Estimating the higher-order co-moment with non-Gaussian components and its application in portfolio selection

Abstract

The estimation of higher-order co-moments of asset returns play an important role in higher-order moment portfolio selection. We improve the estimation of higher-order co-moments by using non-Gaussian components in the observed factor models and construct a portfolio selection method, labelled as Non-Gaussian Component (NGC) portfolio. We assume the non-normality of asset returns is driven by the independent non-Gaussian components in the observed factors. Through identifying and extracting those non-Gaussian components, the parameters in the portfolio objective function have been significantly decreased. We show that the non-Gaussian components can be estimated consistently by the independent component analysis and higher-order cumulant tests. Simulation studies confirm the good finite sample properties of our estimation procedure and further the performance of the NGC portfolio. Empirical results show that the NGC portfolio outperforms the benchmark portfolios, and only a few non-Gaussian components are needed to optimize the objective function.

Keywords:

• Portfolio selection
• non-Gaussian distributions
• higher-order multi-cumulant
• observed factor models

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 When $z_t$ has nonzero means, similar notations can be obtain by ${\overline{z}}_t=z_t-E[z_t]$.

2 If considering no short selling, ${\omega }_i\ge 0$ for $\mathrm{\forall }i$ should be added.

3 For a 100-asset(N = 100) portfolio optimization, we need average 2 minutes to obtain the portfolio weights when using Boudt et al. [16]'s co-moments decomposition, but only average 5 seconds for that when using the multi-cumulant decomposition.

4 For convenience, we denote ${\kappa }_{{\tilde{h}}_j}^{(k)}$ and ${\sigma }_{{\tilde{h}}_j}$ as ${\kappa }_j^{(k)}$ and ${\sigma }_j$ for short.

5 We set the mixing matrix as identity to consider extreme case: the observed factors $f_t$ are independent. In this case, independent component analysis is redundant, and can be regarded as a lower benchmark of the NGC portfolio.

6 When N = 500, we only consider T = 756(3 years) and T = 1260(5 years) to get a reliable result, because the sample covariance matrix is not invertible when T = 252(1 years).

7 Since MV and RMV portfolio have different objective function, we only report the objective value of the FM and NGCP portfolio.

8 The number of non-Gaussian components is larger than one because we assume that at least one non-Gaussian component exists.

Additional information

Funding

Wanbo Lu's research is sponsored by the National Science Foundation of China [grant numbers 71771187, 72011530149, 72163029], and the Fundamental Research Funds for the Central Universities [grant number JBK190602] in China.