<p>Value at Risk (VaR) approach has been extensively used by investment and commercial banks since its development by JP Morgan in 1990s. As time passes, it has become interesting to investigate whether VaR could be used also by other financial intermediaries like pension funds and insurance companies. The aim of this paper is to outline Value at Risk (VaR) methodology by giving more emphasis on parametric approach which is used for empirical section and to investigate the applicability and usefulness of VaR in pension funds. After providing theoretical framework for VaR approach, the paper continues with pension fund systems in general and especially highlights AP funds of Swedish National pension fund system by trying to show why VaR could be an invaluable risk management tool for these funds together with other traditional risk measures used. Based on this given theoretical frame, a practical application of VaR –parametric or covariance/variance method- is executed on 50 biggest investments in the fixed income and equity portfolios of three selected Swedish national pension funds – AP1, AP2 and AP3. Results of one day VaR (DEAR) estimations on 30/12/2005 for each fund have been presented and it is aimed to show the additional information that could be obtained by using VaR and which is not always apparent from other risk measures employed by funds. According to the two traditional risk measures which are active risk and Sharpe ratio; AP2 and AP3 lie in the same risk level for 2005 which can create a contradiction by considering their different returns. On the other hand, obtained DEAR estimates show their different risk exposures even with the 50 biggest investments employed. The results give a matching relationship between return of funds and DEAR estimates meaning that; the fund with the highest return has the highest DEAR value and the fund with the lowest return has the lowest DEAR value; which is consistent with the main rule- “higher risk, higher return”. Thus, we can conclude that VaR could be applied additionally to get a better picture about real risk exposures and also to get valuable information on expected possible loss together with other traditional risk measures used.</p><p>Key words: Value at Risk, DEAR, Pension funds, Risk management, Swedish pension plan, AP1, AP2, AP3</p>

Το ζητούμενο σε κάθε επιχείρηση είναι η αντιμετώπιση καταστάσεων οι οποίες μπορεί να παρουσιάσουν αυξημένη πιθανότητα απωλειών. Για να επιτευχθεί ο συγκεκριμένος στόχος είναι αναγκαίος ο εντοπισμός και ο καθορισμός της σημαντικότητας των επικείμενων κινδύνων. Αυτούς τους κινδύνους μπορούμε να τους κατατάξουμε σε επιχειρησιακούς, μη επιχειρησιακούς και χρηματοοικονομικούς. Η διαχείριση του κινδύνου δεν έχει ως πρώτο σκοπό την αποφυγή του κινδύνου, αλλά την ελαχιστοποίησή του, αφού πρώτα εντοπιστεί και καθοριστεί το πόσο σημαντικός είναι. Στόχος είναι να ποσοτικοποιηθεί ο κίνδυνος και να υπολογίζεται ένα μέτρο συνολικού κινδύνου, έτσι ώστε δίνοντας μια τιμή σε αυτόν, να αποφασίσουμε αν θα πάρουμε το ρίσκο να τον αναλάβουμε ή όχι, με μεγαλύτερη ευκολία. Ένα μέτρο συνολικού κινδύνου, προκύπτει από την προσέγγιση της δυνητικής ζημίας {VAR(Value−At−Risk)}. Η προσέγγιση αυτή αποτελεί μια ποσοστιαία κατανομή κέρδους και απώλειας σε ένα συγκεκριμένο χρονικό διάστημα. Μπορεί να χρησιμοποιηθεί από οποιοδήποτε οργανισμό εκτίθεται σε χρηματοοικονομικό κίνδυνο και συνοψίζει τη χειρότερη ζημία με δεδομένο διάστημα εμπιστοσύνης. Σκοπός της παρούσας εργασίας είναι η περιγραφή του τρόπου λειτουργίας της προσέγγισης της δυνητικής ζημίας (VAR). Για την αξιολόγηση του κινδύνου η δυνητική ζημία (VAR) χρησιμοποιεί τρεις μεθόδους προσομοίωσης, την Ιστορική, την Monte Carlo και την Variance−covariance προσομοίωση. Παρουσιάζονται οι μέθοδοι αυτοί, τα πλεονεκτήματα και τα μειονεκτήματά τους. Η εργασία καταλήγει σε μελέτη μιας εφαρμογής, με τη μέθοδο της Ιστορικής προσομοίωσης. / The aim of enterprises is to remedy situations, which may identify increased probability losses. In order to achieve this particular objective, it is necessary to determine the importance of imminent risks. These risks can be classified into operational, not operational and financial. The primary aim of Risk management is not to evade risk, but to minimize it. The risk must be located and we have to determine its importance. The objective is to quantify the risk and calculate one measure of total risk. One measure of total risk, is the Value at Risk (VAR) approach. In its most general form, the Value at Risk (VAR) measures the potential loss in value of a risky asset or portfolio, over a defined period for a given confidence interval. The aim of this essay is the description of Value at Risk (VAR) approach. For the evaluation of the risk the Value at Risk (VAR) approach uses three methods of simulation. The Historical, the Monte Carlo and the VarianceCovariance simulation. These three methods are presented along with their advantages and disadvantages. The essay is concluded with an application using the method of Historical simulation.

Στόχος μιας επένδυσης είναι το κέρδος, όπως αυτό εκφράζεται μέσω της απόδοσης. Στην εργασία αυτή μελετάμε την έννοια και τις διάφορες μορφές απόδοσης, καθώς και διάφορα μοντέλα πρόβλεψής της, όπως το Μοντέλο Τυχαίου Περιπάτου. Στη συνέχεια εξετάζουμε την σχέση κινδύνου-απόδοσης και τον τρόπο με τον οποίο ενδείκνυται να διαχειριζόμαστε χαρτοφυλάκια επενδυτικών προϊόντων. Για τον σκοπό αυτό είναι ιδιαιτέρως χρήσιμη η εύρεση του Tangency Portfolio, η εκτίμηση των E(R) και σR, και τέλος η μελέτη της συσχέτισης μεταξύ των τοποθετήσεων ρίσκου που αποτελούν το χαρτοφυλάκιό μας. Ακολουθεί αναφορά σε επενδύσεις σταθερού κέρδους, όπως είναι τα ομόλογα, και εισάγεται η έννοια της Value at Risk (VaR), με τις δύο βασικές της παραμέτρους, τον χρονικό ορίζοντα (Τ) και το επίπεδο εμπιστοσύνης (1-α). Η VaR εκτιμάται παραμετρικά, μη παραμετρικά και με την χρήση Pareto Tails. Τέλος, εισάγεται η έννοια των συζεύξεων (copulas), και μελετώνται μέσω αυτών οι τιμές της VaR ενός επενδυτικού χαρτοφυλακίου. Κλείνουμε με μια εφαρμογή στο λογισμικό XPlore, όπου χρησιμοποιούνται πραγματικά δεδομένα τραπεζικών προϊόντων για τη μελέτη της VaR. / Objective of an investment is profit, as this is expressed through returns.We study the meaning and various forms of returns, as well as various models of anticipation of returns, such as the Random Walk Model.We focus at the risk-return relationship, and the way in which it is appropriate to manage portfolios of various investment products. To accomplish this, it is useful finding the tagency portfolio, estimating E(R) and sR, and eventualy studying the correlation between the various risk investments, which consist part of a portfolio.We continue with an extended reference to bonds, and introduce the concept of Value at Risk (VAR), with the it's two basic parameters, time horizon (T) and level of confidence (1-a).VaR is estimated parametricaly, non-parametricaly and with the use of pareto tails. Finally, we introduce the concept of copulas , and with their aid, we try to estimate the VaR of an investment portfolio. We conclude with an example of Value at Risk estimation, using real data, taken from the site of the National Bank of Greece.

Στην παρούσα εργασία γίνεται μια ανασκόπηση της μεθόδου μέτρησης κινδύνου Value at Risk (VaR). Παρουσιάζουμε μερικούς βασικούς τρόπους μέτρησης του Value at Risk και εφαρμόζουμε σε δεδομένα ενός χαρτοφυλακίου συναλλαγματικών ισοτιμιών και στον γενικό δείκτη του χρηματιστηρίου Αθηνών διαφορετικά μοντέλα GARCH (IGARCH, TGARCH, EGARCH, GARCH) για την εκτίμηση του VaR με ορίζοντα μιας ημέρας (1- day ahead). Εφαρμόζουμε διαφορετικές υποθέσεις για την κατανομή των αποδόσεων (normal, student's-t, ged), χρησιμοποιούμε διαφορετικά μεγέθη δείγματος (250, 500, 750, 1000) και επίπεδα εμπιστοσύνης για το VaR (95% και 99%). Στην συνέχεια τα αποτελέσματα τού κάθε μοντέλου ελέγχονται με βάση τον έλεγχο του Kupiec για την καταλληλότητα τους. / In the present diplomatic essay we present a review of the method for risk measurement Value at Risk (VaR). We present a few basic ways of measuring Value at Risk and apply to data of an exchange rates portfolio and Athens stock exchange index different GARCH (IGARCH, TGARCH, EGARCH, GARCH) models for the estimation of the 1-day ahead VaR. We use various assumptions for the distribution of the returns (normal, student's-t, ged), various sample sizes (250, 500, 750, 1000) and VaR confidence levels (95% and 99%). Then the results of each model are tested using Kupiec test for their performance.

The diploma thesis deals with the risk management in the insurance practice. The thesis is divided into two parts -- the literature review and the empirical part. In the first section are identified risks endangering the insurance company in their business activities. There are described arrangements risks prevention and elimination. There are also given the basic risks quantification methods. The thesis also describes the system of risk management in Solvency II directive. Basic processes, procedures and methods of the risk management in AXA insurance company are described in the empirical section. In addition is performed a quantification of risks of the selected insurer. Based on this quantification of risks and the risk management analysis, there are suggested further methods and arrangements which may lead to improved risk management for selected insurer.

The diploma thesis deals with energy commodities investments. The content of thesis is trough analysis of markets to identify key factors affecting supply, demand and prices of energy commodities. By correlation analysis examines the relationships between energy commodities, stocks and the business cycle. Processing time series models create predictions of energy commodities prices. Using the Value at Risk method to quantify the risk, which investor has to accept in the case of investing in energy commodities. In conclusion, based on the results obtained, formulates investment recommendation.

This diploma thesis deals with transferring the risk of a insurance company to another subject. The basic requirement is to homogenize the selected insurance portfolio. The amount of capital required is determined by identifying and quantifying the risk. Adjusted indicator of Economic value added (EVA) determines the optimal ratio of the retention and the risk transferred. There are several factors that can affect the amount of the retained risk. The main objective is to determine the amount of the optimal retention itself and select the appropriate type of reinsurance. The recommendation is based on the current development of expenses on insurance claims.

The diploma thesis deals with current issues of risk management in a selected insurance company. The thesis is conceptually divided into two parts the literature recherche and the empirical part. The first section introduces the individual risks and the basic methods of the quantification of the risks which affect the functioning of commercial insurances. A new system of European insurance regulation, Solvency II, is also described. The empirical part of the diploma thesis deals with the risk quantification of the selected insurance company according to the standard and internal model. The thesis is concluded with the evaluation of the risk management in the selected insurance company and of the company preparedness for the regulatory regime Solvency II. Based on this quantification, the recommendations are put forward to improve the risk management of the selected insurer.

Submitted by Andrea Virginio Machado (andrea.machado@fgv.br) on 2008-09-18T17:56:39Z No. of bitstreams: 1 063202009_Dissertacao_Ilton_Gurgel_Soares.pdf: 848570 bytes, checksum: 327ca1afb361db0553d90dc7ad8107e4 (MD5) / Approved for entry into archive by Francisco Terra(francisco.terra@fgv.br) on 2008-09-18T18:17:34Z (GMT) No. of bitstreams: 1 063202009_Dissertacao_Ilton_Gurgel_Soares.pdf: 848570 bytes, checksum: 327ca1afb361db0553d90dc7ad8107e4 (MD5) / Made available in DSpace on 2008-09-18T18:17:34Z (GMT). No. of bitstreams: 1 063202009_Dissertacao_Ilton_Gurgel_Soares.pdf: 848570 bytes, checksum: 327ca1afb361db0553d90dc7ad8107e4 (MD5) / O objetivo do presente estudo é avaliar a existência de quebra estrutural no Value-at-Risk (VaR) das empresas que negociam suas ações na bolsa de valores de Nova Iorque (NYSE). O evento que justi ca a suspeita de mudança estrutural é a lei de governança corporativa conhecida como Sarbanes-Oxley Act (ou simplesmente SOX), a mais profunda reforma implementada no sistema de legislação nanceira dos Estados Unidos desde 1934. A metodologia empregada é baseada em um teste de quebra estrutural endógeno para modelos de regressão quantílica. A amostra foi composta de 176 companhias com registro ativo na NYSE e foi analisado o VaR de 1%, 5% e 10% de cada uma delas. Os resultados obtidos apontam uma ligação da SOX com o ponto de quebra estrutural mais notável nos VaRs de 10% e 5%, tomando-se como base a concentração das quebras no período de um ano após a implementação da SOX, a partir do teste de Qu(2007). Utilizando o mesmo critério para o VaR de 1%, a relação encontrada não foi tão forte quanto nos outros dois casos, possivelmente pelo fato de que para uma exposição ao risco tão extrema, fatores mais especí cos relacionados à companhia devem ter maior importância do que as informações gerais sobre o mercado e a economia, incluídas na especi cação do VaR. Encontrou-se ainda uma forte relação entre certas características como tamanho, liquidez e representação no grupo industrial e o impacto da SOX no VaR.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2017. / Submitted by Gabriela Lima (gabrieladaduch@gmail.com) on 2017-12-05T12:41:14Z No. of bitstreams: 1 2017_IramAlvesdeSouza.pdf: 1901766 bytes, checksum: 4e8857aa24a5d2e0703cc7665a45b8b6 (MD5) / Approved for entry into archive by Raquel Viana (raquelviana@bce.unb.br) on 2018-01-30T15:47:19Z (GMT) No. of bitstreams: 1 2017_IramAlvesdeSouza.pdf: 1901766 bytes, checksum: 4e8857aa24a5d2e0703cc7665a45b8b6 (MD5) / Made available in DSpace on 2018-01-30T15:47:19Z (GMT). No. of bitstreams: 1 2017_IramAlvesdeSouza.pdf: 1901766 bytes, checksum: 4e8857aa24a5d2e0703cc7665a45b8b6 (MD5) Previous issue date: 2018-01-30 / A gestão de riscos e capital constituem-se em instrumentos fundamentais para a sustentabilidade do sistema bancário. Nesse sentido, o processo de mensuração e gestão dos riscos de mercado vem evoluindo rapidamente ao longo dos últimos anos, em especial, quanto aos tipos e características dos instrumentos financeiros negociados no mercado, como também no aumento da exigência de requerimento mínimo de capital para cobertura de perdas financeiras ou econômicas resultantes da flutuação nos valores de mercado de posições detidas pelas Instituições Financeiras. O presente trabalho é um estudo de caso, do tipo exploratório, descritivo e de carácter qualitativo e quantitativo. O objetivo principal é mensurar o Value at Risk - VaR diário de uma carteira de negociação (Trading Book), com base nas abordagens padronizada e modelos internos, considerando também no cômputo do VaR o uso do indicador de giro do volume de negócios (IGN) observado a partir da liquidez dos instrumentos financeiros registrados na carteira. A metodologia utilizada para cálculo do indicador IGN, levou em consideração os estudos publicados no artigo “Portfolio Turnover and Common Stock Holdings Periods”, e foi ajustado para capturar as características e a liquidez dos instrumentos financeiros negociados em mercado. O trabalho aborda em seu referencial teórico os principais métodos de mensuração do VaR, como também as dissemelhanças nas abordagens padronizada e modelos internos, identificando fatores relevantes que podem ser utilizados gerencialmente pela instituição para traçar políticas ou estratégias que reduzam ou controlem o nível de requerimento de capital de sua carteira de negociação exposta aos riscos de mercado. / Risk and capital management are fundamental instruments for the sustainability of the banking system. That way, the process of measuring and managing market risks has been evolving rapidly over the last few years, especially with regard to the types and characteristics of the financial instruments traded in the market, as well as on the increased needs of minimum capital requirements for hedging of financial or economic losses resulting from the fluctuation in the market values positions held by Financial Institutions. The present work is a case study, exploratory, descriptive and qualitative and quantitative features. The main objective is to measure the Value at Risk (VaR) of a trading book, based on the standardized approaches and internal models, also considering in the VaR calculation the use of the turnover indicator (IGN) observed from the liquidity of the financial instruments registered in the portfolio. The methodology used to calculate the IGN indicator took into account the studies published in the article "Portfolio Turnover and Common Stock Holdings Periods" and was adjusted to capture the characteristics and liquidity of the financial instruments traded in the market. The work addresses in its theoretical reference the main methods of measurement of VaR, as well as the dissimilarities in the standardized approaches and internal models, identifying relevant factors that can be used by the institution to manage policies or strategies that reduce or control the level of capital requirement of its trading portfolio exposed to market risks.