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Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model

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  • Kim, Young Shin
  • Giacometti, Rosella
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.
  • Mignacca, Domenico

Abstract

In 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.

Suggested Citation

  • Kim, Young Shin & Giacometti, Rosella & Rachev, Svetlozar T. & Fabozzi, Frank J. & Mignacca, Domenico, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Working Paper Series in Economics 44, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    • Handle: RePEc:zbw:kitwps:44
    DOI: 10.5445/IR/1000029307
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    More about this item

    Keywords

    portfolio risk; portfolio optimization; portfolio budgeting; marginal contribution; fat-tailed distribution; multivariate normal tempered stable distribution;
    All these keywords.

    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

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