VALUE-AT-RISK IN MUTUAL FUNDS WHICH METHODOLOGY OF ESTIMATION

2ème Conférence Euro-Africaine en Finance et Economie (CEAFE) Février 2008 EcolePolytechnique, 2ème Conférence Euro-AfricaineenFinance etEconomie (CEAFE) 5-6 Juin 2008 THEME: Markets’ microstructure VALUE-AT-RISK IN MUTUAL FUNDS WHICH METHODOLOGY OF ESTIMATION GALLALI Mohamed Imen * GUESMI Ahlem† Abstract: The spectacular explosion experienced by collective investment organisms or mutual funds, this few last years, drove supervising and controlling organisations of these funds, to impose some risk management directives based on value-at-risk. However, the concept’s flexibility raises many questions concerning the choice of the most accurate and suitable estimation’s model. The purpose of this work consists in selecting between the three estimation’s methods, namely, parametric method, historical simulation and Monte Carlo simulation, to determine the most pertinent methodology providing the prediction of potential losses which confront Tunisian open-end funds’ portfolios. For this purpose, we tried, firstly, to present the different estimation’s approaches of VaR. Secondly, we analysed the statistical descriptive characteristics of 14 mixed open-end Portfolios, subject of this study. After that, empirical study’s results have been exposed, and therefore, allowed us to highlight the Monte Carlo simulation superiority, in expecting potential losses inherent to Tunisian mutual funds portfolios. Key words: Value-at-risk – open-end funds – Monte Carlo Simulation – Historical Simulation – Parametric Method. Classification JEL: G10, G11, G23, C13, C14, C15 * Maitre assistant à l’Ecole Supérieur de Commerce (ESC), Université la Manouba. † Enseignante chercheur à FSJEG de Jendouba. Téléphone: 22 534 907 / 72 590 492 E-mail: guesmi_ahlem@yahoo.fr. (Auteur à contacter) Adresse : 54, Route de Tunis Km2, Zarzouna 7021, Bizerte. Ecole polytechnique de Tunis 1 2ème Conférence Euro-Africaine en Finance et Economie (CEAFE) Février 2008 THEME: Microstructure des marchés VALUE-AT-RISK EN SICAV QUELLE METHODOLOGIE D’ESTIMATION GALLALI Mohamed Imen ‡ GUESMI Ahlem§ Résumé: L’expansion spectaculaire qu’ont connue les organismes de placements collectifs, ces dernières années, a suscité les organismes de contrôle et de supervision de ces fonds, à imposer des directives de gestion des risques y afférents, basées sur le concept VaR. Toutefois, la souplesse que confère ce concept, soulève plusieurs interrogations en matière du choix du modèle d’estimation le plus adéquat. Le but de ce travail, consiste à opter pour l’une des trois méthodes d’estimation, à savoir, la méthode paramétrique, la simulation historique et la simulation Monte Carlo, afin de pouvoir déterminer la méthodologie la plus pertinente assurant la prévision des pertes potentielles que confrontent les portefeuilles SICAV tunisiennes. Pour cela, on a essayé, tout d’abord, de présenter les différentes approches d’estimation de la VaR. En second lieu, on a analysé les caractéristiques statistiques descriptives des 14 portefeuilles SICAV mixtes sujet de notre étude. Par la suite, les résultats de notre étude empirique ont été explicités, et nous ont permis de mettre en exergue la supériorité de la simulation Monte Carlo à prévoir les pertes potentielles inhérentes aux portefeuilles Sicav. Mots clefs : Value-at-risk – SICAV – Simulation Monte Carlo – Simulation Historique – Méthode Paramétrique. Classification JEL: G10, G11, G23, C13, C14, C15 ‡ Maitre assistant à l’Ecole Supérieur de Commerce (ESC), Université la Manouba. § Enseignante chercheur à FSJEG de Jendouba. Téléphone: 22 534 907 / 72 590 492 E-mail: guesmi_ahlem@yahoo.fr. (Auteur à contacter) Adresse : 54, Route de Tunis Km2, Zarzouna 7021, Bizerte. Ecole polytechnique de Tunis 2 2ème Conférence Euro-Africaine en Finance et Economie (CEAFE) Février 2008 INTRODUCTION: These last years has been marked with a spectacular expansion of mutual funds, associated with a more and more exigent investors’ behavior, especially with the increase of financial turbulence and the multiplication of financial institutions’ crises. In addition, we noticed, during these years, a gigantic development of financial innovations and an important growth of derived instruments, in term of transaction volume and of complexity. This development of financial instruments list, negotiated on an organized market, and in which mutual funds can invest, has obliged these funds to devote more efforts to measure and control risk, according to the investment policy followed by each fund. These events aroused several interrogations concerning the efficiency of traditional tools of measure, of prediction and control of risks related to financial activities. In fact, it appeared clear that, the common point of all financial crises, is nothing else than, a failing system of measuring, managing and controlling risks. Thus, these factors have supported the appearance of new market risk measures, such as Value-at-Risk. For this reason and for the purpose to secure mutual funds against risk exposition, many monitoring commissions of financial sector in Europe, have promulgated lows requiring from mutual funds to establish a risk management structure. Indeed, in the sixth of April 2005, the French financial market authorities (AMF)** , recommended the use of VaR when measuring their risks and also, determining their engagement level. These arrangements were supposed to be applied since the first of January 2006. Moreover, in the second of august 2007, the monitoring commission of the Luxembourgian†† financial sector emitted a circular, in which, it recommended the adoption of value-at-risk based approach models, in their global risk management processes, attached to the whole portfolio’s positions. Indeed, after the low of 2002, the list of financial instruments, in which mutual funds can invest, has been extended. Thus, in addition to bank deposits, money market instruments, and investment funds shares, mutual funds can use derived instruments. Hence, they must require more efforts to measure and monitor their risks. Those events give rise to our research. Indeed, we propose, in this paper, to study the value-at-risk, as a new alternative of mutual funds risk measure recommended by monitoring and controlling authorities, through the application of its principal estimation’s methodologies: the parametric method, the historical simulation and the Monte Carlo simulation, For this fact, this study will be applied on Tunisian market real data: the open-end funds portfolios, in order to opt for the best relevant VaR estimation method, allowing to measure and well predict risks inherent to these portfolios. Thus, this article will relate to the application of three VaR estimation methodologies to the entire mixed open end portfolios of Tunisian market, with the number of 14. We speak about, parametric approach, called analytic, and based on hypothesis concerning the probability density function of portfolio’s outputs. The second approach is called general or non parametric, it presents a historical type and it is based on empirical distribution of portfolio’s outputs. This approach gathers the historical simulation and the Monte Carlo Simulation. ** Autorité des marchés financiers, AMF « Note d’accompagnement des textes soumis à consultation publique » Paris le 06 Avril 2005, calcul de l’engagement des OPCVM sur instruments financiers à terme. †† Circulaire CSSF 07/308, commission de surveillance du secteur financier, Luxembourg le 02 Août 2007, lignes de conduite des OPCVM relatives à l’emploi d’une méthode de gestion des risques financiers et l’utilisation des instruments dérivés. Ecole polytechnique de Tunis 3 2ème Conférence Euro-Africaine en Finance et Economie (CEAFE) Février 2008 Thereafter, we will carry out a backtesting, by comparing the obtained previsions to observed realizations, in order to validate the relevance of these methods and determine the predictive capacity of each one. This article is organized as follows: the first section presents a literature review. The second one introduces the estimation methods of VaR. while the third part provides a data statistical descriptive study and describes the choice of parameters and estimation tools; the fourth section presents estimation results, methods validation, and interprets. Finally, the fifth section concludes. 1. Literature review: Since its appearance in this last decade, the value at risk has been imposed as an undeniable market risk measure, with consideration to its principal contribution which lies in its aptitude to transform complex risks to only one quantifiable number, simple and comprehensible from everyone. Thus, during these last years, and after the free disposal of the VaR methodology by the JP Morgan American bank in 1994, the use of VaR, as a management risk standard, was spread by banks, little by little. Since that, the literature on VaR, its measure, its evaluation and its methodologies, has seen unprecedented expansion [Duffie and Pan (1997), Dowd (1998), Sawnders (1999), Jorion (2007)]. Indeed, since its appearance, the VaR has overshot its first purpose as a simple risk measure to become a tool of management and control of all types of risk [Smith & al. (1995), Mausser &Rosen (1998), & Jorion (1999)]. This fact drove regulators, such as the Basle comity for banking supervision and especially, the Federal Reserve, to recommend the use of VaR by banks in their risk control strategies, in January 1998, [Kupiec & O’Brein (1996)]. In this context, Blesjer & Shumacher (1999), tried to evaluate VaR in central banks. On the other hand, Dornbusch (1998) has recommended the use of VaR, not only in the microeconomic scale as well by financial as non financial institutions, but in the macroeconomic scale in order to measure and manage the country risk as a whole. Nevertheless, although that this concept found its origin in the banking domain, the generalization of its use, as well by financial institutions as non financial ones [Bodner & al (1998)], is largely due to the fact that VaR is characterized by its measure simplicity and interpretation, even more its attractive usage thinks to its application in normal market conditions. Therefore, the VaR concept has supported the appearance of many estimation methodologies which integrate evaluation models by joining portfolio’s returns to different risk factors. Those different methods, such as parametric method, Monte Carlo simulation and historical simulation, were the subject of several studies throughout the literature, from the VaR measure [Linsmeier & Pearson (1996), Duffie & Pan (1997), Engle & Manganelli (1999)], to the theoretical evaluation of VaR properties and other dynamic measures of risk[Artzner & al (1998]. However, the choice of the VaR methodology to adopt in risk measure seems to be very important, given that the capacity of each method to predict the future exposition to risks relies on several criteria, particularly, portfolio returns’ features and managers’ objectives. Consequently, many researches tried to make comparisons between VaR methodologies. In fact, due to the lack of data on reel portfolios, this evaluation of VaR techniques has been based on artificial portfolios [Christoffersen, Hahn & Inoue (2001), Kupiec (1995), and Pritsker (1997)]. Hence, Beder (1995) compared VaR models based on simulation with parametric ones for options’ portfolios, and concludes that, for the same portfolio, there exist Ecole polytechnique de Tunis 4 2ème Conférence Euro-Africaine en Finance et Economie (CEAFE) Février 2008 disparities in the VaR measured through different estimation’s methods. In a similar study, Hendricks (1996) found the same conclusions, when analyzing an offshore currency portfolio. Linsmeier and Pearson (1996) carried out a comparison between the three estimation methods and concluded that the better method doesn’t exist. It depends on dimensions fixed by risk managers. However, Bollen and Moosa (2002) found, in a comparison between parametric method and historical simulation, that this last approach provides skewed estimations. Similarly, following an undertaken study on interest rate structure in the German case, Vlaar (2000), distinguished that better results are obtained with an approach combined from parametric method and Monte Carlo simulation. Moreover, Campbell & al. (2001) leads to the empirical validation of VaR approach according to parametric method, despite its restrictive hypothesis. Yet recently, Pritsker (2006), based on historical simulation introduced by Boudoukh & al. (1998) and Barone-Adesi (1998), proved the under reaction of historical VaR to conditional risk variations. Nowadays, VaR practices become various and its application field is widening day after day. Value-at-risk is not a simple tool of risk measure any more, but, it goes beyond its first aim, to become a criterion of investment choice, of performance evaluation and even of resources allowance. Accordingly, this acronym becomes a benchmark used, beyond the banking word, by market professionals and funds managers, risk management’s responsible, institutional and even non financials firms. So, what about value-at-risk and mutual funds? 2. Methodology of VaR Estimation: The concept of VaR can be defined as the maximum awaited loss of an asset or a portfolio value in a determined period and with a pre-specified confidence level (or probability rate) under normal completion conditions [Jorion (2007), Coronado (2000)]. Analytically, VaR is defined as: Prob(Lh £VaRh,p)) = p (1) With, h: time horizon. P: probability threshold Lh: maximum awaited loss for the horizon h. The VaR acronym should be confused neither to the awaited loss, nor to the maximum amount of loss that we risk to undergo. It is, simply, the maximum level of loss that will not be exceeded under a defined threshold of probability. It is its conceptual simplicity, in addition to its flexibility and its adaptation to managers’ objectives, which makes VaR more and more popular. The choice of one method to the detriment of another depends on several criteria: financial series’ specificity, risk factors’ complexity, managers’ expectation… For this reason, we will study three VaR methods, in the purpose to determine the most appropriate of them to the prevision of losses related to Tunisian open-end funds’ portfolios. Ecole polytechnique de Tunis 5 ... - tailieumienphi.vn