Every portfolio should be rebalanced to its targeted asset allocation, we are taught.  Indeed, there may be no other precept as routinely and studiously practiced among financial advisors.   But does rebalancing either increase expected return or reduce risk?  If so, why? 

The answers to those questions reveal that it may be prudent to rebalance, but not for the reasons you think.

In the investment field – as in almost no other – it is well known that you can never assume historical patterns will continue. This is because of the arbitrage principle: if prices follow a predictable pattern, investors will arbitrage that pattern out of existence.

Hence, when an investment strategy seems a good idea for whatever reason, somebody often trots out a claim that there’s a mathematically-certain reason why it works. You need the mathematical reason to make it a law of nature, immunizing it against the vicissitudes of history and data. Knowing only that it worked in the past, or that it seems like a good idea, isn’t enough.  It may not work in the future. The advocate of an investment strategy therefore has strong motivation to say – and usually to believe – that there’s a mathematical reason why it works, even if there isn’t one.

For example, people have advanced mathematical arguments why dollar-cost averaging and so-called fundamental indexing must work. The mathematical arguments are wrong – usually because the claimant hasn’t taken the trouble to state clearly what criteria would establish that the strategy “works.”

Let’s take the case of rebalancing. It is widely believed that there is a mathematical reason why rebalancing should work. This belief is in error – at least, it is in error under all the mathematical models of securities prices that are generally accepted and applied by both the academic and practical investment communities.

But there do seem to be reasons to believe that rebalancing will have benefits. Those reasons are so far only empirical, and more in the nature of anecdotal evidence than clear-cut statistical evidence, and therefore may not be reliable in the future. Nevertheless those reasons point – as do so many things since the financial crisis – toward the need for an improved theory of financial markets, one that takes into account the likelihood and pattern of financial bubbles and crises and derives from it amendments to our models of securities price movements.

The case of rebalancing

Rebalancing began as an afterthought, then became conventional wisdom in no time flat.

The models on which “modern portfolio theory” or MPT were built were – and are – one-period models. They apply to one of many decisions in an investor’s lifetime, for only a short period of time, such as a year. They ignore all the decisions the investor might make and objectives the investor might have after that.

This may suggest to you that the models have limited value – and you’d be right. The models did, however, at least force the investing world to recognize two principles: (1) it’s better to diversify; and (2) you can’t get more return without more risk.

Harry Markowitz’s mean-variance algorithm appeared to show a portfolio manager how to “optimize” a portfolio’s asset mix. But because the model is so sensitive to inputs that they have to be jerry-rigged to produce reasonable outputs, that optimization, even for a single period, doesn’t actually work very well in practice. Even if it did, there would be the problem of what to do in the next period, and why. That was taken care of by simply assuming – as an afterthought – that you apply the same optimal asset mix again and again, to every period. Hence, you need to rebalance, because by the time you get to the end of the period your asset mix may not be the same as the one you decided on at the beginning.

This afterthought was fueled by the assumption that the standard deviation of returns over short time periods was an investor’s measure of risk. As we’ll soon see, that assumption can be severely mistaken. But once that assumption was made, it was natural to assume that an investor wanted to keep his or her risk constant; that was done by rebalancing periodically to the original mix.