Vast Portfolio Selection with Gross-exposure Constraints

By Jianqing Fan, Jingjin Zhang, K. Yu. Journal of the American Statistical Association, 2012

317 citations recorded by the source corpus.

This article introduces the large portfolio selection using gross-exposure constraints. It shows that with gross-exposure constraints, the empirically selected optimal portfolios based on estimated covariance matrices have similar performance to the theoretical optimal ones and there is no error accumulation effect from estimation of vast covariance matrices. This gives theoretical justification to the empirical results by Jagannathan and Ma. It also shows that the no-short-sale portfolio can be improved by allowing some short positions. The applications to portfolio selection, tracking, and improvements are also addressed. The utility of our new approach is illustrated by simulation and empirical studies on the 100 Fama–French industrial portfolios and the 600 stocks randomly selected from Russell 3000.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/bcec2a5642c0d606203cc9cae4b2fff81390e4aa

Citations in the corpus

• An Overview on the Estimation of Large Covariance and Precision Matrices (2015, unknown): “Examples include high dimensional discriminant analysis (Cai et al., 2011), portfolio allocation (Fan et al., 2008, 2012), principal component analysis, and complex data visualization (Tokuda et al., 2011).”
• Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data (2017, unknown): “The second approach consists in imposing constraints on the portfolio weights (Jagannathan and Ma (2003), Pesaran and Zaffaroni (2008), DeMiguel et al. (2009a), El Karoui (2010), Fan et al. (2012), Gandy and Veraart (2013)) or penalties (Brodie et al. (2009)).”
• Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks (2017, unknown): “6), with Markowitz (1952) portfolio selection listed as a major motivation; for example, see Frahm and Memmel (2010), Wang et al.”
• Do High-Frequency Data Improve High-Dimensional Portfolio Allocations? (2013, unknown): “A related result for general gross portfolio constraints is put forward by Fan et al. (2012b) and applied to evaluate covariance matrix estimates using HF data, e.g., in Fan et al. (2012a).”
• Large Covariance Estimation by Thresholding Principal Orthogonal Complements (2011, unknown): “The maximum elementwise estimation error ‖Σ̂K̂ − Σ‖max appears in risk assessment as in Fan, Zhang and Yu (2012).”
• Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice (2017, unknown): “For any fixed vector of portfolio weights, the next theorem, of which a similar version may be found in Fan et al. (2012), utilizes the short selling constraint to derive an upper bound on the distance between the predicted portfolio variance and the actual portfolio variance.”