November 2000
But Does It Make Sense?
| "You may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra." |
| -- William Clifford |
ATHEMATICS IS A WONDERFUL THING THAT can be used to help explain a number of natural phenomena. Yet even so, there's no guarantee that any given mathematical relation -- no matter how elegant -- actually describes the real world.
Oftentimes, relationships that seem to be quite powerful are simply spurious. Statistics can help weed these out, but some still slip by. (Statistical tests are described in The Quantitative Approach.)
When we originally created our quantitative portfolios, we tested them for statistical significance, 
but one thing we didn't do was step back and ask, "Does this really make sense?" That's what we want to consider here, specifically in regard to Portfolio 4.
As you may recall, P4 is sector weighted. We created regression relations for each of the S&P 500's eleven sectors, then selected the top stocks in each. As you'd expect, the significant factors varied from sector to sector.
Now we need to examine if each sector's factors make sense. Not only does this apply to which factors are included (or excluded) from each regression, but their magnitude as well. The latter characteristic is given by the size and sign of each factor's coefficient.
The Factors
In September 2000, we listed all the factors and their coefficients. The coefficient table is reproduced below. It's what we'll focus on.|
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Coefficients for each factor are shown for the eleven S&P 500 sectors. A dash (-) is used for those which were not statistically significant. Coefficients appearing in red are negative. |
Growth investors should be heartened by the fact that long-term future earnings growth rate was the factor most frequently appearing across all sectors. At the other extreme was return on invested capital and forward four-quarters P/E, which were only used twice.
Most sectors had three or four significant factors, but consumer staples and basic materials only had one -- price-to-cash-flow. If you're only going to have factor, this is a good one. Discounted cash flow has traditionally been a standard measure of a company's worth. It's more top-line oriented than per-share earnings so is a reasonable standard for industries with high depreciation such as those in the basic materials sector. In this case, these factors make good sense.
Reading the Signs
The "sign" of the coefficients -- whether they're positive or negative -- is also important. Coefficients given in red in the accompanying table are negative while those in black are positive.All sectors with debt/capital in their regressions had negative
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What is puzzling is the negative coefficients for return on invested capital in both the healthcare and transports regressions. This implies companies with greater return on invested would score lower than those with smaller returns. This makes no sense.
The same holds for the consumer cyclicals' and transports' negative coefficients for price/cash flow and long-term future earnings growth rate. In general, these should be positive relations. While statistically significant, these relations are called into question.
Measuring the Size
The coefficient's size also has a bearing on the regression equation. The larger the absolute value of the coefficient, the more impact the factor has on the score. It's the absolute value that's important here since a large negative coefficient will have as much impact as a large positive coefficient -- just in the opposite direction.The largest coefficients are associated with long-term future earnings growth rate. This again supports the relevance of this factor. Not only does it appear most frequently, it has some of the greatest bearing in the regressions' outcomes.
What doesn't make sense is our old friend the transports again. While this sector's regression equation has the two largest coefficients in absolute terms (12.1698 and 13.1588), both are negative in relation to factors that should be positive (return on invested capital and long-term future earnings growth rate, respectively).
Applying Common Sense
Given these general observations, here's how we'd evaluate the regressions for each sector:- Basic Materials and Consumer Staples - Both of these sectors have only one factor: price/cash flow. As suggested above, this is a reasonable factor for these particular sectors. The coefficients, however, are quite small (0.0547 and 0.0196, respectively). Although this is OK, we can't help but wonder if there are other, more relevant factors not tested in our regressions.
- Cap Goods, Communications Services, Financials, Energy, and Utilities - All these factors make sense. Cap goods has a negative coefficient for debt/capital and also utilizes price/book, price/cash flow, and earnings surprise. Communications services relies on price/book and long-term future earnings growth rate. Financials includes positive coefficients for long-term future earnings growth rate, peg ratio, and earnings surprise. Energy has negative price/book and positive long-term future earnings growth rate and peg ratio. Utilities, major borrowers, have a relatively large and negative coefficient for debt/capital and also rely on long-term earnings growth rate and price/book. All of these factors are reasonable for their respective sectors.
- Consumer Cyclicals, Healthcare and Technology - While most factors for these sectors are understandable, each has one screwy one. Consumer cyclicals has that negative coefficient for long-term future growth rate. Healthcare has a negative coefficient for return on invested capital. Technology has a relatively large negative coefficient for earnings surprise -- the very factor some quants feel is the most important in valuing techs. These may all be spurious or perhaps we just haven't recognized the appropriate explanation.
- Transports - This one's really goofy. This regression has more factors than that of any other sector. That's OK, but the coefficients are off the wall. As mentioned earlier, those associated with return on invested capital and long-term future earnings growth rate are not only negative, but large. This is clearly counter-intuitive. Add to that the negative coefficient for the peg ratio, and you probably have a spurious regression relation.
At this point though, we aren't ready to trash any our regressions. When we created the portfolios, we decided to let them run for 12 months starting on July 1, 2000. It'll be interesting to see how they fare, particularly the transports. What this analysis does give us is a good indication of where changes need to be made when we run our next regressions.
In the meantime, we'd like your input. What do you think of the models? What would you question or change? E-mail us and you too can become part of this work in progress.
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