Evolution of financial risk measurement over the last 40 years: the special case for the banking industry. A survey
DOI:
https://doi.org/10.14422/icade.i105.y2018.002Keywords:
value-at-risk, expected shortfall, Tail VaR, Coherent risk measures, Spectral risk measures, Expectiles, Basle Committee on Banking SupervisionAbstract
The aim of this paper is to offer an overview, a survey of the evolution of financial risk measurement and management over the last 40 years, with special mention to banking. After a period based on the principles of the Modern Portfolio Theory (MPT), the introduction of Value-at-Risk (VaR) 25 years ago implied a great revolution. Since then, the introduction of new quantitative measures, with increasing mathematical complexity, has not stopped, in a continuous interaction between academics, professionals and regulators, in response to successive financial and banking crises. Among these, three risk measures stand out: coherent risk measures (specifically the Expected Shortfall), spectral risk measures and based on expectiles. We conclude that VaR and Expected Shortfall (ES) continue to be, despite their limitations, the two most used measures both from the internal point of view of the banks, as well as by the regulator and supervisor of their solvency. Finally, some of the open research lines in this field that address the challenges in the future of measuring financial risk in banking are presented.References
Abad, P., Benito, S. y López, C. (2014). A comprehensive review of Value at Risk methodologies. Spanish Review of Financial Economics, 12(1), 15-32.
Acerbi, C. (2002). Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking and Finance, 26 (7), 1505-1518.
Acerbi, C., y Szekely, B. (2014). Backtesting Expected Shortfall. Introducing three model-independent, non-parametric back-test methodologies for Expected Shortfall. MSCI (December). Geneva.
Acerbi, C., y Tasche, D. (2002a). On the coherence of expected shortfall. Journal of Banking and Finance, 26 (7), 1487-1503.
Acerbi, C., y Tasche, D. (2002b). Expected Shortfall: A natural coherent alternative to Value at Risk. Economic Notes. Banca Monte dei Paschi di Siena SpA, 31 (2), 379-388.
Artzner, P., Delbaen, F., Eber, J. M. y Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9 (3), 203-228.
Artzner, P., Delbaen, F., Eber, J. M. y Heath, D. (1997). Thinking coherently. Risk, 10 (11), 68-71.
Balbás, A. (2007). Mathematical methods in modern risk measurement: A survey. Revista Real Academia de Ciencias, Serie A. Matemáticas, 101 (2), 205-219.
Balbás, A. y Ibáñez, A. (1998). When can you immunize a bond portfolio? Journal of Banking and Finance, 22 (12), 1571-1595.
Balbás, A., Ibáñez, A. y López, S. (2002). Dispersion measures as risk immunization measures. Journal of Banking and Finance, 26 (6), 1229-1244.
Balbás, A., Garrido, J. y Mayoral, S. (2009). Properties of distortion risk measures. Methodology and Computing in Applied Probability, 11 (9), 385-399.
Basak, S. y Saphiro, A. (2001). Value-at-Risk based management: Optimal policies and asset prices. The Review of Financial Studies, 14 (2), 371-405.
Basle Committee on Banking Supervision (BCBS) (2018a). Frequently asked questions on market risk capital requirements. Basle, (March).
Basle Committee on Banking Supervision (BCBS) (2018b). Revisions to the minimum capital requirements for market risk. Consultative Document. Basle, (March).
Basle Committee on Banking Supervision (BCBS) (2017a). Basel III: Finalising post-crisis reforms. Basle, (December).
Basle Committee on Banking Supervision (BCBS) (2017b). Stress testing principles. Consultative Document. Basle, (December).
Basle Committee on Banking Supervision (BCBS) (2016). Standards. Minimum capital requirements for Market Risk. (January).
Basle Committee on Banking Supervision (BCBS) (2013). Fundamental review of the trading book: A revised market risk measure. Consultative Document. Basle, (October).
Basle Committee on Banking Supervision (BCBS) (2012). Fundamental review of the trading book. Consultative Document. (May).
Basle Committee on Banking Supervision (BCBS) (2011a). Basel III: A global regulatory framework for more resilient banks and banking systems. Revised edition. Basle, (June).
Basle Committee on Banking Supervision (BCBS) (2011b). Messages from the academic literature on risk measurement for the trading book. Basle Committee on Banking Supervision Working Paper N.º 19.
Basle Committee on Banking Supervision (BCBS) (2009a). Principles for sound stress testing practices and supervision. (May).
Basle Committee on Banking Supervision (BCBS) (2009b). Revisions to the Basel II market risk framework. Basle, (July).
Basle Committee on Banking Supervision (BCBS) (1996). Amendment to the Capital Accord to incorporate market risks. (January).
Basle Committee on Banking Supervision (BCBS) (1988). International convergence of capital measurement and capital standards. (July).
Baumol, W. J. (1963). An expected gain confidence limit criterion for portfolio selection. Management Science, 10 (1), 174-182.
Bayer, S. y Dimitriadis, T. (2018). Regression based Expected Shortfall backtesting. University of Konstanz, Department of Economics. arXiv:1801.
Belles-Sampera, J. Guillén, M. y Santolino, M. (2014). Beyond Value-at-Risk: GlueVaR distortion risk measures. Risk Analysis, 34 (1), 121-134.
Bellini, F. y Bignozzi, V. (2015). On elicitable risk measures. Quantitative Finance, 15 (5), 725-733.
Bellini, F. y di Bernardino, E. (2017). Risk management with expectiles. The European Journal of Finance, 23 (6), 487-506.
Bellini, F., Bernhard, K., Müller, A. y Gianin, E.R. (2014). Generalized quantiles as risk measures. Insurance: Mathematics and Economics, 54 (2), 41-48.
Berkowitz, J. (2001). Testing density forecasts, with applications to risk management. Journal of Business & Economic Statistics, 19 (4), 465-474.
Black, F. y Scholes, M., (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81 (3), 637-654.
Brockmann, M. y Kalkbrener, M. (2010). On the aggregation of risk. Journal of Risk, 12 (3), 48-65.
Burzoni, M., Peri, I. y Ruffo, C. M. (2017). On the properties of the Lambda Value at Risk: robustness, elicitability and consistency. Quantitative Finance, 17 (11). DOI: 10.1080/14697688017.1297535
Carabias, S. (2000). Análisis estocástico de los procesos de inversión. Tesis Doctoral. Madrid: Universidad Complutense de Madrid.
Carabias, S. (2003). Análisis estocástico de los procesos de inversión. Icade: Revista de las Facultades de Derecho y Ciencias Económicas y Empresariales, 59, 311-324.
Carabias, S., Gimeno, R. et al. (1999). Evolución del tratamiento matemático de los problemas dinámicos a lo largo del siglo XX. Icade: Revista de las Facultades de Derecho y Ciencias Económicas y Empresariales, 47, 13-36.
Chen, J. M. (2018). On exactitude in financial regulation: Value-at-Risk, expected shortfall, and expectiles. Risks, 6 (2), 61, 1-28.
Christoffersen, P. (1996). Evaluating interval forecasts. International Economic Review, 39 (4), 59-96.
Cont, R., Deguest, R. y Scandolo, G. (2010). Robustness and sensitivity analysis of risk measurement procedures. Quantitative Finance, 10 (6), 593-606.
Coronado, M. (1999). Predicción de crisis bancarias: El Value at Risk (VaR) como medida del riesgo de mercado. Tesis Doctoral. Madrid: Universidad Pontificia Comillas.
Coronado, M. (2001a). Comparing different methods for estimating VaR for actual non-linear portfolios: Empirical evidence. Finance India Quarterly Research Journal. 15 (2), 503-531.
Coronado, M. (2001b). Aplicación de la Teoría de los Valores Extremos en la gestión de riesgos financieros: Posibilidades y limitaciones para el cálculo del Value-at-Risk. En Matemática Financiera y Actuarial, Vol. 1, (pp. 343-400). Bilbao: Servicio Editorial de la Universidad del País Vasco.
Coronado, M. (2001c). VaR estimation under non-linearity and non-normality. En Financial Markets, Risk Management and Corporate Governance, Vol. 1, (pp. 148-182). Hammam-Sousse: CR Univers Multimedia Publications.
Costanzino, N. y Curran, M. (2015). Backtesting general spectral risk measures with application to expected shortfall. Journal of Risk Model Validation, 9 (1), 21-31.
Costanzino, N. y Curran, M. (2018). A simple traffic light approach to backtesting expected shortfall. Risks, 6 (2). https://doi.org/10.3390/risks6010002.
Daníelsson, J. y Zhou, C. (2017). Why risk is so hard to measure? Systemic Risk Centre Discussion Paper 36 (February). London School of Economics.
Daníelsson, J., Jorgensen, B. N., Samorodnitsky G., Sarmad, M. y de Vries, C. G. (2013). Fat tails, VaR and subadditivity. Journal of Econometrics, 172 (2), 283-291.
Daníelsson, J., Embrechts, P., Goodhart, C., Keating, C., Muennich, F., Renault, O. y Shin, H. S. (2001). An Academic response to Basle II. Financial Markets Group (FGM) Special Paper N.º 130, London School of Economics.
Daouia, A. Girard, S. y Stupfler, G. (2018). Estimation of tail risk based on extreme expectiles. Journal of the Royal Statistical Society, Series B, 80, 263-292.
Davis, M. H. A. (2016). Verification of internal risk measure estimates. Statistics and Risk Modeling, 33 (3-4),67-93.
Deprés, M., Villegas, R. y Ayora, J. (2017). Manual de regulación bancaria en España. Madrid: Ed. Funcas.
Dimitriadis, T. y Bayer, S. (2017). A joint quantile and Expected Shortfall regression framework. Working Paper University of Konstanz, Department of Economics (august).
Domar, E., y Musgrave, R. A. (1944). Proportional income taxation and risk taking, Quarterly Journal of Economics, 57(May), 388-422.
Donnelly, C. y Embrechts, P. (2010). The devil is in the tails: actuarial mathematics and the subprime mortgage crisis. ASTIN Bulletin, 40 (1), 1-33.
Dowd, K. (2005). Measuring market risk, 2nd edition. West Sussex: Wiley.
Dowd, K. (1998). Beyond Value at Risk. The new science of risk management. London: Wiley.
Dowd, K. y Blake, D. (2006). After VaR: The theory, estimation and insurance applications of quantile-based risk measures. The Journal of Risk and Insurance, 73 (2), 193-229.
Dowd, K., Cotter, J. y Sorwar, G. (2008). Spectral risk measures: Properties and limitations. Journal of Financial Services Research, 34 (1), 61-75.
Du, Z. y Escanciano, J. C. (2017). Backtesting Expected Shortfall: Accounting for Tail Risk. Management Science, 63 (4), 940-958.
El Methni, J. y Stupfler, G. (2017). Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions. Statistica Sinica, 27 (2), 907-930.
Embrechts, P. (2017). A Darwinian view on internal models. Journal of Risk, 20 (1), 1-21.
Embrechts, P., Liu, H. y Wang, R. (2017). Quantile-based risk sharing. Working Paper RiskLab, Department of Mathematics, ETH Zurich, Forthcoming: Operations Research.
Embrechts, P. y Wang, R. (2015). Seven proofs for the subadditivity of Expected Shortfall. Dependence Modeling, 3 (1), 126-140.
Embrechts, P., Wang, B. y Wang, R. (2015). Aggregation-robustness and model uncertainty of regulatory risk measures. Finance and Stochastics, 19 (4), 763-790.
Embrechts, P. y Hofert, M. (2014). Statistics and quantitative risk management for banking and insurance. Annual Review of Statistics and its Applications, 1 (1), pp. 493-514.
Embrechts, P., Puccetti, G., Rüschendorf, L., Wang, R. y Beleraj, A. (2014). An academic response to Basle 3.5. Risks, 2 (1), 25-48.
Emmer, S., Kratz, M. y Tasche, D. (2015). What is the best risk measure in practice? A comparison of standard measures. Journal of Risk, 18 (2), 31-60.
Fama, E. (1965). The behavior of stock market prices. Journal of Business, 38, 34-105.
Feng, M. B. y Tan, K. S. (2012). Coherent distortion risk measures in portfolio selection. Systems Engineering Procedia, 4, 25-34.
Fishburn, P. C. (1977). Mean-risk analysis with risk associated with below-target returns. American Economic Review, 67 (2), 116-126.
Fisher, L. y Weil, R. L. (1971). Coping with the risk of interest rate fluctuations: Returns to bond-holders from naive and optimal strategies. Journal of Business, 44 (4), 408-431.
Fissler, T. y Ziegel, J. F. (2016). Higher order elicitability and Osband's principle. The Annals of Statistics, 44 (4), 1680-1707.
Fissler, T., Ziegel, J. F. y Gneiting, T. (2016). Expected Shortfall is jointly elicitable with Value at Risk. Implications for backtesting. Risk, 1, 58-61.
Föllmer, P. C. y Schied (2002). Convex measures of risk and trading constraints. Finance & Stochastics, 6 (4), 429-447.
Fong, H. G. y Vasicek, O. A., (1984). A risk minimizing strategy for portfolio immunization. The Journal of Finance, 39 (5), 1541-1546.
Frittelli, M. y Rosazza, E. (2002). Putting order in risk measures. Journal of Banking and Finance, 26 (7), 1473-1486.
Gneiting, T. (2011). Making and Evaluating Point Forecasts. Journal of the American Statistical Association, 106 (494), 746-762.
Goodhart, C. (2011). The Basle Committee on Banking Supervision. A history of the early years (1974-1997). Cambridge: Cambridge University Press.
Grootveld, H. y Hallerbach, W. (1999). Variance vs downside risk: Is there really that much difference? European Journal of Operational Research, 114 (2), 304-319.
Guégan, D. y Hassani, B. (2015). Distortion risk measure or the transformation of unimodal distributions into multimodal functions. En Bensoussan A. et al. (Eds), Future Perspectives in Risk Models and Finance, (cap 2, pp.71-88). Cham: Springer.
Harmantzis, F. C., Miao, L. y Chien, Y. (2006). Empirical study of value-at-risk and expected shortfall models with heavy tails. The Journal of Risk Finance, 7 (2), 117-135. DOI: 10.1108/15265940610648571
Jorion, P. (2007). Value at Risk. The new benchmark for managing financial risk. 3rd edition. New York: McGraw-Hill.
Jorion, P. (1997). Value at Risk. The new benchmark for controlling derivatives risk. Chicago: Irwin.
Kaplanski, G. y Kroll, Y. (2002). VaR Risk measures versus traditional risk measures: An analysis and survey. Journal of Risk, 4 (3), 1-27.
Kato, K. (2018). Asymptotic analysis for spectral risk measures parameterized by confidence level. Journal of Mathematical Finance, 8 (1), 197-226.
Keçeci, N. F., Kuzmenko, V. y Uryasev, S. (2016). Portfolios dominating indices: Optimization with second-order stochastic dominance constraints vs. minimum and mean variance portfolios. Journal of Risk and Financial Management, 9 (4), 1-14.
Kerkhof, J. y Melenberg, B. (2004). Backtesting for risk-based regulatory capital. Journal of Banking and Finance, 28 (8), 1845-1865.
Konno, H. y Yamazaki, H. (1991). Mean absolute deviation portfolio optimization model and its application to Tokyo Stock Market. Management Science, 37 (5), 519-531.
Kou, S. y Peng, X. (2016). On the measurement of economic tail risk. Operations Research, 64 (5), 1056-1072.
Kou, S., Peng, X. y Heyde, C.C. (2013). External risk measures and Basel Accords. Mathematics of Operations Research, 38 (3), 393-417.
Krätschmer, V., Schied, A. y Zähle, H. (2014). Comparative and qualitative robustness for law-invariant risk measures. Finance and Stochastics, 18 (2), 271-295.
Kratz, M., Lok, Y. y Mcneil, A. (2018). Multinomial VaR backtests: A simple implicit approach to backtesting expected shortfall. Journal of Banking and Finance, 88 (3), 393-407.
Kuan, C. Yeh, J. y Hsu, Y. (2009). Assessing value at risk with CARE, the Conditional Autoregressive Expectile models. Journal of Econometrics, 150 (2), 261-270.
Lambert, N., Pennock, D. M. y Shoham, Y. (2008). Eliciting properties of probability distributions. Proceedings of the 9th ACM Conference on Electronic Commerce, 129-138. New York: ACM Press.
Lintner (1965). The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47 (1), 13-37.
Longerstay, J. et al. (1996). RiskMetrics™. Technical Document. Morgan Guaranty Trust Company, Fourth Edition, New York (December 17).
Longin, F. M. (2001). Beyond the VaR. The Journal of Derivatives, 8 (4), 36-48.
Longin, F. M. (2000): From Value at Risk to stress testing: The extreme value approach. The Journal of Derivatives, 24 (7), 1097-1130.
Macaulay, F. R. (1938). Some theoretical problems suggested by the movements of interest rates: Bond yields and stock prices in the United States since 1856. New York: National Bureau of Economic Research.
Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 36, 394-419.
Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7 (1), 77-91.
Markowitz, H. M. (1959). Portfolio selection: Efficient diversification of investments, 2nd edition. New York: John Wiley & Sons.
McNeil, A. J. y Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance, 7 (3-4), 271-300.
Moldenhauer, F. y Pitera, M. (2018). Backtesting Expected Shortfall: is it really that hard? (March). arXiv:1709.01337v2.
Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica 34 (4), 768-783.
Nadarajah, S., Zhang, B. y Chan, S. (2014). Estimation methods for expected shortfall. Quantitative Finance 14 (2), 271-291.
Newey, W. K. y Powell, J. L. (1987). Asymmetric least squares estimation and testing. Econometrica, 55 (4), 819-847.
Nolde, N. y Ziegel, J. F. (2017). Elicitability and backtesting: Perspectives for banking regulation. The Annals of Applied Statistics, 11 (4), 1833-1874.
Ogryczak, W. y Ruszczynski, A. (1999). From stochastic dominance to mean-risk models: Semideviations as risk measures. European Journal of Operational Research, 116 (1), 33-50.
Ogryczak, W. y Ruszczynski, A. (2001). On consistency of stochastic dominance and mean semideviation models. Mathematical Programming, 89 (2), 217-232.
Ogryczak, W. y Ruszczynski, A. (2002). Dual stochastic dominance and related mean risk models. SIAM Journal of Optimization, 13 (1), 60-78.
Osband, K. H. (1985). Providing incentives for better cost forecasting. Tesis doctoral. University of California, Berkeley (December).
Patton, A. J., Ziegel, J. F., y Chen, R. (2017). Dynamic semiparametric models for expected shortfall (and Value-at-Risk). ERID Working Paper N.º 250. Duke University. arXiv:1707.05108 [q-fin.EC].
Pflug, G. (2000). Some remarks on the Value at Risk and the conditional Value at Risk. En Uryasev, S. (Ed.), Probabilistic Constrained Optimization: Methodology and Applications (pp. 272-281). Dordrecht: Kluwer.
Pitera, M. y Schmidt, T. (2018). Unbiased estimation of risk. Journal of Banking and Finance, 91 (6), 133-145.
Raupach, P. (2015). Calculating trading book capital: Is risk separation appropriate? Deutsche Bundesbank Discussion Paper 19/2015.
Righi, M. B. y Ceretta, P. S. (2015). A comparison of Expected Shortfall estimation models. Journal of Economics and Business, 78 (3-4), 14-47.
Rocco, M. (2011). Extreme Value Theory for finance: A survey. Banca d'Italia Ocassional Paper N.º 99 (july).
Rockafellar, R. T. et al. (2006). Generalized deviations in risk analysis. Finance & Stochastics, 10 (1), 51-74.
Rockafellar, R. T. y Uryasev, S. (2000). Optimization of conditional Value-at-Risk. Journal of Risk, 2 (3), 21-41.
Ruszczynski, A. y Shapiro, A., (2007). Optimization of convex risk functions. Mathematics of Operations Research, 31 (3), 433-452.
Savage, L. (1971). Elicitation of personal probabilities and expectations. Journal of the American Statistical Association, 66 (336), 783-801.
Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. The Journal of Finance 19 (3), 425-442.
Sy, W. (2006). On the coherence of VaR risk measures for Levy stable distributions. Working Paper Australian Prudential regulation Authority. http://dx.doi.org/10139/ssrn674989
Taleb, N. N. (2015). Silent risk. Lectures notes on probability. Vol.1. Descartes Publishing.
Taleb, N. N. (2014). Silent risk. Lectures on fat tails, (Anti)Fragility, and asymmetric exposures. SSRN Electronic Journal. 10139/ssrn392310.
Taleb, N. N. (2007). The Black Swan. The impact of the highly improbable. New York: Random House, Inc.
Triana, P. (2009). Lecturing birds on flying, can mathematical theories destroy the financial markets? Hoboken: Wiley.
Uryasev, S. (2000). Conditional Value-at-Risk: Optimization algorithms and applications. Financial Engineering News, February, 1-5.
Waltrup, L. S., Sobotka, F., Kneib, T. y Kauermann, G. (2015). Expectile and quantile regression–David and Goliath? Statistical Modelling, 15 (5), 433-56.
Wang, S. S. (2002). A risk measure that goes beyond coherence. En Proceedings of 2002 AFIR (Actuarial Approach to Financial Risk), Cancún (México).
Wang, S. S. (2000). A class of distortion operators for pricing financial and insurance risks. Journal of Risk and Insurance, 67(1), 15-36.
Wang, S. S. (1996). Premium calculation by transforming the layer premium density. ASTIN Bulletin 26 (1), 71-92.
Wang, S. S., Young, V. R. y Panjer, H. H. (1997). Axiomatic characterization of insurance prices. Insurance: Mathematics and Economics, 21 (2), 173-183.
Weber, S. (2006). Distribution-invariant risk measures, information, and dynamic consistency. Mathematical Finance, 16 (2), 419-41.
Wilmott, P. and Orrell, D. (2017). The Money formula. Dodgy finance, pseudo-science, and how mathematicians took over the markets. Chichester: Wiley & Sons.
Wong, W. K. (2008). Backtesting trading risk of commercial banks using expected shortfall. Journal of Banking and Finance, 32 (7), 1404-1415.
Yamai, Y. y Yoshiba, T. (2005). Value-at-Risk versus Expected Shortfall. A practical perspective. Journal of Banking and Finance, 29 (4), 997-1015.
Yamai, Y. y Yoshiba, T. (2002a). Comparative analyses of Expected Shortfall and Value-at-Risk (3): Their validity under market stress. Monetary and Economic Studies, Institute for Monetary and Economic Studies (IMES), Bank of Japan, 20(3), 181-237.
Yamai, Y. y Yoshiba, T. (2002b). Comparative analyses of Expected Shortfall and Value-at-Risk (2): Expected utility maximization and tail risk. Monetary and Economic Studies, Institute for Monetary and Economic Studies (IMES), Bank of Japan, 20 (2), 95-115.
Yamai, Y. y Yoshiba, T. (2002c). Comparative analyses of Expected Shortfall and Value-at-Risk:Their estimation error, decomposition and optimization. Monetary and Economic Studies, Institute for Monetary and Economic Studies (IMES), Bank of Japan, 20 (1), 87-121.
Yamai, Y. y Yoshiba, T. (2002d). On the validity of Value-at-Risk: Comparative analyses with Expected Shortfall. Monetary and Economic Studies, Institute for Monetary and Economic Studies (IMES), Bank of Japan, 20 (1), 57-85.
Yoshiba T. (2016). Risk aggregation with copula for banking industry. En Anderssen R. et al. (eds.) Applications + practical conceptualization + mathematics = fruitful innovation (pp. 246-259). Tokyo: Springer.
Ziegel, J. F. (2016). Coherence and elicitability. Mathematical Finance, 26 (4), 901-918.
Ziegel, J. F.; Krüger, F.; Jordan, A. y Fasciati, F. (2017). Murphy diagrams: Forecast evaluation of Expected Shortfall. Discussion Paper Series, No. 632. University of Heidelberg, Department of Economics. DOI: http://dx.doi.org/10.11588/heidok.00022950
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