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 November 2007 All in the Results A Returns Based Review of Quantitative Models 3, 4, and 5
Many investors build their portfolios to fit certain styles. With studies showing that asset allocation is a major determinant of long-term performance, style-based investing has become ever more firmly entrenched. Software is available to assist in the task, making returns-based analysis a relatively simple, economical, and straightforward way to evaluate and classify portfolios.
Of course like all quantitative processes, it’s garbage in, garbage out. If the benchmarks aren’t true to their assigned style or if returns are too spotty to create a statistically significant data set, the results will be marginal at best. Similarly, since this approach doesn’t really evaluate the actual holdings of the portfolio, it can create some spurious results. Consider, for example, a portfolio consisting entirely of Asian stocks. If it is evaluated against a set of domestic indexes, it will have a higher r-squared against some rather than others, yet that certainly doesn’t mean they define its style. In this case, you know they don’t, but what about other instances when you don’t have any additional knowledge about the portfolio’s actual holdings? When conducted properly, returns-based style analysis can be an effective means of evaluating a portfolio’s style. The best way to assure this is to know some background about its actual holdings. We have a great deal of background on quantitative Models 3, 4, and 5. Not only did we create them, we limited them to investing solely within their benchmark indexes. As a result, these are prime candidates for returns-based style analysis.
Portfolios 3 and 4
Being based on data form the 1990s, you would expect both to have a growth bent, and indeed they do. Throughout their existence, their average betas and earnings growth rates have always been well above those of the S&P 500. Inasmuch as they can only hold stocks from within the index, you’d reasonably expect returns-based style analysis to clearly portray them as large cap growth. That’s exactly what you see on Chart 1 which shows the average capitalization and style for each model over the past seven years. We used the Wilshire Large Growth Index and the Wilshire Large Value Index to represent large growth and value. The Wilshire Small Growth Index and the Wilshire Small Value index are proxies for small growth and value. Charts 2 and 3 use the same capitalization and style proxies, but plot the models’ “composition” over 3-year rolling periods (see color key at the bottom of Chart 6). Surprisingly, they suggest both models were small cap value in the early periods. The small cap aspect isn’t nearly as far out there as the value metric. Although the S&P 500 is considered a large cap index, its smallest components typically fall well within the range of small caps, generally defined as capitalizations less than $2 billion. P3 in particular has always had a high exposure to tech stocks, and back in the 1990s, many of them were rapidly growing smaller components of the S&P 500. Nevertheless, the average market cap has always been well above small cap levels. P4 has always been more diversified and even in the bubble days tended to gravitate towards the larger companies in the index. For that matter, the market cap of both has always been around that of the index, often even higher. So the small cap characterization is certainly not correct. The value attribution is even more off base. Although not explicitly designed to be so, both models have always had a growth tilt. This was especially true from 2000-2002 when growth stocks sported historically high P/Es. From a holdings-based standpoint, neither P3 nor P4 has ever been value portfolios. Of course this isn’t a holdings-based analysis, it’s returns based. But that’s even more perplexing since neither model has ever traded like small caps – especially in the early part of the decade. Back then, small caps held up relatively well in comparison to the major selloff that swamped overvalued large caps. P3 and P4 fell just as hard or even harder than most. At their low points (October 7, 2002) they were off 77.2% and 57.2%, respectively while two days later, small caps (as measured by the Russell 2000) hit their low of “only” -36.8%. (For the record, on the same day, the Dow Industrials and the S&P 500 hit bottom, off 30.3% and 46.6%, respectively.) For 3-year rolling periods ending after December 2005, the style attribution makes more sense. Both P3 and P4 are primarily large cap growth, with the latter showing a growing position in smaller growth stocks in the most recent past. This is an accurate portrayal of the model’s recent composition. The risk and return tradeoff is accurately captured on Chart 4. P3 has the greatest risk and least return. As of the end of September 2007, it was still underwater from inception, confirming the return value. It’s also always been the riskiest model as measured by both beta and standard deviation. The sector balance of P4 has helped it reduce risk, and return to positive territory. On September 30, 2007, its price return from inception was +1.2%. Risk has always been lower than P3, while above that of the S&P 500. This, too, is accurately captured on Chart 4. Chart 5 shows the models’ upside and downside capture. This is an important statistic when assessing volatility and downside protection.
To calculate upside capture, you compare the model’s return to that of the benchmark for each month in the measurement period when the index was up. This isn’t simply a “batting average” where you only consider the number of times it surpasses the index, it’s a measure of magnitude measuring the percent of the benchmark’s gain it captures. The average over the entire measurement period is the upside capture. Obviously, a higher figure is preferred. The downside capture calculation does the same for down market periods. This time, however, lower figures are most preferred. (In fact, negative downside captures are preferred since that indicates the model actually went up when the market went down. As you’d guess, they’re pretty rare.) P3 ends up with a downside capture of 125% and only a 30% upside capture. That’s certainly not optimal and helps explain how it so quickly dug itself a hole in the bear market and why it still hasn't emerged after a 5-year bull run. P4 also has a 30% up market ratio, but much less downside (slightly under 70%) than P3. Again this is attributable to its diversification. It’s also very consistent with the model’s slow and steady recovery back to the upside. It finished September 2007 on the plus side not because it rose faster than P4, but rather because it didn’t have so much ground to recover following the bear market.
Portfolio 5 Although it can go anywhere, P5 has always maintained a major mid cap exposure. At times it’s been mid cap growth, usually it’s been mid cap value, but it’s always been heavily invested in mid caps. This is clearly illustrated in Chart 1 where P5 falls near the center of both capitalization and style. This is an excellent representation of this model.
Chart 6 also captures this consistency. Although it may not look like it at first, the 3-year rolling periods always have an almost even distribution of capitalizations and styles. As you’ll recall, the chart is created with the Wilshire large, small, growth, and value indexes anchoring the corners, there isn’t a real mid cap or blend index. The equal mixture of all options reflects this and again, is an excellent representation of P5’s composition and style. P5 has always been the best and most consistent performer of all the quantitative models. Part of this (perhaps most of it) is due to the fact that P5 didn’t get its start until January 1, 2002 when there was less than nine months left in the bear market. This prohibits direct comparisons with P3 and P4, but doesn’t diminish its results. As of September 30, 2007, P5 was up 57.8% from its inception. Chart 4 shows its annualized return as just under 10%. Its risk (standard deviation) is also relatively low, actually below that of the S&P 500. This reflects the effects of its diversification as well as mid caps’ stellar run over the past five-plus years. That also comes through on Chart 5 where P5’s upside and downside capture are slightly below 100%. Again, however, this may be the result of a relatively stable market run with no real correction, and no real bear market over the measurement period. Even so, these results can be comforting to nervous investors when things get rough – even over the short-term.
Believe It or Not With this background, the returns-based analysis seems quite reasonable, particularly in regard to P5. Perhaps a little more analysis can explain why the rolling periods so clearly miscast P3 and P4, perhaps not. If nothing else, this serves to show that returns-based analysis should probably not be the sole method of evaluation. Like almost any investment evaluation tool, there is no stand alone solution. The more corroborating evidence from various and distinct factors, the stronger the conclusion. Search this site! Just enter you key word or words: Get current quotes or follow your own custom portfolio,
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HE INTRODUCTION OF MODERN Portfolio Theory has had some broad-ranging implications. One of the most widely used is “returns-based style analysis”. Introduced about twenty years ago by William Sharpe, returns-based style analysis is a means of evaluating a portfolio’s style based on its actual returns. This is a quantitative approach which regresses a portfolio’s returns against those of benchmarks with clearly defined styles to determine the portfolio’s style. Portfolios can then be plotted based on capitalization and style for comparison and grouping. The Morningstar “stylebox” is perhaps the best known example of such a plot.
