Thursday, November 12, 2009

Portfolio Rebalancing Experiment

Following up on last week’s musings on using portfolio rebalancing with a 100% stock portfolio, I decided to run an experiment using real stock prices. The goal is to see what benefit rebalancing brings over buy-and-hold.

Fairly arbitrarily, I decided to divide the portfolio into half Canadian and half U.S. stocks. Each half consists of one individual stock and two index ETFs (one large cap ETF and one small cap ETF). The starting portfolio contains equal values of 6 different equities:

BMO – Bank of Montreal stock
XIU – iShares Canadian Large Cap ETF
XCS – iShares Canadian Small Cap ETF
BRKB – Berkshire Hathaway stock
VV – Vanguard U.S. Large Cap ETF
VB – Vanguard U.S. Small Cap ETF

The starting portfolio size for the experiment is $400,000 (Canadian). Because XCS began trading 2007 May 18, the experiment begins on that day with money divided equally among the 6 equities, rounded to the nearest 100 shares, except for BRKB which is rounded to the nearest share (because of its high price). Two different portfolios start this way: one is buy-and-hold and the other uses rebalancing.

The following costs are assumed:

– Trades cost $9.95 (Canadian or U.S. depending on the shares bought or sold).
– Bid-ask spreads are two cents, except for BRKB whose spreads are one dollar.
– Currency conversion costs 0.5% on top of the exchange rate in each direction.
– Funds are in a tax-sheltered account so that no capital gains taxes are paid.

The buy-and-hold portfolio does no trading for the roughly 2.5 years from portfolio inception to the present. The other portfolio rebalances whenever the allocations drift too far from equal allocations in the 6 equities. It was surprisingly difficult to settle on a set of rules for how to do the rebalancing.

To minimize currency conversion costs, I wanted to rebalance from one Canadian equity to another or one U.S. equity to another, where possible. I settled on the following rules to trigger a trade:

– If the total Canadian side gets outside the range 45% to 55%, then rebalance.
– If one of the Canadian equity’s proportion of the Canadian side is outside the range 33.3% plus or minus 5%, then rebalance the Canadian side. Handle the U.S. side similarly.

For the actual rebalancing, I usually sold one overweight stock and bought one underweight stock. All trades were in multiples of 100 shares (except BRKB).

The initial portfolio size and rebalancing rules are set so that the typical trade size is about $10,000. In cases where two equities were roughly equally underweight or overweight, the buy or sell was split into two separate trades. I used my judgement rather than trying to define all the rules completely precisely.

However, I did not use any discretion in deciding when to rebalance. Whenever the portfolio was out of balance, I brought it back into balance that day.

The following chart shows how the rebalanced portfolio fared against the buy-and-hold portfolio. The red triangles mark the 8 rebalancing days that were needed over the 2.5 years.

In the end, the rebalanced portfolio won out by 3.95% (about 1.6% per year), but it wasn’t a smooth ride. For the first year and a half, rebalancing lost money. Rebalancing seemed to do a good job of exploiting the high volatility earlier this year.

Overall, this experiment doesn’t prove one way or the other whether this strategy will profit over buy-and-hold. If a basket of equities each rise at about the same average rate of a long period of time, then rebalancing can capture extra profits from the relative volatility. However, if one or more of the equities’ average growth rate is significantly lower than the others, then continually rebalancing into the underperforming equity will hurt returns.


  1. Interesting results. How did you handle dividends in the experiment?

    Did this exercise give you any ideas for further study?

  2. Ace: I should have mentioned dividends. Dividends were collected as cash into the accounts. The rebalanced portfolio got a total boost of about 0.4% more than the buy-and-hold portfolio due to capturing more dividends. This happened mainly because the rebalanced portfolio was selling BRKB (which doesn't pay dividends) and buying the other equities.

    I certainly have thoughts on further study, but this exercise was fairly labour-intensive. Collecting historical prices and dividends involves going to web sites and cutting and pasting, etc. I don't have an automated setup for this right now. I would like to choose different baskets of ETFs and stocks and try this experiment over other periods of time, etc., but that's not likely to happen soon.

  3. I suppose if you wish to maximize the potential of profiting from portfolio re-balancing, you could rebalance a portfolio of two highly volatile stocks that have not, in the past, moved in tandem. But then your two stocks could underperform the market, or the stocks could start moving in tandem.

    Alternatively, you could try to stay diversified and rebalance a portfolio of, say, a US and EAFE ETF. But then you'll find the re-balancing pay-off is fairly modest.

    I suppose you took a middle of the road approach that I suspect a lot of investors and active mutual fund managers take: some mix of the core market with trading in individual stock picks. If active mutual funds are any indication, I doubt there is much of a pay-off from this approach versus just holding the market.

  4. Blitzer68: You're probably right that the expected payoff of rebalancing over a long period is modest, but it's hard to know without actually running the experiment.

  5. I appreciate your posts since I think they help to educate investors, which is the point of your blog. So thanks for all your posts.

    One tricky thing with experiments on past investment performance is it's not like an experiment of the natural world, where you expect a certain regularity to continue. I'm thinking about the sun rising in the morning, that sort of thing. The correlation between investments seem to be less predictable. Perhaps it's because people are involved.

    Reminds me of the life of a chicken who is hand fed by a farmer every day of the chicken's life. That chicken must be near certain that he'll be fed every day to come. Of course, that's true until the farmer wrings its neck for dinner.

    I can't remember the moral of the story. It's either don't be hand fed by farmers if your a chicken or beware of past investment patterns.

  6. Blitzer68: Even some aspects of the natural world can suffer from the chicken and farmer problem. A particular valley might be free of molten rock for 10,000 consecutive days and then suddenly the nearby volcano erupts.

    The main danger of maintaining a particular balance of a basket of equities is that one of them will go to zero dragging the entire portfolio to zero.

    Experiments can be illuminating, but you can't count on the future being the same as the past. The biggest problem with many "experiments" is that they aren't really experiments at all. If you try thousands of different variations of an idea across many time periods and report on the most favourable case, then you are data mining. Data mining is often used for marketing purposes, but it isn't really illuminating at all.

  7. Michael: Like blitzer68, I appreciate your educational posts... I especially appreciate that you take the time to do what I would call 'primary research'. To your point about the labour involved: I wrote a program to collect and analyze public data (from Yahoo and Google Finance) for my blog. If it would reduce the cutting/pasting, I'd be happy to collaborate on something. My e-mail is in my blogger profile.

  8. Graham's classic, "Intelligent Investor" looks at the same issue in a much longer time period. It's a slow read, but quite interesting. He also concludes that regular rebalancing is a valuable exercise.