Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model
AbstractIn this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization. --
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Bibliographic InfoPaper provided by Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering in its series Working Paper Series in Economics with number 44.
Date of creation: 2012
Date of revision:
portfolio risk; portfolio optimization; portfolio budgeting; marginal contribution; fat-tailed distribution; multivariate normal tempered stable distribution;
Find related papers by JEL classification:
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-09 (All new papers)
- NEP-ECM-2012-09-09 (Econometrics)
- NEP-RMG-2012-09-09 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000.
"Sensitivity Analysis of Values at Risk,"
2000-05, Centre de Recherche en Economie et Statistique.
- C. Gourieroux & J.P. Laurent & O. Scaillet, 2000. "Sensitivity analysis of values at risk," THEMA Working Papers 2000-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Gouriéroux, Christian & Laurent, J.P. & Scaillet, Olivier, 1999. "Sensitivity Analysis of Values at Risk," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 00 Jan 2000.
- Christian Gourieroux & J. P. Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Econometric Society World Congress 2000 Contributed Papers 0162, Econometric Society.
- Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
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