Sparse Mean-Variance Portfolios: A Penalized Utility Approach

Strategic Bayesian Asset Allocation

“…Our work builds on other Bayesian stock selection strategies, such as those based on factor modeling, see Black and Litterman (1992); Carvalho et al (2011); Aguilar and West (2000); Puelz et al (2015); Getmansky et al (2015). Our main assumption is predictability Barberis (2000); Kandel and Stambaugh (1996) of stock returns, which is the main justification of an advice that an investor should heavily invest into stocks.…”

“…Robust minimax optimization techniques were recently proposed to account for uncertainty in covariance matrix and to solve for the worst-case scenario, see Ismail and Pham (2019). Puelz et al (2015) use Bayesian techniques to design a mean-variance portfolio with small number of assets and analyzes the trade off between optimality and number of assets to be included. Kozak et al (2018) design sparse factor models for analysis of large number of cross-sectional stock returns.…”

“…One approach to stabilize the solution and to find sparse portfolios is to add a regularization penalty to the objective function Brodie et al (2009). Another, interpretation of the penalized objective Puelz et al (2015) is that it allows to incorporate investor's preference with regards to number of stocks to be included into portfolio minimize…”

“…We propose a Bayesian regularization based on returns and volatility that simultaneously performs assets selection and optimal portfolio allocaiton. Our approach builds on the sequential asset allocation framework of Black and Litterman (1992) which incorporates investors' preferences on the returns and the stock selection approach by Puelz et al (2015) who uses the methodology of decoupling shrinkage and selection (DSS) Hahn and Carvalho (2015) to select stocks using regularized linear model.…”

“…The perspective of the investor is to maximize alpha risk-adjusted returns relative to a benchmark index. Incorporating investor's preferences using regularization is performed using the approach related to Black and Litterman (1992) and Puelz et al (2015). We show how to tailor MCMC algorithms to calculate portfolio weights and perform selection.…”