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 January 2007 Weight Watching A Comparison of Dollar Weighting and Equal Weighting Portfolio 3
Actually the same is true for investment portfolios. A slightly different weighting with the exact same assets can result in dramatically different results. Most investors put much more effort into deciding what to buy rather than how it and their other holdings fit together in their portfolio. Many don't even know how to weight a portfolio or why it's important. That's a shame since it doesn't require a lot of work to make weighting work for you. All it takes is a little thought and consistent application.
All of our model portfolios are dollar weighted rather than equal weighted. That means the more expensive the holding, the more impact it has on overall return. That's not a bad approach if all the holdings are priced about the same, but it can skew performance if they aren't. Portfolio 3 is one of our quantitative large cap models. It's been around since mid-2000 so it has a suitable history to study the impact of dollar weighting. We already know the results of this scheme, what remains is to compare them to an identical but equal weighted portfolio.
Weights and Measures Many investors don't. They focus on finding securities they feel have the greatest potential for gain. Once they've found them, they simply buy whatever amount they can afford and then sit back and wait for above average returns. That approach can work, but it's truly dependent on the investor's security selection. The holdings are more of a conglomeration than a cohesive portfolio. There really is no weighting scheme here. More sophisticated investors realize that by carefully blending their holdings, they can control risk and possibly even enhance portfolio return. Once they determine what to buy, they tailor the purchase to fit with the other holdings in the portfolio. There are two primary ways to do this. The first is dollar weighting and is probably the most popular approach. It arguably originated with the old commission schedules which marked up costs for trading odd lots. For an equity investor, a "round lot" was any number of shares evenly divisible by 100 (e.g. 100, 200, 500, or 1,000 shares). These were easily quoted and traded so carried the most favorable commissions. "Odd lots" were any other number of shares. Brokers had to break up round lots to create with them and charged higher commissions to make up for their trouble. Investors tried to minimizes their costs by trading in round lots whenever possible. As a result, portfolios were often constructed with round lots, often of 100 shares each. By buying the same number of shares for all holdings, investors -- whether they knew it or not -- were building dollar weighted portfolios.
Although commission structures have changed to no longer favor round lots, many investors still use this approach today. Indeed, it's how all of our model portfolios are created. On the other hand, equal weighting is also an easy and understandable way to build a portfolio. With the same number of shares of each holding, a dollar weighted portfolio gives the appearance of being evenly distributed -- although it's not. To truly make an even distribution, you'd need to "equal weight" the portfolio. To do so, you wouldn't buy the same number of shares of each stock but rather the same dollar amount. To see the difference between the two approaches and their effects on return, consider two $6,000 portfolios holding the same two securities, Stock A and Stock B. Stock A sells at $10 per share while stock B sells for $50 a share. Finally, suppose that at the end of one year, Stock A has risen 50% while Stock B has declined 50%. Intuitively, you'd think the portfolio would have broken even with one stock up and the other down an equal percentage. That's exactly what happens with an equally weighted portfolio. In this case, the $6,000 portfolio would have been divided equally between 300 shares of Stock A (300 x $10 = $3,000) and 60 shares of Stock B (60 x $50 = $3,000). At the end of the year, Stock A would be worth $4,500 (300 x $15) while Stock B would be worth $1,500 (60 x $25) for a total of $6,000. But that's not the case with the dollar weighted portfolio. In that case, 100 shares would have originally been purchased for each stock ((100 x $10) + (100 x $50) = $6,000). By the end of the year, however, the value would have fallen to $4,000 ((100 x $15) + (100 x $25)). The gain in Stock A clearly didn't offset the loss in Stock B. Obviously the difference in these two examples and between the approaches themselves is the greater impact of Stock B in the dollar weighted portfolio. Although it lost the same percentage as Stock A gained, the two don't offset because Stock B's higher price (and greater relative weight) gives it more impact on the overall return. When portfolios are constructed in this manner, gains (or losses) in lower priced components are overshadowed by those of their pricier counterparts.
Equal Weights vs. Equal Dollars To test the impact on P3, we constructed equal weighted versions of each of the actual dollar weighted portfolios from the past five years. We then compared the results.
Despite having over six years worth of data for P3, we only went back 5 years to November 1, 2001. While it would have been informative to have gone all the way back to the model's July 2000 inception, the Baseline database, the source of our return data, didn't have information on stocks of firms such as Enron which appeared in the portfolio but are no longer with us. There were still a few survivorship issues in the five year data, but not enough to prevent us from getting meaningful results. Reproducing five years' returns required building 30 bi-monthly portfolios. Once created, we had Baseline calculate their two-month returns and then combined all 30 together to create Chart 1. We then added the actual returns from dollar weighted P3 to generate the comparison. With the exception of early 2002 and a brief period in late 2005, the dollar weighted model trailed the equal weighted version. At its greatest extreme (mid-2004) the equal weighted model was over 18% ahead. The lead dwindled after late-2004, but still existed -- albeit to a lesser extent -- at the end of October 2006. Sometimes cumulative charts like this can be misleading, especially if one series outperforms the other by a considerable amount at the outset. When that happens, the difference can be exaggerated, particularly if the gap was closing throughout the period. To see if this was happening, we also considered the annual returns of both series. Here again, we looked at annual returns with October year ends. The results appear in Chart 2. Periods were split 3-2 with the equal weighted model leading in 2002, 2003, and 2006. Even so, the greatest one-year difference (17%) favored the dollar weighted portfolio and occurred in 2005. For the full 5-year period, the equal weighted portfolio was ahead by 6%.
All Else Isn't Equal
First of all, it's important not to lose sight of the fact that both the equal and dollar weighted versions of the model employed the exact same stocks. In other words, differences in returns didn't originate from superior stock selection in one model versus the other. Timing wasn't an issue, either, since both versions were created and altered at the same time. Buying and selling was not a distinguishing feature. The only thing that really did have an impact was the actual weighting of holdings in the portfolios. Over the 5-year measurement period, equal weighting won out, but that doesn't necessarily mean it's always the best approach for P3. You can see that from Chart 2. Not only did equal weighting fail to dominate in all 5 annual periods, the greatest differential favored dollar weighting in 2005. You can see this same result in Chart 1. Although equal weighting ends up ahead at the end of five years, there are distinct periods (e.g. early 2002 and late 2005) where dollar weighting is superior. If the two were compared for only four years ending in October 2005, they would have finished in a dead heat. Although neither is shown to be superior to the other, market conditions may be the deciding factor. When leadership is broad, such as in 2003-2004, equal weighting shines. As the overall market forges ahead, all shares benefit to roughly the same extent. In a dollar weighted portfolio where the highest priced stocks may for one reason or another fail to participate, performance falls off relative to the equal weighted alternative. But in a narrower market -- a so-called "stock-picker's market" -- high priced shares are often the result of singular outperformance. As part of the few market leaders, they're able to propel the dollar weighted portfolio ahead. This is precisely what occurred in 2005 when riskier stocks dominated the market. Judging from Chart 1, dollar weighting hasn't really served P3 very well -- at least over the 5-year period ending October 31, 2006. But that's more a function of the prevailing market conditions rather than a fundamental characteristic of P3. Just as it was able to close the wide performance gap that opened in mid-2004, dollar weighted P3 may now be poised to move ahead of its equal weighted counterpart. While the effect of dollar weighting is worth keeping an eye on, there's little evidence that P3 would be better off in the long run if it were equal weighted. So far it doesn't appear that one weighting scheme is superior to the other. Search this site! Just enter you key word or words: Get current quotes or follow your own custom portfolio,
courtesy of E-Line Financials:
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ITH THE HOLIDAYS NOW BEHIND us, many are once again concerned about their weight. After a few minor lapses at festive parties, the difference can be noticeable.
