Global financial crisis and dependence risk analysis of sector portfolios: a vine copula approach

ABSTRACT

We use regular vine (r-vine), canonical vine (c-vine) and drawable vine (d-vine) copulas to examine the dependence risk characteristics of three 20-stock portfolios from the retail, manufacturing and gold-mining equity sectors of the Australian market in periods before, during and after the 2008–2009 global financial crisis (GFC). Our results indicate that the retail portfolio is less risky than the manufacturing counterpart in the crisis period, while the gold-mining portfolio is less risky than both the retail and manufacturing sector portfolios. Both the retail and gold stocks display a higher propensity to yield positively skewed returns in the crisis periods, contrary to the manufacturing stocks. The r-vine is found to best capture the multivariate dependence structure of the stocks in the retail and gold-mining portfolios, while the d-vine does it for the manufacturing stock portfolio. These findings could be used to develop dependence risk- and investment risk-adjusted strategies for investment, rebalancing and hedging which more adequately account for the downside risk in various market conditions.

KEYWORDS:

• Vine copulas
• risk analysis
• dependence structure
• retail and manufacturing stocks

JEL CLASSIFICATION:

• C32
• C51
• G11

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The acronyms DIISR, NAB and CWT stand for the ‘Department of Innovation, Industry, Science and Research’, the ‘National Australian Bank’ and the ‘Common Wealth Treasury’, respectively.

² The concept of dependence risk refers to the risk stemming from a specific type of dependence relationship which two variables have in times of financial turbulence and in well-behaved financial stock markets (Hernandez 2015). The dependence risk that two stock return series have in the centre of a joint distribution is reflected as mild swings in the return distribution, as opposed to the dependence risk in the tails which is characterized by large swings in the return distribution. Besides, the dependence risk of two variables could be linear, nonlinear, symmetric or asymmetric.

³ The acronym GFC refers to the global financial crisis that took place in the United States during the 2008–2009 period and after the collapse of the Lehman Brothers Holdings Inc, which then spread to most international financial markets. This period is characterized by a significant degree of financial market uncertainty, volatility and risk.

⁴ It should be noted that the limitation of the bivariate copulas, relative to the pair vine copulas, becomes evident when the former are used in isolation (e.g. using only the Gaussian or only the Student-t bivariate copula to model a multivariate data set). On the other hand, the strength of the pair vine copulas to a great extent stems from the simultaneous use of a wide array of bivariate copula families to model a multivariate distribution.

⁵ A detailed explanation of the connection between Sklar’s theorem and pair vine copula models can be found in Brechmann and Schepsmeier (2011).

⁶ While the pair vine copula approach can handle portfolios of a larger size, we only consider 20-stock portfolios since the estimation of the dependence matrix becomes quite complex as the number of stocks increases. This is due to the consideration of almost all existing bivariate copula families in the modelling. The summary statistics for the constituents of these two portfolios are presented in Table 1A (Appendix).

⁷ Since the dependence structure corresponding to each financial period scenario is recorded in tables as part of the recording stage, the counting stage of the technique is only implemented to the full sample period scenario of each portfolio. The output from the counting, recording and classification stages is summarized in the grouping stage. Also, only the Kendall’s tau and the dependence structure matrices of the retail and manufacturing portfolios for the one period scenario are shown.

⁸ The strong relationship of dependence the Australian economy has with the mining and energy sectors is a common feature shared by the Canadian economy.

⁹ It should be noted that the iron ore commodity plays a key role in the Australian resources economy. For instance, in 2011, Australia occupied the first place in exports of iron ore worldwide, producing 40% of the global iron ore exports. During the global financial crisis (in the period October 2008 to December 2009) iron ore prices suffered a sharp decline, losing 48% of their value (from US$138 per tonne to US$71 per tonne) (Bingham and Perkins 2012).

¹⁰ The acronyms DIISR, NAB and CWT stand for: The Department of Innovation, Industry, Science and Research; the National Australian Bank and the Common Wealth Treasury, respectively.