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How does rebalancing affect return?

I recently came across an article from William Bernstein explaining how periodic rebalancing is likely to affect the return in your portfolio.

The language in the article is a bit technical, but the message is important. The following is my attempt to put it in everyday terms (with some of my own explanations/interpretations mixed in).

What we’d expect: weighted-average returns

Imagine a portfolio made up of a 75/25 allocation between a stock index fund and a bond index fund.

If, over the next 10 years, the stock market were to earn an 8% return, and the bond market were to earn a 4% return, we might expect the portfolio (with its 75/25 allocation) to earn a return equal to the weighted average of the two–a 7% return.

Weighted Average Return = .75 (8%) + .25 (4%) = 7%

If the portfolio is rebalanced regularly throughout the 10-year period, however, the results are different. In fact, in most cases, the portfolio ends up earning a return that’s slightly greater than the weighted-average return of its components. (Bernstein refers to this additional return as the “rebalancing bonus.”)

Why does this happen?

In short, it’s because regular rebalancing is a way to force yourself to buy low and sell high.

The idea is that decreasing your exposure to the portion of your portfolio that’s just performed best, while increasing your exposure to the portion of your portfolio that’s underperformed should improve your performance. It doesn’t always work, but apparently it works more often than not.

How much additional return can we get?

Well, that depends on a couple variables. Specifically, it depends upon:

  • The volatility of each of the asset classes, and
  • The correlation between the two asset classes.

In order to maximize the rebalancing bonus, we want the volatility of each asset class to be high, and we want the correlation between the two to be low.

How we can profit from this information

It’s common sense that we can reduce portfolio volatility by adding an asset class that has little correlation to the rest of the portfolio. What’s fascinating to learn is that if the asset has an expected return equal to the rest of the portfolio, including it in the portfolio would not only decrease volatility but probably increase return as well.

Alternatively, if the asset has an expected return that’s less than the rest of the portfolio (as would be the case with adding a bond component to a stock portfolio), including it in the portfolio is unlikely to decrease expected return as much as we’d intuitively expect.

In other words, some of the return we sacrifice by including an asset class with a lower expected return than the rest of the portfolio is made up for in the form of a rebalancing bonus.

Takeaway #1: When constructing a portfolio, the correlation of the asset classes involved will affect not just your portfolio volatility, but your overall return as well.

Takeaway #2: Any asset that’s both highly volatile and uncorrelated to the stock market (gold, for instance) can make a lot of sense as a small portion of a portfolio due to the fact that it’s likely to contribute a greater return for the portfolio than would be indicated by the asset’s stand-alone return.

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Comments

  1. I recommend Valuation-Informed Indexing. That’s changing your stock allocation in response to big price changes.

    Many Passive Investors have a hard time buying into this concept. But it’s really just Rebalancing Plus. You describe rebalancing as a means of buying low and selling high. Valuation-Informed Indexing takes that logic a bit further and thereby provides (I believe) even greater benefits.

    Rob

  2. Haha, I literally just made a comment on your blog much to that effect. Neat how across-blog conversations are so effective at tying ideas together that way.

  3. Rick Francis says:

    Mike,
    I see how rebalancing with a very volatile and uncorrelated assert class would increase that asset class’ returns. However, it seems to me that there would be a point where the returns are low enough that even including the “rebalancing bonus” you still shouldn’t include a particular asset class.
    I’ve heard that gold has a pretty dismal long term investment record, so I wonder if it might be better to stick with a less volatile uncorrelated assert class with better long term returns like bonds?
    -Rick Francis

  4. Hi Rick.

    You’re absolutely right: There must be a point at which an asset’s stand-alone return is low enough that the rebalancing bonus would not make up for it.

    As to gold vs bonds though, I don’t think it’s a clear-cut answer.

    When most people quote super-low long-term gold returns, they’re usually looking at a period dating back to 1900 or so. The problem there is that we were on the gold standard for the bulk of that time period (up until 1970 or so, I believe).

    As a result, I’d argue that the period from 1900 all the way up to the point at which we dropped the gold standard offers roughly zero predictive value in terms of what we can expect in the future.

    Over the period 1970-2008, gold prices increased at a rate of 8.75% per year. 10-year T-Bonds earned 8.04% over that period according to my data.

    Of course, I’m not saying that we should necessarily expect gold to outperform bonds. (Its winning margin is pretty slim, and 39 years isn’t a terribly long period from which to draw conclusions.)

    I just think that coming to the opposite conclusion–“bonds outperform gold over long periods”–is similarly questionable.

  5. Hey this was a pretty interesting article; rebalancing made sense but didn’t know it would raise above the weighted expected returns, but reading now feels somewhat obvious haha…

    Also did not know that about the gold… where do you find that data? j/w..

  6. SJ: Frank from BadMoneyAdvice sent me this link: http://goldinfo.net/londongold.html

    Basically I just plugged year-by-year prices into excel, then calculated the return.

  7. Rick Francis says:

    Mike,

    I looked at a graph of the yearly gold price data- and I have to ask is the current price of gold is inflated? The price has nearly doubled in the last four years! I suspect because people are fearful of stocks and have fled to gold- a trend that could reverse very quickly.

    If the current market is a bubble then it would certainly skew the average return figures for gold, especially since we don’t have that many years of data.

    >I just think that coming to the opposite conclusion–”bonds >outperform gold over long periods”–is similarly questionable.

    Since the statistics for gold are complicated by the gold standard why not choose some other commodity? I’m sure there must be historical data for other commodities. Oil has been pretty volatile recently and I don’t know of any currency pegged to the price of oil. I suspect there are hundreds of years of data on corn prices- and it seems that it could be more volatile as the yearly production would vary with weather conditions.

    -Rick Francis

  8. I want to be clear upfront that I’m far from an expert on commodities (gold or otherwise).

    As to the question of whether gold is currently inflated or not, I guess my reply is “compared to what?”

    With stocks (and bonds), there’s an inherent value that’s a function of the fact that the security should actually be earning a return (dividends or interest) for its holder. We can therefore compute whether we’re paying a lot or a little for each dollar of earnings at any point in time. That is, stocks have a value other than what you can get for them on the open market.

    With gold, its only value is in what somebody is willing to pay for it.

    It seems then, that asking if gold is currently inflated is simply the same as asking “is it priced higher now than it will be in the near future?” And to that, my answer is simply “I haven’t a clue.”

    I like the idea of considering other commodities. Are you suggesting considering them for their own sake in a portfolio? Or simply to use historical data from other commodities as a proxy for historical data for gold?

    If option #2, then: Do other commodity prices behave the same way that gold does (or, more to the point, “will”)? It seems at first glance to me that the cross-comparison between commodities is rather more of a stretch than a cross-comparison between stocks.

    Sorry if I’m rambling…As I mentioned, I’m entirely inexperienced regarding commodities, so I’m simply typing as I think this through…

  9. Rick Francis says:

    I can’t prove that the price of gold is going to drop but such a rapid run up makes me concerned that it might. Of course bonds could get hammered in the future by a combination of rising interest rates and high inflation too so I think it makes sense to find alternatives.

    I don’t think the other commodities would be a very good proxy for valuating gold pre 1970- they would correlate but not perfectly. Bonds have a long track record so predictions of long term rates of return should be fairly accurate. There should be commodities with long records so you could calculate dependable statistics for them. I don’t have those statistics, but my feeling is that investing in any single commodity has uncompensated risk that could be diversified away through investing in many different commodities.

    I’m not sure if it would be practical for a small investor. There are some commodity ETFs, but what I would really want is something similar to a commodity index fund.

    -Rick Francis

  10. Sorry to change the subject from gold, but I have a question about the first example you gave.

    Assuming that the 8% and 4% returns over the next ten years are geometric (i.e. compounded) averages, would not the expected 7% return for the 75/25 portfolio be attained only assuming constant rebalancing? Surely you will agree that if you did not rebalance at all, but allowed the stocks (8%) to run you would do better than 7%? (I get 7.12%.)

  11. Frank, absolutely. I simply meant that the weighted average would give us a decent estimate. I should have said “roughly equal to.”

    Bernstein’s point–which I tried to simplify and surely distorted somewhat in the process–is that the return earned when rebalancing is still (more often than not) going to be greater than that earned by “letting it ride” (particularly when the asset classes involved are volatile, and/or have low correlation).

  12. Niklas Smith says:

    A very interesting post. I believe the idea of combining uncorrelated but volatile investments like gold and shares in the same portfolio is the one applied in Harry Browne’s “permanent portfolio”, which overall has very low volatility. But I am wary of gold because it does not provide an income stream so there is no objective way of valuing it. Perhaps the 25% gold allocation of the “permanent portfolio” is too much for my taste, but I could see the point of a smaller allocation (5-10%, possibly).

    Also, you say: “What’s fascinating to learn is that if the asset has an expected return equal to the rest of the portfolio, including it in the portfolio would not only decrease volatility but probably increase return as well.” This is surely a good argument for having a diverse holding of index funds for different stock markets, rather than just one index fund for all of your equities. The only problem is that stocks are globally quite well correlated, I suppose.

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