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<p>This paper examines the reduction of extreme downside risk for a U.S. investor holding the S&amp;P500 by constructing multivariate portfolios with developed and emerging European stock indices. Portfolio optimization is conducted using parametric Value-at-Risk under alternative distributional assumptions, including the normal, logistic, hyperbolic secant, and Laplace distributions. The non-Gaussian models capture fat tails while relying on fully invertible closed-form distributions, ensuring numerical stability in optimization. The analysis covers daily data from 2016 to 2024 and distinguishes between pre-crisis and crisis subsamples. Results show that portfolio composition is largely invariant to the chosen VaR specification, but downside risk estimates and back-testing performance differ substantially. Emerging market portfolios consistently provide superior hedging effectiveness due to lower correlation structures, particularly during crisis periods. The back-testing results show that the portfolio with developed stock indices performs better in the pre-crisis sub-sample, satisfying both coverage and independence criteria, whereas in the crisis sub-sample the emerging markets portfolio exhibits superior performance.</p>

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International diversification with parametric value-at-risk portfolios beyond normality

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Dejan Živkov,
  • Sanja Lončar

摘要

This paper examines the reduction of extreme downside risk for a U.S. investor holding the S&P500 by constructing multivariate portfolios with developed and emerging European stock indices. Portfolio optimization is conducted using parametric Value-at-Risk under alternative distributional assumptions, including the normal, logistic, hyperbolic secant, and Laplace distributions. The non-Gaussian models capture fat tails while relying on fully invertible closed-form distributions, ensuring numerical stability in optimization. The analysis covers daily data from 2016 to 2024 and distinguishes between pre-crisis and crisis subsamples. Results show that portfolio composition is largely invariant to the chosen VaR specification, but downside risk estimates and back-testing performance differ substantially. Emerging market portfolios consistently provide superior hedging effectiveness due to lower correlation structures, particularly during crisis periods. The back-testing results show that the portfolio with developed stock indices performs better in the pre-crisis sub-sample, satisfying both coverage and independence criteria, whereas in the crisis sub-sample the emerging markets portfolio exhibits superior performance.