Do coherent risk measures identify assets risk profiles similarly? Evidence from international futures markets
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Author(s)Sharif Mozumder , M. Humayun Kabir ,Michael DempseyLink to ORCID Index: https://orcid.org/0000-0002-9059-0416
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DOIhttp://dx.doi.org/10.21511/imfi.14(3-2).2017.07
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Article InfoVolume 14 2017, Issue #3, pp. 361-380
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The authors consider Lévy processes with conditional distributions belonging to a generalized hyperbolic family and compare and contrast full density-based Lévy-expected shortfall (ES) risk measures and Lévy-spectral risk measures (SRM) with those of a traditional tail-based unconditional extreme value (EV) approach. Using the futures data of leading markets the authors find that ES and SRM often differ in recognizing the risk profiles of different assets. While EV (extreme value) is often found to be more consistent than Lévy models, Lévy measures often perform better than EV measures when compared with empirical values. This becomes increasingly apparent as investors become more risk averse.
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JEL Classification (Paper profile tab)C52, G13
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References38
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Tables5
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Figures5
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- Figure 1. Conditional and unconditional quantiles in excess of threshold (2): long position in S&P 500
- Figure 2. Conditional and unconditional quantiles in excess of threshold (1.5): long position in FTSE100
- Figure 3. Conditional and unconditional quantiles in excess of threshold (2): long position in DAX
- Figure 4. Conditional and unconditional quantiles in excess of threshold (2): long position in Hang Seng
- Figure 5. Conditional and unconditional quantiles in excess of threshold (2): long position in Nikkei 225
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- Table 1. Generalized Pareto distribution (GDP) parameter estimates for futures indexes
- Table 2. Conditional maximum likelihood estimates for futures indexes
- Table 3. Anderson-Darling and left-truncated Anderson-Darling goodness-of-fit tests
- Table 4. Estimates of ES and Lévy spectral risk measures for futures position
- Table 5. Frequency distribution of significant estimates of ES and Lévy spectral risk measures
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- Acharya, V., Engle, R., Richardson, M. (2012). Capital shortfall: a new approach to ranking and regulating systemic risks. American Economic Review, 102(3), 59-64.
- Acharya, V., Pedersen, L., Philippon T., Richardson, M. (2010). Measuring Systemic Risk (Technical report, Department of Finance, NYU).
- Acerbi, C. (2002). Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance, 26, 1505-1518.
- Acerbi, C. (2004). Coherent representation of subjective risk aversion. In G. Szego (Ed.), Risk Measures for the 21st Century (pp. 147-207). Chichester: John Wiley and Sons Ltd.
- Adam, A., Houkari, M., Laurent, J. (2008). Spectral risk measures and portfolio optimization. Journal of Banking and Finance, 32(9), 1870- 1882.
- Anna, C., Rachev, S., Fabozzi, F. (2005). Composite Goodness-of-Fit Tests for Left-Truncated Loss Samples (Working Paper). Department of Statistics and Applied Probability. University of California, Santa Barbara.
- Artzner, P., Delbaen, F., Eber, J. M., Health, D. (1999). Coherent Measure or Risk. Mathematical Finance, 9, 203-228.
- Bertoin, Jean. (1996). Levy Processes. Cambridge University Press: Cambridge, UK.
- Barndorff-Nielson, O. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society. London A, Issue 353, 401-419.
- Barndorff-Nielson, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scandinavian Journal of Statistics, 5, 151-157.
- Barndorff-Nielsen, O. (1995). Normal Inverse Gaussian distributions and the modeling of stock returns (pp. 401-419). Research report no 300. Department of Theoretical Statistics, Aarhus University, A 353.
- Bingham, N. H., Kiesel, R. (2001). Modeling asset returns with hyperbolic distributions. In Return Distributions on finance (pp. 1-20). Butterworth-Heinemann.
- Brownlees, C., Engle, R. (2012). Volatility, Correlation and Tails for Systemic Risk Measurement (Working Paper Series). Department of Finance, NYU.
- Chen, Z., Wang, Y. (2008). Two sided coherent risk measures and their application in realistic portfolio optimization. Journal of Banking and Finance, 32(12), 2667-2673.
- Christoffersen, P. (2003). Element of Financial Risk Management. Academic Press.
- Cotter, J., Dowd, K. (2006). Extreme spectral risk measures: An application to futures clearinghouse margin requirements. Journal of Banking and Finance, 30, 3469-3485.
- Deng, X., Zheng, Y., Shao, P. (2009). Portfolio optimization based on spectral risk measures. International Journal of Mathematical Analysis, 34, 1657-1668.
- Dowd, K. (2005). Measuring Market Risk. John Wiley & Sons Ltd.
- Dowd, K., Cotter, J., Sorwar, C. (2008). Spectral Risk Measures: Properties and Limitations. Journal of Financial Services and Research, 34, 61-75.
- Dowd, K., Cairns, A. J. C., Blake, D., Coughlan, C.D., Epstein, D., Khalaf Allah, M. (2010). Backtesting Stochastic Mortality Models: An Ex Post Evaluation of Multiperiod-Ahead Density Forecasts. North American Actuarial Journal, 14(3), 281- 298.
- Eberlein, E., Hammerstein, E. A. (2002). The Generalized Hyperbolic and Inverse Gaussian Distributions: limiting cases and approximation of processes (FDM preprint 80). University of Freiburg.
- Eberlein, E., Prause, K. (2002). The Generalized Hyperbolic model: financial derivatives and risk measures. Proceedings of the Mathematical Finance – Bachelier Congress 2000, Springer, 245-267.
- Fajardo, J. (2015). Barrier style contracts under Lévy processes: An alternative approach. Journal of Banking & Finance, 53, 179-187.
- Fajardo, J., Mordecki, E. (2006). Symmetry and duality in Lévy markets. Quantitative Finance, 6(3), 219-227.
- Fajardo, J., Mordecki, E. (2014). Skewness premium with Lévy processes. Quantitative Finance, 14(9), 1619-1626.
- Fuse, G., Meucci, A. (2008). Pricing discretely monitored Asian options under Lévy processes. Journal of Banking & Finance, 32(10), 2076-2088.
- German, H. (2002). Pure jump Lévy processes for asset price modeling. Journal of Banking & Finance, 26(7), 1297-1316.
- Giannopoulos, K., Tunaru, R. (2005). Coherent risk measures under filtered historical simulation. Journal of Banking and Finance, 29(4), 979-996.
- Grootveld, H., Hallerbach, W. G. (2004). Upgrading value-at-risk from diagnostic metric to decision variable: A wise thing to do? In Szego (Ed.), Risk Measures for the 21st Century (pp. 33-50). Wiley, New York.
- Inui, K., Kijima, M. (2005). On the significance of expected shortfall as a coherent risk measure. Journal of Banking and Finance, 29(4), 853-864.
- Kim, Y. S., Rachev, S. T., Bianchi, M. L., Fabozzi, F. J. (2008). Financial market models with Lévy processes and time-varying volatility. Journal of Banking and Finance, 32(7), 1363-1378.
- Kyprianou, A. (2006). Introductory Lectures on Fluctuations of Levy Processes with Applications. Springer.
- Prause, K. (1999). The Generalized Hyperbolic Model: Estimation, financial derivatives and risk measures (PhD Thesis, University of Freiburg).
- Sorwar, G., Dowd, K. (2010). Estimating financial risk measures for options. Journal of Banking and Finance, 34(8), 1982-1992.
- Sato, Ken-Iti. (1999). Levy Processes and Infinitely Divisible Distributions. Cambridge University Press: Cambridge, UK.
- Schoutens, W. (2003). Lévy Processes in Finance: Pricing Financial Derivatives. John Wiley & Sons Ltd.
- Wächter, H. P., Mazzoni, T. (2013). Consistent modeling of risk aversion behavior with spectral risk measures. European Journal of Operational Research, 229, 487-495.
- Wong, H. Y., Guan, P. (2011). An FFT-network for Lévy option pricing. Journal of Banking & Finance, 35(4), 968-999.
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An evaluation and comparison of Value at Risk and Expected Shortfall
Tom Burdorf , Gary van Vuuren
doi: http://dx.doi.org/10.21511/imfi.15(4).2018.02
Investment Management and Financial Innovations Volume 15, 2018 Issue #4 pp. 17-34 Views: 1269 Downloads: 262 TO CITE АНОТАЦІЯAs 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.
