# Big Data Challenges of High-Dimensional Continuous-Time Mean-Variance Portfolio Selection and a Remedy

Risk Analysis, 37, 1532-1549.

34 Pages Posted: 26 May 2016 Last revised: 27 Sep 2017

See all articles by Mei Choi Chiu

## Mei Choi Chiu

Hong Kong University of Science & Technology (HKUST) - Department of Mathematics

## Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

## Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: April 22, 2016

### Abstract

Investors interested in the global financial market have to analyze financial securities internationally. The optimal global investment decision involves processing a huge amount of data for a high-dimensional portfolio. This paper investigates the big data challenges of two mean-variance optimal portfolios: continuous-time precommitment and constant-rebalancing strategies. We show that both optimized portfolios implemented with the traditional sample estimates converge to the worst performing portfolio when the portfolio size becomes large. The crux of the problem is the estimation error accumulated from the huge dimension of stock data. We then propose a linear programming optimal (LPO) portfolio framework, which applies a constrained ℓ1 minimization to the theoretical optimal control to mitigate the risk associated with the dimensionality issue. The resulting portfolio becomes a sparse portfolio that selects stocks with a data-driven procedure and hence offers a stable mean-variance portfolio in practice. When the number of observations becomes large, the LPO portfolio converges to the oracle optimal portfolio, which is free of estimation error, even though the number of stocks grows faster than the number of observations. Our numerical and empirical studies demonstrate the superiority of the proposed approach.

Keywords: High-Dimensional Portfolio Selection, Continuous-Time Mean-Variance Portfolio, Constant-Rebalancing Portfolio, Machine Learning, Constrained $\ell_1$ Minimization, Sparse Portfolio

JEL Classification: C44, C61, G11

Suggested Citation

Choi Chiu, Mei and Pun, Chi Seng and Wong, Hoi Ying, Big Data Challenges of High-Dimensional Continuous-Time Mean-Variance Portfolio Selection and a Remedy (April 22, 2016). Risk Analysis, 37, 1532-1549., Available at SSRN: https://ssrn.com/abstract=2784245 or http://dx.doi.org/10.2139/ssrn.2784245