Asset allocation with gross exposure constraints for vast portfolios

Jianqing Fan Jingjin Zhang Ke Yu

Statistics Theory and Methods mathscidoc:1912.43435

Unpublished paper: Bendheim Center for Finance, Princeton University
Abstract Markowitz (1952, 1959) laid down the ground-breaking work on mean-variance analysis without gross exposure constraints. Under this framework, the theoretical optimal allocation vector can be different from the estimated one due to intrinsic difficulty of estimating a large covariance matrix and return vector. This can result in adverse performance in portfolio selected based on empirical data due to noise accumulation on estimation errors (Jagannathan and Ma, 2003; Fan, Fan and Lv, 2008). 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 as empirically selected ones based on estimated covariance matrices and there is no noise accumulation effect from estimation of covariance matrices. This gives theoretical justification to the empirical results
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@inproceedings{jianqingasset,
  title={Asset allocation with gross exposure constraints for vast portfolios},
  author={Jianqing Fan, Jingjin Zhang, and Ke Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114416041967995},
  booktitle={Unpublished paper: Bendheim Center for Finance, Princeton University},
}
Jianqing Fan, Jingjin Zhang, and Ke Yu. Asset allocation with gross exposure constraints for vast portfolios. In Unpublished paper: Bendheim Center for Finance, Princeton University. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114416041967995.
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