The theory behind investing in a multi-asset portfolio is pretty straight forward when simplifying it. You select a diverse set of uncorrelated assets, assign target weights and then you’re done. Not that tricky.

It is mainly the managing part of the investment process that is more challenging. First, you have to work to maintain your conviction to stick to the strategy and remembering why you chose the strategy in the first place. Secondly, you have to deal with rebalancing the portfolio, as uncorrelated assets are guaranteed to develop in different directions with some assets zigging when others are zagging.

**The topic of rebalancing is one which I find is underserved in the literature and one that I get a bunch of questions about.** Usually, it is the theory behind a portfolio that is the most exciting to write about and which is the key topic that sells and attracts more clients. The science of rebalancing, however, is just something that is covered briefly, at most.

While I have been writing about portfolio rebalancing in the past, I have recently found renewed inspiration for this topic. That inspiration turned into this post, where we are looking more closely at rebalancing luck, and if there is an optimal time in a month to rebalance a portfolio.

Recently, I have been quite tied up at work, which has meant that I have not been able to spend as much time as I would have wanted to write these Insights posts. It is a shame, as I enjoy working on them and trust that they can even be useful for others at time as well. So please bear with me, and I will at times be able to produce these nuggets again, as I have more good topics lined up after this post. But now, let’s jump right into the topic of rebalancing.

**When is the optimal time to rebalance an investment portfolio?**

Rebalancing is a core part of managing a diversified portfolio which holds more than one asset, especially when the assets you own have low or negative correlation with each other. By rebalancing when the portfolio weights have drifted away from the aimed allocations, you will capture a *rebalancing premium* (also called a “rebalancing boost” by some) by selling the assets that have performed relatively well and buy those that have performed relatively poorly.

If you are an investor who has opted to leave behind a stock-only portfolio and instead invest with a broadly diversified portfolio, you need to make a decision of when you should be rebalancing your investments. Whether you invest using the All Seasons Portfolio strategy, or any other diversified portfolio based on a similar philosophical framework, such as Harry Browne’s Permanent Portfolio or the Golden Butterfly, rebalancing is something you should always keep at the top of your mind.

While you can add many nuances to how you go about with rebalancing, the most opted for solutions, among both retail investors and institutional investors, is to decide on a rebalancing frequency and stick with it. This approach is short, sweet, and simple, and suits most investors, as it eliminates all complicated elements of investing and still gets the work done.

**The most common rebalancing frequencies are annual, semi-annual, quarterly, and monthly rebalancing.** It is especially common for retail investors to take a moment during the Christmas holidays and near the year-end to review how the portfolio has done over the year, and to make any rebalancings and trading before the end of the tax year. Furthermore, the most common approach is to just follow the calendar, for example that quarterly rebalancing is carried out at the end of each financial quarter (March, June, September, and December).

In addition to rebalancing frequency, you can add more flavor to your rebalancing strategy, such as **rebalancing spans** (you rebalance when the holdings have drifted X% from their aimed weights) or apply **rebalancing rules based on trend and partial rebalancing** (which I have written about previously in an article about strategic rebalancing).

The aim of this current post is not to dive into any complicated rebalancing rules, but let us stick with just talking about rebalancing frequency.

What we want to find out is whether it matters when you rebalance a portfolio. Longer frequencies, like annual rebalancing, allow for capturing more of established trends, while shorter frequencies, such as monthly rebalancing, can help you capture more of the swings that occur over a year.

While we are not going to analyze today which is best of monthly, quarterly, or annual rebalancing frequencies, **we are going to review if it matters when within a month you pick your rebalancing date**.

Most rebalancing rules are designed so that the rebalancing shall occur on or around the last trading date of a period, for example on the last day of the month or quarter, or that if you rebalance annually or semi-annually, it is often done in December or June/December. **But is this kind of calendar-based rebalancing optimal? **

## Rebalance Timing Luck

The inspiration to write this article about the timing of rebalancing a portfolio comes from a series of articles on the topic of Rebalance Timing Luck published by Newfound Research (founded by Corey Hoffstein). Speaking of, make sure to also follow his podcast Flirting With Models (not to be confused with supermodels, but rather the sexy kind of models where you analyze data), consisting of interviews with people in the quantitative investment universe. This is a podcast I have high on my listening list, as it is educational, insightful and entertaining.

**The foundation of their rebalance timing research comes from that when two portfolios are managed with the exact same strategy in the same manner, with the sole difference being when rebalancing occurs, one of the portfolios is destined to perform better than the other, and that outperformance can only be explained by luck, as there is little to no alpha in setting a rebalancing schedule. **

Even though the audience of Newfound Research’s work is institutional investors, I saw an opportunity to conduct a similar test but which is easy to replicate also for retail investors. Newfound’s results show that rebalance timing luck has an impact on a portfolio’s performance and can make a portfolio manager seem skilled or unskilled, even though he/she uses the exact same strategy and identical rebalance frequency as his/her peers. There is therefore definitely career risk involved for asset managers, which boils down to luck, as the contribution of timing the rebalancing event can only be measured ex-post (see “Rebalance Timing Luck:* The Dumb (Timing) Luck of Smart Beta*” by Hoffstein et. al. 2020).

Note that when rebalancing a factor-based portfolio, as tested by Newfound, it can change the whole constituent composition if annual rebalancing is done in January versus July (different companies can rank higher or lower in e.g. momentum factor rankings between these dates), especially if turnover is high. Hence, the test we are carrying out is somewhat different, as the held assets will always remain the same (there is no constituent substitution), but we will find out if rebalance timing luck applies to diversified portfolios made up of assets with low correlation.

## Testing rebalancing timing luck versus randomly assigned rebalancing dates in a month

While Newfound focused their research on equity factor strategies designed to capture value, momentum, quality, and low volatility tilts, we will here zoom out to a broader and less granular portfolio – something closer to what retail investors hold in multi-asset portfolios. As this blog is about the All Seasons Portfolio and other all-weather strategies, and with retail investors in mind, we will find out whether the concept of rebalance timing luck applies also for rebalancing a diversified portfolio.

To allow our research to include the longest history, we will not be using the All Seasons Portfolio as the guineapig (historical data for TIPS and Commodities were not easily available found for the period before the 1990s). As we have good access to data for stocks (S&P 500), bonds (10-year Treasury Bonds proxied by 10Y constant maturity bonds), gold, and cash (3-month Treasury Notes; proxied by 3M constant maturity bonds), we will instead use Harry Browne’s Permanent Portfolio (with a 25% capital allocation to each) as the portfolio in this test. Note that as we are only testing whether the timing of rebalancing matters for portfolios with identical strategies and identical rebalance frequencies, the exact portfolio is not as important for demonstrating the point.

In our test, we will be looking at a Permanent Portfolio over the period 1 January 1979 to 31 December 2022 (1979 was the first full year of daily gold price data in USD I found). This period still gives us 516 rebalancing occasions, as we will be rebalancing our portfolio monthly.

Also, for properly conducting the test for finding out if *luck *is better than the convention of rebalancing on the last trading day of each month, we are using 100 portfolios for which we generate randomly assigned rebalancing dates in each month (i.e. that the rebalancing date is a randomly chosen day in a month, and that the date is assigned for each month individually). The only constraint we have implemented for generating the rebalancing dates is that at least 5 days must have passed between rebalancings (i.e. that a rebalancing cannot occur both the last day of a month and the first day of the next month).

We will then compare the results of the portfolios with randomly assigned rebalancing dates against a portfolio which rebalances on the last trading date of each month, which is the current most-applied convention (the zero hypothesis H0). If the average of the random rebalancing is greater than the conventional rebalancing strategy, then we can conclude (with statistical significance) that rebalancing luck is a proven risk factor, and that you are better off avoiding rebalancing on the last day of each month.

Additionally, we are reviewing if there are any other fixed days of the month that are better for rebalancing a portfolio than the last trading day. For example, if a portfolio which is consistently rebalanced X number of days before the end of the month, if it fares better than if rebalancing was carried out at the end of the month.

What can we expect? To set the scene, the empirical results in Newfound’s study suggest that strategies with lower turnover rate should be less impacted by rebalance timing luck than strategies with high turnover rate. In a Permanent Portfolio, the turnover will be low, as all we do is rebalancing between the same set of assets. On the other hand, they also found that higher portfolio concentration (fewer holdings) increase the magnitude of rebalance timing luck, which in our case should be an offsetting factor to the lower turnover rate (we only have 4 assets in the tested Permanent Portfolio that we are going to test, while Newfound’s portfolios held more than 100 individual stocks; additionally 4 uncorrelated asset classes can increase the effects of rebalance timing luck vs. 100 investments in the same asset class). Thirdly (and lastly), higher frequency of rebalancing (monthly versus annually) further lessens the exposure to timing luck. In our experiment below, we are rebalancing our example portfolio on a monthly basis. **Hence, any visible impact from rebalance timing luck will thus be an important takeaway from this analysis. **

### Rebalance timing for a Permanent Portfolio 1979-2022

Let us begin with reviewing the performance curves of our 100 portfolios with random rebalancing dates each month. I include also the end-of-month portfolio for comparison, as well as two alternative portfolios rebalancing 7 and 14 days respectively before month-end.

Note the dispersion of results. The difference in CAGR for this Permanent Portfolio between the high and low was 1 percentage point (5.71% for the best performer, versus 4.72% for the worst), with the average CAGR being 5.24%. At the same time time, rebalancing this Permanent Portfolio on the last trading date of each month would have given you a CAGR of 5.07%.

The immediate take-away is therefore that if you would have picked a random day in each month for rebalancing your permanent portfolio, **on average, you would have been better off than trading on the last day of the month, as is convention**. Let’s now continue by testing if this outperformance is statistically significant.

### Statistical analysis of rebalancing dates

To determine whether the improvement in the average end result of H(A) (our alternative hypothesis of randomly selected rebalancing dates) is statistically significant, we can conduct a hypothesis test using a t-test. The null hypothesis (H0) (rebalancing on the last trading date of each month) is that there is no difference between the two rebalancing strategies, and the alternative hypothesis (HA) is that H(A) is better than H(0).

To conduct the t-test, we first need to calculate the t-statistic, which is given by:

t = (x̄A – x̄0) / (s / √n)

where x̄A is the average end result of H(A), x̄0 is the end result of H(0), s is the standard deviation of H(A), and n is the sample size.

Assuming a significance level of 0.05, we can compare the calculated t-statistic to the critical t-value with n – 1 degrees of freedom, which can be obtained from a t-distribution table or calculator.

If the calculated t-statistic is greater than the critical t-value, then you can reject the null hypothesis and conclude that the improvement in H(A) is statistically significant.

Let us now take the data we gained from running the test for our 100 portfolios and insert it in our formula. With a sample size of 100 and a standard deviation of 68.4439, we can calculate the t-statistic as:

t = (x̄A – x̄0) / (s / √n) t = (946.68 – 879.73) / (68.4439 / √100) t = 9.782

where x̄A = 946.68, x̄0 = 879.73, s = 68.4439, and n = 100.

Using a t-distribution table or calculator with 99 degrees of freedom (n – 1), we can find the critical t-value at a significance level of 0.05 to be approximately 1.984.

**Since the calculated t-statistic (9.782) is greater than the critical t-value (1.984), we can reject the null hypothesis and conclude that the improvement in H(A) is statistically significant at the 0.05 level. Therefore, based on this analysis, it appears that rebalancing on a random date each month is a better strategy than rebalancing on the last trading day of the month.**

### What day us best for rebalancing a portfolio?

Having concluded that rebalancing a portfolio on the last day of each month appears to be a suboptimal strategy, we wonder, is there a more optimal day to perform the rebalancing on?

Likely, in real life, we don’t find it attractive to every month assign a rebalancing date randomly, but rather would prefer a fixed day of every month to avoid the struggle imposed by the randomness factor in our workflow.

Let us therefore continue to review if any one day is better than end-of-month, i.e., that we pick a day X number of days before the end of each month and see if we can find a rebalancing strategy that seems to be better.

In the below chart, we see the equity curves of 28 identical Permanent Portfolios, again with the only difference being on what date in a month the rebalancing is carried out. In contrast to the first test we conducted above where the rebalancing was random, each portfolio this time is rebalanced on the same day each month. If such date would not be a trading date in any month (for example that the rebalancing date falls on a Saturday), the rebalancing is carried out on the immediately preceding trading day.

Also here we find a rather wide dispersion of results.

**Compared with the average compounded annual growth rate of 5.27% of all 28 portfolios, rebalancing at month-end returned 5.07% per year, i.e. 0.20 percentage points below the average portfolio. The best portfolio, on the other hand, returned 5.62% (10 days before month-end), while the worst portfolio gave a return of 4.97% (14 days before end-of-month). **

Notably, over the period 1979-2022, there was a cluster of underperformance when rebalancing around mid-month, with the three worst performing portfolios were the ones for which rebalancing was carried out 12, 14, and 15 days before the end of the month (all with CAGRs or 4.97 and 4.98%).

If you, on the other hand, are looking for the optimal days to rebalance a portfolio, picking a day which is between 7 and 10 days before end-of-month appears to yield the best results (10 days before was also our best performing portfolio). The average CAGR of these four portfolios was 5.46%, which is almost 0.20 percentage points above the average of the whole sample, and 0.39 percentage points over the last trading day of each month.

## Optimal rebalancing during the QE era

Moving on to more recent timeframe, has the strategy to avoid the last trading date for the monthly rebalancing held up?

The test above covered a period of 43 years, and with the advent of computers and quant strategies, it is likely that the markets have become more efficient and that a monthly rebalancing arbitrage should thus disappear over time.

To test this, let us conduct the same test as above, but narrowing down the timeframe to only look at *modern *times. For this, we will consider the era of central bank quantitative easing as our “modern era”, which can be claimed to have started around November 2008.

Remember that as we are only testing rebalancing dates and their impact on portfolio return, it is not important to our test that it is covering a period of mainly one macroeconomic environment (rising economic growth, falling inflation and falling rates).

If we review the below equity curves of the same portfolios, we immediately find that the average portfolio (gold line) now is below the line for the portfolio for which the rebalancing was carried out on the last trading date (black line). It thus appears like the edge of randomness has disappeared, but that does not mean that rebalance timing luck is gone. The latter is proven by the best performing portfolio is not the end-of-month portfolio, but it is less profitable to try to chase the luck.

**Running the same statistical analysis as before, with a standard deviation of 6.464, the t-statistic in this test is -10.1317. As this is less than the critical point for 0.05 significance level at 1.984, we cannot conclude that random picked dates is a better rebalancing strategy than rebalancing at the end of each month. **

Continuing in the same spirit as earlier, below follows also the CAGR analysis of fixed rebalancing dates. While the CAGR has been lower for Permanent Portfolios in general over the last 14 years as this has been a period favoring stocks (and being detrimental to e.g. gold), the dispersion is lower with less variance around the average CAGR of 4.38%.

While the results are less convincing than for our longer period test, there still seems to be some relative increased probability of slight outperformance around the 7-10 days prior to month-end mark (which now extends to 13 days), albeit this is in the same range as if you would be rebalancing on the last trading date of the month.

**This means that if you want to avoid rebalancing on the last trading monthly date for some reason, it is the 7-10 day window you should be considering instead. **

One reason for why someone would want to avoid the last trading date is to circumvent the largest capital flows when the behemoths rebalance. Most large asset managers (both active and passive) typically carry out their rebalancing on or near the last day of the month or quarter, why there will be more liquidity on the market around these days. This could have an impact on prices overall, as capital would be flowing from relative outperformers to relative underperformers on a larger scale.

For example, if bonds have outperformed stocks by a great deal in a quarter, 60/40 portfolio managers will be selling bonds and buying stocks. When you consider the size of the asset management industry, the volume of these trades could be large and can move prices. In a world with growing tendency of indexing, opportunities can also present themselves to trade against such expected rebalancing behavior. For the more passive investors, though, it could prove simpler to just avoid the grand rebalancing circus altogether by rebalancing 7-10 days earlier.

## When should a portfolio be rebalanced?

**As there is no rebalancing schedule that is superior to others, it shows that rebalancing timing luck is an uncompensated source of risk when constructing a portfolio.** Any edge there may have been for rebalancing on set dates which deviate from the last trading date of each month, appears to have been arbitraged away as markets have become more efficient. Most investors are there wise to not be picking up pennies in front of steamrollers.

It matters less nowadays on what day of the month you rebalance your portfolio, but any rebalance timing luck becomes visible with less frequent rebalancing schedules. This aligns with the empirical evidence presented by Newfound Research. Note also that my test was conducted for a monthly rebalancing frequency, why the results might differ for schedules of quarterly or less frequent rebalancing. One can assume that there would be a larger impact if we rerun the test for quarterly rebalancing (also Newfound concluded that there is more rebalancing luck associated with less frequent rebalancing). Depending on the reception of this post, I might revisit this topic in the future to also review other rebalancing frequencies.

One middle-way solution, as also suggested by Antti Ilmanen (AQR Capital Management) in his book **Investing Amid Low Expected Returns** (one of the most insightful and best books in portfolio management I have read), is to spread out the rebalancing over a longer period but so that you only do a partial rebalancing with each rebalancing event. For example, instead of an annual rebalancing all the way back to the aimed allocations, you do quarterly rebalancing a quarter of the way back to targets (for example, if stocks have drifted from 30% weight to 34%, with the first rebalancing, you sell it down to 33%, rather than all the way to 30%). This procedure allows you to still capture most of trends while getting the benefits from a rebalancing premium also during a year. The downside is that this approach is slightly more cumbersome to administer for retail investors.

Our research show, however, that if you want to avoid the last trading date each month for rebalancing your portfolio, **it has been advantageous to use the window of 7-10 days before the end-of-month** to match the expected return, even though the difference is not as significant as it has been over the decades leading up to 2008.

If you have made it this far, I thank you for having dedicated a few moments of your time to read this article. I hope you found it useful in your planning for portfolio rebalancing and that it has helped your thinking around this subject.

As mentioned in the intro, I am aiming to release a few more insights posts in the near future (separate from my monthly All Seasons Portfolio performance updates), so make sure to hit the subscribe button at the bottom of the page to not miss anything.

Thanks again for your attention, and please feel free to reach out in the comments!

-Nicholas

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