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 ....................................................................................................................................................