Methodology applied for theAGEFI Asset Management Awards

October 2002

Noël AmencProfessor of Finance, Edhec Business SchoolDirector of Research, Misys Asset Management Systems

Lionel MartelliniProfessor, Marshall School of Business, USC Los AngelesAssociate Researcher, Edhec Business School

Daphné SfeirAssociate Researcher, Edhec Business School

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EDHEC is one of the top five business schools in France. Its reputation is built on the high quality of its faculty and the privileged relationship with professionals that the school has cultivated since its establishment in 1906. EDHEC Business School has decided to draw on its extensive knowledge of the professional environment and has therefore focused its research on themes that satisfy the needs of professionals.

EDHEC pursues an active research policy in the field of finance. EDHEC-Risk Institute carries out numerous research programmes in the areas of asset allocation and risk management in both the traditional and alternative investment universes.

Copyright © 2015 EDHEC

31 - For an exhaustive analysis, it would be useful to consult Amenc and Le Sourd (2002), and Grandin (1998).

I. Introduction: Why use a new methodology for the Agefi Asset Management Awards?Fund performance measurement is an important issue both for professionals, for whom it is thejustification of their remuneration, and for researchers, for whom the right evaluation of returns and risks constitutes the very core of modern portfolio theory.

This twofold academic and professional issue underlies extensive research and numerous methodsfor evaluating the performance of funds.1

Indeed, the diversity of the resulting models and methods has consequences on fund performancerankings and the evaluation of fund performance.

Identifying the best managers actually presupposes taking two areas into account - the risk and the management style. The modelling of those two areas is subject to substantial debate and theoretical and statistical options.

I.1 A risk-adjusted measureFor all rankings, it is appropriate to measure risk-adjusted performance. It would be unfair to reward a manager whose apparent performance superiority is merely down to taking greater risks than his colleagues.

This area of risk-adjusted return has given rise to different indicators and methods. Among the best known is the Sharpe ratio, which relates the excess return of a portfolio with respect to the risk-free asset and its total risk measured by its standard deviation. As a robust indicator, which does not depend on any choice of benchmark, the Sharpe ratio is considered to be an absolute portfolio performance measure, and that is the strength that probably leads to its principal weakness. The fund with the best Sharpe ratio is not necessarily the one that performed best in comparison with the precise risk, for two main reasons:• Firstly, since the Sharpe ratio bases the only risk measure on the standard deviation of the distribution of returns, it is fairly easy to manipulate it by seeking returns in "non-normal" risks(extreme credit, liquidity and volatility variation risks).• Secondly, the Sharpe ratio, by not taking the benchmark that represents the statistical allocation of the funds into account to measure the excess performance, rewards the performance of the market in which the fund is invested as much as it rewards the performance of the fund itself.

To respond to this second point of criticism, the promoters of rankings and performance analysis firms have tried to "relativise" the Sharpe ratio. This approach, which is often called a "risk-adjusted rating" or "rating" was developed from the grouping of funds into "peer groups" and the calculation of the return and risk related to the peer group. This rating system, although it has the advantage of simplifying the presentation, does have numerous disadvantages that were highlighted by Sharpe himself in 1998.

Among the criticisms, the most important is based on the difficulty in defining homogenous peergroups a priori. The promoter of rankings is confronted with two major difficulties:i) It is appropriate to be able to dispose of reliable information on the fund compositions, and information that is representative of the funds' investment policy over the period. For instance, a study carried out in 1995 on the data provided by the two main American disseminators of information on mutual funds showed that only 1/5th of the portfolios contained in "Morningstar Ondisc" updated less than three months previously and only half of the funds in the "Value Line Fund Analyser" detailed their composition. This inadequacy generally leads the promoters of rankings to rely on very broad categories which are themselves defined from very rough benchmarks that do not truly reflect the funds' asset allocation policy.

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The difficulty in knowing the reality of the funds' investments can also lead the person responsible for measuring the funds to rely on the manager's stated objectives and investment styles. In that case, investment management firms are free to choose the benchmarks and categories that are favourable to them.ii) As we stressed previously, it appears that the methods that aim to relativise the Sharpe ratio, either through peer groups or through the choice of a benchmark to replace the risk-free rate, come up against a real problem in defining the categories or benchmarks. Even if we did dispose of a reliable description of the portfolios, the classification problem would not be resolved.

On the one hand, a priori categorisation is faced with a veritable dilemma: either the peer groups chosen are too broad to correspond to the managers' specialisation and in that case they include funds that practice very different investment management and that have performances that are not comparable. In that way, a "domestic stocks" or "international stocks" category does not recognise allocation by style. Or the categories are too narrow to account for the multi-style or multi-class diversification strategies of numerous funds.

On the other hand, it is appropriate to underline the fact that assigning funds to categories, on the basis of their composition, presupposes that an objective relationship exists between the characteristics of the securities held and the definition of the category. However, although it is relatively easy to obtain a consensus on the segmentation of classes, sectors or countries, style analysis, on the other hand, relies on more subjective classification criteria. The growth or value qualification of a security, for example, which is based more often than not on microeconomic attributes whose value, and therefore whose significance for the ranking, vary according to market conditions, is neither stable nor objective.

In a study carried out by Bienstock and Sorensen (1992) for a sample of 3,000 stocks, it appears that only 20% of the securities can, in a significant way, be classified as value or growth.

In a recent article, Haslem and Scheraga (2001), showed, on this subject, that the Morningstar style classification for funds invested in large caps – large growth, large blend and large value – was not consistent with a "clustering" type statistical approach, which allows the funds to be grouped together according to their behaviour, without any a priori choice.

In effect, the difficulties in categorising portfolios a priori according to their financial characteristics often lead professionals to challenge the classification of their fund when it is not favourable to them.

I.2 The measurement of alphasThe concern to relativise the performance with regard to the risk taken by the manager led researchers and professionals to attempt to go beyond market risk analysis alone in favour of sophisticated models that really allowed all of the portfolio risks to be highlighted and the "normal" returns arbitrated by the market to be evaluated. Consequently, the models allowed the excess performance ("abnormal return" or alpha) to be measured in relation to the risks taken by the manager.

This approach aims to measure not only the level of risk to which the portfolio is exposed but also the manager's skill in doing better than the market in terms of reward for risks. The implementation of this type of fund performance evaluation generally relies on explicit or implicit factor models.

The explicit factor models, of which the best known is the firm Barra's, provide us with a meaningful understanding of the sources of portfolio risk and return but, like all models, remain

subject to specification risk. Today, for example, it seems difficult, after the Internet bubble and its subsequent disintegration, for the risk of a security to be taken from a model defined in the 1980s or 1990s.

To handle the model risk, it has been proposed to turn to the virtues of inductive statistics and notably to the technique of principal component analysis. This involves extracting the fund returns alone without imposing an a priori model structure. This type of technique therefore allows the model risk to be avoided at the cost of an increase in the sample risk, since the choice of period conditions the extraction of the factors. The sample risk can be particularly high in the case of non-stationary phenomena, which is the case of the returns on financial assets.

Although the sample risk can pose a serious problem for implementing risk management tools based on the implicit multi-factor approach, the same cannot be said for performance measurement that is carried out ex-post, over a homogenous period and defined arbitrarily for all of the funds. The main criticism aimed at the extraction of alphas carried out from implicit multi-factor models is their lack of readability. The reader must place blind trust in a model designed as a "black box", which renders the interpretation and verification of the results difficult.

I.3 The objectives of the Amenc – Martellini – Sfeir method proposed for the Agefi Asset Management AwardsThe objectives of the performance analysis method proposed for the Agefi Awards are intended to be a response to both the theoretical and practical difficulties in setting up a fund performance measure and ranking.

The method promoted actually aims to propose:• A true evaluation of the excess performance of the funds in regard to all of the portfolio risks• A use of analysis peer groups based on an objective statistical approach• A method that gives access to results that are easy to interpret and justify.

To do this, we propose to use the conceptual framework from the risk and performance style analysis proposed by the Nobel Prize winner William Sharpe (1992) and to adjust it to the problematic of fund ranking and measurement.

Our methodological note will therefore present the conceptual framework proposed by William Sharpe (II), we shall analyse the conditions for adapting it to fund performance measurement (III) and we shall then conclude with the details of the methodology proposed (IV).

II. Return-Based Style AnalysisIt is widely recognised that asset allocation makes a large contribution to the variation in return of an investor's portfolio. This is particularly true if the portfolio is spread between several funds with each containing several securities.

Asset allocation is generally defined as the allocation of the investor's portfolio between the main asset classes. It should be noted that the asset classes are to be considered in the broad sense and that we can speak more accurately of "style allocation"; it does not only involve stocks and bonds, but also different investment styles (for example, large/small cap, value/growth, etc.).

Sharpe (1988, 1992) introduced the following model to provide an objective breakdown of the manager's true style, as opposed to the style breakdown announced by the manager. This method is known as return-based style analysis.

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Model:

where: Ri = excess return (net of fees) of a given portfolio or fund Fk = excess return in relation to index j for period t wik = weight of the style (the sum of the weights is equal to one) eit = error term

Style analysis is a particular case of a multiple linear regression (statistical terminology) and a factor model (financial terminology). Such factor models are typically evaluated on the basis of their capacity to explain the returns of the assets considered (i.e. the Ri). A useful quantity is the proportion of variance "explained" by the asset classes selected. By using the usual definition, we have, for manager i:

The right-hand side of this equation is equal to 1 minus the proportion of "non-explained" variance.The resulting value of R² thus indicates the proportion of variance "non-explained" by the n assetclasses/styles. From a technical point of view, the optimal weights of the styles are obtained as asolution to a programme minimising the variance of the residual term; this is the traditional approach of "estimation of the least squares" (statistical terminology) or "minimisation of the tracking error" (financial terminology).

Style analysis is however distinguished from the standard linear regression by the fact that specificconstraints are imposed on the coefficients such that they can be directly interpreted as weights:• Constraint on the portfolio: the sum of the coefficients must be equal to one• Positivity constraint: the wik coefficients must be positive.

It should be noted that the presence of these constraints distorts the results of the standard regression. In particular, the confidence intervals for the coefficients are no longer directly available in an explicit way. They can however be estimated numerically by using a method introduced by Lobosco and DiBartolomeo (1997), which we shall discuss in detail in the appendix.

The constraint on the portfolio and the positivity constraint can in fact be relaxed sometimes, inparticular when we carry out style analysis for hedge funds, since the hedge fund manager has thepossibility of using a leverage position and taking both long and short positions in traditional assets (see Agarwal and Naik (2000)).

Style analysis without the positivity constraints is sometimes called semi-strong style analysis, while style analysis without constraints imposed on the factor weightings is referred to as weak style analysis.

III. Return-Based Style Analysis and Performance MeasurementPrimarily, the model separates the fund return into two components:• The “Style”: (share attributable to market movements)• “Skill”: eit (manager-specific share).

The "skill" term can itself be attributed to:• The manager's exposure to asset classes not included in the analysis• The manager's active anticipations: active selection within the asset classes and/or timing in relation to the classes• Statistical error: if it is equal to zero, Var(eit) can be considered as the risk of the share of returnthat comes from the selection.

As a result, it is tempting to use style analysis for performance measurement and performance attribution.

III.1 Identification of the style modifications based on the RBSA methodIt is important to check the consistency of the styles to verify that they correspond to significantdimensions of fund behaviour.

There are numerous reasons for which funds with a consistent style are liable to be favoured byinvestors, from both the single and multi-manager perspectives.1. Single manager perspective. There is academic evidence that style persistence has an influence on performance. A study by Coggin, Fabozzi and Rahman (1993) showed in particular that specialised investment management was profitable: certain managers do seem to be able to outperform a given style benchmark, even though they fail to outperform the market as a whole. In addition, funds that performed badly in the past are more inclined to carry out consequential style modifications (Chan, Chen, Lakonishok (1999); Eichholts et al. (1997)). More generally, this is consistent with the common intuition that better performance can be obtained by specialists who concentrate on a given segment of the market (it has been said that this can explain the success of alternative investment strategies).2. Multi-manager perspective. Identifying style modifications is essential in multi-management. In practical terms, an investor who constructs a portfolio of funds will have to take into account the eventuality of fund managers deviating from their stated or identified styles. This eventuality introduces additional variability from the whole portfolio in relation to the benchmark (this is denoted by the term "non-intentional style bias").

III.2 Benchmarking based on the RBSA methodStyle analysis can be used to construct a customised benchmark, or normal portfolio, for eachmanager. We obtain the benchmark by taking the best passive substitute for the manager's portfolio, or .

A customised benchmark of that sort can then be used to estimate:• The total excess return2 (in relation to the benchmark)• The separation of the excess return into a selection skill term and a timing skill term.

A separation of the excess return term can be obtained through the following two steps. We firstlydefine RBi, the customised benchmark of the fund obtained over a long period of analysis. We then carry out dynamic style analysis to obtain a normal portfolio at the current date RNit.

We obtain the following interpretation:• Rit - RBi = Rit - RNit + RNit - RBi represents the total excess return• Rit - RNit represents the selection skill• RNit - RBi represents the timing skill

A common procedure is then to measure the performance in terms of the information ratio based on the style IR = E(excess return) / sigma(excess return).

72 - The excess return is sometimes called "alpha" in the professional literature. We prefer to avoid this terminology, because we reserve the term "alpha" for the abnormal risk-adjusted return of the fund, i.e. the mean excess return in relation to the normal return of a fund estimated by a multifactor model.

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The information ratio provides a practical measure of the manager's past skill in beating a benchmark for a given amount of relative risk. In other words, it provides a risk-adjusted performance measure, where the risk is measured in relative terms (relative to the benchmark). However, if we have to produce a ranking of the different managers through the various styles, we also need to take a risk-adjusted performance measure into account, where the risk must be understood in an absolute sense.

III.3 Performance measure based on the RBSA methodIt is tempting to interpret the "skill" or total excess return term eit in style analysis as an abnormal return measure. There are, however, two important drawbacks to this:1. Introducing the constraint on the portfolio and the positivity constraint into style analysis distorts the results of the standard regression. As a result, the standard properties desirable in linear regression models are not respected. In particular, the correlation between the error term and the benchmark can be non-null (Deroon, Nijman, Terhorst (2000)).2. As we recalled above, an analysis of that sort does not provide an explanation for the abnormal return, on a risk-adjusted basis. Instead, we need to use a complete multi-factor model, which provides a measure of the abnormal return of the fund as the mean excess return in relation to the "normal return" given by the following relationship (direct generalisation of the CAPM's security market line)

where:• Alpha = represents the abnormal performance of the fund• Ri = return (net of fees) of a given portfolio or fund• rf is the risk-free rate• bik = sensitivity of the fund to factor k• Fk = return of factor k for period t

While this equation provides a satisfactory theoretical response to the problem of risk-adjusted performance measurement, in practice, one important question remains: the choice of factors.

There are four types of factor models:1. Implicit factor models. In this approach, we carry out a factor analysis (for example, a principal component analysis) to extract the factors from return series statistically. It is without doubt the best approach, because it avoids the problems of including bad factors or omitting good factors. Nevertheless, the factors can be difficult to interpret.2. Explicit macroeconomic factor models. In this approach, economic variables are used as factors. For example Chen, Roll, Ross (1986) use the inflation rate, the growth in industrial production, the difference between long-term and short-term interest rates and the difference in ratings between bonds.3. Explicit microeconomic factor models. In this approach, microeconomic attributes are used as factors. The BARRA model constitutes a popular example of this type of model.4. Explicit factor models made up of indices. In this approach, market indices are used as factors. This is consistent with the idea of using portfolio returns as factors. The most popular example of this approach is the CAPM (Sharpe (1964)), where the return of the market portfolio, approximated by a broad index, is used as a factor. The idea of using "replicating portfolios" as an approximation of the true factor, which is unknown, is also found in Fama and French (1992).

In this context, we propose to approach the two style analysis imperfections (the distortion of theresults of the linear factor model, due to the presence of constraints, and the absence of an appropriate risk adjustment) by using a multi-index factor model, which can be written in the

following way:

This factor model is similar in form to the one used by Elton et al. (1993) to estimate the performanceof the managers' fund.

This equation can be seen as a weak form of style analysis, consisting of relaxing the positivity constraint and the constraint on the portfolio, and including a constant term in the regression. We also work in terms of excess returns.

From a practical point of view, this approach also allows us to consider the question of benchmarkingand performance measurement in a unified manner: once the appropriate indices have been selected, they can be used for both return-based style analysis (RBSA) (strong form of style analysis with positivity constraint and constraint on the portfolio) and for an abnormal return measure (weak form applied to the excess returns).

It should be noted however that the estimations of the risk premium terms obtained by means ofhistorical regressions must be considered with care because the sample errors can introduce bias into the results (see for example Merton (1980), who addresses the difficulty in estimating expectedreturns).

IV. Application to the AGEFI rankingsWe give details here of the application of our method to fund rankings within the framework of the Investment Management Awards organised by Agefi.

Step 1: Setting up the databaseThe database used for the Awards is made up of information on fund returns provided by Europerformance. It is made up of FCP and SICAV (mutual funds) marketed in France under Frenchor foreign law approved by the COB, with at least three years of weekly or daily historical valuations.Funds that exhibit historical discontinuity for one of the weeks that make up the period being studied will be excluded from the analysis.

If the fund has two shares, we retain the C share or, failing that, the D share. Treasury funds andsector funds are excluded, together with limited guarantee funds and "bear" investment management. Funds that have changed category during the period are also withdrawn from the database. An asset value screen is applied at 10 million euros. Finally, firms that do not dispose of a sales outlet in Paris are not taken into account for this prize.

Following this screening process, we retained a total of 2,097 funds. 8 funds drawn from this population were withdrawn before the analysis for the following reasons:• 1 fund does not have any Europerformance categories (UNKNOWN category)• 7 funds have "non communicated" performances for September 14 and 21.

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For the analysis, therefore, we retained a total of 2,089 funds, of which around 50% are stock funds, 30% bond funds and 20% diversified funds. A more precise breakdown figures in the table below.

The period selected for the analysis covers 157 weeks of weekly performances from the week of 28/06/99-02/07/99 to the week of 24/06/02-28/06/2002 included.

Example: For funds that value on a Monday, we actually retain the period from Monday, June 28,1999 to Monday, June 24, 2002, and for those that value on a Friday, we cover the period from July 2, 1999 to June 28, 2002.

The database prepared by EUROPERFORMANCE was extracted over a period of slightly more than three years, beginning on June 1, 1999, with rolling weekly performances and identification of the exact calculation day for all the weekly performances of each fund.

Step 2: Selecting a set of categoriesWe think that return-based style analysis and decomposition-based style analysis work better when they are associated with each other. We suggest using a classification arrangement based firstly on the Europerformance categories, and then on the investment styles such as they were deduced from the return-based style analysis.

In more precise terms, we use a decomposition-based method for the observable attributes, for example the geographic zone. We use a return-based method for the non-observable characteristics,in particular the investment styles, as opposed to the investment styles that the managers themselves say that they use, and for which the information may be missing or uncertain.3

We initially distinguish the following three categories: "stocks", bonds", and "diversified". It should be noted that the "guaranteed funds" category is excluded from the analysis.

i) "Stock" FundsWe use the information provided by Europerformance to divide the funds into four zones: France,International, Euro Zone and Emerging Markets. We then carry out return-based style analysis toevaluate the funds' exposures to the following styles:• Growth• Value• Small Cap

3 - It should be noted that the groups generated from return-based style analysis and cluster analysis and used to benchmark the performance of funds may not correspond to the predefined categories used for the final rankings.

NB: For the "emerging markets" category, we shall not single out the growth, value and small capinvestment management styles.

ii) "Bond" FundsWe use the information provided by Europerformance to divide the funds into two zones: Euro and International. We then carry out return-based style analysis to evaluate the funds' exposures to the management styles linked to the rating (treasury, corporate or high yield) and the maturities (short term, medium term or long term).

iii) Diversified FundsWe use the information provided by Europerformance to divide the funds into three categories: Euro, International and Convertible Bonds.

Step 3: Selecting a set of indices to carry out the return-based style analysisFor each sub-category, we need to select a set of indices that will be used to benchmark the fundreturns in a return-based style analysis.

i) "Stock" FundsWe use a set of MSCI indices as regression variables:4

• France:MSCI France ValueMSCI France GrowthMSCI France Small Cap

• Europe:MSCI AC Europe ValueMSCI AC Europe GrowthMSCI Europe Small Cap

• International:MSCI World Index ValueMSCI World Index GrowthMSCI World Index Small Cap

ii) "Bond" FundsThe indices used correspond to both different ratings and different maturities.Euro Segment:SSB EMU GBI 1-3Y (Euro Short-term Treasury Bond Index)SSB EMU GBI 3-5 Y (Euro Medium-term Treasury Bond Index)SSB EMU GBI 7-10Y (Euro Long-term Treasury Bond Index)SSB EUROBIG Corporate (Euro Investment Grade Corporate Bond Index)LB Euro High Yield Index (Euro High Yield Bond Index)

International Segment:SSB WGBI GBI 1-3Y (World Short-term Treasury Bond Index)SSB WGBI GBI 3-5Y (World Medium-term Treasury Bond Index)SSB WGBI GBI 7-10Y (World Long-term Treasury Bond Index)ML Global Broad Market CorpLB Global High Yield

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4 - The MSCI Value and Growth Indices cover the full range of developed, emerging and All Country MSCI Equity Indices, including Free indices where applicable. The indices use Price/Book Value (P/BV) ratios to divide the standard MSCI country indices into two sub-indices: Value and Growth. All securities are classified as either "value" securities (low P/BV securities) or "growth" securities (high P/BV securities), relative to each MSCI country index. In this manner, the definition of value and growth is relative to each individual market as represented by the MSCI index. Country Value/Growth indices are aggregated into regional Value/Growth indices. The MSCI Small Cap Indices target 40% of the eligible Small Cap universe within each industry group, within each country. MSCI defines the Small Cap universe as all listed securities that have a market capitalisation in the range of USD 200 - 1,500 million.

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The choice of this set of indices is consistent with what has been used in academic studies on theperformance of fixed-income portfolios (Blake, Elton and Gruber (1993)).

Furthermore, the indices used for the convertible bond funds are the following:• For France, we chose the "SG Convertible France" index• For the Euro Zone, we picked the "Exane Euro Convertible" index• For the International category, the "UBS Warburg Global Convertible" index was selected.

iii) Diversified FundsFor these funds, a necessarily broader selection of indices was taken:• Euro: use of indices from the "Euro stocks" categories and a selection of "Euro bond" indices (only SSB EMU GBI, SSB EUROBIG Corporate Bond Index and LB Euro High Yield Index)• International: use of indices from the "international stock" and "international bond" categories (only SSB WGI, ML Global Broad Market Corp and LM Global High Yield)• Convertible bonds: use of all the "Convertible" bond indices (France, Europe and International).

To conclude for this step, it is appropriate to note the following important points:• To avoid multi-collinearity problems, we decided to regress onto a subset of stock and bond indices for a given geographic zone, instead of regressing onto all the indices.• For the index database, in accordance with the problematic of the differences in valuation daysbetween the funds, Europerformance calculated weekly performance for each day of the week.Each fund is therefore compared to a set of indices that values at the same date as the fund.

Step 4: Making up peer groupsPeer groups are made up according to the process described below. We represent each fund through a vector of the fund's style weights. We then carry out a grouping by cluster by minimising the distances between the funds within the groups and maximising the distances between the funds that belong to different groups, with the distance being defined by appropriate metrics in the space of the funds' style weights.

The goal is to make the different management styles appear. Each fund is represented by a vector of the fund's style weights (coefficients of the constrained regression) in a Euclidean space. To do this, we carry out a grouping by cluster in SAS by minimising the distances between the funds within the groups and maximising the distances between the funds that belong to different groups, with the distance being defined by appropriate metrics in the Euclidean space of the funds' style weights. We use Ward's (minimum variance) method.

The number of groups is imposed in an exogenous manner, in order to be sure to obtain a reasonablenumber of different classes. The decision rule is as follows: Indices with coefficients lower than 10% are removed. In theory, this threshold should be affected by the number of indices used in the regression (it is easier for an index to explain 10% of the style when 2 indices are used than when 10 indices are). In this context, a pragmatic approach consists of qualitatively analysing the dominant styles for each cluster and possibly introducing regressors with an explanation percentage lower than 10% if they are deemed relevant.

In total, on the basis of the clusters obtained, Agefi chose the following 15 categories:1- French Stocks other than Small Caps2- Euro Stocks other than Small Caps3- Small Caps (France + Euro)4- French and Euro Stocks (all styles included)5- Emerging Market Stocks6- International Stocks (all styles included)

7- International Stocks Small Caps8- Euro Bonds9- International Multi-Issuer Bonds10- International Treasury Bonds11- International Corporate Bonds12- International High Yield Bonds13- Euro Diversified14- International Diversified15- Convertible Bonds

Agefi's choice of categories was made on the basis of representativeness. That meant that, from allthe clusters, only the categories in which there were a significant number of funds were retained.One of the striking results of this study is that style management in France today seems to be limited to the distinction by size (Large versus Small). The Growth versus Value distinction is not yet as structuring as it is in the US, for example. We only found a very limited number, which would not justify a prize category, of funds invested in French stocks and European stocks that displayed a chief characteristic labelled Growth or Value.

Step 5: Carrying out a risk-adjusted analysis of the performance of each fundWe propose to measure the risk-adjusted performance by the constant (or alpha) of the unconstrained regression of the excess return of a fund onto the excess return of the different indices. The risk-free rate used in the calculation of the excess returns is EURIBOR.

In order to avoid model definition and multi-collinearity problems, an additional step can lead to the selection, for each fund, of a subset of sub-indices that have been identified as having a more than marginal contribution to the explanation of the fund return (for example, a style weight greater than 10%). In particular, we use potentially different models (i.e. different sets of indices) for different groups, but the same model (i.e. the same set of indices) within a given group (cf. step 4).

A ranking can then be carried out for each group on the basis of the alphas.

Remarks:i) Even when several clusters are grouped together in a broader single category, a different choiceof indices is retained in the alpha calculation phase for each of the groups, in order to measure the relative performance of each fund by using an appropriate benchmark;ii) All the funds for which the method had not given sufficient explanatory power were excluded from the analysis. Within the framework of this study, the explanatory power is classically measured in terms of R2 (percentage of the variance of fund returns explained by the unconstrained regression). The decision rule involves eliminating the funds with an R2 lower than the mean R2 over the whole database minus 2 standard deviations. In total, 270 funds were eliminated from the study in that way.

Following this process, 1,931 funds were ranked.iii) The mean R2 over the funds taken into account in the rankings is 67% and its standard deviationis 17%.

5. ConclusionIn order to provide a coherent methodological framework for evaluating the risk-adjusted performance of mutual funds in the presence of different investment styles, we have used two important conceptual tools from modern portfolio theory.

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1. Style analysis to establish static peer groups of comparable managers, and also to check the consistency of their style from a dynamic point of view.2. A customised multi-factor model to estimate the additional risk-adjusted performance (alpha) within each group.

We believe that this approach provides a better balance between the theory and the practice. It should be noted that the use of an implicit factor model may be a better way to proceed from a conceptual point of view, since this type of model allows the problems of including bad factors or omitting good factors to be avoided. Nevertheless, this solution may not be as practical to implement as a multi-index model, and its black box aspect means that it is not an entirely appropriate solution for the specific context of rankings, for which transparency is a key success factor.

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• Coggin, D., Fabozzi, F., and S. Rahman, 1993, “The investment performance of US equity pensionfund managers: an empirical investigation”, Journal of Finance, vol XLVIII, 3, 1039-1055.Deroon,

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AppendixIn this appendix, we describe Lobosco and DiBartolemeo's (1997) two-step procedure, which allowsthe statistical significance of the style weights to be determined.

Firstly, calculate the standard deviation n of the returns unexplained by the K indices for each fund n in the universe of N funds.

Then carry out a style analysis for each index k using the remaining K-1 indices as explanatory variables, and keep the standard deviation σk of the residuals of the style analysis for each index inrelation to the remaining indices. Lobosco and DiBartolemeo (1997) show that the standard deviation of the style weight of index k for fund n is given by:

where T is equal to the number of observations of the series of returns and i denotes the number of market indices with non-zero style weights (take this as equal to K).

Then calculate the style weight divided by its standard deviation and compare its absolute value to 2 to check whether it is statistically significant at the 95% threshold.

15

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