rather erratic and unpredictable trajectory and if one’s portfolio is perfectly aligned with a given target AA at the beginning of the year, the current positions after a few months or a year will drift away from the intended target.

In the illustration below, the target AA is 25% of four assets (say US stocks, Int’l stocks, Bonds, Gold). After some period of time (say a couple of quarters), the current asset allocation starts shifting (say gold suddenly picks up in value while Int’l stocks crater for whatever reason). Rebalancing would then be the fact of exchanging shares (e.g. sell/buy) between the four asset classes to come back to the plan of record (i.e. the target AA). Rebalancing methods (as discussed below) regulate WHEN to decide to rebalance.

All-in-one funds (e.g. Target-Date or LifeStrategy kind of funds) automatically perform rebalancing on behalf of their investors, but passive investors choosing to use more than one fund (e.g. a three-funds portfolio, or more) will have to rebalance by themselves.

Note that rebalancing is typically something to perform across one’s entire portfolio, across all investment accounts (taxable and tax-deferred). It is certainly easier to act on tax-deferred accounts where exchanges have no tax impact (nor transaction costs), while more care should be exercised with taxable accounts, to avoid triggering capital gains and other cost issues. This article will not cover tax implications, nor transaction costs.

The baseline method: annual rebalancing

The simplest rebalancing method is to pick a fixed date in the year (early January, some sort of anniversary, whatever) and rebalance one’s portfolio at this date, irrespective of the current state of the portfolio. Many backtesting tools make such implicit assumption, e.g. a rebalancing towards the target AA on January 1st. Here is an illustration of what would have happened to the current AA over a period of 20 years. Click on the image below to see a bigger version.

Many graphs in this article will use the same format, so let’s unpack it:

  • Such graph shows what happens to a portfolio made of a given initial investment over a time period of 20 years. No addition (contribution) or withdrawal is performed during this period of time, to simplify.
    • Most graphs below will use the same time period (1995-2014) as this is a particularly eventful period.
  • The initial (and fixed target) AA is 50% US stocks (blue line), 20% Int’l stocks (green line) and 30% US bonds (purple line).
  • The lines wiggle over time as the current AA of the portfolio evolves with the vagaries of the stock market.
  • Rebalancing events occur every now and then and are shown with the red triangle mark labeled with the corresponding date. The asset allocation is then reset to its target.
  • The underlying data set is a set of weekly returns (total returns, dividends included) for each asset class. The author’s spreadsheet computes on a weekly basis if rebalancing is warranted or not.
    • In this precise case, rebalancing events occur every 52 weeks, to approximate annual rebalancing.
    • Note that 52 weeks is 364 days, not exactly a full year, so there is a little bit of calendar drift over time as the rebalancing labels show.
    • Rebalancing labels show Mondays, but actual rebalancing would obviously happen on the first tradable day of the week.
    • The 15-Dec-08 rebalancing event is the most dramatic event of the graph, due to the financial crisis unfolding in Q4-08.
  • The thin orange line near the bottom illustrates the S&P 500 price trajectory. This helps to appreciate when large movements of the stock market occurred (e.g. big bull market run-up; big stock market crises).

To illustrate how things can be different over time, the following chart displays annual rebalancing between 1980 and 1999 (essentially one long bull market with a few hiccups along the way, notably in Oct-87).

Such annual periodic rebalancing method has the great virtue of simplicity and is used by many investors. We will use its properties as the ‘baseline method’ when analyzing more complex methods.

Rebalancing triggers

A common criticism of annual (or periodic) rebalancing is that a fixed rebalancing date is very arbitrary and doesn’t account for those ‘special moments’ in time where markets go haywire, leading to sudden sizable changes in one’s portfolio.

For example, if the stock market drops 30% in just a few weeks (as happened in March 2020), a cold blooded investor might perceive that stock suddenly got much ‘cheaper’ (relatively speaking) and might wish to use its ‘excess’ bonds to quickly buy more stocks while they are ‘cheap’. Fact is rebalancing can be perceived as ‘selling high and buying low’, by virtue of selling shares in positions which seem more highly valued than others (the shares one would buy when rebalancing). Let’s take an example.

Let’s say we start with $1000 with a 60/40 asset allocation, therefore $600 in stocks and $400 in bonds. Let’s say stocks drop by 33% while bonds stay stable. The portfolio is now $402 in stocks and $400 in bonds, essentially a current AA of 50/50. One could be tempted to use the 10% ‘excess’ bonds to restore the 60/40 target allocation, while perceiving that those good stable bonds are used as ‘dry powder’ to buy stocks on a fire sale, hence selling bonds ‘high’ to buy stocks ‘low’. Please note that the author is NOT stating that such perception is correct, just that it speaks strongly to one’s intuition.

Subsequently, one might be tempted to define rebalancing triggers (aka rebalancing bands), i.e. dynamic rules allowing to decide when to rebalance in an event-driven manner instead of a calendar manner. This implies to monitor one’s current AA very frequently (say weekly or monthly), but simple scripts (say with Google Sheet) can easily automate such process. The two main types of triggers are fixed bands and relative bands (which are sometimes combined), a less commonly used type is called adaptive bands. Let’s explore those variants.

Rebalancing with fixed (absolute) bands

Let’s keep exploring the 50/20/30 asset allocation from the previous graph. One could decide to rebalance when one of the asset classes drifts by an absolute 5% or more from their target (i.e. if US stocks go above 55% or below 45%; or if Int’l stock go above 25% or below 15%; of if US bonds go above 35% or below 25%). Assuming a weekly monitoring process of sorts is in place, here is what would have happened.

Note that such ‘fixed band’ approach keeps the virtue of simplicity, but applying the same 5% absolute variation to a 50% (target) position or a 20% (target) position seems rather inconsistent. Still, such approach is certainly a good way to be more reactive to ongoing events, whether they follow quite dramatic changes (e.g. end of 2008) or slower cumulative changes (e.g. big bull market by the end of the 90s or the slowly-unfolding Internet crisis which followed).

Let’s look more carefully at how the Internet and the Financial crises unfolded. The following chart hones on the 2000 to 2011 time period and the scale of the S&P 500 price (thin orange line) is expanded to show the events. The Financial crisis in 08/09 is the most glaring with four rebalancing events in quick succession (the first two just a few weeks apart!), certainly frazzling the nerves of most investors. It then took nearly two years for rebalancing in the reverse direction. Note that rebalancing triggers just perform simple percentage math, which led (in hindsight) to rather poor market timing calls in Q4-08 (while the rebalancing events in 2009 were more fortunate). The Internet crisis unfolded much more slowly, but the same type of observations apply. Rebalancing is just a discipline, there is NO market timing magic here.

The fixed (absolute) bands approach suffers from clear inconsistencies though. Let’s say that we express the 50% US allocation as two 25% positions of the same asset class (or something very similar, e.g. total-market vs. S&P 500 index). Quite clearly, fixed bands will then not behave the same way and this makes little sense.

A sounder variation of fixed bands consists of assessing a cumulative drift from the target AA. Just sum up the positive differences (for each asset class) between the current AA and the target AA, then use such cumulative drift as the trigger to rebalance. This solves the previously described consistency issue (and other similar issues) while keeping the math trivial.

Rebalancing with relative bands

A variation on the previous idea is to use relative bands, say rebalancing when an asset class is more than 20%, relatively speaking, from its target. Using such logic on our 50/30/20 allocation:

  • 20% of 50% is 10%, so one would rebalance if US stocks exceeds 60% of the current AA or is below 40%.
  • 20% of 20% is 4%, so one would rebalance if Int’l stocks exceeds 24% of the current AA or is below 16%.
  • 20% of 30% is 6%, so one would rebalance if US bonds exceeds 36% of the current AA or is below 24%.

Here is what would have happened when starting in 1995, a slightly different pattern than the fixed band approach, but not that dissimilar.

This relative band approach is more consistent than the fixed band method, while keeping computations to a very simple formula. Still, for large positions (e.g. 50% of the portfolio), a relative band could end up being uncomfortably large. One could, of course, tune how reactive the algorithm is, by using narrower or wider bands. Here is the same chart using a 15% relative band.

Combining fixed and relative bands

A fairly common practice (popularized by Larry Swedroe) consists of combining fixed (absolute) and relative bands. A ‘5/25’ rebalancing algorithm would use fixed (absolute) 5% bands in combination with 25% relative bands. Fixed bands would be used for any asset class weighing 20% or more in the target AA and relative bands would be used for smaller positions. This is certainly useful when asset allocations use smaller positions (e.g. a 10% tilt towards something like Small-Cap-Value, Gold or REITs). If a position is only 10% of one’s portfolio, waiting for it to go to 15% or 5% (a fixed 5% difference) would take quite a rare chain of events…

As a side note, the 5/25 numbers are often touted as a typical recommendation, but as we could see from the previous sections, a 25% relative band is actually VERY wide (in other words, it could let the current AA drift away a lot from the target AA) and seems a rather odd choice.

With the 50/30/20 allocation we’ve been illustrating, only fixed bands would be activated with such combined algorithm, so there is no point providing a graph of such approach in this specific case. To better observe the dynamics, we can adjust a bit the asset allocation, carving out 10% for Small-Cap-Value while reducing US stocks to 45% and Int’l to 15% (just as an example), as illustrated below.

Looking carefully at the first three rebalancing events, we can see that the ones in Mar-96 and Sep-97 were triggered by the 5% fixed rule, while the next one (in Feb-99) was triggered by the relative rule (with a 20% band) on the smaller SCV position. This being said, if one would disable the relative rule, a rebalancing event would have occurred in Mar-99 based on solely using the fixed rule.

Rebalancing with adaptive bands

As was hinted at, fixed bands as well as relative bands have the virtue of simplicity, but anybody with a bit of a mathematical bent would quickly sense that those are rather inconsistent methods, which are ok for some simple asset allocations, but less so for other cases. As to the combined approach, this seems a rather unsatisfying kludge.

Such considerations led to in-depth discussions on the Bogleheads forum, from which emerged a more mathematically consistent approach dubbed ‘adaptive bands’, which can be implemented with a simple (albeit non intuitive) spreadsheet formula. The point of this blog is not to delve in such detailed discussions, but interested readers can start reading here. In essence, a 20% adaptive band would be triggered by a 20% drop (or increase) of a given asset class in absence of changes to the other asset classes. Note that 20% is then an absolute number, which consistently applies irrespective of how large or small the asset class target is in the overall AA. It is also a truly symmetrical band, based on geometric math (while simple relative & fixed bands formulas suffer from asymmetry).

Here is an illustration of 20% adaptive bands with the same parameters as before, followed by the same graph using 30% adaptive bands (hence less frequent rebalancing events).

In all fairness, although adaptive bands are more consistent than previous schemes and more directly applicable to any type of asset allocation, the primary net effect is probably a form of intellectual satisfaction for math-minded investors. For other investors, just picking fixed and/or relative bands that fit a specific portfolio would probably work better, if only because of the more intuitive nature of corresponding formulas. Such considerations are essentially behavioral, but this is important too. Matching one’s strategy with one’s skills and psychology is the best way to stay the course…

One-way rebalancing

In combination with some of the methods previously described, some people like to add another constraint which can be expressed as “only rebalance out of stocks, never into stocks”. The author assumes that the intent is to mitigate emotions along the lines of “don’t catch a falling knife” when a deep crisis is unfolding in real time and nobody knows (in foresight) the outcome. Avoiding to sell ‘safe’ bonds under such circumstances will probably provide emotional comfort to some.

This is all understandable at the ‘gut feeling’ level, but backtesting shows that really strange situations can occur. In the graph below, the same target AA as before is used, started again in 1995, using fairly narrow 15% relative rebalancing bands, but the time period was extended till mid-2020.

If you’re looking for rebalancing events between 1999 and 2017, well, there were none. Stocks dropped precipitously during the Internet crisis and just never recovered enough before the Financial crisis hit, i.e. not coming back where one could ‘rebalance out of stocks’ (i.e. US stocks exceeding 60%, the target AA). It took until 2017 (nearly 20 years!) for the current AA to catch up with the target AA for US stocks, finally triggering a rebalancing event (then another one, ironically enough right before the Covid-19 crisis started).

One might argue that you would only use one-way rebalancing in the depth of a crisis while not being shy to rebalance ‘when things are getting better’, but this is the kind of logic that is hard to put in a formula and relies more on intuition than anything else. And intuition might not be one’s best friend in troubled financial times.

More on data sources

This analysis is based on straightforward data sources, to avoid conclusions to be affected by other types of ‘noise’ (e.g. a fund or an index changing strategy mid-way, expense ratios varying greatly over time, etc).

In addition, to test rebalancing triggers, one needs data sources with extensive AND frequent/reliable history (e.g. weekly data, dividends included). As an acceptable approximation, monthly data is acceptable for some of the older years, notably for slow-changing bonds. To keep the weekly rhythm consistent across series (notably for trigger-based rebalancing methods), the author interpolated monthly returns to equivalent weekly returns (which should work reasonably well for bonds).

The author honed on the following indices as data sources. Note that most tests only used Total-US-Market (TSM), International Stocks and US Aggregate Bonds. With such data set, the author was able to study ~40 years of history (from 1980 to mid-2020). This is a marked change from known rebalancing studies which are often limited to time periods of 20 years or less (again, compare the first two charts to see how things can differ between two time periods). It is also a marked change from studies solely focusing on two asset classes (e.g. US stocks vs. bonds) where older data is available, but suffers from significant issues with granularity (e.g. due to history only recording quarterly dividends) and a certain lack of realism (most passive investors use 3 funds/asset-classes or more).

Wilshire 5000 Total Market TR USDTSM
Russell 2000 TR USDSCB
Russell 2000 Value TR USDSCV
FTSE Nareit All Equity REITs TR USDREITs
LBMA Gold Price AM USDGold
Bloomberg Barclays US Aggregate Bond TR USDBonds
Bloomberg Barclays US Treasury Long TR USDLTTs

Using such indices has the great virtue of simplicity and consistency, and remains fairly realistic as modern passive index funds have quite a remarkable track record of very closely following their index benchmark. The absence of an expense ratio (ER) is not an issue since modern funds have a very low ER, plus most of the computations are made of relative comparisons between numbers (therefore a roughly identical -small- ER adjustment to all data series would not change the outcomes).

Still, to check that the tests weren’t somehow skewed by such index-centric approach, the author also used another data set made of real-life funds (see below). Some of the choices may seem odd, but it is quite difficult to find funds with enough history back in the 80s. Even with such long-lived funds, this led the author to have to approximate some of the missing early years (e.g. use small-caps in lieu of small-caps value) while accepting some historical disruptive changes (e.g. NAESX used to be an active fund before it became a passive index fund in 1990, etc). For gold, there was just no good solution the author could find besides the price index, but few tests used this series anyway.

Vanguard 500 Index Fund Investor SharesTSMVFINX
Vanguard Small-Cap Index Fund Investor SharesSCBNAESX
Vanguard International Growth Fund Investor SharesInt’l VWIGX
Vanguard Intermediate-Term Tax-Exempt Fund Investor SharesBondsVWITX
Fidelity Real Estate Investment PortfolioREITsFRESX
LBMA Gold Price AM USDGoldLBMA index

Long story short, the top level findings were very similar to the findings determined with the index-centric data set. The latter being more consistent, more extensive and closer to modern passive investing, the author decided to use the index-centric data set for the graphs and numbers being published in this entire article.

For general context, here are two growth charts tracking the investment of $1 on 31-Dec-79, until 30-Jun-2020, for the various asset classes of interest represented by their index. Note that the vertical scale is logarithmic.

Next Steps

After this introduction to the most typical rebalancing methods and the type of backtesting one can perform, the next part of this article (Part 2) will tackle an assessment of the so-called ‘rebalancing bonus’, to try to quantify if a given rebalancing method or another truly provides improved benefits. And then we will address a few miscellaneous topics in Part 3.