Abstract
Forecasting portfolio risk requires both, estimation of marginal return distributions for individual assets and dependence structure of returns as well. Due to the fact, that the marginal return distribution represents the main impact factor on portfolio volatility, the impact of dependency modeling which is required for instance in the field of Credit Pricing, Portfolio Sensitivity Analysis or Correlation Trading is rarely investigated that far. In this paper, we explicitly focus on the impact of decoupled dependency modeling in the context of risk measurement. We do so, by setting up an extensive simulation analysis which enables us to analyze competing copula approaches (Clayton, Frank, Gauss, Gumbel and t copula) under the assumption that the “true” marginal distribution is known. By simulating return series with different realistic dependency schemes accounting for time varying dependency as well as tail dependence, we show that the choice of copula becomes crucial for VaR, especially in volatile dependency schemes. Albeit the Gauss copula approach does neither account for time variance nor for tail dependence, it represents a solid tool throughout all investigated dependency schemes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The analysis is based on applied loss functions in an empirical setup.
- 2.
We applied the CPA test proposed by Giacomini and White (2006) to prove this fact. Results are available upon request.
- 3.
The empirical backtesting performance would get rejected by statistical backtesting criteria, “conditional coverage”, by Christoffersen (1998).
- 4.
Results are available upon request.
- 5.
The “first best” solution is always the original model.
References
Ane, T., & Kharoubi, C. (2003). Dependence structure and risk measure. The Journal of Business, 76(3), 411–438.
Christoffersen P. (1998). Evaluating interval forecasts. International Economic Review, 39(4), 841–862.
Fantazzini, D. (2009). The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study. Computational Statistics and Data Analysis, 53(6), 2168–2188.
Giacomini, R. and H. White (2006). Tests of Conditional Predictive Ability. Econometrica, 74(6), 1545–1578.
Joe, H. (1996). Families of m-variate distributions with given margins and m (m-1)/2 bivariate dependence parameters. In L. Ruschendorf, B. Schweizer, M. D. Taylor (Eds.), Distributions with fixed margins and related topics (Vol. 28, pp. 120–141). IMS Lecture Notes Monograph Seriex.
Nelson, R.B. (1990). An Introduction to Copulas. New York: Springer.
Sklar, C. (1959). Fonctions de repartition a n dimensions et leurs marges (Vol. 8, pp. 229–231). Publicationss de Institut Statistique de Universite de Paris.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Berger, T. (2014). Misspecified Dependency Modelling: What Does It Mean for Risk Measurement?. In: Huisman, D., Louwerse, I., Wagelmans, A. (eds) Operations Research Proceedings 2013. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-07001-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-07001-8_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07000-1
Online ISBN: 978-3-319-07001-8
eBook Packages: Business and EconomicsBusiness and Management (R0)