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 January 2006 Fundamental Change A New Look at P3's Underlying Stock Selection Formula
Among them, are basics that are often forgotten in the giddiness of the preceding bull market. For example:
Many new investors of the 1990s learned these lessons the hard way. After watching their portfolios soar for a decade, their gains dissipated in the ensuing bear market. To a certain extent, quantitative Portfolio 3 is in the same boat. The idea was to create a model that would be comprised of stocks with the fundamental features most closely linked to performance. Using data from the S&P 500 from the decade of the '90s, we ran a multiple regression analysis (for more on how this works, see The Quantitative Approach) for one-year return versus seven fundamental factors (see The Starting Point). The resulting formula is P3's stock selection process.
As a quantitative model, there's no subjective input. The formula alone determines the holdings. Needless to say, the 2000-2002 bear market was difficult for P3 as the 1990s' growth-oriented model consistently relied upon over-priced favorites from the previous decade. No wonder it lost 78% -- that's not a typo -- between October 1, 2000 and September 30, 2002. History will probably view the 1990s as an anomaly for investment return. The fundamental factors that produced market leaders during that time are equally anomalous. Too bad for P3.
Another Look But it doesn't have to be that way. Knowing what we now know about the unique 1990s' market conditions and their effects on P3's regression formula, what if we re-ran the process using data from the last five years? Instead of encompassing an ever-increasing equity run-up, the period from July 1, 2000 through June 30, 2005 was almost evenly divided between bull and bear markets. No particular large cap style dominated the period so if fundamental factors are important in determining investment return, a new regression analysis should reveal which can best handle both up and down cycles.
Before looking at the results, a few points need elaboration. First, the critical underlying assumption is that fundamental factors do influence return. A technician or a pure stock picker might not agree, but most investors do. That's why they spend their time poring over P/Es, Price-to-Book ratios, cash flows, and earnings statements. Rather than proving this relation, the regression study provides a way to test this assumption. Which brings up the second point: Contrary to how it may at first appear, this is not data mining. One of the worst abuses of statistical analysis is the process of building a hypothesis based on patterns observed in historical data. This essentially turns the process on its head since statistical analysis is a means of testing hypotheses, not creating them. In re-running P3's regression analysis with data from a different time period, we didn't look for new factors, but instead used the same as in the original study. We expected the resultant weightings to be different but only because both bull and bear conditions were represented. Ideally, this is what we would have liked to have had in the original study. The third and final point concerns the means of testing the results. If you look back over the past five years to generate a regression formula for return and then simply apply it over the same five years, you'll obviously get wonderful results. How could you not? The approach is circular. The way to truly test the findings is out of sample, in a different time period. That's what's been going on with P3. Its regression formula was based on data from the 1990s, but it was launched out of sample on July 1, 2000. What we've found is that the fundamental characteristics that allow stocks to outperform in a bull market fare quite poorly in a bear market. As you'll notice from Chart 1, P3 fell dramatically in 2000 at the start of the bear market. Although it's managed to beat the S&P 500 since 2002, it's never been able to dig itself out of the bear market hole. In revisiting P3's regression model, we need to test the results outside the July 1, 2000 - June 30, 2005 period. There's only a few months to compare, but even so, you can begin to see some interesting patterns.
New Numbers While it's possible that each of the eight fundamental factors have a significant impact on investment return, they don't have to. In fact, they didn't, not in P3's initial regression nor in the new one. In both cases, the regression analysis started with all eight variables and then through a "stepwise" process, removed the ones that weren't statistically significant. The original as well as the revised results are summarized on Chart 2. The only similarity between the two regressions is that both found Long-Term Debt to Capital to lack statistical significance. They differed on the significance of the remaining factors, and gave them different signs (positive or negative) when included in the final regression. What a difference a bear market makes.
The weightings of the various factors illustrate the original regression's growth bias while the revised version puts more emphasis on traditional valuation. You can see this from the fact that the new regression uses negative coefficients for Price/Book, Price/Cash Flow, and the PEG ratio. With a negative coefficient, higher values for these factors result in lower stock ratings. In other words, the more "overvalued" a stock becomes, the lower the revised regression rates it. This isn't the case with the original regression. In fact, the exact opposite holds true: Its positive coefficients for Price/Book, Price/Cash Flow, and Forward P/E reward stocks that trade at high valuations. This is the momentum approach that as so popular in the 1990s when stocks that were rising in value were the most likely to keep appreciating. While it worked well when almost all stocks were rising, Chart 1 clearly shows it didn't fare nearly as well when they sold off.
The original regression shows a higher correlation between the fundamental factors and annual return. Correlation is measure of the strength of the relation given in by the regression equation. It ranges from +1 to -1. Series with a +1 correlation move in perfect tandem while those with -1 move in exact opposite ways. Those with 0 correlations aren't related at all. Since most stocks were moving in the same direction -- up -- in the 1990s, it stands to reason that the original regression would have a stronger correlation with return. By squaring the correlation value, you arrive at the coefficient of determination, commonly referred to as R2. In this case, it represents the proportion of the total variation in the annual return explained by the variation in the fundamental factors. Because the original regression's correlation is higher, so is its R2. From Chart 2 you'll notice that it accounts for over 65% of the variation in return while the new regression only explains about 38%. Again this is understandable given how market conditions in the past five years have been much more changeable than they were in the decade of the 1990s. The important question then is how do the two regressions compare when actually put into practice?
Head to Head P3 was reoptimized based on closing prices from June 15th, August 15th, and October 14th. Although the first date was still within the new regression's ("Alt-P3" for convenience) sample period, we used it to create a portfolio based on those closing prices, but effective July 1. We then compared portfolio composition and period returns for both versions of P3 from July 1 through November 30. Chart 3 shows a comparison of the models' sector weightings in each of the reoptimizations. In each instance, Alt-P3 has less of a bias toward traditional growth sectors, particularly Technology and Healthcare. Even so, it's no more broadly-based than the actual P3 as both have representation in 8 of the 10 S&P sectors in two of the periods and are in 9 in the third. Neither regression has Telecom exposure in any of the three periods.
With each successive reoptimization, Alt-P3 strays further from the index sector weightings. By the October period, its deviation from the S&P 500's weightings is greater than that of P3. This was somewhat unexpected since Alt-P3 has a broader focus than the more growth-oriented P3. The periodic returns for the five months was more predictable. As shown on Chart 4, P3 bested both Alt-P3 and the benchmark S&P 500 for all three optimizations as well as the overall period. That's pretty understandable given that large cap growth (as measured by the S&P Barra Growth and Value Indexes) outperformed large cap value in each of the periods except September - October when both were unchanged. In this instance, a growth bias was helpful. Nevertheless, Alt-P3's results are still encouraging. It was ahead of the index for two of the three optimization periods as well as the full five months. Tempering this promising start is the fact that the one period in which it didn't beat the S&P 500 was September - October when all stocks were down. This might suggest that like P3, it, too, will fall behind in a down market. The hope was that in virtue of being more broadly based, this problem would diminish. Of course five months is an extremely short period to gauge anything about an equity model. That's why we only consider changes to our quantitative models on a three-year basis. Historically that's been long enough to cover both bull and bear periods so should provide a balanced overview. The second three-year period will be up on June 30, 2006, P3's sixth anniversary. By then we'll have 12 months of data on Alt-P3. That's still a relatively short time, yet it may be sufficient to suggest substituting its regression for P3's original. That's a decision for next summer. In the meantime, we'll continue to monitor the results from both. Just on the face of it, however, it's hard to believe that P3 couldn't benefit from a more broadly-based regression than one stemming from the anomalous market of the 1990s. Wasn't that one of the lessons of the equity bubble? Search this site! Just enter you key word or words:
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S DIFFICULT AS THEY ARE TO ENDURE bear markets do two very valuable things: First, they leave behind true buying opportunities as few, if any, stocks remain overpriced in their wake. Secondly, and perhaps even more importantly, bear markets teach investors hard lessons they should have already known.
