DOCSLIB.ORG

VALUE at RISK - a Comparison of Value at Risk Models During the 2007/2008 Financial Crisis

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
VALUE at RISK - a Comparison of Value at Risk Models During the 2007/2008 Financial Crisis ÖREBRO UNIVERSITY Business School Master Thesis in Finance Supervisor and Examiner: Håkan Persson Spring 2011 VALUE AT RISK - A comparison of Value at Risk models during the 2007/2008 financial crisis Jonna Flodman 860224 Malin Karlsson 870402 ABSTRACT The financial crisis of 2007/2008 brought about a debate concerning the quality of risk management models, such as Value at Risk (VaR) models. Several studies have tried to make conclusions about multiple VaR models in periods around the crisis. The conclusions differ, but the Extreme Value Theory (EVT) is considered to be a good prediction model in times of unstable financial markets. In this thesis, the VaR for six financial instruments; the OMXS 30, the OMX Stockholm Financials PI, the OMX Stockholm Materials PI and the currencies USD/SEK, GBP/SEK and EUR/SEK are estimated with the Historical Simulation, the Monte Carlo Simulation and the Variance- Covariance Method, with a 95 percent confidence interval. The risk is estimated both for single instruments as well as portfolios in times before, during and after the crisis with the purpose of concluding which of the VaR models more accurately predict risk for specific instruments/portfolios in different time periods of the crisis. No direct conclusions can be made about the accuracy of the models before, during or after the crisis. The only clear conclusion can be drawn for the single instruments regarding the EUR. All methods predict more accurate results for this instrument compared to the other instruments. The clearest conclusion for the portfolios is that portfolios holding larger weights of indexes show on larger VaR estimations. Also, the modified Monte Carlo Simulation and the Variance-Covariance Method estimate lower risk in general than the Historical Simulation. Keywords: Value at Risk, financial crisis, Historical Simulation, Monte Carlo Simulation, Variance- Covariance Method, individual financial instrument, portfolios, OMXS 30, OMX Stockholm Financials PI, OMX Stockholm Materials PI, USD/SEK, GBP/SEK, EUR/SEK TABLE OF CONTENT 1. INTRODUCTION ............................................................................................................................................ 1 1.1 BACKGROUND ............................................................................................................................................... 1 1.2 PROBLEM ...................................................................................................................................................... 2 1.3 PURPOSE ....................................................................................................................................................... 2 1.4 DELIMITATIONS ............................................................................................................................................. 2 2. THEORETICAL FRAMEWORK ......................................................................................................................... 4 2.1 PORTFOLIO THEORY – RETURN AND RISK ........................................................................................................... 4 2.1.1 STATISTICAL TERMS ............................................................................................................................... 6 2.2 VALUE AT RISK ............................................................................................................................................... 6 2.2.1 HISTORY OF VALUE AT RISK ................................................................................................................... 7 2.3 MODELS FOR CALCULATIONS OF VALUE AT RISK .......................................................................................... 9 2.3.1 THE HISTORICAL SIMULATION ............................................................................................................... 9 2.3.2 THE MONTE CARLO SIMULATION .......................................................................................................... 9 2.3.3 THE VARIANCE- COVARIANCE METHOD .............................................................................................. 10 2.4 OTHER VALUE AT RISK METHODS ................................................................................................................ 13 2.5 PREVIOUS STUDIES ...................................................................................................................................... 13 2.6 THE UNDERLYING ASSETS ............................................................................................................................ 15 2.6.1 INDEX ................................................................................................................................................... 16 2.6.2 CURRENCIES ......................................................................................................................................... 17 3. METHOD..................................................................................................................................................... 18 3.1 SCIENTIFIC METHODS .................................................................................................................................. 18 3.1.1 A QUANTITATIVE APPROACH .............................................................................................................. 18 3.1.2 DEDUCTIVE APPROACH ....................................................................................................................... 18 3.1.3 VALIDITY .............................................................................................................................................. 18 3.1.4 RELIABILITY .......................................................................................................................................... 19 3.1.5 SOURCE CRITICISM .............................................................................................................................. 19 3.2 METHOD USED IN THIS THESIS .................................................................................................................... 19 3.2.1 CHOSEN FINANCIAL INSTRUMENTS ..................................................................................................... 19 3.2.2 THE SOURCE OF DATA ......................................................................................................................... 20 3.2.3 VALUE AT RISK CALCULATIONS ............................................................................................................ 20 4. EMPIRICAL RESULTS AND ANALYSIS ........................................................................................................... 26 4.1 INDIVIDUAL FINANCIAL INSTRUMENTS ....................................................................................................... 26 4.1.1 OMXS 30 .............................................................................................................................................. 26 4.1.2 OMX STOCKHOLM FINANCIALS PI ....................................................................................................... 29 4.1.3 OMX STOCKHOLM MATERIALS PI ........................................................................................................ 32 4.1.4 CURRENCY, USD/SEK ........................................................................................................................... 35 4.1.5 CURRENCY, GBP/SEK ........................................................................................................................... 38 4.1.6 CURRENCY, EUR/SEK ........................................................................................................................... 40 4.2 FINANCIAL INSTRUMENTS IN PORTFOLIOS ................................................................................................. 43 4.2.1 PORTFOLIOS 2006 ................................................................................................................................ 43 4.2.2 PORTFOLIOS 2008 ................................................................................................................................ 45 4.2.3 PORTFOLIOS 2010 ................................................................................................................................ 47 4.2.4 PORTFOLIOS 2011 ................................................................................................................................ 48 5. CONCLUSIONS ............................................................................................................................................... 50 6. DISCUSSION ................................................................................................................................................ 51 6.1 COMMENTS................................................................................................................................................. 51 6.2 FURTHER STUDIES ....................................................................................................................................... 52 7. REFERENCES ............................................................................................................................................... 53 ARTICLES ........................................................................................................................................................... 53 LITTERATURE ....................................................................................................................................................
Load more

Recommended publications
  • Estimating Value at Risk
    Estimating Value at Risk Eric Marsden <[email protected]> Do you know how risky your bank is? Learning objectives 1 Understand measures of financial risk, including Value at Risk 2 Understand the impact of correlated risks 3 Know how to use copulas to sample from a multivariate probability distribution, including correlation The information presented here is pedagogical in nature and does not constitute investment advice! Methods used here can also be applied to model natural hazards 2 / 41 Warmup. Before reading this material, we suggest you consult the following associated slides: ▷ Modelling correlations using Python ▷ Statistical modelling with Python Available from risk-engineering.org 3 / 41 Risk in finance There are 1011 stars in the galaxy. That used to be a huge number. But it’s only a hundred billion. It’s less than the national deficit! We used to call them astronomical numbers. ‘‘ Now we should call them economical numbers. — Richard Feynman 4 / 41 Terminology in finance Names of some instruments used in finance: ▷ A bond issued by a company or a government is just a loan • bond buyer lends money to bond issuer • issuer will return money plus some interest when the bond matures ▷ A stock gives you (a small fraction of) ownership in a “listed company” • a stock has a price, and can be bought and sold on the stock market ▷ A future is a promise to do a transaction at a later date • refers to some “underlying” product which will be bought or sold at a later time • example: farmer can sell her crop before harvest,
    [Show full text]
  • The History and Ideas Behind Var
    Available online at www.sciencedirect.com ScienceDirect Procedia Economics and Finance 24 ( 2015 ) 18 – 24 International Conference on Applied Economics, ICOAE 2015, 2-4 July 2015, Kazan, Russia The history and ideas behind VaR Peter Adamkoa,*, Erika Spuchľákováb, Katarína Valáškováb aDepartment of Quantitative Methods and Economic Informatics, Faculty of Operations and Economic of Transport and Communications, University of Žilina, Univerzitná 1, 010 26 Žilina, Slovakia b,cDepartment of Economics, Faculty of Operations and Economic of Transport and Communications, University of Žilina, Univerzitná 1, 010 26 Žilina, Slovakia Abstract The value at risk is one of the most essential risk measures used in the financial industry. Even though from time to time criticized, the VaR is a valuable method for many investors. This paper describes how the VaR is computed in practice, and gives a short overview of value at risk history. Finally, paper describes the basic types of methods and compares their similarities and differences. © 20152015 The The Authors. Authors. Published Published by Elsevier by Elsevier B.V. This B.V. is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or and/or peer peer-review-review under under responsibility responsibility of the Organizing of the Organizing Committee Committee of ICOAE 2015. of ICOAE 2015. Keywords: Value at risk; VaR; risk modeling; volatility; 1. Introduction The risk management defines risk as deviation from the expected result (as negative as well as positive). Typical indicators of risk are therefore statistical concepts called variance or standard deviation. These concepts are the cornerstone of the amount of financial theories, Cisko and Kliestik (2013).
    [Show full text]
  • Value-At-Risk Under Systematic Risks: a Simulation Approach
    International Research Journal of Finance and Economics ISSN 1450-2887 Issue 162 July, 2017 http://www.internationalresearchjournaloffinanceandeconomics.com Value-at-Risk Under Systematic Risks: A Simulation Approach Arthur L. Dryver Graduate School of Business Administration National Institute of Development Administration, Thailand E-mail: [email protected] Quan N. Tran Graduate School of Business Administration National Institute of Development Administration, Thailand Vesarach Aumeboonsuke International College National Institute of Development Administration, Thailand Abstract Daily Value-at-Risk (VaR) is frequently reported by banks and financial institutions as a result of regulatory requirements, competitive pressures, and risk management standards. However, recent events of economic crises, such as the US subprime mortgage crisis, the European Debt Crisis, and the downfall of the China Stock Market, haveprovided strong evidence that bad days come in streaks and also that the reported daily VaR may be misleading in order to prevent losses. This paper compares VaR measures of an S&P 500 index portfolio under systematic risks to ones under normal market conditions using a historical simulation method. Analysis indicates that the reported VaR under normal conditions seriously masks and understates the true losses of the portfolio when systematic risks are present. For highly leveraged positions, this means only one VaR hit during a single day or a single week can wipe the firms out of business. Keywords: Value-at-Risks, Simulation methods, Systematic Risks, Market Risks JEL Classification: D81, G32 1. Introduction Definition Value at risk (VaR) is a common statistical technique that is used to measure the dollar amount of the potential downside in value of a risky asset or a portfolio from adverse market moves given a specific time frame and a specific confident interval (Jorion, 2007).
    [Show full text]
  • How to Analyse Risk in Securitisation Portfolios: a Case Study of European SME-Loan-Backed Deals1
    18.10.2016 Number: 16-44a Memo How to Analyse Risk in Securitisation Portfolios: A Case Study of European SME-loan-backed deals1 Executive summary Returns on securitisation tranches depend on the performance of the pool of assets against which the tranches are secured. The non-linear nature of the dependence can create the appearance of regime changes in securitisation return distributions as tranches move more or less “into the money”. Reliable risk management requires an approach that allows for this non-linearity by modelling tranche returns in a ‘look through’ manner. This involves modelling risk in the underlying loan pool and then tracing through the implications for the value of the securitisation tranches that sit on top. This note describes a rigorous method for calculating risk in securitisation portfolios using such a look through approach. Pool performance is simulated using Monte Carlo techniques. Cash payments are channelled to different tranches based on equations describing the cash flow waterfall. Tranches are re-priced using statistical pricing functions calibrated through a prior Monte Carlo exercise. The approach is implemented within Risk ControllerTM, a multi-asset-class portfolio model. The framework permits the user to analyse risk return trade-offs and generate portfolio-level risk measures (such as Value at Risk (VaR), Expected Shortfall (ES), portfolio volatility and Sharpe ratios), and exposure-level measures (including marginal VaR, marginal ES and position-specific volatilities and Sharpe ratios). We implement the approach for a portfolio of Spanish and Portuguese SME exposures. Before the crisis, SME securitisations comprised the second most important sector of the European market (second only to residential mortgage backed securitisations).
    [Show full text]
  • Value-At-Risk (Var) Application at Hypothetical Portfolios in Jakarta Islamic Index
    VALUE-AT-RISK (VAR) APPLICATION AT HYPOTHETICAL PORTFOLIOS IN JAKARTA ISLAMIC INDEX Dewi Tamara1 BINUS University International, Jakarta Grigory Ryabtsev2 BINUS University International, Jakarta ABSTRACT The paper is an exploratory study to apply the method of historical simulation based on the concept of Value at Risk on hypothetical portfolios on Jakarta Islamic Index (JII). Value at Risk is a tool to measure a portfolio’s exposure to market risk. We construct four portfolios based on the frequencies of the companies in Jakarta Islamic Index on the period of 1 January 2008 to 2 August 2010. The portfolio A has 12 companies, Portfolio B has 9 companies, portfolio C has 6 companies and portfolio D has 4 companies. We put the initial investment equivalent to USD 100 and use the rate of 1 USD=Rp 9500. The result of historical simulation applied in the four portfolios shows significant increasing risk on the year 2008 compared to 2009 and 2010. The bigger number of the member in one portfolio also affects the VaR compared to smaller member. The level of confidence 99% also shows bigger loss compared to 95%. The historical simulation shows the simplest method to estimate the event of increasing risk in Jakarta Islamic Index during the Global Crisis 2008. Keywords: value at risk, market risk, historical simulation, Jakarta Islamic Index. 1 Faculty of Business, School of Accounting & Finance - BINUS Business School, [email protected] 2 Alumni of BINUS Business School Tamara, D. & Ryabtsev, G. / Journal of Applied Finance and Accounting 3(2) 153-180 (153 INTRODUCTION Modern portfolio theory aims to allocate assets by maximising the expected risk premium per unit of risk.
    [Show full text]
  • Portfolio Risk Management with Value at Risk: a Monte-Carlo Simulation on ISE-100
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE International Research Journal of Finance and Economics ISSN 1450-2887 Issue 109 May, 2013 http://www.internationalresearchjournaloffinanceandeconomics.com Portfolio Risk Management with Value at Risk: A Monte-Carlo Simulation on ISE-100 Hafize Meder Cakir Pamukkale University, Faculty of Economics and Administrative Sciences Business Administration / Accounting and Finance Department, Assistant Professor E-mail: [email protected] Tel: +9 0258 296 2679 Umut Uyar Corresponding Author, Pamukkale University Faculty of Economics and Administrative Sciences, Business Administration Accounting and Finance Department, Research Assistant E-mail: [email protected] Tel: +9 0258 296 2830 Abstract Value at Risk (VaR) is a common statistical method that has been used recently to measure market risk. In other word, it is a risk measure which can predict the maximum loss over the portfolio at a certain level of confidence. Value at risk, in general, is used by the banks during the calculation process to determine the minimum capital amount against market risks. Furthermore, it can also be exploited to calculate the maximum loss at investment portfolios designated for stock markets. The purpose of this study is to compare the VaR and Markowitz efficient frontier approach in terms of portfolio risks. Along with this angle, we have calculated the optimal portfolio by Portfolio Optimization method based on average variance calculated from the daily closing prices of the ninety-one stocks traded under the Ulusal-100 index of the Istanbul Stock Exchange in 2011. Then, for each of designated portfolios, Monte-Carlo Simulation Method was run for thousand times to calculate the VaR.
    [Show full text]
  • Evaluating Covariance Matrix Forecasts in a Value-At-Risk Framework
    Evaluating Covariance Matrix Forecasts in a Value-at-Risk Framework Jose A. Lopez Christian A. Walter Economic Research Department Group Risk Management Federal Reserve Bank of San Francisco Credit Suisse Group 101 Market Street Nueschelerstrasse 1 San Francisco, CA 94705 8070 Zurich, Switzerland Phone: (415) 977-3894 Phone: +41 1 333 7476 Fax: (415) 974-2168 Fax: +41 1 333 7516 [email protected] [email protected] Draft date: April 17, 2000 ABSTRACT: Covariance matrix forecasts of financial asset returns are an important component of current practice in financial risk management. A wide variety of models, ranging from matrices of simple summary measures to covariance matrices implied from option prices, are available for generating such forecasts. In this paper, we evaluate the relative accuracy of different covariance matrix forecasts using standard statistical loss functions and a value-at-risk (VaR) framework. This framework consists of hypothesis tests examining various properties of VaR models based on these forecasts as well as an evaluation using a regulatory loss function. Using a foreign exchange portfolio, we find that implied covariance matrix forecasts appear to perform best under standard statistical loss functions. However, within the economic context of a VaR framework, the performance of VaR models depends more on their distributional assumptions than on their covariance matrix specification. Of the forecasts examined, simple specifications, such as exponentially-weighted moving averages of past observations, perform best with regard to the magnitude of VaR exceptions and regulatory capital requirements. These results provide empirical support for the commonly-used VaR models based on simple covariance matrix forecasts and distributional assumptions.
    [Show full text]
  • Procyclicality and Value at Risk
    Procyclicality and Value at Risk Peter Youngman In the years leading up to the financial crisis, banks of the internal-models approach of Basel II, whereby around the world, including those in Canada, became banks are permitted to compute regulatory capital based more heavily involved in financial markets. Securities and on their own models, subject to certain qualitative and derivatives that banks actively buy and sell in financial quantitative standards.1 markets make up the “trading book.” Prudential regula- Simply stated, a VaR model is a model of the distribution of tions governing the trading book differ in many important future profits and losses of a bank’s trading portfolio.V aR respects from those governing the “banking book,” which models combine information on a bank’s trading positions is the more traditional stock of loans and mortgages across various products with statistical estimations of the originated and held by banks. In the initial phase of the probability distribution of the underlying market factors and current financial crisis, banks suffered severe losses from their relation to each other. The final output of aV aR model instruments held in the trading book: in many cases, sev- is a VaR estimate, which is defined as the maximum amount eral times what standard models would have predicted of money that a bank would expect to lose over a defined (Standard & Poor’s 2008). Given the significance of the period and with a defined confidence level. For example, trading book to international banks and its prominent role if a bank has a 99 per cent, 1-day VaR of $100 million, this in the recent crisis, it is important that regulatory reforms means that 99 times out of 100, the bank’s trading portfolio aimed at reducing the procyclicality in the financial should not lose more than $100 million the next day.
    [Show full text]
  • Modelling Credit Risk
    Centre for Central Banking Studies Modelling credit risk Somnath Chatterjee CCBS Handbook No. 34 Modelling credit risk Somnath Chatterjee [email protected] Financial institutions have developed sophisticated techniques to quantify and manage credit risk across different product lines. From a regulator’s perspective a clear understanding of the techniques commonly used would enhance supervisory oversight of financial institutions. The initial interest in credit risk models originated from the need to quantify the amount of economic capital necessary to support a bank’s exposures. This Handbook discusses the Vasicek loan portfolio value model that is used by firms in their own stress testing and is the basis of the Basel II risk weight formula. The role of a credit risk model is to take as input the conditions of the general economy and those of the specific firm in question, and generate as output a credit spread. In this regard there are two main classes of credit risk models – structural and reduced form models. Structural models are used to calculate the probability of default for a firm based on the value of its assets and liabilities. A firm defaults if the market value of its assets is less than the debt it has to pay. Reduced form models assume an exogenous, random cause of default. For reduced form or default-intensity models the fundamental modelling tool is a Poisson process. A default-intensity model is used to estimate the credit spread for contingent convertibles (CoCo bonds). The final section focusses on counterparty credit risk in the over-the-counter (OTC) derivatives market.
    [Show full text]
  • Value at Risk (VAR) Models
    Lecture 7: Value At Risk (VAR) Models Ken Abbott Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material. Risk Management's Mission 1. To ensure that management is fully informed about the risk profile of the bank. 2. To protect the bank against unacceptably large losses resulting from concentration of risks 3. In other words: NO SURPRISES • Two analogies: •Spotlight •coloring book 2 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material. Methodology Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material. Different Methodologies • Example of one-asset VaR • Price-based instruments • Yield-based instruments • Variance/Covariance • Monte Carlo Simulation • Historical Simulation 4 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material. Variables in the methods 1. Interest rate sensitivity – duration, PV01, 2. Equity exposure 3. Commodity exposure 4. Credit – spread duration 5. Distribution/Linearity of price behavior 6. Regularity of cash flow/prepayment 7. Correlation across sectors and classes 5 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Methodology: What Are We Methodology: WhatAreTrying We -4.00 We want to estimate the worst 1% of the possible outcomes.
    [Show full text]
  • Value at Risk Models in Finance
    EUROPEAN CENTRAL BANK WORKING PAPER SERIES ECB EZB EKT BCE EKP WORKING PAPER NO. 75 VALUE AT RISK MODELS IN FINANCE BY SIMONE MANGANELLI AND ROBERT F. ENGLE August 2001 EUROPEAN CENTRAL BANK WORKING PAPER SERIES WORKING PAPER NO. 75 VALUE AT RISK MODELS IN FINANCE BY SIMONE MANGANELLI 1 AND ROBERT F. ENGLE 2 August 2001 1 Simone Manganelli, European Central Bank, Kaiserstraße 29, 60311 Frankfurt am Main, Germany. E-mail: [email protected] 2 Robert F. Engle, New York University and UCSD. E-mail: [email protected] © European Central Bank, 2001 Address Kaiserstrasse 29 D-60311 Frankfurt am Main Germany Postal address Postfach 16 03 19 D-60066 Frankfurt am Main Germany Telephone +49 69 1344 0 Internet http://www.ecb.int Fax +49 69 1344 6000 Telex 411 144 ecb d All rights reserved. Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged. The views expressed in this paper are those of the authors and do not necessarily reflect those of the European Central Bank. ISSN 1561-0810 2 ECB • Working Paper No 75 • August 2001 Contents Abstract 4 Non-technical summary 5 1 Introduction 6 2 VaR Methodologies 7 2.1 Parametric Models 8 2.2 Nonparametric Methods 10 2.3 Semiparametric Models 12 3 Expected Shortfall 20 4 Monte Carlo Simulation 22 4.1 Sumulation Study of the Threshold Choice for EVT 22 4.2 Comparison of quantile methods performance 24 5 Conclusion 28 References 29 Appendix A: Tables 31 Appendix B: Figures 35 European Central Bank Working Paper Series 36 ECB • Working Paper No 75 • August 2001 3 Abstract Value at Risk (VaR) has become the standard measure that financial analysts use to quantify market risk.
    [Show full text]
  • Market Risk Measurement, Beyond Value at Risk
    Box 13 MARKET RISK MEASUREMENT, BEYOND VALUE AT RISK Financial risk management has evolved dramatically over the last few decades. One of the most widespread tools used by financial institutions to measure market risk is value at risk (VaR), which enables firms to obtain a firm-wide view of their overall risks and to allocate capital more efficiently across various business lines. This box places the VaR approach into a broader risk measurement context and compares the metric with alternatives. VaR summarises in a single number the risk of loss of a portfolio over a defined time horizon and a given confidence level α so that the probability of exceeding this loss is equal to p = 1- α. If it is assumed, for example, that the VaR of a portfolio over a one-week period is equal to -1.5% of its value with a 95% confidence level (α), this implies that the investor could expect the portfolio to exceed this loss with a probability of 5% (p = 1- α). VaR depends on two arbitrarily chosen parameters: the confidence level α, which indicates the probability of an outcome of less than or equal to VaR; and the holding period or the period over which the portfolio’s profit or loss is measured. VaR owes its prominence as a risk measure in the financial markets to several positive characteristics of the metric. It enables risk managers to aggregate the risks of sub-positions into an overall and consistent measure of portfolio risk while simultaneously taking into account the various ways in which different risk factors correlate with each other.
    [Show full text]