Black-Litterman model with copula-based views in mean-CVaR portfolio optimization framework with weight constraints

This study examines the portfolio optimization problem by exploiting daily data of 10 international Exchange Trade Funds (ETF) from 2012 to 2022. We extend the Black-Litterman (BL) approach using ARMA-GARCH-copula-based expected returns as a proxy for investor views and use the CVaR metric as a risk measure in the optimization procedure. The BL approach provides a Bayesian methodology for combining the equilibrium returns and the investor views to produce expected returns. We use Regular Vine (R-vine) copula since it provides a flexible multivariate dependency modeling. The suggested approach is compared against the copula-CVaR portfolio, which likewise a BL copula approach avoids excessive corner solutions that many optimization approaches would generate in case of extreme values of estimated parameters. We compare the performance of these two approaches using out-of-sample back-testing against two benchmarks: Mean–Variance optimizations (MV) and equal weights portfolio (EW). To further reduce the sensitivity of considered strategies to input parameters, we evaluate out-of-sample performance at three levels of maximum weight constraints: 30%, 40%, and 50%. Moreover, in this paper, we consider different levels of view confidence—τ in the Black-Litterman model as it significantly affects the obtained results and inferences. We calculate and report the portfolios’ tail risks, maximum drawdown, turnover, and the break-even point for all optimization approaches. Our empirical analysis indicates better performance for the CBL portfolio regarding lower tail risk and higher risk-adjusted returns, and the copula-CVaR portfolio is better regarding lower turnover and higher break-even point.