## Tuesday, October 5, 2010

### A Portfolio Rebalancing Trap

The idea behind rebalancing a portfolio is to maintain your intended asset allocation percentages. A side benefit is that rebalancing involves selling one asset when its price is high and buying another when its price is low. I’ll show that this process can actually lose money if you’re not careful.

It is tempting to rebalance whenever assets differ from their target amounts by some fixed dollar amount. However, this doesn't always work well. Portfolio size matters. Larger portfolios should wait for larger deviations from target levels when the deviations are measured in dollar amounts.

I’ll use a very simple example to illustrate the problem. In a real portfolio, there are many factors that mask what is going on making it difficult to judge whether rebalancing is profitable or not.

A Fictitious Portfolio

Suppose that Jim’s portfolio consists of just two ETFs: BND and STK. Jim’s intended asset allocation is 50/50. Initially Jim has 1000 shares of each and they trade at \$20 per share for a total portfolio value of \$40,000.

A few months later, BND is down to \$18 and STK is up to \$22. Both assets are \$2000 away from their target amounts in Jim’s portfolio. So, Jim decides to rebalance. He sells 100 shares of STK and buys 100 shares of BND. Before costs, this leaves an extra \$400 in his account.

After another few months, BND and STK have both returned to \$20. Jim decides to rebalance again by selling 100 shares of BND and buying 100 shares of STK. Jim’s portfolio is now back to exactly what it would have been if he had never done any rebalancing, except that he has an extra \$400 (less costs).

Suppose that each trade costs Jim a \$10 commission and the bid-ask spread is 4 cents. This means that Jim pays an extra 2 cents per share on each buy order and receives 2 cents less per share than the going price on each sell order. In total, Jim made 4 trades and traded 400 shares. He paid \$40 in commissions and \$8 in spread costs. His profit from rebalancing twice is \$352.

A Larger Portfolio

Suppose that Sue’s portfolio is very similar to Jim’s except that hers is 20 times larger. She starts with 20,000 shares of each of BND and STK at \$20 per share each. Sue plans to rebalance her portfolio whenever BND and STK differ from their target levels by \$2000 or more, just as Jim did. The big difference here is that it will take a much smaller move in ETF prices to trigger Sue to rebalance.

After a couple of days, BND is down to \$19.90 and STK is up to \$20.10. Both assets differ from their target amounts in Sue’s portfolio by \$2000 and Sue rebalances by selling 100 shares of STK and buying 100 shares of BND. The big difference from Jim’s case is that this leaves only an extra \$20 (less costs) in Sue's account.

After another couple of days, BND and STK return to \$20 triggering Sue to sell 100 shares of BND and buy 100 shares of STK. Sue’s costs will be the same as Jim’s: \$48. But her profit before costs is only \$20. She actually lost \$28 doing this rebalancing. Sue would have been better off to have done nothing.

Even though both Sue and Jim traded the same number of shares, Sue lost money and Jim made money. The lesson is that the threshold for rebalancing can’t be just some fixed dollar amount of deviation from target amounts.

Real Portfolios

It’s important to keep in mind that while this problem is fairly easy to see in this example, it is difficult to see it in a real portfolio. Equity prices don’t behave simply the way they did in this example. They move around randomly and rarely sit at nice round figures.

However, losses from rebalancing are still a real possibility. Hyper-active rebalancing can make you lose money whether you realize it or not. This is particularly true when rebalancing between assets denominated in different currencies. Currency conversion charges effectively raise spread costs by roughly a factor of 10 to 100.

One of the best ways to rebalance is to put new money into whichever asset class is below target. When percentages get far enough away from target that this doesn’t work and you plan to rebalance by buying and selling, make sure that trading costs don’t eat up your gains.

1. You explained that perfectly. You must be careful when rebalancing. when we do rebalance I believe it usually is once a year. So its probably more out of balance than your example. The frequency we rebalance depends on the individual. But isn't the rule of thumb, once a year?

2. I tend to rebalance when I have more funds to add to my portfolio, and use that money to create the balance. It is rare I "move" from one area to another, I simply buy more as needed, which still can cause problems, but less shuffling of the deck chairs on the Titanic.

3. @50plusfinance: I prefer to rebalance based on when my portfolio gets out of balance by more than some threshold amount. I'm still working on what the threshold should be. I don't see any problem with rebalancing only once per year. At least that approach won't generate excessive trading costs.

@Big Cajun Man: Rebalancing with new money works well while you're adding a significant amount of money compared to your total savings. Presumably, your savings will grow over time and you may have to actually sell then buy to rebalance.

4. Michael, I read an academic study that reviewed rebalancing strategies in a hypothetical portfolio (like your example) for 1 - 4 years. They found that 4 years was optimal and, by extension, longer is probably better. I believe that holds in any bull market. If I find the reference, I'll pass it on to you.

The only optimal times to rebalance are market tops and bottoms. We both know how likely investors are to do THAT :) Your advice to "rebalance" using new money (or dividend income, I would add) is wise. The next best advice is probably to set a percentage threshold after which an investor will rebalance, as opposed to a dollar limit. For example, if the allocation to a certain asset (class) is >5%, rebalance. This should keep costs down.

One last caution: thinking about the mechanics of trading, high volatility could throw a wrench in the works. Remember September and October 2008? Some days the market would move 4-5% in a day. Imagine selling bonds, waiting three days for settlement, then buying stocks. You could be paying up at 8% higher prices than you planned!

5. @Robert: Any study of rebalancing strategies between stocks and bonds will discover that stocks have outperformed over the long ran and that it is best to never rebalance. However, people hold bonds to lower volatility.

In my case, I don't hold bonds for the long term. I'm looking at rebalancing among stock ETFs. Since the presumption going in is that we can't predict which ETF will outperform over the long run, there is reason to believe that rebalancing can be profitable.

All results I've had so far indicate that the threshold level for rebalancing (the 5% you mention) depends on portfolio size. Small portfolios would lose money if they traded every time they were out by 5%, and large portfolios would be leaving profits on the table if they had such a wide margin. In the cases of rebalancing between assets in different currencies or when capital gains are involved, 5% seems to be too narrow. This subject is more complex than it is made out to be.

6. I believe I saw another study once that showed markets do have some momentum for these purposes - rebalancing to get a 0.1% difference is a waste of time. But of course if you wait 4 years, where those 4 years ends would make a big difference with recent price histories.

1 year feels a bit more natural to me (and the 1-year cycle probably has some impact on investor psychology that makes it a useful anchor) but of course there's no way I can prove that :)

I'll probably end up looking at a combination of factors but if you periodically review the asset allocation you want, deviation from that would seem to be the biggest thing to look at. You just need to consider whether the trading commissions or changes to contributions are worth it.

7. @Richard: On a million dollar portfolio, 0.1% is \$1000. If all I had to do to make \$1000 is tap two trades into my computer, I'd do it. If \$1000 is a waste of time, then going to work each day is a much bigger waste of time.

8. "If \$1000 is a waste of time, then going to work each day is a much bigger waste of time." You had me laughing out loud at this.

And to Richard, if the markets have momentum (and I believe they do), why would you set a time-based rebalancing trigger, instead of a momentum-based rebalancing trigger?
That's what I've been trying, since January. DecisionMoose offers some ideas.

9. @Michael James - if you're in a market when you can move 0.1% in a month (ie not this year) then based on the relative size of the move you're either trading on volatility or getting out in the first day or a long-term trend. There are probably a few ranges - if you rebalance every day when the difference is big enough you can capture all the volatility, whereas if you rebalance every 3-6 months you may miss out on further trends if you rebalance 6 months after a trend turns when the average trend lasts 3-5 years. It sounds dangerously under-researched to me so I wouldn't be afraid of rebalancing if the difference is big enough :)

@Robert - the idea (if it does work) would be to ensure you don't reduce your exposure well before the average length of a trend. What momentum indicators would you use?

10. Richard: I've been tracking the relative movements over 50 days and 200 days (equal-weighted average) between stocks and bonds, with confirmation that the 5 day average is positive. I've been watching this for a year, but haven't traded on it (no need in the last year).

It's something I update manually once each week. It's not a crystal ball, but it gives a clear(ish) idea of the movements of the market.

11. Robert: interesting - are you looking at this as a signal to sell at the top and buy at the bottom, or do you start to buy in when prices go off a peak and start to sell out as they begin climbing?