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On How the Value at Risk of a Bank Can Be Estimated Using Expected Shortfall Methodology
Company: Lund University
Year Of Publication: 2007
Month Of Publication: June
Pages: 105
Download Count: 423
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Comment Num: 0
Language: EN
Who Can Read: Free
Date: 6-6-2007
Publisher: Administrator
Background: There is a well-known (theoreticaland practical) problem with VaR as a risk measure; its lack of subadditivity. If 99 % VaR can be estimated well using ES-methodology, banks could avoid problems with eg. limit structure, while still fulfilling the Basle internal model requirement of reporting a 99 % VaR figure. Purpose: To investigate how well ES - estimated using different approaches and confidence levels - suits for estimating the 99 % VaR of a bank. Methodology: The 99 % VaR estimation performance - both in terms of exceedance frequency (Kupiec test) and in terms of exceedance independence(longest-run test) - of two ES approaches and six VaR approaches is evaluated and compared. The study is limited to linear equity and currencyportfolios where each portfolio consists of either one or more (between four and eight) assets. The time series used are seven Morgan Stanley equityindices (1972-2006), DAX (1972-2006) and the prices of six currenciesmeasured in euros (german D-Mark prior to euro introduction) (1984-2006). Conclusions: In general, ES methodology seems to work just as well for the purpose of estimating 99 % VaR as does VaR methodology. If the ES confidencelevel is chosen not with the intention of resembling the results of the corresponding VaR method as closely as possible, but instead with the intention of leading to an exceedance frequency as close to 1 % as possible,results better than the ones of the VaR methods can be obtained. This is because these VaR estimates are greater, compensating for the way VaR methods (especially equally weighted historical simulation) underestimatethe true VaR. When using volatility-weighted historically simulated ES, 97.3 % seems to be an appropriate confidence level for representing 99 % VaR, whereas a confidence level of about 97.6 % looks optimal when equally weighted historically simulated ES is used. The earlier mentioned of the methodologies (unlike the later mentioned) fulfils the independence criterion. Also, its optimal confidence level is much more robust to volatility trend changes. In addition this, the volatility- weighted approach in general results in smaller average VaR estimates (for a given number of exceedances) and is better at predicting really big losses.
Tenland, Thomas Sign in to follow this author
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