How do you define style? When it comes to mutual fund investing, this is no idle question. After all, every advisor looks at the world of mutual funds and analyzes them by their stated investment styles — growth, value, whatever. The trouble is, mutual funds don't always behave as their names suggest. (For example, the Gabelli Small Cap Growth Fund, despite its name, has always had strong value leanings.) And some do not even have stated style mandates. Because the goal is to create properly diversified portfolios, advisors have to be certain that the small cap value fund they are putting clients into really acts like a small cap value fund.
That is, of course, what style analysis is all about. For example, by visiting morningstar.com, an advisor can see what style category Morningstar places a fund in based on its proprietary analysis. Yet, advisors should know that there are different ways of analyzing funds. So, it is important for the users of the various style analysis models to understand how the different quantitative models work and to be familiar with their limitations before relying on them.
Furthermore, style models can be used to provide a more detailed description of investment style than is revealed by a fund category assignment. Rather than stating that a fund belongs in, say, the “large-cap growth” category, many equity style models assign a pair of numerical scores for size and value/growth orientation that can be plotted on an x-y grid. The position of a fund's point on the grid makes distinctions such as “core growth” and “high growth” visually apparent. If done accurately, such plots are extremely useful in showing the distinctions between the investment styles of funds that fall into the same style category. This is why the ability to create such plots is an essential feature of many of the commercially available style analysis software packages that are used by advisors and institutional investment professionals.
There are two main approaches to style analysis: holdings-based and returns-based. Each has its fans, and the debate over which provides the better results is a hot one. Not surprisingly, much of the discussion has turned on the relative accuracy in describing a fund's allocation among asset classes or equity styles. This isn't some arcane argument among propeller heads: Under a holdings-based analysis, Oakmark Select I is a mid-cap value fund; under a returns-based analysis, it is large-cap value.
So, which is more accurate, holdings-based or returns-based? To find out, I recently conducted a study that compared both models over a large set of U.S. equity funds.
To generate style plot points from holdings-based analysis, I used the 10-factor style model that Morningstar introduced in 2002 to analyze stocks and equity funds and to construct equity style indexes. This model assigns an x-y coordinate pair to most U.S. stocks each month. The x-coordinate represents the value/growth orientation and the y-coordinate represents size. The coordinate pairs of the stocks in a portfolio can be rolled up into the portfolio's “centroid” by taking the asset-weighted average of the stock locations. A centroid represents the overall investment style of the portfolio. The portfolio centroids of a fund from different points in time can be averaged to measure the fund's long-term style.
Using the Morningstar style model, I divided the stock universe into style-specific portfolios to construct the reference portfolios used in the returns-based style model. The style plot points of the reference portfolios are the average portfolio centroids derived from their holdings. Using the same underlying model to construct the reference portfolios as is used for the holdings-based analysis should increase the likelihood that the two methods will produce similar results.
For a returns-based model, I used a standard regression model that does not constrain the coefficients to be non-negative. In the study, I argue that such constraints would preclude the model from ever generating the appropriate style plot points for funds that have strong value or growth orientation — such as “deep value” or “high growth” — or an extreme size bias — such as “giant-cap” or “micro-cap.”
I also argue that the model proposed by finance professors Eugene Fama and Kenneth French, which has become popular with academic researchers and some institutional practitioners, contains overly restrictive constraints when implemented as a model of fund style.
I applied the estimated regression coefficients to the centroids of the reference portfolios to estimate style plot points that ought to be comparable to the time-averaged centroids obtained through holdings-based style analysis. I also constructed confidence regions around the returns-based estimated centroids to gage their statistical precision.
I first compared the results of the two methods for category averages. I then performed the analysis on 1,909 distinct U.S. equity mutual funds from the nine U.S. diversified equity Morningstar categories (“Large Value,” Large Blend,” etc.).
I found that the degree of similarity of the results of the two methods varies widely across funds. In some cases, the dissimilarity is to be expected, but in other cases, it is quite surprising. I found, for instance, that high R-squared values do not necessarily mean that returns-based style centroid estimates are reliable. Even when modeling portfolios of funds that all belong to the same style category, I found that the returns-based method can give extreme results with large confidence regions, although the R-squared values are high. To get an overall picture, I looked at the overall correlation between the centroid coordinates generated by the two methods. I found that although the overall correlation between the results of the two methods is high, there are many funds in which the two methods give contrary results, especially in the estimation of the size orientation of small-cap funds.
I explored whether goodness-of-fit statistics (such as R-squared) for the style regressions can systematically explain the extent of the differences. I found that they are significantly related to differences in the results of the two models, but the goodness-of-fit of the style regression cannot be regarded as the sole factor leading to the differences. Other possible sources of differences include style inconsistency (which is demonstrated by a simple simulation) and correlation between selection and style effects. These possibilities require further investigation.
Thus, if a fund's portfolio is primarily composed of direct stock holdings, holdings-based analysis should be the primary means of assessing investment style. In the absence of such information, and under the right conditions, returns-based style analysis can be used to estimate investment style. But users of returns-based style analysis need to be aware of the conditions under which it produces inaccurate results. Users of all models need to keep in mind that quantitative techniques can complement, but never replace, qualitative knowledge of a fund's style and strategy.
Writer's BIO: Paul D. Kaplan Ph.D., CFA, is director of research at Morningstar, [email protected].
Morningstar's 10-factor holdings-based methodology is used to determine the style of an individual stock. Separate value and growth “style scores,” each based on five factors, are calculated for each stock. The methodology places a 50/50 weight on future/historical measures.
|Value Score Components and Weights||Growth Score Components and Weights|
|Forward-looking measures 50%||Forward-looking measures 50%|
|•Price to projected earnings||•Projected Earnings growth|
|Historical Measures 50%||Historical Measures 50%|
|•Price to book 12.5%||•Book value growth 12.5%|
|•Price to sales 12.5%||•Sales growth 12.5%|
|•Price to cash flow 12.5%||•Cash flow growth 12.5%|
|•Dividend yield 12.5%||•Trailing earnings growth 12.5%|
|•Large Cap||Top 70% of market|
|•Mid Cap||Next 20% of market|
|•Small/Micro Cap||Next 10% of market|
Key Findings of the Morningstar Study
Holdings-based and returns-based style analysis results, while often similar, can differ substantially.
Differences in the results of the two methods can be the result of poor statistical fit of the returns-based model or inconsistently style orientation on the part of the fund manager.
High R-squared statistics do not necessarily mean that the results of returns-based style analysis are accurate.