Identifying Sparse L2-Norm Regularized Portfolios via Semi-Definite Relaxation

Posted: 1 Sep 2015

See all articles by Min Jeong Kim

Min Jeong Kim

Korea Advanced Institute of Science and Technology (KAIST)

Yongjae Lee

UNIST

Woo Chang Kim

Korea Advanced Institute of Science and Technology (KAIST)

Date Written: July 15, 2015

Abstract

For portfolio management in the real-world, it is required that a portfolio has a manageable number of assets and stable performance. However, much research has pointed out that the Markowitz model, which is a classical model in portfolio theory, forms a portfolio with many different assets that may have unstable performance. Therefore, in this paper, we focus on developing a portfolio selection model which constructs a sparse and stable optimal portfolio. In order to achieve our research goal we introduce a L2-norm regularization and a cardinality constraint on portfolio weights to the Markowitz model. Moreover, using semidefinite relaxation, we formulate a convex optimization problem for the proposed model. The outcomes of our empirical test show that portfolios obtained by our model have desired cardinalities and better out-of-sample performances than those of Markowitz optimal portfolios.

Keywords: Portfolio selection, L2-norm regularization, Cardinality constraint, Semi-definite relaxation

Suggested Citation

Kim, Min Jeong and Lee, Yongjae and Kim, Woo Chang, Identifying Sparse L2-Norm Regularized Portfolios via Semi-Definite Relaxation (July 15, 2015). Available at SSRN: https://ssrn.com/abstract=2653592 or http://dx.doi.org/10.2139/ssrn.2653592

Min Jeong Kim

Korea Advanced Institute of Science and Technology (KAIST) ( email )

373-1 Kusong-dong
Yuson-gu
Taejon 305-701, 130-722

Yongjae Lee

UNIST ( email )

gil 50
Ulsan, 689-798
Korea, Republic of (South Korea)

HOME PAGE: http://https://felab.unist.ac.kr/yongjaelee

Woo Chang Kim (Contact Author)

Korea Advanced Institute of Science and Technology (KAIST) ( email )

373-1 Kusong-dong
Yuson-gu
Taejon 305-701, 130-722
Korea, Republic of (South Korea)

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