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 March 2004 The Right Balance
P5 is our multi-cap portfolio. It's based on the Morningstar "stylebox" that divides equities into nine different combinations of style and growth. (For a more detailed description, click here.) We backtested it using ten years of data and then started following it out of sample effective January 1, 2002. Throughout that entire time we calculated its performance based on a very simple, elegant formula. Unfortunately, although easy to use, it really doesn't capture the nature of the model. Now that this has come to light, it's time to correct the situation.
The ProblemThe theory behind Portfolio 5 is pretty simple and should yield a procedure you can easily apply to your own investments. In essence, there are only nine different potential holdings such as "large cap growth" and "small cap core". Each is represented by an exchange traded fund (ETF) that can be purchased throughout the day like a common stock.Every three months, the portfolio's model reconfigures the combination of these nine potential holdings to produce what it projects to be the optimal mix. While in theory it's possible that it might call for the use of all nine potential categories, in practice the model has never used more than three. The limited holdings and relatively low trading level make this an ideal portfolio for the individual investor. This is truly something you can do at home. But it turns out the performance that has been reported here and on the home page, actually hasn't been calculated accordingly. The backtest was, but until now, the ongoing results weren't. Here's the problem: Starting with the out of sample results in 2002, we calculated daily portfolio results by simply applying the model's recommended weighting times the closing value of the ETFs. For example, the current mix (effective January 7, 2004) is 82% mid cap growth (IJK) and 18% mid cap value (IJJ). To calculate any given day's value of P5 we multiplied .82 x IJK's closing price and added it to .18 x IJJ's close. Simple, right? Well, simple but wrong. Think about it: If you, as an investor, were applying this model, you would have rebalanced your portfolio on January 7 by making the appropriate transactions to result in 82% IJK and 18% IJJ. You would have then left it alone until the next optimization in three months. But that's not what the simple calculation method does. By applying the 82%/18% breakdown each day, it treats P5 as being rebalanced daily. To do this at home, you'd have to buy or sell enough of each holding every day so that it would start at the 82%/18% mix the next day. Although even large portfolios would only need to trade a small number of shares each day, this would be cost prohibitive. In other words, daily rebalancing would require a lot of trading with very little to show for it. In a trendless market or one in which the model's constituents move in tandem, there may not be much difference in the return from daily and quarterly rebalancing. But in a trending market where holdings move in different directions or magnitudes, there's the potential for quite a disparity. For instance, consider January 5, 2004. On that day, traders excited about the prospect for fourth quarter earnings and just happy to be back from the holidays, sent stocks soaring. Growth issues were clearly preferred to value. As a result, mid cap growth (IJK) jumped 1.13% while mid cap value (IJJ) climbed a more modest 0.60%. If you were investing $10,000 based on this model, you would have started the day with $8,200 in IJK and $1,800 in IJJ. At the close of trading on January 5, these amounts would have
Now .1% may not seem like such a big deal, but remember, this difference was the result of just one trading day. With about 65 trading days in the quarter, this minor difference could compound and grow dramatically before the next rebalancing -- especially if the market holds the trend throughout the period. Also remember both holdings moved up in this example. The difference between the two has the potential to be even exaggerated if they move in opposite directions over the course of a quarter. The SolutionTechnically, there's nothing inherently wrong with calculation P5's returns with daily rebalancing. Still, this model was designed to be efficient not only from a risk and return standpoint by from an investing one as well. Given this, the best solution is to go back and recalculate performance based on quarterly rebalancing.The good news is the backtest was already done this way. It was done using historical data, monthly, and quarterly returns. No problem there. The mistake -- and that's what it is -- didn't start until January 1, 2002. That, then, is the starting point for the recalculation. While not as simple as the original percentage-times-share price calculation, this one still isn't too complex. It helps to be working with ETFs. Essentially it's done this way:
By applying this formula, we recalculated the daily values of P5 from January 1, 2002 forward. These are now the "official" values and are the source of the returns on reported in Historical Performance as well as on the Home Page. The ResultsA funny thing happened in making major changes in reported performance: There weren't any.
As you'll notice from Chart 1, it really didn't matter how often P5 was rebalanced, the daily and quarterly results plot right on top of one another. The greatest cumulative differences had quarterly rebalancing ahead by 0.31% on January 16, 2002 and daily rebalancing ahead 1.01% on May 15, 2002. The standard deviation -- the daily average variance from the mean was .1043 and .1039, respectively. Like the performance difference, this is negligible. The only noticeable trend occurred early in 2002 as the bear market came to an end. This is shown on Chart 2 which compares the cumulative performance of the S&P 1500 Super Composite vs. the cumulative difference between quarterly and daily rebalancing.
As you'll notice there, the difference between the two rebalancing methods grows in February and March 2002 until the quarterly optimization occurs in April. The same happens in early October 2002, immediately before that quarterly rebalancing. Both are likely attributable to a trending market (down in the first instance and sharply up in the second) catching the quarterly-rebalanced portfolio overweighted in the wrong direction. Yet at the end of the two-year period, these short-term differences really didn't make a difference. As of December 31, 2003, the two-year returns of the two methods differed by a mere 0.04%. Over the one-year periods, quarterly rebalancing was behind by 0.32% in 2002 and ahead by 0.50% in 2003. These results are summarized on Chart 3. These were definitely not the results we were anticipating. The market did trend sharply downward in the first half of 2002 only to reverse course in the last nine months of 2003. Under these conditions, we would have expected a greater difference in returns. So is the rebalancing period irrelevant? Contrary to what these two year's worth of data indicate, we'd still argue no.
If you'll notice from Chart 3, the short-term differences are greater than the results over the full two years. This period covers a sharp market decline and an almost equally sharp upturn. We would suggest that had the trend continued in one direction only, the differences between the two rebalancing methods would have been more pronounced. As it is, they essentially cancelled out. That's the hypothesis, anyway. It's not conclusive from the 2002-2003 data, but Chart 2 certainly seems to support it. We'll continue to calculate and compare the two methods of rebalancing and revisit this question when we have more data in hand. One thing is certain, however: If P5 is to be a quarterly-rebalanced model, its returns should be calculated accordingly. From now on that's how we'll do it. It's fortunate there wasn't much difference between the results of the two calculation methods, but this was probably more luck than statistics. That's one of the reasons why P5 is still a work in progress. Search this site! Just enter you key word or words:
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OMETIMES THE BEST SOLUTION IS the simplest and most elegant. Other times it isn't. We've been calculating Portfolio 5's returns by the former method when it turns out the latter is more appropriate.
