Title: Dynamic Black Litterman copula based optimal portfolios with tail constraints
Authors: Maziar Sahamkhadam - Linnaeus University (Sweden) [presenting]
Andreas Stephan - Jonkoping University (Sweden)
Ralf Ostermark - Abo Akademi (Finland)
Abstract: The original Black-Litterman (BL) approach assumes normality, constant conditional distribution and no tail dependency, neither symmetric nor asymmetric. We estimate returns conditional distribution from a dynamic BL approach and model the tail dependency by applying truncated regular vine (Rvine) copula. Furthermore, reward-risk ratio optimizations generally consider only two portfolio characteristics, expected return and risk. It is shown that including tail constraints leads to more flexible portfolio strategies, combining tail and classical risk-return optimization techniques. Conditional Value-at-Risk (CVaR) is used as downside risk measure and added in classical reward-risk optimization. To examine the performance of the suggested forecasting models and optimization techniques, we perform out-of-sample back-testing for several portfolio strategies applied to a data set consisting of 30 stocks listed on the Stockholm exchange. We compare the results with benchmark portfolios including equally weighted (EQW) portfolio and portfolios obtained from dynamic BL model with out copulas. The results show more flexibility and frequent out-performance for the tail constraint augmented portfolios. In general, the suggested version of BL approach outperforms the benchmark models regarding both portfolio return and risk measures.