Raphaëlle Bellando
email: raphaelle.bellando@univ-orleans.fr

Zahra Ben Braham
email: zahra.benbraham@gmail.com

Sébastien Galanti
email: sebastien.galanti@univ-orleans.fr.

Zahra Ben Braham

« The performance of portfolios based on analysts' recommendations: the Tunisian case »

Keywords: Financial Analyst Recommendations, Broker, Emerging Stock Markets, Portfolio Analystes Financiers, recommandations, courtiers, marchés émergents, portefeuilles. JEL Classification Code : G24 ; O16 ;

This article aims at measuring recommendation value on the Tunisian market and uses a database of 6646 recommendations (2005)(2006)(2007)(2008)(2009). We apply the methodology of calendar-time portfolio analysis. This consists in simulating a portfolio that would include stocks depending on the recommendations issued. In order to measure abnormal (or "excess") returns, the raw return of the portfolio is then compared to the evolution of the stock index and to the prediction of the Capital Asset Pricing Model. Portfolios following buy recommendations have raw monthly returns around 2% to 3%, but their excess return is not statistically different from zero. The portfolios following sell recommendations have a positive raw return but a significant negative excess return, which is explained mainly by the strong uprising trend of the Tunisian market on the sample period.

Furthermore, although portfolios that follow upgraded recommendation have a positive raw return, the abnormal returns of upgrade or downgrade portfolios are not significantly different from zero. We build long-short portfolios, some of which earn a positive significant excess risk-adjusted return of 1.19% per month. Finally, the fact that "sell" signals are largely more informative than "buy" signals suggests that the market trend on a five years scale probably influences the ability of analysts to pick stocks that evolves reversely from the trend.

La performance des portefeuilles construits selon les recommandations des analystes financiers : le cas tunisien.

Résumé

Cet article cherche à mesurer la valeur des recommandations des analystes financiers de la bourse de Tunis. En utilisant une base de 6646 recommandations émises de 2005 à 2009, nous appliquons la méthodologie des portefeuilles en temps calendaire. Cela consiste à inclure dans un portefeuille les titres conditionnellement aux recommandations émises. On mesure les rendements bruts et anormaux de ces portefeuilles. Le rendement anormal est évalué, d'une part, par comparaison à l'indice de marché, et d'autre part par comparaison à la prédiction du Modèle D'Evaluation des Actifs Financiers. Les portefeuilles qui suivent les recommandations d'achat ont des rentabilités brutes de 2 à 3%, mais leur rentabilité anormale n'est pas statistiquement différente de zéro. Les portefeuilles suivant les recommandations de vente ont des rentabilités brutes positives mais des rentabilités excédentaires significativement négatives, ce que nous expliquons par une forte tendance haussière du marché sur la période. De plus, les rentabilités anormales des portefeuilles qui suivent des révisions à la hausse ou à la baisse des recommandations ne sont pas significatives. On construit des portefeuilles consistant à acheter les titres recommandés à l'achat et vendre les titres recommandés à la vente, dont certains atteignent une rentabilité anormale corrigé du risque de 1,19% par mois. Nous interprétons le fait que les signaux de vente sont bien plus importants que les signaux d'achat comme une conséquence de l'influence de la tendance boursière sur l'habilité des analystes à identifier les titres qui vont évoluer en sens inverse de la tendance.

SECTION I: INTRODUCTION

Financial analysts are an important element of financial decision-taking in the Stock

Exchanges throughout the world. Most often employed by brokerage houses, they produce earnings and stock price forecasts, and also investment recommendations, all of which are signals used by stock markets participants.

In practice, recommendations are disclosed in a variety of forms, but financial medias are used to subsume them into five items: strong buy, buy, hold, sell or strong sell a given stock.

Those item are usually coded on a numerical scale. In this paper, we will code strong sell as 1, and so on until strong buy as 5.

Since the 1930's, many studies aimed at measuring the value of recommendations. If one investor follows the recommendations closely, will he earn a positive return? A return that is higher than the stock market growth rate? We review here only the most salient articles2 .

The studies of [START_REF] Stickel | The anatomy of the performance of buy and sell recommendations[END_REF] and [START_REF] Womack | Do brokerage analysts recommendations have investment value[END_REF] analyze the impact of the recommendations on the market price. By calculating an average return for days following the recommendation, they assess the value of the information brought by the analysts. Lehavy, McNichols and Trueman ( 2001 ) complete this study by building calendar-time portfolios.

Into these portfolios, they incorporatestocks according to the recommendations disclosed by the analysts through time. It allows estimating if, for an investor, the strategy consisting in following the recommendations of the analysts is profitable. Jegadeesh, Kim, [START_REF] Jegadeesh | Analyzing the analysts: When do recommendations add value[END_REF], [START_REF] Green | The Value of Client Access to Analyst Recommendations[END_REF] use a similar method. The main results validate the hypothesis according to which following analysts recommendation gives a return in excess of the market (or other benchmark) that is statistically significant. However, if transaction costs are taken into account, the gains are sometimes close to zero, and sometimes positive. Although the profitability of recommendations for an investor has then to be tempered, these results nevertheless underline that the information disclosed by analysts do have accuracy. However, most of the studies cited above examine American stock markets. Do the same results apply to other markets? Does it differ according to whether they are developed markets, or emerging -and then, smaller, less liquid, and less efficient-markets? page 4 / 29

In their paper, [START_REF] Jegadeesh | Value of analyst recommendations: International evidence[END_REF] study the returns of portfolios based on recommendations from G7 countries (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002). They confirm that the distribution of sell and strong sell recommendations is smaller in the US than in other G7 countries. However, they do not conclude that US recommendations are less accurate. Indeed, portfolios based on upward revisions to "buy" recommendations (upgrades) or downward revision to "sell" recommendations (downgrades) exhibit a higher return in the US. According to the authors this demonstrates a superior ability of analysts working on US markets. They analyze the return of a portfolio consisting in purchasing the stock for which an upgrade is observed, and selling the stocks for which a downgrade is observed. Alike other studies, they compute the average monthly return in excess of the market risk-adjusted return (i.e. the average alpha of the Capital Asset Pricing Model -CAPM), in an equally-weighted portfolio (all stocks have equal weights). This excess return is 5.79% in the US, 2.74% in Japan, and lies between 1% and 2% in Canada, Great-Britain, France and Germany. In Italy the return is not significantly different from zero. Lai and Teo (2008) analyze the value of recommendations on height Asian markets3 (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003). They distinguish local and foreign analysts. They show average monthly excess returns of 2,4% to 3% depending on the panel of analyst4 . Interestingly, this places emerging markets in an intermediary position, between the US and the other G7 countries. Chang (2010), studying the profitability of recommendations in Taiwan (1998Taiwan ( -2002)), distinguishes local, foreign and "expatriates" (foreign analysts physically operating in the country where the stock is listed). The monthly average excess return is again between 2% and 2.5%, confirming the previous result5 .

These last two articles illustrate that emerging markets are often studied to compare the ability of local and foreign analysts, in order to test the "home bias".

Recently, other studies endeavored to analyze the impact of recommendations in emerging markets by themselves, no matter the origin of the analyst. The question is to know whether those markets, often perceived as complicated, less well known, and more risky, offer profitable investment opportunity as long as one follows the recommendations, or not. page 5 / 29

In a study about eleven emerging markets6 , [START_REF] Moshirian | The value of stock analysts' recommendations: Evidence from emerging markets[END_REF] analyze the price impact of recommendations. They show that upgrades have more impact than in G7 countries expect the US, and less impact than in the US, c=onfirming again an intermediary position of those countries. This illustrates that the greater information asymmetries supposed to apply in emerging markets can be mitigated using recommendations. However, their study only measures price impact and do no build calendar-time portfolios, as in previous works.

Our article analyzes recommendations of financial analysts from Bourse de Tunis (Tunis Stock Exchange) and examines their value for investors. Using a database of 6646 recommendations about a maximum of 55 firms listed in Tunis between January 2005 and December 2009, we assess whether we confirm the main results of the literature concerning the excess return of portfolio based on recommendations on emerging markets.

The originality of this article lies, first, in the use of a unique dataset collected by hand from the main brokers of the Tunisian market. Second, our methodological strategy is to build calendar-time portfolios that follow recommendations -this has not been done yet, to the best of our knowledge, for an emerging country outside the Asian area. Third, our result contrast with the literature, concerning the returns of portfolio based on the levels of recommendations vs portfolios based on recommendation revisions. Finally, our conclusion put forth what we believe is a phenomenon that has not been paid sufficient scrutiny: the role of the market trend on the ability of analysts to pick over-or under-performing stocks.

We follow the methodology of calendar-time portfolios, as in Barber, Lehavy andTrueman (2001), or in Lai andTeo (2008), for example. We reconstruct portfolios that follow the recommendations. For example, a "buy" portfolio contains stock for which the analysts recommend "buy", in a given month. We then study the return of this portfolio. It is first compared to the market return. We obtain an "abnormal" or "excess" return: if it is positive, following recommendations gives a higher return than a passive market following. Then, the return is compared to the risk-adjusted return of the CAPM. If this abnormal return is positive, the analysts are able to pick stocks which return is in excess of the reward for the assumed risk.

Our main results show that portfolios based on the level of recommendations outperform those based on the revisions of recommendations, in contrast with the previous literature about big developed markets and about the emerging Asian markets studied in Lai and Teo page 6 / 29 (2008). On the other hand, the strategy consisting in buying a portfolio based on buy recommendation, and selling the portfolio based on sell recommendations (the "long-short" portfolio) gives an monthly return between 1.57% (abnormal return) and 1.19% (risk-adjusted abnormal return), which is comparable to most developed countries except the US, and slightly under the emerging Asian countries. The local analysts of the Tunisian market do add value to the investors willing to invest on this market.

We also confirm that "sell" recommendations are more profitable than "buy" recommendations. At the end of the article we provide a possible explanation by discussing the role of the market trend. We observe a strong growth of the Tunisian market in the period under study (2005)(2006)(2007)(2008)(2009). To compare the asymmetry between "buy" and "sell" recommendations' profitability with the market trend is an aspect that has been under-studied.

We hypothesize that analysts, in a bull market, do not clearly discriminate the stocks that will over-perform the market, and pick more easily the stocks which price will increase less. Our database does not allow us to test this point but we emphasize it as an interesting project of future research.

The remainder of this article is built as follows. The second section presents the data and the construction of portfolios. The third section describes the size, returns, and abnormal returns of the portfolios. The fourth section tests for the significance of the abnormal returns obtained, and the last section concludes.

SECTION 2:DATA AND RESEARCH METHODOLOGY

The Data

We gathered the recommendations published by the four main broker of Tunis market place. The recommendation disclosure is monthly. It is also important to analyze changes of recommendations. In the mind of the investors, a reiterated "buy" recommendation can have a different meaning than a recommendation change from "sell" to "buy". In line with [START_REF] Moshirian | The value of stock analysts' recommendations: Evidence from emerging markets[END_REF] and [START_REF] Jegadeesh | Value of analyst recommendations: International evidence[END_REF],

we define upgrade and downgrades by comparing two consecutive recommendations about the same stock from the same intermediary. When unchanged, the recommendation is a reiteration. When moving from any category 1-4 to any superior category, it is an upgrade.

When moving from any category 5-2 to any inferior category, it is a downgrade. We confirm, as in all the previous literature, the prevalence of reiterations. Comparing upgrades and downgrades, we remark that they split exactly even (50% -50%). It is consistent with [START_REF] Moshirian | The value of stock analysts' recommendations: Evidence from emerging markets[END_REF] who find 51.7% upgrades and 48.2% downgrades, and with [START_REF] Jegadeesh | Value of analyst recommendations: International evidence[END_REF] who find 46% upgrades and 54% downgrades.

page 8 / 29

Portfolios construction

We now turn to the construction of calendar-time portfolios. The stocksare integrated into the portfolios depending on the recommendation issued each month by analysts. We aim at simulating what would an investor do when taking into account all the signals sent by the four brokers of the market place. It is as if each portfolio would have four pockets, one for each broker. For the moment we consider three kinds of strategies, depending on which signal is taken into account.

Strategies based on "broad" categories: All-Buy portfolio and All-Sell portfolio

This strategy only focuses on the level of the recommendation and dismisses the recommendations revisions.

-All-Buy portfolio: each month, a stock is included in the portfolio as many times as it is recommended "strong buy" or "buy" by an intermediary.

-All-Sell portfolio: each month, a stock is included in the portfolio as many times as it is recommended "strong sell" or "sell" by an intermediary

Strategies based on « extreme » categories: Strong Buy portfolio and Strong Sell portfolio

We imagine an investor that would focus only on the most salient levels of recommendations.

-Strong Buy portfolio: each month, a stock is included in the portfolio as many times as it is recommended "strong buy" only by an intermediary.

-Strong Sell portfolio: each month, a stock is included in the portfolio as many times as it is recommended "strong sell" only by an intermediary

In the four previous portfolios, one stock is excluded only when there is a recommendation change. For example, if a broker changes his rating about a stock from "buy" in month t to "sell" in month t+1, then the stock would be excluded from All-Buy portfolio in t+1 and would enter All-Sell portfolio at the same time.

page 9 / 29 Moreover, if, on the same month, two brokers recommend to "Buy" a security, and a third one recommends to "Sell" the same security, then, the security will be present two times in the All-Buy portfolio (two shares of the same firm); and one time in the All-Sell portfolio.

Strategies based on the revision of recommendations: upgrade portfolio and downgrade portfolio

In contrast with the two previous ones, this strategy simulates an investor that would react only to recommendation changes.

-Upgrade portfolio: each month, a stock is included in the portfolio as many times as it is upgraded by an intermediary.

-Downgrade portfolio: each month, a stock is included in the portfolio as many times as it is downgraded by an intermediary

The security in question is kept in the portfolio only if there is another revision in the same direction on the following month, and is excluded in the contrary.

The performance of a portfolio: abnormal returns

The returns of each of the six portfolios are computed following the duration between two consecutive recommendations, i.e. a month. Recall that a security can be integrated several times in a portfolio when several brokers disclose the same signal about it.

As usual in the field, the portfolio return, R p,t , is defined as:

𝑅 𝑝,𝑡 = � 𝑥 𝑖,𝑝,𝑡-1 𝑟 𝑖,𝑡 𝑛 𝑝,𝑡-1 𝑖=1
Where 𝑟 𝑖,𝑡 is the return for stock i between month t-1 and t,computed as𝑟 𝑖,𝑡 = ln (

𝑃 𝑖,𝑡 𝑃 𝑖,𝑡-1
),

with𝑃 𝑖,𝑡 the stock i's price at the day of recommendation release in month t, and where𝑛 𝑝,𝑡-1 is the number of securities in month t-1 in portfolio p, and finally where 𝑥 𝑖,𝑝,𝑡-1 is the weight of security i in the portfolio in month t-1.

page 10 / 29

The portfolio is weighted according to market capitalization7 , or « value-weighted », according to capitalization in time t-1, defined as𝐶 𝑖,𝑡-1 :

𝑥 𝑖,𝑝,𝑡-1 = 𝐶 𝑖,𝑡-1 / � 𝐶 𝑗,𝑡-1 𝑛 𝑝,𝑡-1 𝑗=1
The performance of the portfolio is measured with abnormal returns. The aim is to assess the quality of the information content of recommendations. The first way to achieve this is to compare the return with the market return. The difference is denoted as:

𝐴𝑅1 𝑝,𝑡 = 𝑟 𝑝,𝑡 -𝑟 𝑚,𝑡
With𝑟 𝑚,𝑡 the return of the market index (Tunindex). It is weighted by the capitalization of stocks included in it.

The second way to measure performance is to adjust stocks return for their systematic risk, as measured by the beta parameter of the CAPM8 . This measure captures the expected return conditional to the risk of the stock. Comparing it with the observed return of the recommended stock gives an idea of the ability of analyst to pick stocks with observed returns that differ from the returns predicted by the model. Indeed, this difference is measured by Jensen's alpha. A buy (sell) recommendation is supposed to entail a positive (negative) alpha:

the observed return is significantly above (below) the predicted risk-adjusted return.

Using the estimated beta9 for each stock, 𝛽 𝑖,𝑡 , we use the standard CAPM to compute the expected return of the stock, 𝑟ĩ ,𝑡 :

𝑟ĩ ,𝑡 = 𝑟 𝑓 + 𝛽 𝑖,𝑡 (𝑟 𝑚,𝑡 -𝑟 𝑓 )
Where𝑟 𝑓 is the risk-free rate (see appendix A1 for its determination).We then compute the abnormal return of the stock with the alpha 10 , defined as:

𝑎𝑟 𝑖,𝑡 = 𝑟 𝑖,𝑡 -𝑟ĩ ,𝑡
Then the abnormal return of the whole portfolio is:

page 11 / 29
𝐴𝑅2 𝑝,𝑡 = � 𝑥 𝑖,𝑝,𝑡-1 𝑎𝑟 𝑖,𝑡 𝑛 𝑝,𝑡-1

𝑖=1

We now to the results obtained.

SECTION 3: SIZE, RETURNS AND PERFORMANCE OF PORTFOLIOS BASED ON ANALYSTS'

RECOMMENDATIONS

Here we present information about the size of the portfolios obtained (3.1), the returns observed (3.2), and finally the cumulated abnormal returns (3.3). In this last subsection, we build "long-short portfolios", in order to fully assess the value of recommendations.

The number of stocks in each portfolio

As there are 54 firms and 4 brokers, the maximum size of a portfolio is 216 stocks for a given month, if all were recommended by all brokers with the same recommendation. The evolution of the size of portfolio is given in figure 3.

Figure3: evolution of the number of stocks in the portfolios. Statistics are reported in Figure 4 11 . We compare the maximum, minimum, and average number of stocks (n) in a given portfolio on the whole period. We also note the maximum, minimum, and average number of different stocks (nd) in the portfolio. We confirm the domination of buy recommendation, as All-Buy portfolio and Strong-Buy portfolio are the largest ones, and the scarcity of revisions, as the upgrade portfolio and downgrade portfolio are relatively small. Note :nis the number of stocks in the portfolio, nd is the number of unique stocks in the portfolio.

We also report n/nd in the table. We interpret the ratio as a rough measure of the consensus between brokers for a given month. Of course this makes sense only after May 2006, when a second broker enters the market place. When n/nd=1, no stock has a same recommendation made by different brokers. The disagreement is high. When n/nd=4, all stocks have received the same recommendation by the 4 brokers. Brokers all agree about stocks 12 .

The evolution of this ratio is given in figure 5.

11 Appendixes A2 et A3 give the monthly details. 12 As the upper bound of n/nd evolves with the entry of new brokers, we verified that our results are not explained by structure effects, by calculating the gap between the ratio and its upper bound. The average values of this gap (respectively 0.92, 1.30, 1.40, 1.34, 1.93 and 1.86 for the six portfolios) confirm our comments.

page 13 / 29 We note that the revisions, in addition to being scarce, are less consensual (ratio close to 1). When an upgrade occurs, it is most often made by a unique broker (34 cases on 38), and similarly for downgrades (39 cases on 41) 13 . For the other portfolios, the degree of agreement seems higher. The All-Buy portfolio ratio is often higher than 2: on average, each stock receives a "buy" or "strong buy" recommendation by at least two brokers. In the contrary, sales are only recommended by around 1.5 brokers on average. Finally, the overall rising trend of the ratio is nothing else than the consequence of the entry of new brokers.

As a whole, portfolios based on the levels are bigger, because this size is related to a relatively high degree of agreement and to the entry of new brokers; and portfolios based on revisions are smaller, probably because revisions are scarcer and less consensual.

Portfolio returns

We first examine the raw returns, and secondly the abnormal returns.

The figure 6 illustrates the following salient facts. The All-Buy and Strong Buy portfolios are more profitable and less volatile than their sale equivalent. This shows that analysts meet the minimal quality of information that an investor is entitled to expect. The All-Buy and All- 13 The difference with the total in figure 4 Sell portfolio are finally quite close to the extreme portfolios. All four portfolio based on recommendation levels are less profitable than the market index. The most profitable strategy is the one based on revisions: particularly, the upgrade portfolio is the only one to reach a raw return that is higher than the market. However, we must mitigate this aspect because of the high volatility of returns of this portfolio -probably due to an insufficient diversification. We note that the first three portfolios are quite well correlated with the index. The most deceitful is the downgrade portfolio: its return almost equals the market return. Whereas upgrades seem justified, downgraded stocks do not experience a price decrease, not even a weak increase, but seem to increase relatively sharply. Furthermore this portfolio is the most volatile.

Turning to abnormal returns (figure 7), we note that buy portfolios are performing poorly.

In the contrary, the upgrade portfolio has a positive abnormal return: it outperforms the market index (+1.13%), even when adjusting for the risk of stocks (+0.88%). Again, this must be mitigated by the high volatility observed. Taken as a whole, All-Buy and Strong Buy portfolios exhibit a poor performance whereas the All-Sell and Sell portfolios seem to provide valuable information. Concerning the revisions, the large difference between upgrades and downgrades may come from the initial level of the revised recommendation. Figure A4 in the appendix shows that, unsurprisingly, downgrades concern stocks that were initially recommended to "strong buy" or "buy". And precisely, these levels are the ones for which the quality of information is weak. In the contrary, upgrades concern stock initially recommended at "hold" or "sell" levels.

Portfolios performance in terms of cumulated abnormal returns

To complete the description of abnormal returns, figure 8 provides the cumulated abnormal returns over the sample period, for every portfolio. To ease comparison, we suppose that portfolios based on sale recommendation are sold in order to obtain a positive sign of the return.

We also build "long-short portfolios". We suppose that an investor invests one unit in a buy portfolio and sells one unit of the corresponding sell portfolio in every point of time14 .

Although the Bourse de Tunis does not allow for short sales, this strategy represents the full value that can possibly be extracted from analysts' information. We then construct the three following long-short portfolios:

-Long-short broad level portfolio. Each month, one unit of theAll-Buy portfolio is purchased and one unit of the All-Sell portfolio is sold.

-Long-short extreme level portfolio. Each month, one unit of the Strong Buy portfolio is purchased and one unit of the Strong Sell portfolio is sold.

-Long-short revision portfolio. Each month, one unit of the upgrade portfolio is purchased and one unit of the downgrade portfolio is sold.

page 17 / 29

Note. The graphs report the abnormal returns of the different portfolios (as measured by: AR1, the excess return compared to market index return, and AR2, the excess return compared to the CAPM prediction), cumulated over the sample period (January 2005-December 2009). We consider that All-Sell, Strong-Sell, and downgrade portfolios are sold. The longshort portfolios' abnormal returns consist in the difference between the abnormal returns of its two components (if at least one of the two is non-empty on a given month).

This result differs from the literature according to two aspects. The first difference is that we do not find that revisions entice the most important returns, as it is usually found in studies on international markets [START_REF] Barber | Can investors profit from the prophets? Consensus analyst recommendations and stock returns[END_REF][START_REF] Jegadeesh | Value of analyst recommendations: International evidence[END_REF]Lai et al. 2008). Revisions are seen as more informative than the levels of recommendations; whereas our data suggests the contrary. Nevertheless, a common point with the previously cited articles is that we find that long-short portfolios generate positive excess returns, and that sell or downgrade portfolios are more important than buy or upgrade portfolios in driving this result.

SECTION 4: TESTS ON AVERAGE AND MEDIAN RETURNS AND INTERPRETATIONS

We now examine the performance of the strategies consisting in following analysts' recommendation in the Tunis stock exchange during the 2005-2009 period. We test for the statistical significance of the portfolios returns described in the previous section.

As usual in this literature, we use Student t tests. However, some preliminary tests showed that the distribution of returns do not follow a Gaussian distribution, in particular, they are not symmetrically distributed around the mean. This may disrupt Student t-test, as those suppose the Gaussian distribution.

This is why we add two classical non-parametric tests that have not been used in the articles cited above. First, we use the signed ranks Wilcoxon W test, which tests for median or mean abnormal return being equal to zero under the hypothesis of a symmetric distribution.Second, we use the sign S test, which tests for the median abnormal return being equal to zero.

For brevity, we name « buy portfolios » the All-Buy, Strong Buy, and upgrade portfolios and «sale portfolios» the All-Sell, Strong Sell and downgrade portfolios. We define the following null (H 0 ) and alternative (H 1 ) hypothesis.

For the buy portfolios and long-short portfolios:

H 0 : m = 0 vs H 1 : m > 0, page 18 / 29
with m the median or the mean of the returns.

For the sale portfolios, we test:

H 0 :m = 0 vs H 1 : m < 0.
Figure 9 gives the tests results 15 .

Figure 9. Tests for the nullity of portfolio returns

The table reports the returns and p-values of the tests T (Student) W (Wilcoxon signed-rank) and S (Sign test). P-values are given for a positive median alternative hypothesis (for buy and long-short portfolios) and for a negative median alternative hypothesis (for sale portfolios). The returns in bold indicate returns that are statistically significant at the 5% level all three statistics.

The results are interesting in two aspects: the asymmetry between buy and sale recommendations, and between the levels and revision of recommendations.

The profitability of buy vs sale portfolios.

Since [START_REF] Womack | Do brokerage analysts recommendations have investment value[END_REF], the literature posits that buy recommendations are far more numerous than sell recommendations. This constitutes a positive bias. As investors learn this bias over time, they tend to discount buy recommendations and pay more attention to sell recommendation. When transposed to the framework of calendar-time strategies, this imply that portfolios based on buy recommendation should under-perform those based on sale recommendation. The evidence for this fact is given in the articles of [START_REF] Barber | Can investors profit from the prophets? Consensus analyst recommendations and stock returns[END_REF], Jegadeesh andal (2004, 2006), [START_REF] Green | The Value of Client Access to Analyst Recommendations[END_REF]), Lai and Tao (2008), Chang (2010). We confirm this result in our study.

Nevertheless, as most of those results more significance for long-short portfolios and for sale portfolios, they also document significance for buy portfolios. For example in Green 15 As these are unilateral tests, we checked that p-values given by RATS and STATA softwares do correspond.

T obs Raw return T W S AR1 T W S AR2 T W S All-Buy 60
1,92% 0.000 0.000 0.000 -0,03% 0.570 0.847 0.849 -0,05% 0.611 0.872 0.849

All-Sell 60 0,34% 0.781 0.693 0.500 -1,61% 0.000 0.000 0.010 -1,23% 0.002 0.000 0.010

Long-short broad level 60 1,58% 0.001 0.001 0.002 1,57% 0.001 0.002 0.005 1,19% 0.010 0.010 0.001

Strong Buy 60 1,74% 0.000 0.000 0.000 -0,21% 0.843 0.937 0.965 -0,27% 0.905 0.958 0.939

Strong Sell 44 0,15% 0.574 0.526 0.500 -1,67% 0.033 0.036 0.183 -0,63% 0.216 0.181 0.183

Long-short extreme levels 60 1,62% 0.015 0.015 0.010 1,01% 0.082 0.200 0.398 0,19% 0.387 0.484 0.302 upgrade 39 2,83% 0.008 0.011 0.002 1,13% 0.113 0.100 0.100 0,88% (2008), the raw return of buy portfolio is significant (whereas it is not the case when riskadjusted by the CAPM), and in most variants upgrade portfolios have significant returns. In Chang (2010), the long (buy) portfolio is even more significant than the short (sell) portfolio.

It is not the case in our study. Whereas the raw return of the All-Buy portfolio and the upgrade portfolio are quite different from zero (resp. 1,92% and 2.83%), it is no longer significant when computing excess return, compared to market index (reps.-0.03% and 1,13%)) or risk-adjusted (-0.05% and 0.88%).

Our explanation for it concerns the ability of analyst to order the stocks that are expected to perform, during a bear period. It is the case in our sample (see appendix A3), as the trend is steadily upward from 2005 to 2009. In that framework, it is possible that analyst fail to identify stocks that will perform better than the trend (the raw returns of buy portfolios are positive, but not the abnormal returns). In the contrary, they succeed in identifying stocks that evolves reversely from the trend, i.e. in our case, abnormal return of All-Sell portfolio is highly significant: -1.61% when compared to market index and -1.23% when risk-adjusted.

This drives most of the return of the portfolio that purchases the All-Buy and short-sells the All-Sell. However, as there is no bear period in our sample, we are not able to test this explanation.

The profitability of recommendation levels vs revisions.

Since the article of [START_REF] Jegadeesh | Analyzing the analysts: When do recommendations add value[END_REF], the revisions of recommendations are considered as more susceptible to entail positive abnormal returns than the levels of recommendations do. For this reason [START_REF] Jegadeesh | Value of analyst recommendations: International evidence[END_REF] do not event mention portfolios based on the level of recommendation, but only on upgrades or downgrades. In Lai andTao (2008), the upgrade portfolios bring a higher return than buy portfolios, and downgrade portfolios bring a more negative return than sell portfolios.

In our study in the contrary, level-based portfolios outperform revision-based portfolios.

Considering excess return, upgrade, downgrade, or purchasing upgrade and short-selling downgrade portfolios are never significant. Still, the long-short portfolio gives an abnormal return between 1.09% compared to the stock index (i.e. around 13.9% annualized), and 0.57% when risk-adjusted. Whereas "extreme" levels do not entail real profitability, the portfolio that page 20 / 29 short-sell "All-Sell" obtains a significant abnormal return of 1.61% (21.1% annualized) and of 1.23% (15.8% annualized) when risk-adjusted.

We explain this result as follows. The specificity of the Tunisian market, unlike developed and Asian markets; is that investors seem to wait for a confirmation when a revision occurs 16 .

Instead of reacting quickly, investors postpone their trading decision. It is possible that investors on the Tunisian market are more risk-adverse than on other places; but a more plausible explanation is that they simply follow a different institution which is to wait for a confirmation of the revision. Suppose, for example that an upgrade to "Buy" occurs. Then, investors wait for the next recommendation on this firm. If the "Buy" is reiterated, only then the stock is purchased.

Although this explanation is consistent with our results, we should condition revisions on the current level of the recommendations 17 . For example, the impact of an upgrade depends on whether it is an upgrade to "Strong Buy" or to "Hold". However, the small size of our sample does not allow us to treat this aspect.

SECTION 5: CONCLUSION

Our study undoubtedly has limits and calls for future research. For example, as many results of the literature 18 , we do not account for transaction costs. Indeed, brokerage commissions would surely reduce the returns mentioned in the paper.

However, our results bring evidence of the value of analysts' recommendation on the Tunisian market. Buy recommendations entail returns that are clearly above sale recommendations.

The strategy consisting in buying the upgrade portfolio and selling the downgrade portfolio brings a risk-adjusted return, computing the CAPM alpha, of 0.57% per month, using a valueweighted portfolio. Although not statistically different from zero, it is positive, which indicates that analysts are able to differentiate stocks depending on whether their price is going to rise or fall. This return can be compared to those computed the same way in [START_REF] Jegadeesh | Value of analyst recommendations: International evidence[END_REF]. They are 2.07% in the US, 0.95% in Canada and 0.67% in Britain.

All three are significant. It is 1.10% in Japan, 0.51% in Germany, 0.37% in Italy, and 0.25% 16 We obtain a similar conclusion in a previous study on the Tunisian market about the price impact of recommendation; see Ben [START_REF] Ben Braham | Recommendation Value on an Emerging Market: the Impact of Analysts' Recommendations on Stock Prices and Trading Volumes in Tunisia, working paper[END_REF]. 17 As it is done in Barber and al. (2010). 18 With the exceptions of [START_REF] Barber | Can investors profit from the prophets? Consensus analyst recommendations and stock returns[END_REF] and [START_REF] Green | The Value of Client Access to Analyst Recommendations[END_REF] page 21 / 29 in France, and those four are not statistically different from zero. In Lai and Tao (2008), the average of height emerging Asian countries for the same strategy gives 2.42% and 3.05% 19 .

Our results hence place the Tunisian market closer to European developed country than to Asian emerging markets.

We also show that returns of portfolio for "broad" levels (All Buy and All-Sell) outperform those based on "extreme" levels (Strong Buy and Strong Sell). Furthermore, the poor performance of buy portfolios is probably due to the bullish orientation of the market during our sample period. The analysts are able to pick stocks that are going to deeply under-perform the market. But they are much less able to pick stocks that will do better than the market.

Although the relation between the market trend and the performance of recommendation levels is sometimes evoked in the literature, it has not, as far as we are aware of, been paid enough attention, and this constitutes an interesting perspective for future research. 19 We translate into monthly basis the daily percentage of their

Figure 2 :

 2 Figure 2 : recommendationsrevision by broker

Figure 4 :

 4 Figure 4:statistics about the number of stocks in the porfolios.

Figure 5 :

 5 Figure 5: evolution of the degree of agreement between brokers

Figure 1: distribution of recommendations by broker Tunisie valeurs Amen Invest Cofib Capital Axis Capital Total

	Recommendationlevel Freq. Percent Freq. Percent Freq. Percent Freq. Percent Freq. Percent
	1 (strongsell) 2 (sell)	126 311	15.26	178 304	22.60	37 132	15.25	33 88	22.37	374 835	18.20
	3 (hold)	1200	41.90	907	42.52	327	29.51	158	29.21 2592	39.00
	4 (buy) 5 (strongbuy)	311 916	42.84	461 283	34.88	451 161	55.23	212 50	48.43	1435 1410	42.80
	Total	2864 100.00 2133 100.00 1108 100.00	541 100.00 6646 100.00
	Note : To compute percentages, we group the « sell » and « strong sell » recommendations, and also « buy » and « strong
	buy » recommendations. Source: Auhors.
						TunisieValeurs initiated coverage on
	January 2005 (hence 60 months are available), Amen Invest in 2006 (44 months), COFIB in
	2008 (24 months) and Axis Capital in 2009 (12 months). This amounts to a total of 6646
	recommendations, which are distributed as indicated in the following figure.
					page 7 / 29

Tunisie valeurs Amen Invest Cofib Capital Axis Capital Total

		Freq.	Percent	Freq.	Percent	Freq.	Percent Freq. Percent	Freq .	Percen t
	Downgrade	51	1.81	110	5.29	46	4.36	4	0.81 211	3.27
	Reiteration	2700	96.09	1858	89.37	972	92.13	483	98.37 6013 93.46
	Upgrade	59	2.10	111	5.34	37	3.51	4	0.81 211	3.27
	Total	2810	100.00	2079	100.00	1055	100.00	491	100.00 6435 100.00
	Source : Authors.

  Buy close to Strong Buy, All-Sell close to Strong Sell), slowly the recommendations are more diverse and revisions are more frequent.

	recommendations (almost no revisions), and by the domination of extreme recommendations
	(All-
	120
	100
	80
	60
	40
	20
	0
	janv-05	mars-05	mai-05	juil-05	sept-05	nov-05	janv-06	mars-06	mai-06	juil-06	sept-06	nov-06	janv-07	mars-07	mai-07	juil-07	sept-07	nov-07	janv-08	mars-08	mai-08	juil-08	sept-08	nov-08	janv-09	mars-09	mai-09	juil-09	sept-09	nov-09
					PAN				PVN				PAE			PVE			PAR			PVR
												page 12 / 29

PAN : All-Buy portfolio, PVN : All-Sell portfolio, PAE : Strong Buy portfolio, PVE : Strong Sell portfolio, PAR : upgrade portfolio, PVR : downgrade portfolio This evolution is affected by the entry of new brokers: Amen Invest in may 2006, Cofib in January 2008 and Axis Capital in January 2009. After a period showing a high stability of

Figure 7 : Abnormalreturns All-Buy All-Sell StrongBuy StrongSell upgrade downgrade

  Sell and Strong Sell portfolios show a negative abnormal return, which is a good news since it means that the sale signals do provide a valuable information. The downgrade portfolio shows inconclusive results, as the abnormal returns are weak and very variable.

	The All-
	AR1 : Relative to Tunindex
	Mean	-0,03%	-1,61%	-0,21%	-1,67%	1,13%	-0,09%
	Standard dev.	1,44%	3,19%	1,59%	5,81%	5,67%	7,69%
	Correlation w/ Tunindex	1,40%	-11,58%	1,21%	-41,23%	19,29%	14,70%
	AR2 : Relative toCAPM
	Mean	-0,05%	-1,24%	-0,27%	-0,63%	0.88%	0,23%
	Standard dev.	1,43%	3,26%	1,58%	5,20%	6,85%	7,87%
	Correlation w/Tunindex	1,07%	9,13%	-5,53%	-2,31%	12,87%	25,57%
	Note: Monthlyreturns.
			page 15 / 29

  Table6, panel C), upgrade portfolio are as significant as downgrade portfolio, whereas the size of the excess (abnormal) return is smaller for the upgrade portfolio. In Lai and Tao

	(2006
				0.216 0.115 0.055
	downgade	42	1,83%	0.096 0.175 0.268 -0,09% 0.470 0.174 0.108 0,23% 0.573 0.696 0.500
	long-short revisions	44	0,76%	0.285 0.287 0.382 1,09% 0.207 0.155 0.382 0,57% 0.347 0.229 0.382
				page 19 / 29

Definition of the risk-free rate (Rf) lesSICAVs

  monétaires sont inexistantes sur le marché tunisien et que les produits monétaires existants sont plutôt les billets de trésorerie, les certificats de dépôt, ou encore les comptes de dépôt à terme. Mais ces produits présentent de nombreuses restrictions (un remboursement à échéance, un montant minimal de placement, un blocage obligatoire) et une liquidité réduite.Ils ne sont, donc, pas adaptés à la gestion de portefeuilles boursiers d'où la gestion actuelle de la liquidité disponible en portefeuille.Les taux afférents à ces produits sont de toute façon inexploitables étant donné l'absence de statistiques officielles : ce sont souvent des négociations de gré à gré qui se font au cas par caset pour lesquelles aucun historique de données n'est disponible.

	APPENDIXES A4 Revision distribution conditional on the initial level A2 : Statistique sur les portefeuilles A3
							downgrade upgrade
		Tableau A1. Evolution du nombre de titres total dans les portefeuilles Tableau A2. Evolution du nombre différents de titres total dans les portefeuilles StrongSell 0,0% 6,8%
	SICAV Rendement Tunisie SICAV PAN PVN PAE PVE PAR PVR PAN PVN PAE PVE PAR PVR Moyenne 12 7 12 juil-07 39 22 21 9 4 12 7 12 août-07 41 23 21 10 3 2 12 7 12 sept-07 40 21 21 8 5 6 14 7 14 1 oct-07 41 20 22 8 4 1 15 7 15 nov-07 43 18 21 8 4 1 15 7 15 févr-08 71 27 30 7 2 5 15 7 15 1 mars-08 71 29 30 8 2 15 7 15 avr-08 69 27 31 8 1 3 15 7 15 mai-08 71 23 30 8 8 7 15 7 15 juin-08 71 23 30 8 15 7 15 juil-08 68 23 33 8 6 6 15 7 15 août-08 68 22 33 7 3 2 15 7 15 sept-08 72 22 35 7 6 2 15 7 15 oct-08 73 23 28 7 5 11 25 19 25 6 nov-08 74 26 27 8 2 4 28 18 28 4 5 déc-08 71 27 27 8 4 6 32 18 32 5 4 2 janv-09 95 32 37 11 3 2 31 20 31 6 3 févr-09 94 31 37 11 5 6 PAN PVN PAE PVE PAR PVR PAN PVN PAE PVE PAR PVR 12 7 12 juil-07 26 18 17 7 4 12 7 12 août-07 28 19 17 8 3 2 12 7 12 sept-07 27 17 18 6 5 6 14 7 14 1 oct-07 26 16 18 6 4 1 15 7 15 nov-07 28 15 18 6 4 1 15 7 15 févr-08 33 18 22 4 2 4 15 7 15 1 mars-08 33 19 22 4 2 15 7 15 avr-08 34 19 23 4 1 3 15 7 15 mai-08 36 16 22 4 8 7 15 7 15 juin-08 36 16 22 4 0 15 7 15 juil-08 35 14 22 4 6 6 15 7 15 août-08 36 14 23 4 3 2 15 7 15 sept-08 35 13 24 4 6 2 15 7 15 oct-08 36 13 21 4 5 10 21 14 21 6 nov-08 35 14 21 5 2 3 23 13 23 4 5 déc-08 35 15 20 5 4 6 26 13 26 5 4 2 janv-09 36 18 22 6 3 2 26 15 26 6 3 févr-09 35 17 21 6 5 6 Sell 5,0% 27,7% Hold 27,4% 46,6% Buy 30,8% 18,9% StrongBuy 36,8% 0,0% A1: Année janv-05 févr-05 mars-05 avr-05 mai-05 août-05 sept-05 oct-05 nov-05 déc-05 janv-06 févr-06 mars-06 avr-06 mai-06 juin-06 juil-06 août-06 janv-05 févr-05 mars-05 avr-05 mai-05 août-05 sept-05 oct-05 nov-05 déc-05 janv-06 févr-06 mars-06 avr-06 mai-06 juin-06 juil-06 août-06 juin-05 15 7 15 déc-07 44 18 22 7 4 juin-05 15 7 15 déc-07 28 15 18 5 4 2 2 juil-05 15 7 15 janv-08 73 27 31 7 8 2 juil-05 15 7 15 janv-08 34 18 22 4 8 2 A5
	sept-06 sept-06	29 22	2005 17 13	29 22	6 5 6	3.7 4 5	4	4 mars-09 mars-09	90 35	3.85 31 17	36 21	11 3 6	2	8	8
	oct-06 oct-06 nov-06 nov-06 déc-06 déc-06	30 22 28 21 28 21	2006 20 18 2007 22 18 20 16	30 22 24 20 22 20	7 3 7 9 1 9 8 4 8	3.4 6 3 3.7 10 1 10 6 3 4 3	4.1 avr-09 avr-09 3.7 mai-09 mai-09 juin-09 juin-09	91 36 90 33 93 35	31 17 3.75 30 16 3.7 28 15	35 21 39 21 39 21	11 2 6 11 9 6 11 4 6	2 9 3	1 7 2	1 7 2
	janv-07 janv-07	27 21	2008 21 17	17 17	8 8	3.7 6	6	3.7 juil-09 juil-09	94 38	25 14	3.7	38 21	8 11 4 10	14 14
	févr-07 févr-07	37 27	2009 21 15	16 16	3.3 11 18 10 20 9 11	4 août-09 août-09	94 35	3.65 28 14	40 19	15 12 10 11	10 10
	mars-07 mars-07	36 26	Moyenne 23 18 16 17	11 2 9	3.6 4 2	4	3.9 sept-09 sept-09	99 36	27 15	3.7	41 19	14 5 10	5	1	1
	avr-07 avr-07	37 26	Ecart-type 22 19 15 18	10 3 8	3	1	1	oct-09 100 oct-09 37	0.0758 28 40 14 20	15 3 10	3	1	1
	mai-07 mai-07	37 25	Variance 19 19 14 17	10 6 8	6	2	2	nov-09 105 nov-09 37	0.0058 28 41 16 20	14 10 9 10	5	5
	juin-07 juin-07	40 27	19 15	22 18	9 8 7	8	5	5	déc-09 déc-09	81 37	22 14		30 19	11 3 9	3	1	1
	PAN : « acheter » ou « renforcer », PVN : « vendre « ou « alléger »,PAE : « acheter », PVE : « vendre », PAR,
	PAN : « acheter » ou « renforcer », PVN : « vendre « ou « alléger »,PAE : « acheter », PVE : « vendre », PAR, révisions à la hausse, PVR, révisions à la baisse.
	révisions à la hausse, PVR, révisions à la baisse.
									article, supposing 22 trading days. 2.42% is for
	foreign analysts and 3.05% for local analysts.
								page 22 / 29 page 23 / 29 page 24 / 29 page 25 / 29

Nous avons donc choisi pour le calcul du taux sans risque les SICAVs à cent pour cent obligataires les moins risquées du marché durant la période 2005-2009 selon avec les gestionnaires d'organisme de placement collectif en valeurs mobilières (OPCVM) de la place.

Les rendements des SICAVs étant publiés annuellement, on a reporté ci-dessous les deux séries ainsi que leur moyenne utilisée pour le taux sans risque.

Evolution of the Tunisian Market Index A6 Corrélation des rentabilités anormales cumulées avec les rentabilités cumulées de TUNINDEX

									Tunindex
	350
	300
	250
	200
	150
	100
	50
	0
	janv.-yy	avr.-yy	juil.-yy	oct.-yy	janv.-yy	avr.-yy	juil.-yy	oct.-yy	janv.-yy	avr.-yy	juil.-yy	oct.-yy	janv.-yy	avr.-yy	juil.-yy	oct.-yy	janv.-yy	avr.-yy	juil.-yy	oct.-yy
							AR1								AR2
				Niveaux		Extrêmes		Révisions		Niveaux		Extrêmes		Révisions
	Acheteur	-0,16042337 -0,62544564 0,87077056 -0,23991442 -0,69031043 0,8023743
	Vendeur (-)		0,90660029 0,94621049 -0,64547653 0,8534053		0,85130562 -0,73748851
	Mixte		0,90785922 0,94812837 0,65495263 0,84785537 0,64891527 0,23776146
									page 26 / 29

For a complete survey, seeRamnath et al. (2008)

India, Indonesia, South Korea, Malaysia, Philippines, Singapore, Taiwan, Thailand.

We compute monthly return from the daily rate in the article.

We compute monthly return from the yearly rate in the article.

Argentina, Brazil, China, Chile, Hungary, India, Indonesia, Israel, South Korea, Mexico, South Africa.

We also computed equal-weights portfolios, where the weights are defined as:𝑥 𝑖,𝑝,𝑡-1 = 1/𝑛 𝑝,𝑡-1 . The results obtained at the different stages of the study are very close.

The data available on the Tunisian market is insufficient to use a multiple factor model, as Fama-French model.

For each stock, the beta is estimated on a two year period and then supposed constant for the following year. Another strategy would be to res-estimate each month rolling betas, but this entails a highbetas volatility, partly explained by the number of days without trade.

There are month in which a given recommendation is not disclosed (e.g. "Strong Sell"…). Recall that in this case, no portfolio is built for that month. The return of the long-short portfolio being the difference of two portfolios' return, it is computed if, for a given month, at least one of the two portfolios exists. In the case when one of the two portfolios is empty, its return is considered as zero. It follows that the average return of the longshort portfolio does not necessarily correspond to the simple difference of its two components' average return.

page 16 / 29

The observation of graphs in figure 8 confirms the previous comments. Analysts do add value to portfolios when they issue "sell" or "strong sell" recommendations. It seems clear that the source of the long-short portfolios returns stems from stocks recommended for sale.

In the contrary, the revisions do not look like having a great impact.


Franck Marle

Ludovic-Alexandre Vidal

Jean-Claude Bocquet

Interactions-based risk clustering methodologies and algorithms for complex project management

Project risks have never been so present. First, projects are dealing with bigger stakes and facing stronger constraints. Moreover, projects must cope with an ever-growing complexity. Risks have then increased in number and criticality. Lists of identified project risks thus need to be decomposed, for smaller clusters are more manageable. Existing techniques are mainly mono-criteria, based on risks parameters such as nature or criticality value. Limits have appeared since project risk interactions are not properly considered. Project interdependent risks are indeed often managed as if they were independent. We thus propose an interactions-based clustering methodology with associated tools and algorithms. Our objective is to group risks, so that the interaction rate is maximal inside clusters and minimal outside. The final objective is to facilitate the coordination of complex projects by reducing interfaces when dealing with risks. We first model project risk interactions through binary matrix and numerical matrix representation. Then we define our objective function. A linear programming algorithm and two approximate iterative ones are then presented. Possible refinement through the concept of interactions similarity is also proposed. A case study in the entertainment industry is finally presented, providing us information and points of comparison for global conclusions and perspectives. 1

INTRODUCTION

A project is a temporary and unique endeavor undertaken to deliver a result, which generally corresponds to the creation of a unique product or service which brings about beneficial change or added value (PMI, 2004). A new organization within the firm is then needed to perform a project: new processes which must answer project finalities and objectives in terms of values creation must be set up. These new processes are performed thanks to resources (notably project actors) which belong to the created project organizational system. A project is in essence unique, which means that the project organizational system is to be conceived for each project within a firm (as it is specific to a project). Project organizations are thus in essence temporary organizations. They coexist with permanent organizations which exist within the firm. This coexistence (involving interfaces and dependencies) makes project and project management all the more complex. Moreover, the conception of the project organizational system follows the steps of project phases' identification and analysis, planning and monitoring.

Therefore, when thinking at projects in terms of systems following several phases, many dependencies and interdependencies between phases, sub-systems and other entities can be identified. This can lead to communication and coordination issues when facing decisionmaking situations. Namely, project complexity, described notably in [START_REF] Baccarini | The concept of project complexitya review[END_REF], [START_REF] Edmonds | Syntactic measures of complexity[END_REF], [START_REF] Laurikkala | Reducing complexity of modelling in large delivery projects[END_REF] involves issues in decision-making under complex situations [START_REF] Phelan | From chaos to complexity in strategic planning. 55th meeting of Academy of Management[END_REF], [START_REF] Earl | Complexity in planning design processes[END_REF], [START_REF] Vidal | Measuring project complexity using the Analytic Hierarchy Process[END_REF]. Then, as well as the uncertainty and instability which are inherent to projects, complexity appears to be one of the main risk drivers. Moreover, complexity reduces the awareness of decision-makers and thus the efficiency of their decisions.

As a consequence, this paper proposes an innovative method and its associated tool to assist project risk management under complex contexts by focusing on project risk interdependencies. Our research objective is to group risks into clusters in order to catch inside of them most of project interactions. This is notably to facilitate the coordination among actors involved in the project risk management process.

THE NEED FOR A BETTER CONSIDERATION OF PROJECT RISK

INTERACTIONS

Project systems are in essence risky, as they are unique, constrained, subject to uncertainty and to complexity. They are composed of many interrelated objects of different natures and must reach many objectives which may be interdependent or even contradictory. This involves two things in terms of risk management. First, there are many risks of different natures, and it is even impossible to be completely exhaustive when identifying them. It is then mandatory to group risks into smaller and thus more manageable groups, which is detailed in 2.1. Second, these risks are interrelated, meaning that they are not independent events. This causes some issues in decision-making in project risk management, when decisions are to be made about the prioritization of risks and the risk mitigation actions. These issues are not well addressed by traditional approaches as shown in 2.2. Paragraph 2.3 sets the resulting problem and methodology of this paper.

Classifying project risks by nature and/or by value

Project risk management is classically decomposed into four successive major steps: risk identification, risk analysis, risk response planning and risk monitoring (PMI, 2004).

Risk identification is the process of determining events which, may they occur, could impact positively or negatively project objectives. Risk identification methods are classified according two different families: direct or indirect risk identification [START_REF] Raz | A comparative review of risk management standards[END_REF].

The number of risks in the generated list may vary from some tens to some hundreds. It is then mandatory to decompose it into subgroups in order to have more manageable items. This list is a priori (included in the methodology) or a posteriori classified according to the nature of the risks (financial, human, technical, schedule, etc…). This process is called clustering by nature.

During risk analysis, risks are prioritized, essentially according to their probability and impact. Risk evaluation scales are often defined in terms of criticality, which is generally a function of probability and impact. The main output of risk analysis is a list or graph, which enables decision-makers to categorize risks as high, medium or low in terms of the chosen indicator (criticality whatever its formulation, or other indexes). This is another kind of clustering, called by value.

Next steps are risk response planning and monitoring. We argue that these steps should be performed after an innovative project risk analysis based on risk interactions since current methods have shown their limits.

Limits of traditional approaches

The initial goal of risk clustering processes is to facilitate the management of risks in terms of decision-making. In the case of clustering by nature, the main objective is to facilitate the identification of risk owners, whether individual or entities (due to their skills and competencies), and then to facilitate the allocation of additional or contingency resources. In the case of clustering by value, the main objective is to prioritize risks in order to make decisions about the future mitigation plan and the resulting resource allocation. As they are classifying risks based on one of their characteristics, those methods do not include their possible interactions. Therefore, in both cases, there are lots of interactions between clusters. This can result in a lack of coordination between actors when making decisions, due to the lack of awareness of the global impact of one's decision, mainly outside the considered cluster.

Actually, whatever the criteria used for the decomposition of an initial risk list, and whatever the rigor and detail level used, there will always be interactions between risks which do not belong to the same cluster [START_REF] Marle | Modèle d'informations et méthodes pour aider à la prise de décision en management de projets[END_REF]. This can notably be underlined when looking at projects through systems thinking [START_REF] Simon | The Sciences of the artificial[END_REF], [START_REF] Le Moigne | La théorie du système général[END_REF].

Project management current techniques include classical principles underpinning scientific management: the fragmentation of work and the maximization of visibility and accountability.

We can argue that today projects are generally managed with single-link trees (Work Breakdown Structure, PERT, Organizational Breakdown Structure, risk lists) and not as networks [START_REF] Vidal | Interactions-based clustering to assist project management[END_REF]. In the case of risk management, most of the methods use lists, screening or sorting risks, as seen before. The problem with current methodologies is that project risk interactions are not clearly included, e.g. in Figure 1, where some links are existing though not managed (dotted lines). Risks are indeed interrelated with complex links.

Insert Figure 1 A previous study we had conducted about 23 risk analysis methodologies enabled to identify complexity-related issues [START_REF] Marle | Analysis of current project risk management methodologies and required improvements[END_REF]. For instance, there may be propagation from one « upstream » risk to numerous « downstream » risks, the climax of this phenomenon being the famous dangers of the domino effect. Traditional methodologies are mainly single-risk oriented, analyzing their multiple causes and multiple consequences. However, some works have been done to model more complex interdependencies between risks. Bayesian Networks for instance link several risks, from multiple inputs to multiple outputs, but they have specific validity conditions: links must be oriented, and they are more adapted to acyclic networks.

However, loops are a great danger during projects and are all the more complicated to understand since risks which exist within a loop are likely to be heterogeneous (of different natures). It is possible to tackle this issue using dynamic Bayesian Networks but the effort required to gather conditional probabilities and to run dynamic networks for the huge number of possible loops makes them unsuitable to real project environments.

There is thus crucial need for better awareness, consideration and management of project risks, knowing they are intertwined. We propose in this article such a methodology. Our ambition is not to give "exact" results: we want to assist day-do-day project risk management thanks to our method. This one is notably not based on the mathematics of probabilities. It can thus take into account easily the existence of loops and non-linear couplings for instance.

Problem setting and methodology

As shown by the former paragraphs, risks are managed thanks to the elaboration of smaller clusters. At this stage, a management issue arises, since decisions may be blocked, slowed down or ineffective if interactions are poorly taken into account. Our research problematic is thus to propose a new additional clustering methodology, which could take into account interactions between risks, in terms of existence and strength. First, we identify possible risk interactions. The whole is synthesized thanks to binary matrix representation. The matrix is then transformed to be a numerical one thanks to the use of the principles of the AHP (Analytic Hierarchy Process, a multi-criteria decision-making methodology) [START_REF] Saaty | The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation[END_REF].

These numerical data permit us to develop a linear programming and two approximate iterative algorithms. We then express how these results can still be refined thanks to the introduction of a distance measure and similarity identification process. All the obtained results are then compared to classical decompositions, notably thanks to a case study in the entertainment industry. We then propose some conclusions and call for future perspectives of research around this issue, after studying the implications of our works on day-to-day management.

CATCHING PROJECT RISKS INTERACTIONS THROUGH MATRIX REPRESENTATION

Building up the Risk Structure Matrix (RSM)

The Design Structure Matrix approach

The Design Structure Matrix (DSM) represents relations and dependencies among objects.

The same objects are both in the rows and columns of the square matrix, which is square. The DSM was introduced by Steward [START_REF] Steward | The Design Structure Matrix: a method for managing the design of complex systems[END_REF] with tasks and was initially used basically for planning issues [START_REF] Eppinger | A model-based method for organizing tasks in product development[END_REF]. Since, it has been widely used with other objects, like product components, projects or people [START_REF] Eppinger | Patterns of product development interactions[END_REF], [START_REF] Sosa | The misalignment of product architecture and organizational structure in complex product development[END_REF], [START_REF] Danilovic | Managing complex product development projects with design structure matrices and domain mapping matrices[END_REF], [START_REF] Sosa | A structured approach to predicting and managing technical interactions in software development[END_REF]. As for us, we propose to use the concept of DSM for other conceptual objects, which are risks, in the context of project management. As tasks, projects and people, project risks are (or can at least be supposed as):

 in a finite number (since a project is in essence temporary, with finite resources, objectives, means, etc., i.e. a finite number of elements),  managed during the project management process,  interrelated, (notably because of project and project management complexity factors [START_REF] Vidal | Understanding project complexity: implications on project management[END_REF]) which justifies the use of a methodology for complex interactions management.

We define risk interaction in terms of the existence of a possible precedence relationship between two risks R i and R j . We then define the binary Risk Structure Matrix (RSM). It corresponds to the square matrix with RSM ij =1 (else 0) when there is an interaction from R j to R i . The main advantage of this approach is to overcome the display issue of complex network and to permit easier calculations which are inherent to the matrix format (eigenvalues, matrices product, matrix transposition, etc…). The combination of several individual interactions may form loops in the risk network (for instance, if RSM ij =RSM jk =RSM ki =1, then we have a loop including the three risks R i , R j and R k ).

Building up the RSM

In order to build the RSM, we have to identify the interactions which exist between project risks. The iterative procedure we use is notably addressed in ongoing publications.

Classically, the DSM is re-ordered in a way which permits to show first-level blocks, thanks to the well-established partitioning process [START_REF] Eppinger | A model-based method for organizing tasks in product development[END_REF]. This one applied to the RSM gives three types of information:

 the dependent risks: they are engaged in a potential precedence relationship,  the interdependent risks: they are engaged in mutually dependent relation, directly or with a bigger loop,  the independent risks: the risks are basically non-related.

The aim of this process is basically to obtain a lower block-triangular matrix. Partitioning enables to isolate interdependent risks, but our purpose is different. We aim at grouping risks in clusters with maximal internal interactions and minimal inter-clusters interactions.

In order to do so, we firstly use an AHP-based evaluation to transform the RSM into a numerical matrix which is to catch the strength of local interactions. Indeed, fieldwork proves us that such assessment of interactions is hard to do directly. On the contrary, it can be observed that people find it easier to say that a cause C 1 is more likely to produce an effect E (first level neighbor) than another cause C 2 , or similarly, that an effect E 1 is more likely to be the consequence of a cause C than another effect E 2 . That is why we claim for the use of the principle of pair wise comparisons to assess project risk interactions.

Methodology

Five steps are necessary to carry out our methodology. Figure 2 shows this process with an example for risk R 4 :

Step 1: Decomposing individual sub-problems

The presence of a 1 in the binary RSM expresses the existence of a possible precedence relationship between risks R i and R j . RSM ij =1 implies two possible ways to address the situation. If there is a cause-effect relationship between R i and R j , then it is equivalent to consider R i as a cause of R j or R j as an effect of R i . Similarly as in [START_REF] Chen | Decomposition of interdependent task group for concurrent engineering[END_REF] for design tasks, we combine these visions. Two stages must thus be performed. For each R i , we isolate the risks which are related with R i in column (possible effects) and in row (possible causes). This permits a sanity check because each relationship has to be expressed two times.

This identification enables to generate the Binary Cause or Effect Vectors, which are relative to one risk R i (respectively BCV|R i and BEV|R i ).

Step 2: Evaluating the strength of interactions

We build up two matrices regarding the risk R i based on the two previously isolated sets of risks (in rows and in columns), which constitute the set of alternatives. They are called Cause or Effect Comparison Matrices and are both relative to one risk R i (CCM|R i and ECM|R i ).

Given the AHP numerous applications in the field of project management and project risk management [START_REF] Gourc | Vers un modèle conceptuel du risque pour le pilotage et la conduite des activités de biens et de services[END_REF], we claim for the use of the AHP-based principle of pair wise comparisons to assess project risk interactions (as we define them in this article). The Analytic Hierarchy Process was developed by Thomas Saaty [START_REF] Saaty | A scaling method for priorities in hierarchical structures[END_REF], [START_REF] Saaty | The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation[END_REF]. It is a multi-criteria decision-making method. It permits the relative assessment and prioritization of alternatives. The AHP is based on the use of pair wise comparisons, which lead to the elaboration of a ratio scale. The AHP models the problem as a hierarchy, consisting of an overall goal, a group of alternatives, and a group of criteria which link the alternatives to the goal. Pair wise comparisons are carried out by asking how more valuable an alternative A is to criterion C than another alternative B. Pair wise comparisons finally constitute square matrices, the values of which are between 1/9 and 9, and the diagonal elements of which are equal to 1 while the other elements verify two conditions:

 The i-j th element is equal to the comparison between i and j regarding the considered criterion.

 For i different from j, the i-j th element is equal to the inverse of the j-i th element. This piece of information is processed mathematically, in order to transform the qualitative user information into a mathematical one. Priorities are then determined thanks to these matrices and a global consistency test can be performed to evaluate the coherence of the judgments. The final result is a table which gives a global evaluation of each alternative for the objective and for each criterion.

In our case, we have two parallel pair wise comparison processes to run. The first one consists in the ranking in rows for each project risk. Given the risk R k , the set of alternatives are all the non-zero elements of risks other than the diagonal element in row k. The criterion on which the alternatives are evaluated is the contribution to R k in terms of risk input: in other terms, for every pair of risks which are compared, R i and R j (thus following RSM ki =RSM kj =1), the user should assess which one is more important to risk R k in terms of probability to be a risk input (i.e., a cause) for risk R k . Numerical values express these assessments thanks to the use of the traditional AHP scales. The second one is the ranking in columns, according to the same principles.

Step 3: Consolidating the results Eigenvectors of each matrix ECM|R i and CCM|R i are now to be calculated. It enables to find the principal eigenvectors, relative to the maximal eigenvalue. They are called the Numerical Cause or Effect Vectors and are relative to one risk R i (NCV i and NEV i ). Consistency of the results should be tested thanks to the AHP consistency index.

Step 4: Aggregating the results

For each risk R i , Numerical Cause or Effect vectors are respectively aggregated into Numerical Cause / Effect Matrices (NCM and NEM). The i-th row of NEM corresponds to the eigenvector of CCM|R i , which is associated to its maximum eigenvalue. The j-th column of NCM corresponds to the eigenvector of ECM|R j , which is associated to its maximum eigenvalue.

Step 5: Compiling the results

The two previous matrices are aggregated into a single Risk Numerical Matrix (RNM), the values of which assess the relative strength of local interactions. The RNM is defined by a geometrical weighting operation (based on the possible assumption that both estimations can be considered as equivalent). We choose the geometrical mean instead of the arithmetic mean because it tends to favor balanced values (between the two assessments).

) , ( ) , ( ) , ( j i NEM j i NCM j i RNM   1 ) , ( 0 ), , (    j i RNM j i
The RNM thus permits to synthesize the existence and strength of local precedence relationships between risks as it combines the cause-oriented vision and the consequenceoriented vision of an interaction. Combining these two visions is therefore interesting to avoid any bias or misevaluation which can happen when looking at the problem with only one vision.

Similarly as when performing risk identification and analysis, the identification and evaluation of interactions should be updated during the project.

Insert Figure 2 4 PROPOSED CLUSTERING ALGORITHMS AND REFINEMENTS

Overall problem definition

We want to cluster risks in order to maximize intra-cluster interactions thanks to the use of the RNM. We do insist on the fact that the values of the RNM are local judgements, which implies that risk interactions assessments are in essence relative. However, we do argue that this first clustering is useful, since it permits to focus on the most significant local risk interactions. In order to define our clustering approach, we carried out a literature review on clustering and graph partitioning approaches, notably thanks to the works of Schaeffer [START_REF] Schaeffer | Graph clustering Computer Science Review I[END_REF]. There are mainly two approaches for clustering operations: vertex similarity-based methodologies and cluster fitness measures-based methodologies.

Vertex similarity-based criteria and methodologies

On one hand, there are several clustering algorithms which are based on similarities between the vertices. These methods are based on the assumption that the higher the vertex similarity, the stronger the need to cluster the vertices together. These measures are mainly based on additional properties of vertices which permit to compute a similarity matrix.

Rather than defining similarity measures, dissimilarity measures such as distance measures are usually defined, for instance the traditional Euclidean and Manhattan distances (Ben-Arieh and Sreenivasan, 1999), [START_REF] Hennig | A robust distance coefficient between distribution areas incorporating geographic distances[END_REF]. More advanced distance such as Jaccard distance [START_REF] Dong | A hierarchical clustering algorithm based on fuzzy graph connectedness Fuzzy Sets and Systems[END_REF] or the Levenshtein distance [START_REF] Gusfield | Algorithms on strings, trees and sequences[END_REF]) can be used to answer this issue. Some other coefficients can also be calculated to evaluate vertex similarity and perform the corresponding clustering process: for instance there exists angle measures such as the cosine similarity [START_REF] Lakroum | Clustering of the Poincare vectors Image Processing[END_REF]. Some important works even try to compare such similarity measures and their impact on clustering operations [START_REF] Hartigan | Clustering Algorithms[END_REF], [START_REF] Yin | Similarity coefficient methods applied to the cell formation problem: A taxonomy and review[END_REF]. As noticed by [START_REF] Schaeffer | Graph clustering Computer Science Review I[END_REF], "in some applications, the vertices lack additional properties and there is nothing in the vertices themselves that would allow the computation of a similarity matrix". In this case, vertex similarity measures are often defined thanks to the structural characteristics of the graph. For instance, some measures based on the correlation of the adjacency matrix can be used, such as the Pearson correlation [START_REF] Rodgers | Thirteen Ways toLook at the Correlation Coefficient[END_REF] or the Mahalanobis distance [START_REF] Mahalanobis | On the generalised distance in statistics[END_REF].

Cluster fitness measures-based criteria and methodologies

On the other hand, some clustering processes are based on cluster fitness measures, that is to say functions which assess the overall quality and relevance of a given cluster or of a given global clustering solution. The global objective of these methodologies is to identify clustering solutions which directly fulfil a certain property. For instance, methodologies based on graph density measures have been developed in order to partition the initial graph into subgraphs, the density of which should be inferior and/or superior to chosen values (Karp, 1977), [START_REF] Kim | Graph theoretic sequence clustering algorithms and their applications to genome comparison[END_REF], [START_REF] Zotteri | The impact of aggregation level on forecasting performance[END_REF]. But other cluster fitness measures are used as a criterion for graph partitioning. Indeed, as noticed by [START_REF] Schaeffer | Graph clustering Computer Science Review I[END_REF], "one measure that helps to evaluate the sparsity of connections from the cluster to the rest of the graph is the cut size. The smaller the cut size, the better isolated the cluster". Indeed, cutsize-based measures undoubtedly permit to quantify the relative independence of a subgraph to the rest of the graph and have been used in many clustering processes [START_REF] Shi | Normalized Cuts and Image Segmentation[END_REF], (Kannan and al., 2004). Finding the partition which minimises cut-sizes (with restriction conditions on the orders of the subgraphs) permits to maximise the sum of the edges weights which are internal to the clusters. This cut-based measure seems very interesting in our case. In order to facilitate complex project risk management, one is likely to want to reduce interfaces in terms of number, and above all strength. Reducing interfaces is thus very similar to this problem of graph partitioning which aims at minimising the global cut size (since risk interactions are modelled and assessed thanks to edges and their weights).

Broad definition of the interactions-based project risk clustering problem

Indeed, let us consider a set of project risks (R 1 , R 2 , …,R N ). This set of risks is in essence a complex one, since interactions do exist between risks. Let us suppose we know the RNM of this set of risks (the former steps to build the RNM should have been followed by the user).

Let K be the number of clusters of the optimal clustering solution, which maximises intra- K is not known in advance, but we know some constraints about it. Namely, the goal is to assign project members to clusters in order to manage more properly the risks which belong to a same cluster, i.e. which are strongly interdependent. It is known that people have a limited capacity to manage simultaneously numerous objects. Indeed, the number of factors that most decision-makers can handle simultaneously cannot be higher than 7 to 9 [START_REF] Miller | The magical number seven plus or minus two: some limitations on our capacity for processing information[END_REF]). We follow this hypothesis and in the end the maximum size of a cluster should be 9.

We choose to leave some margin compared to the classical empirical rule of 7 objects to be managed simultaneously. This permits us to know a lower bound of K, which is

1 ) 9 1 ( min    N INT K
, where INT is the integer part of a real number. This problem corresponds to the K-graph partitioning / clustering problem [START_REF] Schaeffer | Graph clustering Computer Science Review I[END_REF] and we define it more precisely in the following of this article.

Formulating a linear programming problem to answer this question

Here is the corresponding quadratic integer programming problem formulation. This problem is to be solved for each value of K which is superior to K min . We first introduce the following decision variables:

1 , 1 , , 1 ,        ik x K k k N i i if risk R i belongs to cluster C k .
The objective function, which is to be maximized, is as following in equation 2

       K k N i N j jk ik j i RNM x x INTRA 1 1 1 ) , ( (2)
Problem constraints are the following (equations 3 and 4).

      K k ik x N i i 1 1 , 1 ,
(3) as we argue for clusters disjunction in order to permit easier management in practice.

      N i ik x K k k 1 9 , 1 , (4)
since we want the maximum size of clusters to be 9 risks. This problem is not linear but we can make it easily linear thanks to the introduction of new decision variables (equation 5) and new constraints (equation 6).

ijk y K k k N i j N i i , 1 , , 1 , , 1 ,          is a binary variable (5)
We define y ijk by adding the constraints:

1 , 1 , , 1 , , 1 ,             jk ik ijk x x y K k k N i j N i i (6)
This equation forces y ijk to be equal to 0 if x ik and x jk are not both equal to 1, i.e. if R i and R j do not belong to the same cluster. All other constraints are kept for problem formulation. The objective function can then be re-written thanks to these new decision variables, in equation 7.

       K k N i N j ijk j i RNM y INTRA 1 1 1 ) , ( (7)
We use OPL (Optimization Programming Language) to solve this problem. However, its complexity is high (2 N-1 ), and problems over 20-21 risks appear to be critical when testing them. We presently work on developing some heuristics to assist problem solving in the software and reduce processing time by avoiding trivial non-solutions. Meanwhile, we have developed some approximate iterative algorithms, which permit us to approximate the optimal solution of the problem.

Using simple heuristics to solve this problem

Both of these heuristics are iterative construction algorithms, but they use two different values for clustering conditions, as described in equations 8 and 9. The first iterative algorithm IA 1 is based on the maximum value between two separate clusters. The second one IA 2 is based on global interactions value between two separate clusters. In the two cases, these values are to be maximized at each step.

) , ( ) , ( max , 1 j i RNM C C Value C j C i        (8)          C j C i i j RNM j i RNM C C Value , 2 ) , ( ) , ( ) , ( (9)
At the initial step, all risks are isolated: every initial cluster is a singleton. The maximum value is obtained for two isolated risks R i0 and R j0 , which are grouped into a first cluster C 1 .

Then, the maximum value for the second step may be obtained for two isolated risks or for cluster C 1 and an isolated risk: in the first case, this forms another cluster C 2 and in the second case, C 1 is updated with the third element. Step by step, clusters are formed with singletons or by expanding (adding one singleton to an existing cluster) or by merging (two existing clusters). At each step, the previously defined value (Value 1 or Value 2 ) is maximized. In the case the maximum size of a cluster is reached, the second maximum value is identified and the clustering operation is done on the corresponding interaction if it does respect the formulated constraints. This procedure is repeated iteratively until reaching a solution which respects all the constraints. Given a possible solution thanks to a clustering method, we can build a K × N matrix (M ki ), so that M ki =1 if risk R i belongs to cluster C k in the final solution. If T (M ki ) is the transpose of this matrix, then:

 H=(M ki ). T (M ki ) is a K × K matrix, the diagonal terms of which correspond to the number of risks which are clustered in cluster K. MCS = Mean Cluster Size is then the average of the diagonal values of this matrix.

 L= T (M ki ).(M ki ) is a N × N matrix, the i-j th term of which is equal to 1 if R i and R j belong to a same cluster. As a consequence, the calculation of

) , ( B A M 
which is the difference of the two matrices L(A) and L(B), obtained thanks to the clustering methods A and B, permits to identify the similarity between two clustering solutions.

Let N 0 be the number of non-zero values in the ) , ( B A M  matrix. We build up the following indicator (Eq. 11) which is a dissimilarity measure when comparing solutions. Note that MCS is taken into account, since, if given a clustering solution, if one risk R i is taken out of the cluster it belongs to, then MCS non-zero values are likely to appear (mean value) in the dissimilarity matrix for this risk R i .

) 2

) ( ) ( ( ) , ( 2 0 B MCS A MCS N N B A     (11)
These other indicators permit to compare the structure of two solutions proposed by different methods.

Refinement of the obtained solutions

Our goal here is to refine our results by identifying within clusters similar situations in terms of causes and effects, i.e. the less distant risks. Many distances (i.e. similarity functions) can be proposed in order to assess the proximity of two risks as seen in 4.1.1. To define them, we build up a symmetrical matrix, the Risk Interaction Matrix (RIM), the i-j th term of which is given by equation 12 :

) , ( ) , ( ) , ( i j RNM j i RNM j i RIM   (12)
At this stage, note that any metric can be used in order to define this distance. As for us, we claim for the use of the Mahalanobis distance [START_REF] Mahalanobis | On the generalised distance in statistics[END_REF], which corresponds to a weighted Euclidian distance (the weights being determined by the covariance matrix ∑), as shown in equation 13. ( 13) Where V i is the i-th column of RIM.

We then use a classical average-linkage clustering algorithm [START_REF] Murtagh | A survey of recent advances in hierarchical clustering algorithms[END_REF] to identify similar situations inside clusters. Such identifications of similar risks (in terms of interactions) within the clusters obtained in 4.2 and 4.3 permit to give information to the person in charge of the management of the cluster: indeed, two similar risks may be handled with similar managing techniques and/or even the same preventive/curative actions.

CASE STUDY

Introduction of the case study

In order to test the proposals and results of our theoretical study, we carried out a case study in the entertainment industry: the chosen project is the production of a family stage musical in Paris. The project notably encompasses stage, costume, lightning and sound design, casting management, rehearsal management, fund raising and overall project management support activities, etc… Project duration is 6 months before the 9 months staging. Overall budget is around 60000€ without salaries. The project team is composed of 18 people. The case study we present here is based on fieldwork and interviews which were conducted with 1 cast member, 2 creatives, and 1 production team member. We introduce below the initial list of risks in table 1.

Insert Table 1

Results of the case study

With the previously introduced data, we built up the RNM. In order to do so, a preliminary interview (which last about 1 hour and a half) was realised with the production team member so he could perform the required pairwise comparisons. Before a meeting with all the participants was organised, the study was presented to them and preliminary qualitative interviews were conducted with them in order to have a general idea of the points which would not make consensus. During the meeting, the evaluations of the production team member were exposed and discussed by all the participants. Some changes occurred while discussing and consensus was reached after the meeting, which last about 3 hours. As a whole, 3 weeks were needed to build up the RNM.

We then processed the algorithms which were presented previously. Their results can be seen next page in Figure 3. They only represent two graphs, since in this case the second iterative algorithm (IA2) gave the same result as the linear programming (LP) algorithm. In this figure, they are compared to the two classical clustering results. A general observation is that there are less arcs (risk interactions) outside the clusters in IA1 or LP than in the traditional approaches. Moreover, it appears that the arcs which remain outside the clusters in IA1 or LP tend to be weighted with low values (low strength of risk interactions) compared to the mean value of interactions.

Insert Figure 3 Indeed, as shown afterwards in Figure 4 . The linear programming and iterative algorithms we developed give very interesting results and perspectives for project risk management since in all cases, more than 70% of the interactions values are kept inside the obtained risk clusters (nearly 5 times best than by nature, and 2 times best than by values).

Insert Figure 4

Practical implications on project management are the following ones. Since the formed clusters are more independent (due to a lower level of interactions between clusters), it seems interesting to propose a complementary organisation. For a given cluster C, the nomination of a risk cluster owner RO(C) seems interesting. This person would then assure the global coordination of the management of the risks which are inside cluster C. Since within cluster C, risks tend to be strongly linked, this person has more easily a global view of the possible implications (propagation effects) of any decisions made for a risk which is inside cluster C.

In this case, the process to nominate the risk cluster owner was discussed: the participants proposed to organise a meeting for each cluster C with the initial risk owners which are present in cluster C and ask them to nominate the risk cluster owner.

In this specific case, one of the decisions was notably to make one cast member (a female performer) the prime interlocutor with the production team members. This corresponded to assign her to the cluster which grouped notably R 10 (low team communication) and R 17 (low team motivation). She was then responsible for the identification of triggering events of risks within this cluster and its communication to the production team. She was also a relay between the production team and the cast to avoid miscommunication. This organisation permitted to create a better ambience and motivation than in former projects which had been carried out by the firm. Discontent was notably detected earlier, before it implied a decrease of motivation and thus a decrease of quality for the show. In other terms, instead of focusing on the project results, thanks to this approach, some root causes of project risks were better addressed than before.

Moreover, these results were refined. Indeed, the risks R 11 (Bad scenic, lightning and sound design) and R 12 (Bad costume design) were analysed as very similar thanks to the Mahalanobis distance-based clustering method we use. The person in charge of the corresponding cluster was informed of this similarity. He then decided to group some management actions of these two risks. For instance, a common monitoring and control process was defined for R 11 and R 12 (identical frequency of milestones during the project, simultaneous check of the risks and their consequences,…).

Finally, in this case, IA2 and LP gave exactly the same result. IA1 gave a slightly different result in terms of risks regrouping and intra-cluster interactions value. As a consequence, the issue of algorithm performance compared to MPT is to be addressed, since results do not differ much, whereas MPT can vary of around 275%. In order to answer it more properly and validate even more this overall approach and its practical implications on project management, new tests are to be carried out on several projects (it is presently being tested on a large infrastructure project).

IMPLICATIONS ON PROJECT MANAGEMENT

Some works in the literature show that, in the context of decision-making within some specific environments, project managers tend to deny, avoid, ignore and/or delay dealing with risks [START_REF] Kutsch | Intervening conditions on the management of project risk: Dealing with uncertainty in information technology projects[END_REF]. For all practical purposes, the gap between expected and real risk management implementation is significant. Our methodology permits greater communication on project risks and better confidence in risk management activities thanks to two aspects.

First, the evaluation of risk interactions which is performed when building up the RNM implies a two-step process (looking in terms of causes, and then of effects). Information can thus be checked and refined since one interaction should be listed twice (from cause to effect, and from effect to cause): this checking process permits a better confidence in risk identification and risk interaction identification. Even if theory is sometimes difficult to implement in real projects, we argue that the theoretical background of our models can easily be implemented and understood at a reasonable level. The fact that it relies on expert judgements, mainly qualitative judgements, makes it a user-friendly and easily computable tool. The case study indeed proved us that, even in project contexts where project members are not used to work with tools built from design engineering and industrial engineering theories, the whole approach is globally understood.

Second, clustering risks in order to maximize the global intra-cluster interactions value permits to facilitate the coordination of risk management activities. Namely, it underlines the need for cooperation and transversal communication within the project team, especially within the current structure of the project or the organization. It permits greater communication between people, since it does not seek the identification of ownership, responsibility and/or accountability, but the identification of risk interdependencies. After the clustering process, coordination is made by the person who is assigned to the cluster, but communication has been facilitated before, meaning we have less defensive phenomena.

However, this implies that the assignment of a cluster to a team member should be done carefully, as they need to manage risks which are of different natures. They must have enough background, enough global overview of the different components of the project and enough authority to be able to manage people from different entities with different interests. Such project team members should then be able to facilitate communication and group decisionmaking. They should also show great adaptability since people may not be used to work together, if they were traditionally managing risks by nature (mainly the same entity). The question is finally to assign the cluster to one of the owners of one or more risks which are inside this cluster, or to assign it to someone who may have a global view and enough authority on most of the risks which are inside the cluster. In some cases, the best assignment is for the most experimented team member or the one who has the highest hierarchical level.

In other cases, the best assignment is for the person who is the owner of most of the risks (in terms of number or global gravity).

As a whole, since our work changes the way risks are grouped together, it changes the way decisions are made. Indeed, with our approach, decisions are made less locally since potential implications and propagation phenomena are handled more easily.

CONCLUSIONS AND PERSPECTIVES

In this study, we made a comparison between several possibilities for grouping risks in a project. Our aim is not to criticize the use of classical approaches, because they may have slightly different objectives: we refer to them as points of comparison. Our objective is the improvement of coordination through the better recognition and handling of risks interactions.

Our works and case study shows potential significant improvements regarding this specific objective.

They also underline the need for a shift in the way project risk management should be approached. Regrouping risks in clusters which maximize the values of risk interactions inside them appears to be a promising approach to handle project risks. Indeed, such clusters are generally to be assigned to project team members. Each person in charge of a cluster can thus manage risks which are closely related in terms of possible causes or consequences. As a whole, this means that complexity-related possible effects can be caught more easily and as a consequence managed more effectively and efficiently. Project coordination is undoubtedly facilitated with this approach since interface problems are considerably reduced (for interclusters links global value is lowered). This new approach is thus a complementary one to traditional project risk management techniques. For instance, classifying risks by criticality value is still useful for prioritization and resource allocation, and can be performed within the formed clusters. But the fact that a risk with a low criticality value may involve a chain of more dangerous consequences could change the decision of treating this risk or not. The identification of clusters then enables to treat risks whether individually or collectively. Sometimes, it will be more efficient to treat a risk which could be a cause of the rest of the cluster in order to dramatically reduce the probability of propagation. In other cases, the mitigation actions should impact the complete cluster, because of its global criticality and its very interrelated nature.

Lots of aspects of this work and its results may however be discussed. We identify several of them hereinafter.

 Trying to integrate more project dynamics in this (quite static) methodology, that is to say trying to integrate the time interval which exists between a given cause and each of its effects.

 Consolidating the constitution of the binary interaction matrix. For the moment, we have essentially focused on the triggering effect of the cause and effect relationships between risks, but others do exist (such as changing the gravity of a consequence knowing that a given cause has occurred or not). It would then be particularly interesting to create a typology of possible interactions between risk parameters (probability, gravity, criticality, non detection, influence capacity,…). This could facilitate the evaluation of the strength of interactions in the RNM.

 Exploring the sensitivity of this methodology since the evaluation of risk interactions is at the basis of this approach. As defined presently in our methodology, this evaluation is in essence subjective. Therefore, the use of fuzzy methods such as the fuzzy AHP needs to be explored in order to reduce the subjectivity of the users' judgements.

 More generally, evaluating with more reliability the relative weights of risk interactions. Formally, the AHP has notably received some criticisms which need to be studied for this issue. Other multi-criteria methods should also be explored (such as MACBETH or ELECTRE) and their results should then be compared to the ones obtained with the AHP.

Future research works are thus to be carried out in order to explore these aspects and develop future implications for project complexity and risk management.

  cluster global interactions value. INTRA value is defined by the sum of the values of all interactions between risks which belong to a same cluster. INTER (Inter-cluster global interactions) value is defined by the sum of the values of all interactions between risks which are not paired inside a same cluster. The sum of INTRA and INTER values corresponds to the sum of all risk interactions values, which is constant. As a consequence, maximizing INTRA is equivalent to minimizing INTER.

4. 4

 4 Developing indicators to compare solutions In order to compare different possible clustering solutions, we introduce some numerical indicators. Given a problem with N risks, the first two indicators we introduce are:  MPT = Mean Processing Time, which is the mean time to obtain the solution of the problem. B are two solutions and INTRA is the value of the intra-cluster global interactions value. These indicators permit to assess the overall performance of each method (in terms of time and capture of interactions inside clusters).

  (synthetic indicators), it must be noted that interactions-based clustering give here much more efficient results in terms of interactions values within clusters, as expressed by the values of INTRA 

Figure 1 .

 1 Figure 1. Classification of projects risks by nature and/or by value

Figure 2 .

 2 Figure 2. How to build the Risk Numerical Matrix (RNM)

Figure 4 .

 4 Figure 4. Performance of the clustering methods -Case study