Thursday, May 13, 2010

Rebalancing Strategies: Periodic versus Thresholds

For investors who maintain constant portfolio allocations to different asset classes, such as stocks and bonds, there is a debate about when to rebalance. Most advice is to rebalance periodically, such as quarterly or yearly. Others suggest a threshold approach where rebalancing is based on when the allocation gets sufficiently far from the target allocation. I am in this latter camp.

The idea behind periodic rebalancing is to have a defined time to look at your portfolio, sell some of the assets that have grown beyond their target percentage, and buy the ones that are below. With the threshold approach, we wait for assets to get a certain percentage away from the target percentage and then rebalance. This could take just hours or it could take years.

Here is a simple example. Sally has her retirement savings equally split between a stock ETF and a bond ETF. (In my case it would be two different stock ETFs because I prefer not to own bonds for the long term.) Over time, the ETFs will rise and fall in value and throw her 50/50 allocation out of whack. Sally could ignore her portfolio until the first trading day each quarter to rebalance. If stocks are up, she would sell some stock ETF shares and buy some bond ETF shares to restore balance.

Another approach would be to set a window of say 45% to 55% and if the allocation gets outside of these thresholds, then rebalance. With either approach there are more choices to make. With periodic rebalancing you have to decide how often, and with threshold rebalancing you have to decide how wide to make the window.

I prefer to rebalance based on thresholds because the profitability of rebalancing depends mainly on how far out of balance the allocation becomes. A criticism of this approach is that it can lead to too much trading during volatile periods, but I'm not concerned with this if the trades themselves are profitable.

Profitability of rebalancing is best illustrated with an example. I'll cook the numbers a little so that we don't have to deal with fractions. Suppose that the stock and bond ETFs are currently trading at $55 each, and Sally owns 990 units of each. Let's assume that over a period of time the bond ETF stays flat at $55, but the stock ETF drops to $45 and then returns to $55. With a 45/55 threshold, this would trigger Sally to do some rebalancing:


Stocks: 990 at $55
Bonds: 990 at $55

Stocks drop:

Stocks: 990 at $45
Bonds: 990 at $55

Sally rebalances by selling 90 bond ETF shares ($4950) and buying 110 stock ETF shares with the proceeds. (We'll look at trading costs later.)

Stocks: 1100 at $45
Bonds: 900 at $55

Stocks rise:

Stocks: 1100 at $55
Bonds: 900 at $55

Sally rebalances:

Stocks: 1000 at $55
Bonds: 1000 at $55

If Sally had done nothing over this period of time, her return would have been exactly zero. By rebalancing, she ended up with an extra 10 shares of each ETF, a gain of $1100 less costs. She made 4 trades and traded a total of 400 shares. Assuming commissions of $10 per trade and losses of one cent per share in bid-ask spreads, Sally's costs are $44 for a total profit of $1056.

Other things that can affect the profitability of rebalancing are capital gains taxes for non-registered accounts and currency conversions if the ETFs are traded in different currencies.

It doesn't matter how long it takes for stocks to drop and rise back up again; these trades profit over the "do nothing" strategy whether they take place over hours or years. This is the reason why I prefer threshold-based rebalancing rather than doing it periodically.

To set thresholds wide enough to create profits after trading costs, it's important to take into account all costs. Capital gains taxes and currency conversion costs can make a big difference. Another thing to consider in very volatile times is that bid-ask spreads can widen dramatically and significant price changes can take place between selling the overweight holding and buying the underweight holding.

In practical terms, by choosing appropriate thresholds, trading will be infrequent. However, I prefer to be ready to pounce if volatility takes my allocation outside the thresholds rather than to miss out by waiting until the next planned rebalance day.

An advantage of periodic rebalancing is that you can ignore your portfolio for months at a time. A possible compromise is to check thresholds perhaps weekly. If price changes don’t last at least a week, conditions may be too volatile to trade at predictable prices. Personally, I tend to check roughly 2 or 3 times per week using rules coded in a spreadsheet.


  1. I'm with you.

    The purpose of rebalancing is to reduce risk and, as one would expect, have a balanced portfolio.

    Allowing the calendar to tell an investor when to do that is absurd.
    Rebalance any time you are out of balance - according to your definition of the term.

  2. @Mark: I'm glad to hear that someone else sees this as I do. There seem to be many commentators who advise checking portfolio balance periodically.

  3. @CC: You make a good point that while new money added is large enough, balance can be maintained most of the time with this new money. Also, when it comes time to pull money out of a portfolio in retirement, you can be selective in what you sell to maintain the desired allocation. All this can reduce the amount of rebalancing, but probably won't eliminate it entirely.

    1. The comment above is a reply to Canadian Capitalist's comment:

      As an investor who regularly adds to the portfolio, I had to rebalance only once so far when the allocations got really out of whack. Almost always, I simply rebalance when adding new money.

      When the portfolio grows large enough that periodic additions become a small proportion of the portfolio, I'll probably fall in the camp that rebalances when the allocation goes out of a range as well. It just makes more sense than rebalancing based on a calendar to me.

  4. Philosophically, I believe in threshold rebalancing. But I set my thresholds based on dollar amount rather than percentage. This way I know my costs should only be a certain percentage of the trade being made. However, because of this, I haven't had to rebalance yet. This is probably an indicator that I have too many ETFs for the size of my portfolio, but that will correct itself with time. :-)

    Although this isn't a revolutionary concept, I came up with the idea while reading David Swenson's 'Unconventional Success' where he argues the best thing to do is "continuous rebalancing". I took it to mean this was in a theoretical case where costs aren't an issue or the portfolio is so large costs are negligible. So I set a cost target approach to the general philosophy.

    For now, I just buy the most underweighted item every time I have enough money to make it worthwhile to execute a trade (sounds like this is basically CC's approach).

    Over time, I'd expect rebalancing trades to occur more and more frequently as my fixed dollar threshold becomes a smaller and smaller percentage of the portfolio.

  5. @Returns Reaper: Using dollar amounts as thresholds is an interesting idea. I tend to think in percentages, but that these percentages are smaller for larger portfolios. I'll have to think about this some more.

  6. @Jason R: Those are interesting observations. I think that the idea behind choosing a fixed asset allocation and sticking with it is that the investor can't predict periods of momentum or long slumps or anything else like this. If the investor believes that he can predict these things, then he will use entirely different strategies from using asset allocation with fixed percentages.

    There are some who suggest letting your asset allocation get out of whack to let the winners "run". However, this usually means an increasing allocation to riskier assets. If you're willing to take on more risk in this way, why not assign a higher percentage to the riskier asset in the first place?

    In the end it comes down to how much risk the investor wants to take on and to what degree he thinks he can predict the future. I prefer a strategy where I don't have to predict the future. I make decisions based on the long-term average returns and volatility of different asset classes, and I don't try to guess the future any more accurately than this.

    1. The comment above was in response to the comment from Jason R that I've reproduced below without the broken links:

      Funny, I recently started researching this topic.

      I found Larry MacDonald's post10 things to know about rebalancing from last December very interesting as well.

      A couple problems I've been considering:

      1. In periods where momentum is a factor (tendency for outperforming stocks/sectors to continue outperforming) this strategy will underperform. In fact it is pretty much opposite to a sector rotation strategy which chooses the best few performing sectors to invest in.
      I'm thinking you minimize this danger by rebalancing only non-correlated assets. This is often quite difficult, as almost all equities indices seem very highly correlated (with just varying degrees of volatility). One might even go so far as to use a momentum strategy with the equities portion of ones portfolio and rebalancing between the total equities/total bond allocation. This is a bit to "active" for me, but just an idea.

      2. The other problem is that in extended periods of equities under-performance (think Japan of the past 20 years) your portfolio gets decimated as you continually allocate more and more to a losing sector. It may be unlikely, but if one considers the demographic shift in North America over the next couple decades you can't rule it out.
      The easiest way I can think of to mitigate this problem is a market timing method which gets you out entirely. For example you might look at Mebane Faber's A Quantitative Approach to Tactical Asset Allocation:

      Any other ideas people have about dealing with these problems in a passive indexing strategy would be welcome!

  7. @Larry: My take on the width of the thresholds is to make them wide enough that the trades are profitable when one asset goes down then up again (or up then down). This is what I did in this article. However, each investor would have to take into account different costs.

    1. The comment above is a reply to Larry MacDonald's comment:

      Put me down for threshold. Then the question is how to do it. How wide the bands, how often to check, rebalance back to the midpoint or somewhere else …. I guess the quick answer is it depends on risk tolerances. Swedroe liked 5/25 -- rebalancing if the change was greater than five percent points or 25 percent (whichever was less). Gobind Daryanani found bi-weekly monitoring of 20-percentage-point bands optimal, etc.

  8. I'm also on the "threshold" camp. But I add an additional criteria on keeping the "cost" of my portfolio down to less than 0.5%. I keep a count of the number of trades I made for the lifetime of the portfolio. My commission is $10. If $10 x # of trades > 0.5% of my portfolio, I know I'm trading too frequently, and I wait until I have accumulated enough cash before I rebalance. Sounds too anal? probably. :P

  9. @P2sam: Keeping portfolio costs down makes a lot of sense. I do this by keeping the thresholds wide enough, but your idea of keeping track of costs as an added check makes sense. You might want to keep track of spread costs as well. If the sell and buy prices of an ETF $10 and $10.02, then a trade costs 1 cent per unit (half the spread).

  10. I see two contradicting conclusions coming from this post.
    1. Cut costs by holding ETFs that comprise VEQT directly instead of bunched up by Vanguard
    2. Rebalance as often as cost allows.

    Extra cost of holding VEQT for a year is 0.32%.
    How does this compare with the extra benefit of constant rebalancing offered by Vanguard?

    1. The value of Vanguard's automatic rebalancing depends greatly on the investor. If you would do your own rebalancing correctly taking costs into account properly, and you wouldn't find this to be a burden, then the value of automatic rebalancing is very low (much lower than 0.32%). However, investors like this are extremely rare. For the typical investor who would ignore rebalancing most of the time, would make mistakes sometimes, and would find the whole business of having to rebalance a bother, Vanguard's asset allocation ETFs are worth the money.

    2. Thank you for your explanation.
      My back of the envelope comparison of VEQT performance vs performance of its parts (as you presented in this post) resulted in significant advantage of VEQT. I am not sure if I accounted for all the intricacies. Do you know of an investment simulator that could do an accurate math over 10 years?

    3. I'm afraid I don't know of any available simulator. You can try looking up the opinions of experts on the value of rebalancing, but be warned that how they measure this value makes a big difference. For example, some say that you should only rebalance every few years. However, the supposed advantage of this approach comes from the fact that stocks tend to go up and you get higher returns when your portfolio is overweighted with stocks. So, infrequent rebalancing is little different from taking on slightly more risk. I prefer to think of rebalancing as a way to limit risk rather than as a way to earn higher returns. I focus on returns to choose rebalancing thresholds mainly to make sure that I'm not losing money on trading costs. Even though I'm pleased to get rebalancing profits from periods of high volatility, this isn't the real reason I rebalance.

    4. thank you.
      Your example of Sally's portfolio shows that rebalancing of 2 20% fluctuations resulted in a 2% gain. Following this logic I'd expect daily rebalancing to have a proportionate benefit (costs put aside). Is this an incorrect understanding?

    5. The two 20% fluctuations gave a 1% gain when measured against the entire portfolio. There is a quadratic relationship here. If the fluctuations had been half as big, the gain would have been 4 times smaller. These larger fluctuations are not common, so we can't expect large gains from rebalancing, except when volatility spikes.

    6. it's a 1% gain over 2 rebalancings of 20%. my mistake.
      If this is a quadratic relation, then 250 of 1% rebalancings between 2 ETFs should gain 1%/20^2*250, which is about 0.5%, which is in the vicinity of extra cost of owning VEQT. Rebalancing between 4 ETFs should generate even more. To me this means that extra fee of 0.32% charged by Vanguard is worth it. Is my thinking correct?

    7. I don't know exactly how much rebalancing would be available, but remember that two assets have to differ by 1% in your example. If the two assets move together by the same amount one day, then there is no rebalancing needed. Further, when you're rebalancing among multiple assets, the individual rebalancing operations involve smaller amounts of money. I doubt it is very easy to estimate the gains. Perhaps some experts have looked at actual results to estimate future gains.