A Maximal Tail Dependence-Based Clustering Procedure for Financial Time Series and Its Applications in Portfolio Selection

Abstract

In this paper, we propose a clustering procedure of financial time series according to the coefficient of weak lower-tail maximal dependence (WLTMD). Due to the potential asymmetry of the matrix of WLTMD coefficients, the clustering procedure is based on a generalized weighted cuts method instead of the dissimilarity-based methods. The performance of the new clustering procedure is evaluated by simulation studies. Finally, we illustrate that the optimal mean-variance portfolio constructed based on the resulting clusters manages to reduce the risk of simultaneous large losses effectively.

Risk, Ruin and Survival

“…This might be disconcerting from the practical point of view, and has therefore given rise to the notion of maximum tail dependence (MTD). Liu et al (2018) have adopted this notion in their real data based explorations of a portfolio selection problem initiated by De , who have proposed to cluster financial assets by tail dependence. In Liu et al (2018), the tail dependence coefficient (TDC) used by De is replaced by the MTD coefficient, and the corresponding techniques of clustering are developed and discussed.…”

“…Liu et al (2018) have adopted this notion in their real data based explorations of a portfolio selection problem initiated by De , who have proposed to cluster financial assets by tail dependence. In Liu et al (2018), the tail dependence coefficient (TDC) used by De is replaced by the MTD coefficient, and the corresponding techniques of clustering are developed and discussed. The obtained results suggest that MTD-based portfolios outperform TDC-based portfolios on avoiding extremely low rates of return.…”

Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”

“…This might be disconcerting from the practical point of view, and has therefore given rise to the notion of maximum tail dependence (MTD). Liu et al (2018) have adopted this notion in their real data based explorations of a portfolio selection problem initiated by De Luca and Zuccolotto (2011), who have proposed to cluster financial assets by tail dependence. In Liu et al (2018), the tail dependence coefficient (TDC) used by De Luca and Zuccolotto (2011) is replaced by the MTD coefficient, and the corresponding techniques of clustering are developed and discussed.…”

“…Liu et al (2018) have adopted this notion in their real data based explorations of a portfolio selection problem initiated by De Luca and Zuccolotto (2011), who have proposed to cluster financial assets by tail dependence. In Liu et al (2018), the tail dependence coefficient (TDC) used by De Luca and Zuccolotto (2011) is replaced by the MTD coefficient, and the corresponding techniques of clustering are developed and discussed. The obtained results suggest that MTD-based portfolios outperform TDC-based portfolios on avoiding extremely low rates of return.…”

A tail-revisited Markowitz mean-variance approach and a portfolio network centrality

“…This is due to the fact that covariance is a measure of portfolio risk based on moments and, as consequence, does not distinguish downside from upside risk. The quantile-based tail measures-value-at-risk (Var), expected shortfall (ES), extreme downside correlations (EDC) and p-tail risk (see, for example (Liu and Wang 2021;Harris et al 2019))-overcome the limitation of covariance in that they are able to capture the downside risk. However, their main drawback is that they are rather insensitive to the shape of the tail distribution since they strongly depend on the a priori choice of the confidence level and/or quantiles, thereby accounting mainly for the frequency of the realizations (not their values) (Kuan et al 2009).…”