Solving High-Order Portfolios via Successive Convex Approximation Algorithms

IEEE Trans. on Signal Processing, vol. 69, pp. 892-904, Feb. 2021.

13 Pages Posted: 25 Oct 2021

See all articles by Rui Zhou

Rui Zhou

Hong Kong University of Science and Technology - School of Engineering

Daniel Palomar

Hong Kong University of Science and Technology (HKUST)

Date Written: February 1, 2021

Abstract

The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows the Gaussian distribution. However, the real world distribution of assets return is usually asymmetric and heavy-tailed, which is far from being a Gaussian distribution. The asymmetry and the heavy-tailedness are characterized by the third and fourth central moments, i.e., skewness and kurtosis, respectively. Higher skewness and lower kurtosis are preferred to reduce the probability of extreme losses. However, incorporating high-order moments in the portfolio design is very difficult due to their non-convexity and rapidly increasing computational cost with the dimension. In this paper, we propose a very efficient and convergence-provable algorithm framework based on the successive convex approximation (SCA) algorithm to solve high-order portfolios. The efficiency of the proposed algorithm framework is demonstrated by the numerical experiments.

Keywords: High-order portfolios, skewness, kurtosis, efficient algorithm, successive convex approximation

JEL Classification: C61, G11

Suggested Citation

Zhou, Rui and Palomar, Daniel, Solving High-Order Portfolios via Successive Convex Approximation Algorithms (February 1, 2021). IEEE Trans. on Signal Processing, vol. 69, pp. 892-904, Feb. 2021., Available at SSRN: https://ssrn.com/abstract=3947795

Rui Zhou

Hong Kong University of Science and Technology - School of Engineering ( email )

China

Daniel Palomar (Contact Author)

Hong Kong University of Science and Technology (HKUST) ( email )

Clear Water Bay
Kowloon, 00000
Hong Kong

HOME PAGE: http://www.danielppalomar.com/

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