Portfolio with Copula-GARCH and Black-Litterman Model Using a Novel View Error Matrix

M-V (Mean-Variance) model's sensitivity to input parameters and its reliance on historical data have long posed challenges in portfolio optimization. In this paper, we address these concerns to some extent by adopting Black-Litterman model to derive posterior expected returns and a covariance matrix. However, Black-Litterman model also has its drawbacks, particularly in handling subjective randomness of investor views. To overcome it, we integrate a GARCH model to better account for forecasted volatility and investor uncertainty. Additionally, we introduce a copula function to capture asset correlations that are overlooked in subjective views. Building on these improvements, we propose a novel view error matrix, combining GARCH model's forecasted volatility with copula function's correlation coefficient matrix. We use Monte Carlo simulation to determine portfolio weights, and conduct a horizontal comparison of the proposed view error matrix using copula-GARCH with three other types given by He and Litterman (SEJ in 334304, He and Litterman, SSRN Electronic Journal, 2002), (Forecasting expected returns in the financial markets, Elsevier, Amsterdam, Idzorek, Forecasting expected returns in the financial markets, Elsevier, 2007) and (Sun in Mathematics 11: 1476, Sun et al., Mathematics 11:1476, 2023). Our findings reveal that: (a) In terms of return and risk, our presented copula-GARCH and (Sun in Mathematics 11: 1476, Sun et al., Mathematics 11:1476, 2023) are effective, but methods of He and (Litterman in SEJ 334304, He and Litterman, SSRN Electronic Journal, 2002) and (Forecasting expected returns in the financial markets, Elsevier, Amsterdam, Idzorek, Forecasting expected returns in the financial markets, Elsevier, 2007) are not effective enough, which tend to over-allocate to one stock; (b) In terms of Sharpe ratio, copula-GARCH achieves superior results compared to (Sun in Mathematics 11: 1476, Sun et al., Mathematics 11:1476, 2023), demonstrating its advantage in risk adjusted performance.