The European investment arena consists of a collection of closely integrated national markets subject to a rapidly evolving mix of national, regional and global influences. This fast-changing, rapidly integrating market invalidates many of the standard techniques of the style analysis toolbox. This article describes the modifications necessary to make style analysis work successfully in the contemporary European context.
Style analysis is a simple and intuitive approach to analysing the key strategic features of a portfolio. It was originated by the Nobel Prize-winning economist William Sharpe. Style analysis does not provide a detailed risk decomposition of a portfolio, but instead a simple strategic overview. It sits midway between an asset allocation breakdown (which gives the proportions invested in very broad asset classes such as stocks, bonds, real estate and cash) and factor modeling (which describes all the risk characteristics of the portfolio). Style analysis works best for equity portfolios, although Sharpe also considered other asset classes in his original proposal.
Sharpe proposed a simple historical approach to estimating the style components of a portfolio. His approach only requires a recent historical sample of returns for the portfolio in question and a corresponding history of returns on a chosen set of style indices. One finds the weighted combination of style indices that best tracks the historical sample of returns on the portfolio. This is equivalent to finding an allocation across the style indices (with weights constrained to be positive and summing to one) that comes closest to reproducing the observed returns on the portfolio.
Sharpe emphasised the simplicity of his estimation approach, and the fact that it only requires easily obtainable data. It is not necessary for the style analyst to be in contact with the portfolio manager; the exercise can be done using publicly available return records. Individual investors working on a home computer can perform style analysis on mutual funds or on personally chosen portfolios. Returns on style indices are easily obtainable, and have become even more diverse and widely available with the increasing popularity of Sharpe’s technique.
The simplicity and limited data requirements of historical style analysis come at a considerable cost. One major problem is the noise in historical returns. Consider a growth-oriented portfolio dominated by a small number of large holdings. Can the historical approach reliably identify the growth style of such a portfolio? Suppose that these dominant holdings happen, by chance, to have some large negative returns in months when the typical growth stock performed well, and some large positive returns in months when most growth stocks underperformed. Under these circumstances the historical approach will mis-classify the growth-style portfolio as a value-style portfolio. This type of mis-classification due to return noise is very common for poorly diversified portfolios. It can also occur due to noise associated with concentrated industry bets, or from any other source of return that is not diversified away in the portfolio.
Style miss-classification
In many cases, return noise leads to serious style mis-classifications. Hence, the historical approach is easy and convenient to apply, but not very reliable. The lack of reliability is most notable if the style indices or managed portfolio are dominated by a small number of assets or have strong industry concentrations.  
Another problem with the historical approach is the implicit assumption of stability. If the environment has changed, eg, the portfolio’s strategy has shifted in the recent past, then the historical record will not reflect the current situation. Aware of these potential problems, the user of the historical approach faces a harsh tradeoff. If a shorter sample is chosen, so that the returns are representative of the current environment, then the estimates are more likely to be badly affected by return noise. If a longer historical period is used to decrease noise, more obsolete data is captured in the estimates. Five years of monthly returns is a typical choice as the historical sample period, balancing these concerns about return noise versus parameter stability. Using weekly or daily returns just creates additional problems, related to transactions noise.
Another limitation of the historical approach is that it can only identify the style of a portfolio, not of an individual asset. Therefore one cannot easily perform ‘what-if’ exercises, describing how the portfolio’s style decomposition will change after adding or removing particular assets. 
Characteristic-based analysis
A more accurate way to measure the style of a portfolio is by directly examining the characteristics of the portfolio’s individual assets. For example, to deduce whether a particular portfolio strategy reflects a bias toward small stocks, one can calculate the weighted average capitalisation of the assets in the portfolio and compare to that of a market index. Of course this defeats one of the objectives of Sharpe’s historical approach, its use only of inexpensive publicly available data. Characteristic-based style analysis uses the full record of holdings in the portfolio and a database of characteristics for all relevant assets.
Characteristic-based style analysis has the advantage that it measures a portfolio’s style in snapshot fashion rather than relying on an historical record. Also, it allows for ‘what-if’ exercises to discern how proposed trades will affect portfolio style.
Characteristic-based style analysis sacrifices some of the features in Sharpe’s historical approach. The increased data requirements are not onerous for institutional investors, but can be prohibitive for individual investors. Importantly, Sharpe’s approach produces a style index combination to match the portfolio’s historical return. This ‘mimicking portfolio’ can be used as a benchmark to evaluate the performance of the portfolio relative to an equivalent combination of style indices. The characteristic-based method does not give a mimicking portfolio return for benchmarking.  
Using underlying security characteristics to measure portfolio style removes some of the weaknesses of the historical method. By taking a further step, and embedding the style analysis in a characteristic-based factor model, we can add additional features. This provides a style return benchmark and a linkage to portfolio risk modeling and full-fledged return attribution.
Characteristic-based factor models are a mainstay of portfolio risk analysis. Factor modeling is distinct from style analysis in the number of categories used: with style analysis only three or four styles are identified (tied to strategic themes rather than statistical fit) whereas with factor analysis 20-60 factors (including industry factors) is typical. The objective of factor analysis differs from that of style analysis. Factor analysis looks for a comprehensive measure of the portfolio’s riskiness and the sources of this risk, not just a limited description of strategic features of the portfolio.
A recent innovation in finance is the use of second-order factor modeling. This approach comes originally from psychometrics, the scientific measurement of personality and intelligence. For example, psychometricians speak of ‘multiple intelligences’ meaning an individual’s measured abilities in specific problem-solving areas such as spatial reasoning, number manipulation, memory and language. These multiple intelligences or first-order factors can be aggregated into a broader category called ‘general intelligence’ or the g-factor. The g-factor captures overall intellectual ability. General intelligence is called a second-order factor since it aggregates at a coarser level a set of more specific factors. Second-order factor analysis is essentially a type of ‘factor analysis of factors’.
Style returns can be defined as second-order factors arising as aggregates from a more detailed factor model. Developed in this way, style analysis can be embedded within a fully-specified risk and performance attribution model.
Table 1 shows four style categories for European equities: size, value, growth and risk, and the constituent factors underlying the definition of each style, based on a Europe-wide equity factor model. Some of the first-order factors (such as foreign exposure and momentum) do not appear in any of the four style categories.
One of the advantages of embedding a style analysis in a full factor model is that industry effects are not confounded with style, a common problem with Sharpe’s historical method. Table 2 shows a 12-month return attribution, relative to a market-wide benchmark, for four European indices designed to capture style tilts (STOXX Large, Small, Value and Growth indices). Much of the relative return of these style indices can be traced to industry concentrations rather than style tilts. For example, the Growth index has a large overweight in healthcare and a large underweight (relative to the market-wide benchmark) in banks. These industry effects are neutralised when style returns are derived from a factor model.
The rapidly changing European market is an exciting environment for equity investment. The best approach to style analysis in Europe is to derive style returns as aggregates of underlying factors in a fully-specified characteristic-based factor model. This approach does not depend upon an unchanged historical environment, and produces style returns that are not confounded by unbalanced European industry weights.  
Gregory Connor is a scientific adviser in the London office of Barra Inc  

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