A Heteroskedastic Black–Litterman Portfolio Optimization Model with Views Derived from a Predictive Regression

The modern portfolio theory in Markowitz (1952) is a cornerstone for investment management, but its implementations are challenging in that the optimal portfolio weight is extremely sensitive to the estimation for the mean and covariance of the asset returns. As a sophisticate modification, the Black–Litterman portfolio model allows the optimal portfolio’s weight to rely on a combination of the implied market equilibrium returns and investors’ views (Black and Litterman, 1991). However, the performance of a Black–Litterman model is closely related to investors’ views and the estimated covariance matrix. To overcome these problems, we first propose a predictive regression to form investors’ views, where asset returns are regressed against their lagged values and the market return. Second, motivated by stylized features of volatility clustering, heavy-tailed distribution, and leverage effects, we estimate the covariance of asset returns via heteroscedastic models. Empirical analysis using five industry indexes in the Taiwan stock market shows that the proposed portfolio outperforms existing ones in terms of cumulative returns.