### Does Rebalancing Really Pay Off??

Investment advice is rife with nostrums that have never been backed up by adequate proof or evidence. Many of these are ritualistically repeated by advisors who assume that, because they have been repeated so often and for so long and by reputable experts, there must be a good reason for them.

No investment advice is more universally offered than the advice – originally posited by William Bernstein – to rebalance your portfolio. Yet, the evidence that this practice is beneficial is shockingly meager.

**The rebalancing bonus?**

The assumption that rebalancing provides a benefit in increased return is encapsulated in the phrase “the rebalancing bonus.” This catch-phrase was originated by Bernstein in an 18-year-old post on his website, efficientfrontier.com, titled “The Rebalancing Bonus.”

In this posting, Bernstein said, “An understanding of the mechanics of rebalancing is fundamental to sound portfolio management, and yet surprisingly little theoretical attention has been paid to this area.” This was true at the time and it is still true now. To this day, little work of theoretical merit has been devoted to the question of whether and when it is beneficial to engage in the practice of rebalancing. Bernstein’s posting remains the best effort to tackle the issue to date, and has had the longest-lasting effects.

Unfortunately, there are flaws in the argument. Bernstein and I have communicated about this and he is well aware of the issues. Nevertheless, many of its implications are still very much alive in the claims for rebalancing often heard voiced by advisors.

I will first point out the flaws in the 1996 posting. From there, I will go on to delineate the issues surrounding the question of rebalancing that remain after removing the misconceptions that it inadvertently perpetuated. Then I will explore these issues through a combination of empirical studies of historical returns with the results of simulations.

**The trouble with Bernstein’s rebalancing bonus**

The odd thing about Bernstein’s rebalancing bonus posting is that he shows what is wrong with it in almost the same breath with which he introduces the term. He establishes a measure that he calls the “Markowitz return” by defining it as the weighted average return. But he says at the same time that “It is surprising that Markowitz considered portfolio return to be the weighted sum of the component returns.”

Yes, that is how Markowitz defined it for his one-period model and in that case it is correct. If a portfolio starts with a specified asset weighting and then holds the assets until the end of a time period without buying or selling, portfolio return over that time period is indeed the weighted average of the raw (i.e., unannualized) asset returns.

However, Bernstein went on to define the Markowitz return over a multi-year period as the average of the annualized asset returns. Over the period 1926-94 he calculated this so-called “Markowitz return” for a stock-bond portfolio with an initial 50-50 mix as 7.85%. This is in fact a meaningless number because it is not a measure of the growth of the portfolio using any discernible asset reallocation strategy, either dynamic or static. Furthermore that return, so defined, is always less than the actual annualized return on a buy-and-hold portfolio over the same time period.

Bernstein then defined the “rebalancing bonus” as the excess return of a rebalanced portfolio over the “Markowitz return.” Since the return on an annually rebalanced portfolio is 8.34% over the same time period, the “rebalancing bonus” is 0.49%. Thus, he compared the return on a rebalanced portfolio with a phantom benchmark that is always less than the return on a buy-and-hold portfolio.

In fact, in the very next sentence, Bernstein pointed out that if the portfolio had not been rebalanced, its return would have been 9.17% – 0.83% higher than the rebalanced portfolio and 1.32% higher than the Markowitz return. Nevertheless he let the definition of “rebalancing bonus” stand, as the difference between the return on a rebalanced portfolio and the Markowitz return. Here we find the accidental – and accidentally misleading – origin of the term “rebalancing bonus.” It is misleading because it identifies the benefit of rebalancing as its incremental return over a meaningless number.