DOCSLIB.ORG

Estimation of Value at Risk with GARCH Family Models

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Estimation of Value at Risk with GARCH Family Models An empirical study in risk management: estimation of Value at Risk with GARCH family models Author: Askar Nyssanov Supervisor: Anders Ågren, Professor Master Thesis in Statistics Department of Statistics Uppsala University Sweden 2013 Abstract In this paper the performance of classical approaches and GARCH family models are evaluated and compared in estimation one-step-ahead VaR. The classical VaR methodology includes historical simulation (HS), RiskMetrics, and unconditional approaches. The classical VaR methods, the four univariate and two multivariate GARCH models with the Student’s t and the normal error distributions have been applied to 5 stock indices and 4 portfolios to determine the best VaR method. We used four evaluation tests to assess the quality of VaR forecasts: - Violation ratio - Kupiec’s test - Christoffersen’s test - Joint test The results point out that GARCH-based models produce far more accurate forecasts for both individual and portfolio VaR. RiskMetrics gives reliable VaR predictions but it is still substantially inferior to GARCH models. The choice of an optimal GARCH model depends on the individual asset, and the best model can be different based on different empirical data. Keywords: Value at Risk, univariate and multivariate GARCH models, classical VaR approaches, evaluation tests 2 Contents I. INTRODUCTION ............................................................................................................. 4 II. THEORETICAL FRAMEWORK .................................................................................... 6 1. UNIVARIATE GARCH MODELS .......................................................................................... 6 1.1 GARCH model ................................................................................................................. 6 1.2 Exponential GARCH (EGARCH) model ............................................................................. 7 1.3 Integrated GARCH (IGARCH) model ................................................................................ 8 1.4 GJR-GARCH Model .......................................................................................................... 8 2. MULTIVARIATE GARCH MODELS ..................................................................................... 9 2.1 GO-GARCH model ........................................................................................................... 9 2.2 DCC-GARCH model ....................................................................................................... 10 3. ERROR DISTRIBUTIONS .................................................................................................... 12 3.1 Normal distribution ...................................................................................................... 12 3.2 Student’s t distribution ................................................................................................. 12 4. VALUE-AT-RISK (VAR) METHODOLOGIES ........................................................................ 13 4.1 Historical simulation..................................................................................................... 14 4.2 Unconditional parametric methods .............................................................................. 15 4.3 RiskMetrics model ........................................................................................................ 16 4.4 GARCH-based models ................................................................................................... 17 5. EVALUATION TESTS ......................................................................................................... 18 5.1 Violation ratio .............................................................................................................. 18 5.2 Kupiec’s test ................................................................................................................. 19 5.3 Christoffersen's conditional test ................................................................................... 19 5.4 Joint test ...................................................................................................................... 20 III. EMPIRICAL RESULTS ................................................................................................. 21 1. DATA .............................................................................................................................. 21 2. ESTIMATION OF VAR ....................................................................................................... 23 2.1 VaR for individual assets .............................................................................................. 24 2.2 Portfolio VaR ................................................................................................................ 26 IV. CONCLUSION ................................................................................................................ 28 V. REFERENCES ................................................................................................................ 30 VI. APPENDIX ...................................................................................................................... 32 3 I. INTRODUCTION Value at Risk (VaR) is one of the widely used risk measures. VaR estimates the maximum loss of the returns or a portfolio at a given risk level over a specific period. VaR was first introduced in 1994 by J.P.Morgan and since then it has become an obligatory risk measure for thousands of financial institutions, such as investment funds, banks, corporations, and so on. Classical VaR methods have several drawbacks. These methods include historical simulation (HS), RiskMetrics, and unconditional approaches. For instance, RiskMetrics method always assumes joint normality of the returns. In the unconditional approach we use a standard deviation to estimate VaR and assume that the volatility constant over time. However, in reality these assumptions do not hold in most cases. On the other hand, the basic driving principle of the historical simulation method is its assumption that the VaR forecasts can be based on historical data. In 1982, Engle, the winner of the 2003 Nobel Memorial Prize in Economic Sciences, introduced ARCH (“Autoregressive Conditional Heteroskedasticity”) models. Then Bollerslev (1986) proposed the generalization of the ARCH process calling it GARCH models. The main advantage of the GARCH models is that they are capable of capturing several major properties of financial time series. In recent years, the estimation of the VaR using GARCH models has become very popular and most widely-used approach in VaR calculation. Many research results have shown that the GARCH models outperform classical VaR methods and make more accurate VaR forecasts. Fuss, Kaiser and Adams (2007) applied three different VaR approaches: the normal, Cornish–Fisher (CF), and the GARCH-type VaR to the S&P hedge fund index series (SPHG). They showed that the GARCH-type VaR gives more accurate VaR forecasts than other VaR methods for most of the hedge fund style indices. Totić, Bulajić and Vlastelica (2011) estimated daily returns of the FTSE100 index using non-parametric, RiskMetrics and GARCH-based VaR methods with the normal and t distributions. According to their study, RiskMetrics and GARCH models performed better than non-parametric approaches. So and Yu (2006) estimated one-step- ahead VaR predictions of 12 stock market indices and four foreign exchange rates using six GARCH models and RiskMetrics. They have concluded that all GARCH models outperform RiskMetrics in estimating 1% VaR and Student’s t distribution produces more accurate VaR forecasts than the normal. Angelidis, Benos and Degiannakis (2004) used AR-GARCH, AR-EGARCH and AR- TARCH models of different orders with the normal, Student’s t and the generalized error distributions to estimate one-step-ahead VaR for five stock indices: S&P 500, NIKKEI 225, FTSE 100, CAC 40 and DAX 30. They came to the conclusion that the sample size is crucial in defining VaR accuracy, leptokurtic distributions make better VaR predictions and the GARCH model fitting the data best depends on specific stock indices. Orhan and Koksal (2012) compared 16 GARCH models in estimating one-step-ahead VaR forecasts using Student’s t and the normal distributions. The data used were stock indices from growing (Turkey, Brazil) and developed (Germany, USA) economies. The conclusion again underlined that GARCH (1,1) results were the most accurate, and Student’s t slightly outperformed the normal distribution. Wong, Cheng and Wong (2003) tested the performance of 9 GARCH models in estimating VaR results for Australia’s All Ordinary Index (AOI) series. Their result showed that GARCH-based VaR models showed poor performance and did not meet Basel’s backtesting criteria. Next I have analyzed some earlier studies on portfolio VaR estimations. Santos, Nogales and Ruiz (2013) compared the performance of three multivariate GARCH models in computing VaR forecasts for equally weighted diversified portfolios with large number of assets. The models used included DCC-GARCH, CCC-GARCH and Asymmetric DCC-GARCH. This study has showed that DCC-GARCH produced more accurate VaR forecasts compared to other models. Morimoto and Kawasaki (2008) conducted a more comprehensive study in order to define the best model in 4 forecasting portfolio VaR. They have evaluated the performance of VECH, BEKK, CCC- GARCH and DCC-GARCH models with
Load more

Recommended publications
  • Estimation and Decomposition of Downside Risk for Portfolios with Non-Normal Returns
    The Journal of Risk (79–103) Volume 11/Number 2, Winter 2008/09 Estimation and decomposition of downside risk for portfolios with non-normal returns Kris Boudt Faculty of Business and Economics, Katholieke Universiteit Leuven and Lessius University College, 69 Naamsestraat, B-3000 Leuven, Belgium; email: [email protected] Brian Peterson Diamond Management & Technology Consultants, Chicago, IL; email: [email protected] Christophe Croux Faculty of Business and Economics, Katholieke Universiteit Leuven and Lessius University College, 69 Naamsestraat, B-3000 Leuven, Belgium; email: [email protected] We propose a new estimator for expected shortfall that uses asymptotic expansions to account for the asymmetry and heavy tails in financial returns. We provide all the necessary formulas for decomposing estimators of value-at-risk and expected shortfall based on asymptotic expansions and show that this new methodology is very useful for analyzing and predicting the risk properties of portfolios of alternative investments. 1 INTRODUCTION Value-at-risk (VaR) and expected shortfall (ES) have emerged as industry standards for measuring downside risk. Despite the variety of complex estimation methods based on Monte Carlo simulation, extreme value theory and quantile regression proposed in the literature (see Kuester et al (2006) for a review), many practitioners either use the empirical or the Gaussian distribution function to predict portfolio downside risk. The potential advantage of using the empirical distribution function over the hypothetical Gaussian distribution function is that only the information in the return series is used to estimate downside risk, without any distributional assumptions. The disadvantage is that the resulting estimates of VaR and ES, called historical VaR and ES, typically have a larger variation from out-of-sample obser- vations than those based on a correctly specified parametric class of distribution functions.
    [Show full text]
  • Capturing Downside Risk in Financial Markets: the Case of the Asian Crisis
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Research Papers in Economics Journal of International Money and Finance 18 (1999) 853–870 www.elsevier.nl/locate/econbase Capturing downside risk in financial markets: the case of the Asian Crisis Rachel A.J. Pownall *, Kees G. Koedijk Faculty of Business Administration, Financial Management, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands and CEPR Abstract Using data on Asian equity markets, we observe that during periods of financial turmoil, deviations from the mean-variance framework become more severe, resulting in periods with additional downside risk to investors. Current risk management techniques failing to take this additional downside risk into account will underestimate the true Value-at-Risk with greater severity during periods of financial turnoil. We provide a conditional approach to the Value- at-Risk methodology, known as conditional VaR-x, which to capture the time variation of non-normalities allows for additional tail fatness in the distribution of expected returns. These conditional VaR-x estimates are then compared to those based on the RiskMetrics method- ology from J.P. Morgan, where we find that the model provides improved forecasts of the Value-at-Risk. We are therefore able to show that our conditional VaR-x estimates are better able to capture the nature of downside risk, particularly crucial in times of financial crises. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Financial regulation; Value-at-risk; Riskmetrics; Extreme value theory 1. Introduction A number of Asian economies have recently been characterized by highly volatile financial markets, which when coupled with high returns, should have been seen as an attractive avenue down which one could diversify portfolios.
    [Show full text]
  • Applied Quantitative Finance
    Applied Quantitative Finance Wolfgang H¨ardle Torsten Kleinow Gerhard Stahl In cooperation with G¨okhanAydınlı, Oliver Jim Blaskowitz, Song Xi Chen, Matthias Fengler, J¨urgenFranke, Christoph Frisch, Helmut Herwartz, Harriet Holzberger, Steffi H¨ose, Stefan Huschens, Kim Huynh, Stefan R. Jaschke, Yuze Jiang Pierre Kervella, R¨udigerKiesel, Germar Kn¨ochlein, Sven Knoth, Jens L¨ussem,Danilo Mercurio, Marlene M¨uller,J¨ornRank, Peter Schmidt, Rainer Schulz, J¨urgenSchumacher, Thomas Siegl, Robert Wania, Axel Werwatz, Jun Zheng June 20, 2002 Contents Preface xv Contributors xix Frequently Used Notation xxi I Value at Risk 1 1 Approximating Value at Risk in Conditional Gaussian Models 3 Stefan R. Jaschke and Yuze Jiang 1.1 Introduction . 3 1.1.1 The Practical Need . 3 1.1.2 Statistical Modeling for VaR . 4 1.1.3 VaR Approximations . 6 1.1.4 Pros and Cons of Delta-Gamma Approximations . 7 1.2 General Properties of Delta-Gamma-Normal Models . 8 1.3 Cornish-Fisher Approximations . 12 1.3.1 Derivation . 12 1.3.2 Properties . 15 1.4 Fourier Inversion . 16 iv Contents 1.4.1 Error Analysis . 16 1.4.2 Tail Behavior . 20 1.4.3 Inversion of the cdf minus the Gaussian Approximation 21 1.5 Variance Reduction Techniques in Monte-Carlo Simulation . 24 1.5.1 Monte-Carlo Sampling Method . 24 1.5.2 Partial Monte-Carlo with Importance Sampling . 28 1.5.3 XploRe Examples . 30 2 Applications of Copulas for the Calculation of Value-at-Risk 35 J¨ornRank and Thomas Siegl 2.1 Copulas . 36 2.1.1 Definition .
    [Show full text]
  • Return to Riskmetrics: the Evolution of a Standard
    Return to RiskMetrics: The Evolution of a Standard Jorge Mina and Jerry Yi Xiao Introduction by Christopher C. Finger RiskMetrics www.riskmetrics.com 44 Wall St. New York, NY 10005 Return to RiskMetrics: The Evolution of a Standard, April 2001. Copyright © 2001 RiskMetrics Group, Inc. All rights reserved. Certain risk measurement technology of RiskMetrics Group, Inc. is patent pending. RiskMetrics, RiskManager, CreditMetrics, CreditManager, LongRun, CorporateMetrics, and DataMetrics, among others, are trademarks or service marks owned by or licensed to RiskMetrics Group, Inc. in the United States and other countries. RiskMetrics Group, Inc. disclaims any and all warranties as to any results to be obtained from any use of the content or methodology provided by RiskMetrics Group, Inc. or any representation or warranty that such content or methodology are in any way guidance for any investor or investors in general to determine the suitability or desirability of the investment in a particular security, or securities in general. RiskMetrics Group, Inc. does not guarantee the sequence, timeliness, accuracy, completeness, or continued availability of such content or methodology. Such content and methodology are based on historical observations and should not be relied upon to predict future market movements. The information contained in this document is believed to be reliable, but RiskMetrics Group does not guarantee its completeness or accuracy. Opinions and estimates constitute our judgment and are subject to change without notice. Foreword This document is an update and restatement of the mathematical models in the 1996 RiskMetrics Technical Document, now known as RiskMetrics Classic. RiskMetrics Classic was the fourth edition, with the original document having been published in 1994.
    [Show full text]
  • Evaluating the Riskmetrics Methodology in Measuring Volatility
    Evaluating the RiskMetrics Methodology in Measuring Volatility and Value-at-Risk in Financial Markets Szil´ard Pafka a,1, Imre Kondor a,b,2 aDepartment of Physics of Complex Systems, E¨otv¨os University, P´azm´any P. s´et´any 1/a, H-1117 Budapest, Hungary bMarket Risk Research Department, Raiffeisen Bank, Akad´emia u. 6, H-1054 Budapest, Hungary Abstract We analyze the performance of RiskMetrics, a widely used methodology for mea- suring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution function, which is an important feature of financial data. Nevertheless, it was com- monly found that RiskMetrics performs satisfactorily well, and therefore the tech- nique has become widely used in the financial industry. We find, however, that the success of RiskMetrics is the artifact of the choice of the risk measure. First, the outstanding performance of volatility estimates is basically due to the choice of a very short (one-period ahead) forecasting horizon. Second, the satisfactory perfor- mance in obtaining Value-at-Risk by simply multiplying volatility with a constant factor is mainly due to the choice of the particular significance level. Key words: RiskMetrics, market risk, risk measurement, volatility, Value-at-Risk 1 Introduction arXiv:cond-mat/0103107v1 [cond-mat.stat-mech] 5 Mar 2001 Risk management is one of the top priorities in the financial industry today. A huge effort is being invested into developing reliable risk measurement meth- ods and sound risk management techniques by academics and practitioners alike.
    [Show full text]
  • Var Vs Cvar in Risk Management and Optimization Stan Uryasev
    VaR vs CVaR in Risk Management and Optimization Stan Uryasev Joint presentation with Sergey Sarykalin, Gaia Serraino and Konstantin Kalinchenko Risk Management and Financial Engineering Lab, University of Florida and American Optimal Decisions 1 Agenda ` Compare Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) ` definitions of VaR and CVaR ` basic properties of VaR and CVaR ` axiomatic definition of Risk and Deviation Measures ` reasons affecting the choice between VaR and CVaR ` risk management/optimization case studies conducted with Portfolio Safeguard package by AORDA.com 2 Risk Management ` Risk Management is a procedure for shaping a loss distribution ` Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular function for measuring risk ` The choice between VaR and CVaR is affected by: ` differences in mathematical properties, ` stability of statistical estimation, ` simplicity of optimization procedures, ` acceptance by regulators ` Conclusions from these properties are contradictive 3 Risk Management ` Key observations: ` CVaR has superior mathematical properties versus VaR ` Risk management with CVaR functions can be done very efficiently ` VaR does not control scenarios exceeding VaR ` CVaR accounts for losses exceeding VaR ` Deviation and Risk are different risk management concepts ` CVaR Deviation is a strong competitor to the Standard Deviation 4 VaR and CVaR Representation 5 VaR, CVaR, CVaR+ and CVaR- CVaR+ Risk CVaR CVaR- VaR x 6 Value-at-Risk X a loss random variable α ∈ [1,0] VaR( )α X= min{ zX | F≥
    [Show full text]
  • Financial Risk Forecasting Chapter 4 Risk Measures
    What is risk? Value–at–Risk Issues Coherence Manipulation ES Scaling Regulations Financial Risk Forecasting Chapter 4 Risk Measures Jon Danielsson ©2021 London School of Economics To accompany Financial Risk Forecasting www.financialriskforecasting.com Published by Wiley 2011 Version 6.0, August 2021 Financial Risk Forecasting © 2011-2021 Jon Danielsson, page 1 of 99 What is risk? Value–at–Risk Issues Coherence Manipulation ES Scaling Regulations Financial Risk Forecasting © 2011-2021 Jon Danielsson, page 2 of 99 What is risk? Value–at–Risk Issues Coherence Manipulation ES Scaling Regulations The focus of this chapter is on Defining and measuring risk • Volatility • VaR (Value–at–Risk) • ES (Expected Shortfall) • Holding periods • Scaling and the square–root–of–time • Financial Risk Forecasting © 2011-2021 Jon Danielsson, page 3 of 99 What is risk? Value–at–Risk Issues Coherence Manipulation ES Scaling Regulations Notation p Probability Q Profit and loss q Observed profit and loss w Vector of portfolio weights X and Y Refer to two different assets ϕ(.) Risk measure ϑ Portfolio value Financial Risk Forecasting © 2011-2021 Jon Danielsson, page 4 of 99 What is risk? Value–at–Risk Issues Coherence Manipulation ES Scaling Regulations Defining Risk Financial Risk Forecasting © 2011-2021 Jon Danielsson, page 5 of 99 What is risk? Value–at–Risk Issues Coherence Manipulation ES Scaling Regulations General Definition No universal definition of what constitutes risk • On a very general level, financial risk could be defined as • “the chance of losing a part
    [Show full text]
  • Risk Management: a Review
    The Research Foundation of CFA Institute Literature Review Risk Management: A Review Sébastien Lleo, CFA Imperial College London The concept of risk has been central to the theory and practice of finance since Markowitz’s influential work nearly 60 years ago. Yet, risk management has only emerged as a field of independent study in the past 15 years. Advances in the science of risk measurement have been a main contributor to this remarkable development as new risk measures have been proposed and their properties studied. These measures, which in the past have only applied to market risk, are now being applied to credit, operational, and liquidity risk as well as to portfolio optimization. A growing emphasis on risk budgeting has also sparked a quest for an integrated risk measurement framework. But risk management is more than the application of quantitative techniques. A long list of past financial disasters demonstrates that a profound and concrete understanding of the nature of risk is required and that adequate internal controls are crucial. The modern study of risk can be traced to Markowitz’s seminal work on portfolio selection.1 Markowitz made the observation that one should care about risk as well as return, and he placed the study of risk at center stage in the new field of financial economics. Since then, the science of risk management has grown and become its own field of study. Initially, risk management was manifest in hedging, that is the elimination of unwanted aspects of risk. Hedging is accomplished primarily through the use of derivatives. (An example would be the hedging of foreign currency risk associated with purchasing foreign currency denominated securities.) In the past 15 years, however, risk management has evolved beyond the practice of hedging and into a complex discipline that revolves around two dimensions: risk measurement and the practice of risk management.
    [Show full text]
  • Coherent Measures of Risk
    Mathematical Finance, Vol. 9, No. 3 (July 1999), 203–228 COHERENT MEASURES OF RISK PHILIPPE ARTZNER Universite´ Louis Pasteur, Strasbourg FREDDY DELBAEN Eidgenossische¨ Technische Hochschule, Zurich¨ JEAN-MARC EBER Societ´ eG´ en´ erale,´ Paris DAVID HEATH Carnegie Mellon University, Pittsburgh In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties “coherent.” We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules, and by quantile-based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods. KEY WORDS: aggregation of risks, butterfly, capital requirement, coherent risk measure, concentra- tion of risks, currency risk, decentralization, extremal events risk, insurance risk, margin requirement, market risk, mean excess function, measure of risk, model risk, net worth, quantile, risk-based capital, scenario, shortfall, subadditivity, tail value at risk, value at risk 1. INTRODUCTION We provide in this paper a definition of risks (market risks as well as nonmarket risks) and present and justify a unified framework for the analysis, construction, and implementation of measures of risk. We do not assume completeness of markets. These measures of risk can be used as (extra) capital requirements to regulate the risk assumed by market participants, traders, and insurance underwriters, as well as to allocate existing capital.
    [Show full text]
  • Market Risk Management for Financial Institutions Based on GARCH Family Models Qiandi Chen Washington University in St
    Washington University in St. Louis Washington University Open Scholarship Arts & Sciences Electronic Theses and Dissertations Arts & Sciences Spring 5-2017 Market Risk Management for Financial Institutions Based on GARCH Family Models Qiandi Chen Washington University in St. Louis Follow this and additional works at: https://openscholarship.wustl.edu/art_sci_etds Part of the Applied Statistics Commons, Finance and Financial Management Commons, and the Longitudinal Data Analysis and Time Series Commons Recommended Citation Chen, Qiandi, "Market Risk Management for Financial Institutions Based on GARCH Family Models" (2017). Arts & Sciences Electronic Theses and Dissertations. 1059. https://openscholarship.wustl.edu/art_sci_etds/1059 This Thesis is brought to you for free and open access by the Arts & Sciences at Washington University Open Scholarship. It has been accepted for inclusion in Arts & Sciences Electronic Theses and Dissertations by an authorized administrator of Washington University Open Scholarship. For more information, please contact [email protected]. Washington University in St. Louis Graduate School of Arts and Sciences Department of Mathematics Market Risk Management for Financial Institutions Based on GARCH Family Models by Qiandi Chen A thesis presented to The Graduate School of Washington University in partial fulfillment of the requirements for the degree of Master of Arts May 2017 Saint Louis, Missouri Contents List of Tables ::::::::::::::::::::::::::::::::::::::: iii List of Figures :::::::::::::::::::::::::::::::::::::: iv Acknowledgments :::::::::::::::::::::::::::::::::::: v Abstract :::::::::::::::::::::::::::::::::::::::::: viii 1 Introduction :::::::::::::::::::::::::::::::::::::: 1 1.1 Background . 1 1.2 Outline . 3 2 Methodology ::::::::::::::::::::::::::::::::::::: 5 2.1 VAR........................................ 5 2.1.1 Calculation . 5 2.1.2 Element Selection . 7 2.2 Time Series and ARIMA Model . 8 2.3 GARCH Family Model .
    [Show full text]
  • Longrun Technical Document
    LongRun Technical Document Jongwoo Kim, Allan M. Malz, Jorge Mina RiskMetrics Group http://www.riskmetrics.com The development of LongRun LongRun was created by the RiskMetrics Group in conjunction with a variety of groups within J.P. Morgan, including risk management services, corporate finance, advisory, foreign exchange, and capital markets. All data used in the production of the RiskMetrics Group's LongRun forecasts are provided by Reuters. LongRun First Edition (version 1.1, April 1999) Copyright 1999 RiskMetrics Group. All rights reserved. CorporateMetrics™ and CorporateManager™ are trademarks or registered trademarks of the Risk- Metrics Group in the United States and in other countries. They are written with the symbol ™ or ® on their first occurrence in this publication, and as CorporateMetrics and as CorporateManager here- after. RiskMetrics® and CreditMetrics® are registered trademarks of J.P. Morgan and Co, Inc. in the United States and in other countries. The RiskMetrics® and CreditMetrics® methodologies, data sets, and related software applications are exclusively managed by the RiskMetrics Group, LLC. Windows NT, Windows 98, and Windows 95 are trademarks of the Microsoft Corporation. RiskMetrics Group does not warrant any results obtained from the use of the LongRun data, methodology, documentation or any information derived from the data (collectively the “Data”) and does not guarantee its sequence, timeliness, accuracy, completeness or continued availability. The Data is calculated on the basis of historical observations and should not be relied upon to predict future market movements. The Data addresses market risk measurement and should not be relied upon to measure all of a company’s other risk types, such as credit, operational, business, legal, or reputational risks.
    [Show full text]
  • Chapter 7 Value at Risk (Var)
    1 CHAPTER 7 VALUE AT RISK (VAR) What is the most I can lose on this investment? This is a question that almost every investor who has invested or is considering investing in a risky asset asks at some point in time. Value at Risk tries to provide an answer, at least within a reasonable bound. In fact, it is misleading to consider Value at Risk, or VaR as it is widely known, to be an alternative to risk adjusted value and probabilistic approaches. After all, it borrows liberally from both. However, the wide use of VaR as a tool for risk assessment, especially in financial service firms, and the extensive literature that has developed around it, push us to dedicate this chapter to its examination. We begin the chapter with a general description of VaR and the view of risk that underlies its measurement, and examine the history of its development and applications. We then consider the various estimation issues and questions that have come up in the context of measuring VAR and how analysts and researchers have tried to deal with them. Next, we evaluate variations that have been developed on the common measure, in some cases to deal with different types of risk and in other cases, as a response to the limitations of VaR. In the final section, we evaluate how VaR fits into and contrasts with the other risk assessment measures we developed in the last two chapters. What is Value at Risk? In its most general form, the Value at Risk measures the potential loss in value of a risky asset or portfolio over a defined period for a given confidence interval.
    [Show full text]