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Value at Risk: A Comparative Analysis

Value at Risk: A Comparative Analysis. Filip Iorgulescu. Introduction. Why is VaR a challenging subject for me?. - scientific but also practical - easy to understood, difficult to determine - a benchmark with certain shortcomings.

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Value at Risk: A Comparative Analysis

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  1. Value at Risk:A Comparative Analysis Filip Iorgulescu

  2. Introduction Why is VaR a challenging subject for me? - scientific but also practical - easy to understood, difficult to determine - a benchmark with certain shortcomings VaR - the number that measures risk, so popular it may not need an introduction The objective: to develop a comparison between different approaches to VaR by the means of a portfolio consisting of three stocks traded at BSE

  3. The Methodology • The analysis focuses on two aspects that are taken into account when computing VaR: - the volatility models - the distributional approaches It was considered that T = 1 day and p = 1% Mainly based on Christoffersen (2002) and Codirlasu (2007) Therefore, I set out from 1-day, 1% VaR formula VaR1% = - (Q1%σ + μ)S

  4. Historical volatility • EWMA volatility model for the three stocks • GARCH volatility model for the portfolio • GARCH volatility models for the three stocks • GARCH volatility models for the stocks along with a dynamic conditional correlation model • Standard N distribution • Historical quantile (last 750 days) • t-Student, NIG and GH distributions • CF approximation • Extreme Value Theory. ES measure was also considered The following approaches were considered:

  5. Welcome to the Championship of VaR measures!!! The pitch is ready… all the tickets are sold… The computed VaR measures were examined according to the following criteria: - precision - level of capital coverage - calculation requirements

  6. Meet the players – The Data Period: 5 Jan 2001 – 9 May 2008 • Main features: - Volatility clustering => conditional volatility models are recommended - Non-normality => other distributional approaches are needed - No unit roots A portfolio consisting of three stocks with equal weights: ATB, AZO and TLV. Arguments: quoted at Category 1 at BSE diversification across industries

  7. Group 1 – Historical volatility

  8. 1-day, 1% VaR graphs Historical volatility approach

  9. VaR GHD seems to be the most appropriate choice under historical volatility approach. • Advantages • Simplest volatility approach • Good precision results • Disadvantages • Strictly dependent on these portfolio allocations • Rather high capital coverage levels

  10. Group 2 – EWMA volatility ES EVT seems to be the most appropriate choice under EWMA volatility approach. • Advantages • Lower capital coverage • No estimations for λ • No strict dependence on current allocations • Disadvantages • Very weak precision results • Carries the limitations of EWMA model

  11. Group 3 – GARCH for the portfolio VaR GHD seems to be the most appropriate choice under GARCH (portfolio) volatility approach. • Advantages • Lower capital coverage • Very good precision • No difficult calculations required • Disadvantages • Strictly dependent on these portfolio allocations

  12. Group 4 – GARCH for the stocks VaR NIG seems to be the most appropriate choice under GARCH (stocks) volatility approach. • Advantages • Lower capital coverage • No strict dependence on current allocations • Disadvantages • Weak precision results • For large portfolios many estimations are needed

  13. Group 5 – GARCH DCC VaR GHD seems to be the most appropriate choice under GARCH DCC volatility approach. • Advantages • Lower capital coverage • Good precision results • No strict dependence on current allocations • Disadvantages • For large portfolios the estimation of the variance and correlation models is very difficult

  14. Complex approaches to VaR are more available to the practitioners. However, are the results worth the effort? Conclusions – The Semifinals • GARCH portfolio has the advantage of precision and smaller calculation effort, but is strictly dependent on current portfolio allocations. • GARCH DCC has the advantage of lower capital coverage but requires many estimations

  15. Taking into account the non-normality of the data proved useful • VaR CF and ES EVT: highest precision results – highest levels of capital coverage • VaR NIG and VaR GHD may prove to be more appropriate risk measures

  16. Conclusions – The Final • VaR GHD under GARCH DCC volatility approach may be considered the “best” risk measure for the analyzed portfolio and the chosen period. Yet, is the effort of estimating a DCC model worth the decrease from 5.21% to 5.07%? • Using more improved volatility models tends to reduce the level of capital coverage

  17. It is recommended to use other distributional approaches to deal with the non-normality of the returns • CF approximation tends to overestimate risk leading to very high levels of capital coverage • NIG and GHD seem to be reasonable distributional approaches • VaR under the EVT approach does not perform very well, while ES leads to nice precision results but at the cost of high levels of capital coverage. Other threshold values should be also considered. Thank you for attending this presentation!

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