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 January 2005 A Portfolio of Outliers
But that's not how it should work. Instead, the model should be constantly reviewed to assure it works as expected and that its outputs are reasonable. If it isn't, it's time to dump the model and start over again.
It takes a little time to get enough data to make a meaningful evaluation. It's been almost five years now since we introduced Portfolio 3, a large-cap quant model. It's time to take a look into the black box. P3's equity selection model is based on a regression study run on the stocks of the S&P 500 during the decade of the 1990s. Essentially, it's an attempt to isolate and maximize those fundamental factors that lead to superior 12-month performance. Every two months we re-screen the S&P 500 and rebalance the portfolio. (For details of how the model was created, click here.) Since its introduction in July 1, 2000, there have been 28 rebalancings. That's enough data to give us a good idea of how the model is actually picking stocks. Growth and DistributionIt didn't take long to realize that P3 is actually a growth model. This was not intended but resulted from the data used to create the regression model. As documented in January 2002, growth stocks dominated in the decade of the '90s and it was their fundamentals that colored the model.Given that and the fact that P3 isn't sector weighted, you would expect it to be dominated by growth stocks. Typically these are found in the Technology, Healthcare, and Financial sectors. Looking back over P3's 28 different formulations, this has pretty much been the case. Technology has always had a major presence while Healthcare and Financials have played lesser, but still significant roles. Non-growth sectors have also been represented. Cyclical Industrials and Materials have most recently been included, but defensive Consumer Staples and Energy stocks have also made appearances. Chart 1 shows the average sector weightings as well as the maximum and minimums. Given that and the fact that P3 isn't sector weighted, you would expect it to be dominated by growth stocks. Typically these are found in the Technology, Healthcare, and Financial sectors.
Looking back over P3's 28 different formulations, this has pretty much been the case. Technology has always had a major presence while Healthcare and Financials have played lesser, but still significant roles. Non-growth sectors have also been represented. Cyclical Industrials and Materials have most recently been included, but defensive Consumer Staples and Energy stocks have also made appearances. Chart 1 shows the average sector weightings as well as the maximum and minimums. Of course P3 utilizes individual stocks and not sector proxies like P5 and P6. Its model assigns values to stocks based on their fundamentals and values derived from its underlying regression formula. The basic formula is:
The top 30 stocks are included in the portfolio and remain there until their value falls below 100. Given its growth bias, you'd expect Tech and Healthcare stocks to receive the highest values, Utilities, Materials, and Consumer Staples to receive the lowest, and stocks from the other five sectors to fall in between. In a normal distribution, P3's stock values would be equally distributed around the average. Most would be clustered around the average with lesser numbers at high and low extremes. In statistics, this pattern is called a bell curve since its trend looks like an outline of a bell. Chart 2 illustrates a normal distribution (green bars) and its trend's bell curve (red line).
If P3 resulted in a normal distribution, stocks from Tech and Healthcare would tend to receive the highest scores and be included in the bars to the right of the chart. Utilities and Materials would receive the lowest scores and fall to the left. Stocks from other sectors, the greatest number, would fall around the average and appear in the taller bars in the middle of the chart. But that's not how P3 has ranked stocks. Chart 3 shows the actual distribution since P3's July 2000 inception. Since it covers 28 different rebalancings, the total frequencies add to 1400 (28 x 500 stocks). Although most stocks fall into a normal pattern, the overall distribution is positively skewed. The easiest way to understand this is to notice that there are a number of outliers (red bars on Chart 3) to the right of the main distribution. Because they are on the positive side the distribution is said to be positively skewed, if they had fallen to the left or negative side, it would be negatively skewed. In a normal distribution, the average and median are equivalent. The average is simply the arithmetic mean of all values while the median is the value falling in the middle of the ranked distribution. In this case, the average value is 0.0842 while the median is -0.0570. The specific values aren't all that important, but their relationship to one another is. On Chart 3, the average falls in the green bar while the median falls in the blue. This is the effect of the outliers pulling the average above the median. This is a statistical characteristic of a positively skewed distribution. A statistical measure (not surprisingly called skewness) provides a mathematical measure of this distortion. A normal distribution has a skewness value of 1, but P3's is 2.35. Statistically, it's moderately positively skewed.
Something to Think AboutAlmost all naturally occurring distributions have some degree of skewness. The fact that P3's is positively skewed is significant for two reasons. First, since the stocks selected for the portfolio are those with the highest values, they come from the outliers on the right of Chart 3. This wouldn't have been the case had the distribution been negatively skewed. Secondly, the distribution is sufficiently skewed so that all of the stocks of P3 come from the outliers. A total of 840 stocks would be needed for the 28 different reformulations (28 x 30). Adding the frequencies from right to left on Chart 3, all of these would be drawn from the red bars, and all are outliers. Of course if only a few rebalancings resulted in significantly skewed distributions, Chart 3's cumulative results would paint a distorted picture of the average distribution. To check this, we looked back at all 28 distributions and found that they all had similar, slightly positively skewed, results.
Chart 4 shows the distribution from the most recent (December 15th) reformulation. It's pretty representative of the other 27. Like the cumulative results on Chart 3, it's moderately positively skewed. More importantly, as denoted by the red bars, all 30 stocks of the portfolio are drawn from the outliers. So P3 is, and has been, a portfolio of outliers. That can explain how stocks from the Materials and Consumer Staples sectors have made their way into it while their sectors have not been highly rated. From a statistical standpoint, this is not necessarily a bad result. If the outliers truly share characteristics of potential outperformance, then the model's doing exactly what it was designed to do. There may indeed only be a handful of stocks from all sectors that have the greatest potential to outperform over the short-term. On the other hand, the model itself may need to be tweaked since it consistently yields a positively skewed distribution. Perhaps if other fundamental factors were included in the underlying model, the results would be more normally distributed. At this point there's not enough evidence to suggest which interpretation is correct. It is worth noting that the model does consistently generate positively skewed results. It's not too soon to consider other fundamental factors that could also be included in the regression process to tweak the model for the future. For now, however, P3 will continue to be a portfolio of outliers. Search this site! Just enter you key word or words:
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Y THEIR VERY NATURE, quantitative equity models are numbers driven. A lot of work goes into finding, testing, and combining the correct factors, but after that the focus changes to updating the inputs and monitoring results. That gives rise to the perception that quant models are some sort of mysterious "black boxes" that generate buy and sell orders. Once created, you let them run, never again looking inside.
