Document Type

Conference Proceeding


The Modelling and Simulation Society of Australia and New Zealand


Faculty of Business and Law


School of Business/Marketing and Services Research Centre




This article was originally published as: Arreola Hernandez, J. , Allen, D. E., & Powell, R. (2013). Dependence estimation and controlled CVaR portfolio optimization of a highly kurtotic Australian mining sample of stocks. In MODSIM2013, 20th International Congress on Modelling and Simulation (pp. 1305-1311). Canberra, Australia: The Modelling and Simulation Society of Australia and New Zealand. Original article available here


The drivers of mining stock prices are known to be several. Sharp spikes on the stocks return distribution have been linked to the presence of unusually high volatility signifying the presence of high levels of kurtosis. The accurate measurement of the stocks’ underlying co-movements for more accurate CVaR portfolio optimization requires, therefore, the utilization of sophisticated and specific-specialized techniques which could adequately capture and model these characteristics. Here this issue is addressed by applying statistical-graphical models for dependence estimation. Twenty mining stocks, out of the 801 listed in the ASX as of December 2012, have been selected for the analysis under the criteria of satisfying the eight years trading period sought, having very weak or no autocorrelation of residuals and displaying the highest kurtosis. Models’ estimations of dependence are compared and inserted into a differential evolution algorithm for non-convex global optimization in order to conduct risk controlled CVaR portfolio optimization (Ardia, Boudt, Carl, Mullen & Peterson, 2011) and be able to identify the one yielding the highest portfolio return. The findings are of relevance in portfolio allocation and portfolio risk management. Energy and mining stock markets are subjected to numerous price drivers holding complex relationships. The dynamics of production and consumption based on seasonality features, transportation and storage, weather conditions, commodity price fluctuations, currency changes, market confidence and expectations, trading speculations and the domestic and international states of the economy impact mining stock prices in particular and unobvious ways reflected in high volatility with sudden spikes in the stock’s return distribution (Pilipovic, 1998). The generation of accurate measurements of the dependence matrix of mining stock’s return series is therefore both, a non-trivial task due to the hard to decipher characteristics present in return series suffering from high levels of kurtosis (Carvalho, Lopes & Aguilar, 2010) and, a crucial element in portfolio optimization and portfolio risk management. The use of graphical techniques in this study is justified on the basis of their utility and suitableness. Graphical models such as pair c-vine copulas, the graphical lasso and adaptive graphical lasso provide, for instance, the visualization and flexibility to represent a problem in a more simplified and dissected form (Lauritzen, 1996). Graphs also appear to be naturally adequate to express the interaction of variables and thus facilitate the analysis of their dependency. The models of dependence estimation and CVaR portfolio optimization, on the other hand, are desirable due to mathematical and statistical framework they provide which may lead to satisfactory results and, their apparent ability to overcome the flaws (i.e. standardized model application to all joint distributions, restrictive and deterministic linear and monotonic modelling functions as in the Pearson and Spearman) traditional measures display when dealing with highly kurtotic data, joint distributions with stronger dependence in the tails and controlled risk non-convex portfolio optimization problems. Findings indicate that the highest portfolio returns are generated by inserting the covariance output matrix from the student-t copula into the differential optimization algorithm and, the student-t copula fitting with separate modelling of the marginal distributions appears to be the most desirable modelling choice. The portfolio return by the adaptive graphical lasso is lower than that of the student-t and is followed by the Gaussian pair c-vine copula. The regular graphical lasso produced the lowest portfolio return and the covariance matrix values were higher for models producing the highest portfolio returns implying that the models generating the lowest portfolio returns underestimated the dependence of the assets. The implications of the findings suggest that specific modelling of each marginal distribution, as compared to modelling based on a Gaussian framework, may lead to an edge in the estimations due to the distribution differences encountered on each marginal. Furthermore, the ability of the model to capture dependence in the tails, as it is the case of the student-t copula, does provide a modelling advantage too. This paper appears to be the first one in, comparing the portfolio performance of the models of dependence estimation in the context of controlled CVaR, applying the models treated to a highly kurtotic mining sample of stocks from the Australian market and modelling separately the distribution of the marginals when fitting the student-t copula.