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 March 2009 Weight Control Sometimes It's Not What You Measure, But How You Measure It
Perhaps the best known example is the difference between the geometric and arithmetic mean. Both are ways of finding the "average" in a distribution, but they can be dramatically different. Not only that, the geometric mean will always be less than the arithmetic mean -- yet they measure the same elements.
In a related, yet different manner, portfolio construction using the same holdings can also vary. For example, some investors believe that equal weighting is more a more effective way of building a portfolio than cap weighting. Under the latter scheme, stocks are weighted based on their relative capitalization, so a $50 billion firm's stock gets five times the weighting of a $10 billion company's. This is a handy way to build an index because market fluctuations automatically adjust the weights of the various holdings. Rebalancing is not necessary.
Equal weighted indexes hold equal amounts of each constituent. As a result, they have more shares of cheaper stocks relative to the more expensive ones. Unlike their cap weighted counterparts, equal weighted indexes need to be periodically rebalanced to return to equal weighting. Each approach has its benefits and drawbacks. In addition to not requiring rebalancing, cap weighted indexes are driven by the largest holdings while barely reflecting any movements in the smaller components. Proponents argue this correctly captures what's going on in the overall market since it's the largest companies that see the greatest number of trades and have the widest distribution of shareholders. On the other hand, advocates of equal weighting point out that there's a whole world of smaller stocks that is almost totally masked by the larger stocks in cap weighted indexes. There are periods (most recently the early part of this decade) when small stocks rally, yet large caps remain lethargic. You'd never know this in a cap weighted environment, but you'd enjoy rising values with an equal weighted portfolio. Both approaches measure the same basket of stocks, but the difference in weighting has a major effect on the returns.
Another Look at Portfolio 4 Portfolio 4 is also cap weighted, but with a twist. Unlike P3, P4 attempts to keep its sector weightings in line with those of the S&P 500. P4 is rebalanced every six months so that the total portfolio value remains virtually unchanged, but the sector weights are adjusted back to those of the index. In addition, stocks are retained or replaced based on the model's quantitative algorithm. This has an interesting, and somewhat unintended effect.
When stocks are considerably cheaper than they were six months ago, more need to be added to the model to maintain the portfolio weight. This is precisely what occurred in December 2008 when the portfolio holdings jumped from 40 to 69. Not only that, in some instances, high priced stocks (think Google in 2007) can represent virtually all of an entire sector while others (think financials in 2008) may require a significant number of stocks just to maintain the correct relative sector weighting. When this happens, it would seem the portfolio would be inordinately driven by the largest holdings, regardless of the sector weightings. Given that there have been times when P4 would have been exposed to these potential distortions, it would be informative to see how differently it would have performed under equal weighting. Intuitively one might think there would be some significant differences, especially when one or two expensive stocks overwhelmed not only the other holdings but the sector weightings as well. Like P3, P4 dates back to July 1, 2000 so there's plenty of data to compare. Using the eight and one-half years from July 1, 2000 through December 31, 2008, we reconstructed P4 with equal weighting. We then compared returns and statistics for the total, and sub-periods.
Small Wonder Before comparing the results, it's necessary to put the observation period into context. P4 was launched at precisely the worst time imaginable -- with the possible exception of October 2008. Shortly after it was introduced, the tech bubble burst and stocks entered a three-year bear market lasting until late 2002. The next five years saw stocks recover somewhat, but P4 was starting from quite a hole. Just as it made its way back to even, the bottom fell out in the final quarter of 2008, leaving it once again well in the red. If it's any consolation, the benchmark S&P 500 followed a similar path. Chart 2 shows the value of $100 invested on June 30 2000 in P4 cap weighted and equal weighted, as well as the S&P 500 and Small Cap S&P 600. It's not pretty, but at least the small cap index shows a $35 profit. The rest of the series incurred considerable losses over the period. The Small Cap S&P 600 is included in this illustration for two reasons: First, as mentioned earlier, small caps held up much better than larger stocks from 2000 - 2007. Secondly, if Cap Weighted P4 was dominated by its largest holdings, presumably Equal Weighted P4 would be free to reflect its smaller components and possibly act more like the small cap benchmark than the large cap S&P 500.
Did it? Well, yes and no. Initially the equal weighted index closely tracks the cap weighted index. Both fall together and hit roughly the same low in late 2002. They start back up together, too, but by mid-2003, they begin to diverge. After that point, P4 Equal Weighted moved well ahead of the cap weighted alternative until they both collapsed with the market in late 2008. There are two things of note here: First, as pointed out previously all of our model portfolios tend to converge when the market enters a prolonged slump. To a certain extent, this is true for most indexes and assets. This phenomenon could account for the fact that the two versions of P4 tended to fall together both in 2000 and 2008. Secondly, a change in process in July 2003 -- precisely when the two began to diverge -- could also help explain Equal Weighted P4's sprint to the upside. Initially, P4 was only rebalanced annually on June 30. After reviewing the results, we determined that was too long to wait in rapidly changing markets. Although the goal was not short-term timing, we concluded that six months was a more appropriate holding period. Of course Cap Weighted P4 also enjoyed semi-annual rebalancing, too, but it lagged behind its equal weighted counterpart. Why? Perhaps it was because the equal weighted version benefited from its smaller holdings that weren't overwhelmed by its larger ones. Typically in the early stages of an economic expansion, smaller companies (and consequently their stocks) tend to be market leader since they often carry less debt so any increase in revenues and earnings falls directly to their bottom lines. As you can see from the relative trajectories of the Small Cap 600 and the Large Cap 500, small stocks not only held up better during the downturn, they accelerated much faster during the upturn. Maybe there is something to this equal weighting.
What About Risk?
Chart 3 shows the composite risk and return for all four series over the observation period using arithmetic means and annualized standard deviations. Although Equal Weighted P4 has slight higher return then Cap Weighted (-1.67% vs. -4.11%), standard deviation is also considerably higher (25.71% vs. 19.73%). Interestingly, Equal Weighted P4's standard deviation is higher than that of the S&P 600, which is almost identical to that of Cap Weighted P4. Although Equal Weighted P4's risk adjusted statistics are marginally higher the those of the cap weighted alternative, the difference is too small to be statistically significant. (Additional MPT statistics appear on Chart 4). So maybe Equal Weighted P4 isn't so much like the small cap benchmark. Indeed, it bears a stronger correlation with the S&P 500 (0.8771) than it does with the S&P 600 (0.7949). Curiously, it's correlation with Cap Weighted P4 is only slightly greater than with the S&P 500 (0.8980). In at least this regard, it appears to march to its own drummer.
This is also supported by the array of annual returns. Ideally, it would be nice to see one type of portfolio construction consistently dominate the other, but that just didn't happen. Chart 5 shows the annual returns of both P4 models as well as that of the S&P 500. Over the eight and one-half years, Equal Weighted P4 outperformed Cap Weighted P4 and the S&P 500 four times -- roughly half. When it did beat the competition, it did so in a dramatic fashion (2003 and 2004), but when it fell behind, it was equally dramatic (2005 and 2008). There's no trend here.
Putting it in Perspective About the only thing that seems clear here is that different styles of portfolio construction lead not only to different return patterns, but different risk profiles as well. Based on the the difference between the equal weighted and cap weighted S&P 500 illustrated on Chart 1, we initially thought Equal Weighted P4 would dominate it cap weighted counterpart, but it didn't do so consistently. Intuitively, equal weighting would seem to make more sense when constructing a quantitative portfolio such as P4. Given that expensive shares can overly influence returns while overwhelming carefully balanced sector weightings, equal weighting would appear to be the better alternative. Even though it may not necessarily improve long-term performance, it would be more consistent with the theory behind the model. Superior returns are only one consideration when constructing quantitative models. While the goal may be to outperform the appropriate index, the underlying algorithm needs to be coherently carried out in the model. In this case, a better argument can be made for equal weighting because it doesn't conflict with the model's sector weighting. Put differently, if sector weighting is thought to be important, the other aspects of the portfolio should allow it to be a contributing factor. Cap weighting doesn't pass this test. When the quantitative models were first created in 2000, it was determined that they would be reviewed in three-year periods. The presumption was that this would prevent short-term changes yet still allow modifications in a timely manner. Not only that, three years (until recently) generally captured most if not all market cycles. Accordingly, P4 will be up for review in mid-2009. At that point, we'll seriously consider changing to equal weighting. It may not bring an immediate improvement to short-term returns, but it could very well improve the integrity of the model. Check back this summer. 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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NE OF THE BIGGEST PROBLEMS in particle physics stems from the fact that the very act of measuring the subatomic world changes the subatomic world. The scientist actually has a bearing on what he or she is measuring just by the act of measuring it. This strange phenomenon is not limited to the realm of physics, a version also infects investment performance results.
