Copula-based Portfolio Optimization

Abstract: This thesis studies and develops copula-based portfolio optimization. The overall purpose is to clarify the effects of copula modeling for portfolio allocation andsuggest novel approaches for copula-based optimization. The thesis is a compilation of five papers. The first and second papers study and introduce copula-based methods; the third, fourth, and fifth papers extend their applications to the Black-Litterman (BL) approach, expectile Value-at-Risk (EVaR), and multicriteria optimization, respectively.The first paper focuses on applying copula-based forecasting models and studying tail dependence and how the risk model choice affects asset allocation. Using international stock markets, an analysis of the performance of several risk modeling portfolio strategies indicates that GARCH-EVT forecasting models, which use Gaussian or Student-t copulas, are best at reducing portfolio risk.In the second paper, vine copulas are applied to study portfolio strategies during the global financial and COVID-19 crises. Overall, we find that the Student-t drawable vine copula models perform best with regard to risk reduction, both for the entire 2005–2012 period as well as during the global financial crisis. For the COVID-19 crisis, however, we find that the asymmetric Joe C-vine copula model performs bestin reducing downside portfolio risk.The third paper includes a methodological contribution in that it incorporates dependency structure modeling with the BL approach and applying tail constraintsin reward-risk maximization. Our empirical analysis and robustness check indicate better performance for the CBL portfolios in terms of lower tail risk and higher risk-adjusted returns compared to the benchmark strategies.The fourth paper investigates EVaR as the risk measure in dynamic copula-based portfolio optimization and compares it to the common variance and conditional Value-at-Risk (CVaR). Using ten S&P 500 industry sectors, EVaR leads to a min-risk dynamic generalized additive models (GAMC-vine) portfolio that achieves higher out-of-sample average return and risk-adjusted ratios. Furthermore, EVaR shows a better portfolio ranking than CVaR and the copula-based variance and EVaR portfolios show higher-order stochastic dominance over CVaR strategies.The fifth paper develops a copula-based multi-objective portfolio (MOP) optimization. Applying the copula-based multi-objective portfolio optimization (MOP) optimization model, we investigate the impacts of objective functions and several multivariate risk models on portfolio performance. In general, there isevidence that the copula-based multicriteria portfolios perform better than those produced using the other predictive models in terms of the downside risk. With regard to portfolio attributes, the dividend yield and beta coefficient significantly reduce portfolio tail risk measures.

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