Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios

By Jianqing Fan, Jingjin Zhang, K. Yu. 2008

69 citations recorded by the source corpus.

Markowitz (1952, 1959) laid down the ground-breaking work on the mean-variance analysis. Under his framework, the theoretical optimal allocation vector can be very different from the estimated one for large portfolios due to the intrinsic difficulty of estimating a vast covariance matrix and return vector. This can result in adverse performance in portfolio selected based on empirical data due to the accumulation of estimation errors. We address this problem by introducing the gross-exposure constrained mean-variance portfolio selection. We show that with gross-exposure constraint the theoretical optimal portfolios have similar performance to the empirically selected ones based on estimated covariance matrices and there is no error accumulation effect from estimation of vast covariance matrices. This gives theoretical justification to the empirical results in Jagannathan and Ma (2003). We also show that the no-short-sale portfolio is not diversified enough and can be improved by allowing some short positions. As the constraint on short sales relaxes, the number of selected assets varies from a small number to the total number of stocks, when tracking portfolios or selecting assets. This achieves the optimal sparse portfolio selection, which has close performance to the theoretical optimal one. Among 1000 stocks, for example, we are able to identify all optimal subsets of portfolios of different sizes, their associated allocation vectors, and their estimated risks. The utility of our new approach is illustrated by simulation and empirical studies on the 100 Fama-French industrial portfolios and the 400 stocks randomly selected from Russell 3000.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/fb1771dd2b2b4667f5b4675b4f38b71be732ee80

Citations in the corpus

Large Covariance Estimation by Thresholding Principal Orthogonal Complements (2011, unknown): “While Fan et al. (2008, 2011) assumed the factors are observable, Bai and Shi (2011) considered the strict factor model in which Σu is diagonal.”
Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data (2010, unknown): “Still, there are some problems in ﬁnancial economics, in which it is only the accuracy of the estimator that matters and positive semi-deﬁniteness is less important, for example in asset allocation and risk management under gross exposure constraints (e.g. Fan, Zhang, and Yu, 2009).”
HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS (2011, unknown): “…we have derived a better convergence rate of ( Σ T ) − 1 than that in Fan, Fan and Lv (2008). b When the operator norm is considered, p is allowed to grow exponentially fast in T in order for ( Σ T ) − 1 to be consistent. b k k This quantity appears in risk assessment as in Fan, Zhang and Yu ( ).”
Vast Portfolio Selection with Gross-exposure Constraints (2012, unknown): “The parameters are calibrated to the market data of 30 industrial portfolios from May 1, 2002, to August 29, 2005, and are taken from Fan et al. (2008).”