An evaluation and comparison of Value at Risk and Expected Shortfall
-
DOIhttp://dx.doi.org/10.21511/imfi.15(4).2018.02
-
Article InfoVolume 15 2018, Issue #4, pp. 17-34
- Cited by
- 1269 Views
-
261 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
As a risk measure, Value at Risk (VaR) is neither sub-additive nor coherent. These drawbacks have coerced regulatory authorities to introduce and mandate Expected Shortfall (ES) as a mainstream regulatory risk management metric. VaR is, however, still needed to estimate the tail conditional expectation (the ES): the average of losses that are greater than the VaR at a significance level These two risk measures behave quite differently during growth and recession periods in developed and emerging economies. Using equity portfolios assembled from securities of the banking and retail sectors in the UK and South Africa, historical, variance-covariance and Monte Carlo approaches are used to determine VaR (and hence ES). The results are back-tested and compared, and normality assumptions are tested. Key findings are that the results of the variance covariance and the Monte Carlo approach are more consistent in all environments in comparison to the historical outcomes regardless of the equity portfolio regarded. The industries and periods analysed influenced the accuracy of the risk measures; the different economies did not.
- Keywords
-
JEL Classification (Paper profile tab)C6, G2, G3
-
References30
-
Tables9
-
Figures9
-
- Figure 1. Example of a risk aversion function ϕ (x)for ES
- Figure 2. Comparison of South Africa’s and the UK’s real GDP growth rates from 2000 to 2017
- Figure 3. Comparison of South Arica’s and the UK’s unemployment rates from 2000 to 2017
- Figure 4. Comparison of South Arica’s and the UK’s M2 money supply rates from 2000 to 2017
- Figure 5. Relative portfolio development from 2003 to 2006. Portfolios rebased to 100 on January 1, 2003
- Figure 6. Relative portfolio development from 2008 to 2011. Portfolios rebased to 100 on January 1, 2008
- Figure 7. Historical simulation ES/VaR ratios for (a) SA 03-05, (b) SA 08-10, (c) UK 03-05 and (d) UK 08-10
- Figure 8. Variance-covariance ES/VaR ratios for (a) SA 03-05, (b) SA 08-10, (c) UK 03-05 and (d) UK 08-10
- Figure 9. Monte Carlo simulation ES/VaR ratios for (a) SA 03-05, (b) SA 08-10, (c) UK 03-05 and (d) UK 08-10
-
- Table 1. BCBS back-testing color table for a 99% confidence level
- Table 2. Correlation between all securities (a) from 2003 to 2005 and (b) from 2008 to 2010 using daily returns. Demarcated areas (boxed) indicate SA securities, remainder UK
- Table 3. JB test results during (a) 2003–2005 and (b) 2008–2010, 99% confidence level, daily returns. Demarcated areas are for SA, remainder UK
- Table 4. Results of a two-sided means test at a 99% confidence level (daily returns)
- Table 5. Historical simulation results of 99% VaR and ES (daily returns)
- Table 6. Variance-covariance method results of 99% VaR and ES (daily returns)
- Table 7. Monte Carlo simulation results of 99% VaR and ES (daily returns)
- Table 8. BCBS back-testing results for VaR at a 99% confidence level
- Table 9. BCBS back-testing results for ES at a 99% confidence level
-
- Acerbi, & Tasche (2003). Expected shortfall: a natural coherent alternative to Value at Risk. Economic Notes, 31(2), 379-388.
- Acerbi (2002). Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking and Finance, 26(7), 1505-1518.
- Acerbi, C., Nordio, C., & Sirtori, C. (2001). Expected shortfall as a tool for financial risk management (Working paper).
- Acerbi, C., & Szekely, B. (2014). Back-testing expected shortfall. Risk Magazine, December 2014.
- Artzner, P., Delbaen, F., Eber, J., & Heath, D. (1999). Coherent Measure of Risk. Mathematical Finance, 9(3), 203-228.
- Basel Committee on Banking Supervision (BCBS) (2016). Minimum capital requirements for market risk.
- Basel Committee on Banking Supervision (BCBS) (1994). Risk management guidelines for derivatives.
- Benninga, S., & Wiener, Z. (1998). Value at Risk (VaR). Mathematica in Education and Research, 7(4), 1-8.
- Brehmer, J. (2017). Elicitability and its Application in Risk Management (Thesis: University of Mannheim).
- Dimsdale, N. (2009). The Financial Crisis of 2007–9 and the British Experience. Oxonomics, 4(1), 1-9.
- Emmer, S., Kratz, M., & Tasche, D. (2015). What is the best risk measure in practice? A comparison of standard measures. Journal of Risk, 18(2), 31-60.
- Hughes, C., & MacIntosh, J. (2008, September 17). Barclays strikes deal for Lehman spoils. Financial Times.
- Gurrola-Perez, P., & Murphy, D. (2015). Filtered historical simulation Value-at-Risk models and their competitors. Bank of England Working Paper, 525, 1-33.
- Hürlimann, W. (2004). Distortion risk measure and economic capital. North American Actuarial Journal, 8(1), 86-95.
- JP Morgan (1996). Riskmetrics Technical Document, JP Morgan/ Reuters (Fourth Edition).
- Li, H., Fan, X., Li, Y., Zhou, Y., Jin, Z., & Liu, Z. (2012). Approaches to VaR. Project: Stanford University.
- Liang, B., & Park, H. (2007). Risk measures for hedge funds: a cross-sectional approach. European Financial Management, 13(2), 333-370.
- Linsmeier, T., & Pearson, N. (1996). Risk Measurement: An Introduction to Value at Risk (Working Paper, 96-04).
- Miletic, S., Korenak, B., & Lutovac, M. (2014). Application of VaR (Value at Risk) method on Belgrade Stock Exchange (BSE) optimal portfolio. Faculty of Business Economics and Entrepreneurship, 1(2), 142-157.
- Nadarajah, S., Zhang, B., & Chan, S. (2013). Estimation methods for expected shortfall. Quantitative Finance, 14(2), 271-291.
- Necir, A., Rassoul, A., & Zitikis, R. (2010). Estimating the conditional tail expectation in the case of heavy-tailed losses. Journal of Probability and Statistics, 2010, 1-17.
- Richardson, M., & Smith, T. (1993). A test for multivariate normality in stock returns. The Journal of Business, 66(2), 295-321.
- Righi, M., & Ceretta, P. (2013). Individual and flexible expected shortfall back-testing. Journal of Risk Model Validation, 7(3), 3-20.
- Petev, I., LSQ-Crest, & Pistaferri, L. (2012). Consumption in the Great Recession. Stanford: The Russell Sage Foundation and The Stanford Center on Poverty and Inequality.
- Sharma, M. (2012). What is wrong with quantitative standard deviation? Research Journal of Finance and Accounting, 3(4), 16-25.
- Sheihk, A., & Qiao, H. (2009). Non-normality of Market Returns. JP Morgan.
- Thadewald, T., & Büning, H. (2004). Jarque-Bera test and its competitors for testing normality: A power comparison. Diskussionsbeiträge, 2004/9. Freie Universität Berlin, Fachbereich Wirtschaftswissenschaft, Berlin.
- Wimmerstedt, L. (2015). Backtesting Expected Shortfall: the design and implementation of different back-test (Thesis: KTH School of Engineering).
- Fong, T., & Wong, C. (2008). Stress testing banks’ credit risk using mixture vector autoregressive models (Working paper). Hong Kong Monetary Authority.
- Yamai, Y., & Yoshiba, T. (2002). Comparative analyses of expected shortfall and Value-at-Risk: their estimation error, decomposition, and optimization. Monetary and Economic Studies, 20(1), 87-121.