Black–Litterman with a Factor Structure Applied to Multi-Asset Portfolios

Abstract

In this article, the author directly incorporates a standard factor structure into the Black–Litterman (BL) framework that can be applied to a wide array of mean–variance optimization problems, but it is especially useful for multi-asset portfolio construction. The author compares the BL model with a direct factor structure to the BL model with view portfolios employed in the existing literature. He argues that when tactical views are quantitatively derived, using a direct factor structure can be applied to a broader set of investment problems than integrating factors via view portfolios. The two frameworks are quite similar when applied to traditional quantitative stock selection portfolio construction. However, the direct factor approach can easily handle two situations that often occur in multi-asset portfolio construction that the view portfolio approach cannot: when the number of factors is greater than the number of assets (e.g., market-timing models) and when uncertainty in asset residuals is heterogeneous. In addition, the author provides the fundamental assumptions with clean notation that underpin the BL model.