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

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

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


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.

Original languageEnglish
Pages (from-to)325-343
Number of pages19
JournalAnnals of Operations Research
Issue number1
StatePublished - Dec 2012


  • Fat-tailed distribution
  • Marginal contribution
  • Multivariate normal tempered stable distribution
  • Portfolio budgeting
  • Portfolio optimization
  • Portfolio risk


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