The Rebalancing Myth

"Rebalancing increases portfolio returns".

is a common refrain, in some form or the other. However, this refrain is also almost certainly false when applied to the real world.


Let us define rebalancing as the process of selling assets that have appreciated in price, and replacing them with assets that have depreciated in price.

Let us define momenting (short for momentum investing) as the process of selling assets that have depreciated in price, and replacing them with assets that have appreciated in price.

Let us define buy-and-hold as the process of not rebalancing or momenting.

Let us define FOO bonus as the excess return earned by strategy FOO over the returns earned by buy-and-hold. Thus the buy-and-hold bonus is 0, by definition.

Thus the above falsehood about rebalancing may be alternatively stated as:

"The rebalancing bonus is positive".

Consider an efficient market populated by rational investors.

If you consider market efficiency and investor rationality to be operational and provisional assumptions (i.e. seem to be true in practice and will be considered so unless refuted) then read on. If you do not believe in even the operational assumptions of market efficiency and investor rationality, then there is little point in reading further.

In other words, the argument that follows is predicated on market efficiency and investor rationality.

Consider that the market is made up of 2 distinct, non-overlapping asset classes: This and That. It does not matter what This and That are composed of. It does not matter how the composition of This and That changes over time (day to day, month to month, year to year, whatever to whatever). It does not matter what procedure one uses to classify individual securities as being either This or being That.

Lemma 1:

If This and That are perfectly correlated with each other in their price and return behavior, then there is no such thing as a Rebalancing Bonus or a Momenting Bonus---both are identically 0.

So, for the rest of the discussion assume that This and That are not perfectly correlated with respect to their price and return behavior.

A market consists of 3 kinds of investors: buy-and-holders, rebalancers, and momenters. There are no other kinds.

Buy-and-holders do not participate in buying/selling activity based on the past behavior of This and That. Therefore:

Lemma 2:

Rebalancers, in order to rebalance, must exchange their relative proportions of This and That with momenters. Conversely, momenters, in order to moment, must exchange their relative proportions of This and That with rebalancers.

Lemma 3:

Rebalancers without Momenters end up being Buy-and-Holders.
Momenters without Rebalancers end up being Buy-and-Holders.

Lemma 4:

Everybody in the market cannot rebalance.
Everybody in the market cannot moment.

Lemma 5:

Everybody in the market cannot earn a rebalancing bonus.
Everybody in the market cannot earn a momenting bonus.

Lemma 6:

A rebalancing bonus necessarily implies a momenting penalty. It involves a transfer of (some fraction of) returns from the momenters to the rebalancers.

A momenting bonus necessarily implies a rebalancing penalty. It involves a transfer of (some fraction of) returns from the rebalancers to the momenters.

Lemma 7:

Buy-and-holders will always see a raw return (i.e. return before transaction costs and taxes) that is intermediate to the raw returns seen by Rebalancers and Momenters.

Lemma 8:

Transaction costs and taxes will erode the raw returns seen by Rebalancers and Momenters so that their net returns will always be lower than their raw returns. Since this transfer of costs is an externality, the sum of rebalancing and momenting is a negative-sum strategy.

Market impact costs can be reasonably ignored in this discussion, since there is just as much demand or dislike, and just as much supply or like, for This or That, either from rebalancers or momenters.

Lemma 9:

Rebalancing or momenting make sense only if they provide net return bonuses when compared to buy-and-hold.

In any case, consider an ideal world without costs. In other words, consider rebalancing and momenting in the best possible light against buy-and-holding.


Now, consider why someone would want to be a Momenter.

It cannot be because he/she knows for certain that the asset which has just appreciated in price will continue to appreciate into the future---remember, this is an efficient market.

It cannot even be because she/she knows with better-than-even probability that it is likely that the asset that has appreciated in price will continue to appreciate into the future---remember, this is an efficient market.


Now, consider why someone would want to be a Rebalancer.

It cannot be because he/she knows for certain that the asset which has just appreciated in price will begin to depreciate into the future---remember, this is an efficient market.

It cannot even be because she/she knows with better-than-even probability that it is likely that the asset that has appreciated in price will begin to depreciate into the future---remember, this is an efficient market.


Some people have data-mined the behavior of markets in the past and concluded that prices moment in the short-term and mean-revert in the long-term. This piece of information, even if true, is completely useless.

If everyone in the market knew that the market moments (or at least, momented in the past) over the short-term, no one would rebalance in the short-term. Momenters would not find rebalancers to match, and everyone would end up being a buy-and-holder.

If everyone in the market knew that the market mean-reverts (or at least, mean-reverted in the past) over the long-term, no one would moment in the long-term. Rebalancers would not find momenters to match, and everyone would end up being a buy-and-holder.

Lemma 10:

In other words, in an efficient market, where prices follow a random walk, rebalancing and momenting, if at all they lead to a bonus over buy-and-hold, can due so only for mathematical reasons, i.e. because of the statistical properties of random sequences and the mathematical nature of the rebalancing and momenting operations.

Rebalancing and momenting cannot lead to a bonus for informational reasons, i.e. cannot lead to a bonus because a subset of the market participants have more information than some other subset of the market participants, about the behavior of price changes---this sort of information imbalance goes against the assumptions of market efficiency and investor rationality.

Whatever the short-term or long-term behavior of markets in the past, this information cannot be used to make momenting or rebalancing decisions, because the very dissemination of this information will perturb the market behavior into the future.

Even the time-period at which the short-term momenting and the long-term mean-reverting tendencies balance out cannot be known with any useful degree of certainty. Whatever period one determines from past market behavior, this period will not be the same in future because the very use of such knowledge in investing strategy will make erode the usefulness of that knowledge.

It does not matter whether a real-world market moments in the short term or mean-reverts in the long term, whatever these phrases might mean. Any deterministic behavior in the market cannot be exploited because doing so will arbitrage the behavior away. To paraphrase Paul Samuelson, "properly anticipated prices will follow a random walk".


Let us now turn to the possible mathematical advantage for rebalancing or momenting.

Mathematical knowledge is still knowledge.

If it can be proved, with certainty, that rebalancing is mathematically superior to momenting, why would anyone moment?? Even if there is no informational advantage (regarding information about market prices and and the economics of the underlying securities), someone who has mathematically demonstrated that rebalancing has a mathematical advantage will never moment.

Likewise, someone who has proved, with certainty, that momenting is mathematically superior to rebalancing, will never rebalance.

Note also that a mathematical proof of either proposition applies to everyone in the market. I.e. if rebalancing is mathematically superior, it is superior for everyone in the market. So, it is simply inconsistent to claim that rebalancing is advantageous for some people, while momenting is advantageous for some other people.

When everyone knows that one or the other of rebalancing or momenting is mathematically superior to the other, why would anyone choose to follow anything other than this mathematically superior strategy.

Even if you replace proved with certainty with proved to happen with a high-degree of probability, the above arguments hold. The only state of affairs at which rebalancers and momenters will find each other equally matched, is when it is mathematically certain that neither has any advantage, informational or mathematical, whatsoever.

In that case, rebalancing or momenting is nothing more than a personal preference. Rebalancing and momenting are not rational investment strategies.


Some concluding remarks.

There exist some people who pay lip-service to the notion of market efficiency and investor rationality, but still continue to believe in the back of their minds, that they are somehow superior to and more disciplined that the majority of the investors in the market, and therefore have an informational advantage over them. Sadly, these people are also in the majority.

There exist some people who claim that the small investor, manipulating small amounts of money, is qualitatively different from the large investor, manipulating large amounts of money. Hence, these people claim, the small investor can follow strategies that, while informationally neutral, can sustain advantages that are impervious to arbitrage by the larger players, because the larger players do not have the guts to engage in arbitrage (or else, these larger players are supposed to march to the drum-beat of different kinds of motivations and rewards, things that are not conducive to arbitrage and performance maximization). The less said about such belief the better, esp. when these people also seek to gain their arbitrage advantage by investing in mutual funds controlling huge amounts of money.

There exist some people who also claim that not only does rebalancing improve returns, but it also reduces risk ("through diversification", they claim). In other words, more returns for less risk. Naturally, those who claim this also claim to believe in market efficiency and investor rationality. The terms that best describe such people are: fool, unscrupulous liar, and unscrupulous lying hypocrite.

I leave it to you to digest these bits of information.


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First version: Thu Nov 9 16:43:02 PST 2000
Last updated: Sun Jun 27 17:00:19 PDT 2004
URL: http://www.reocities.com/krishna_kunchith/markets/rebalance.html