Vine copula modelling of dependence and portfolio optimization with application to mining and energy stock return series from the Australian market

This thesis models the dependence risk profile, investment risk and portfolio allocation features of seven 20-stock portfolios from the mining, energy, retail and manufacturing sectors of the Australian market in the context of the 2008-2009 global financial crisis (2008-2009 GFC) and pre-GFC, GFC, post-GFC and full sample period scenarios revolving around it. The mining and energy portfolios are the base of the study, while the retail and manufacturing are considered for benchmarking purposes. Pair vine copula models including canonical vines (c-vines), drawable vines (d-vines) and regular vines (r-vines) are fitted for the analysis of the portfolios’ multivariate dependence and their underlying sectors’ dependence risk dynamics. Besides, linear and nonlinear optimization methods threaded with the variance, mean absolute deviation (MAD), minimizing regret (Minimax), conditional Value-at-Risk (CVaR) and conditional Drawdown-at-Risk (CDaR) risk measures are implemented to examine the portfolios’ investment risk and optimal portfolio allocation features. The vine copula modelling of dependence aims at examining the dependence risk profile of the portfolios in specific market conditions; studying the changes of the portfolios’ dependence structure between pairs of period scenarios; and recognizing the vine copula models that best account for the portfolios’ multivariate dependence. The multiple risk measure-based portfolio optimization seeks to identify the least and most investment risky portfolios, single out the portfolio that offers the best risk-return trade-off and recognize the stocks in the portfolios that are good candidates for investment. This thesis’ main contributions stem from the “copula counting technique” and “average model convergence” perspectives proposed to handle, analyse and interpret the portfolios’ dependence structure and portfolio allocation features. The copula counting technique aside from simplifying the analysis and interpretation of the assets’ dependence structure, it enables an in-depth and comprehensive analysis of their underlying dependence risk dynamics in specific market conditions. The average model convergence addresses the optimal stock selection and investment confidence problems underlying any type of portfolio optimization, and faced by investors when having to select stocks from a wide array of optimal investment scenarios, in a more objective manner, through model convergence and model consensus. Both, the copula counting technique and average model convergence are new concepts that introduce new theory to the pair vine copula and multiple risk measure-based portfolio optimization literatures. The research findings stemming from the vine copula modelling of dependence indicate that the each of the portfolios modelled has dependence risk features consistent with specific market conditions. Out of the seven portfolios modelled the gold mining and retail benchmark portfolios are found to have the lowest dependence risk in times of financial turbulence. The iron ore-nickel mining and oil-gas energy portfolios have the highest dependence risk in similar market conditions. Out of the energy portfolios the coal-uranium is significantly less dependence risky, relative to the oil-gas. Out of the mining portfolios the iron ore-nickel is the most dependence risky, while the gold portfolio has the lowest dependence risk. The retail benchmark portfolio is significantly less dependence risky than the manufacturing benchmark portfolio in both, tranquil periods and non-tranquil periods. In terms of investment risk, the oil-gas energy portfolio is the most risky. The “copula counting technique” is acknowledged for simplifying the analysis and interpretation of the portfolios’ dependence structure and their sectors’ dependence risk dynamics. The average model convergence provides an alternative avenue to identify stocks with large weight allocations and high return relative to risk. The research findings and empirical results are interesting in terms of theory and practical financial applications. Portfolio managers, risk managers, hedging practitioners, financial market analysts, systemic risk and capital requirement agents, who follow the trends of the Australian mining, energy, retail and manufacturing sectors, may find the obtained results useful to design investment risk and dependence risk-adjusted optimization algorithms, risk management frameworks and dynamic hedging strategies that best account for the downside risk the mining and energy sectors face during crisis periods to the pair vine copula and multiple risk measure-based portfolio optimization literatures. The research findings stemming from the vine copula modelling of dependence indicate that the each of the portfolios modelled has dependence risk features consistent with specific market conditions. Out of the seven portfolios modelled the gold mining and retail benchmark portfolios are found to have the lowest dependence risk in times of financial turbulence. The iron ore-nickel mining and oil-gas energy portfolios have the highest dependence risk in similar market conditions. Out of the energy portfolios the coal-uranium is significantly less dependence risky, relative to the oil-gas. Out of the mining portfolios the iron ore-nickel is the most dependence risky, while the gold portfolio has the lowest dependence risk. The retail benchmark portfolio is significantly less dependence risky than the manufacturing benchmark portfolio in both, tranquil periods and non-tranquil periods. In terms of investment risk, the oil-gas energy portfolio is the most risky. The “copula counting technique” is acknowledged for simplifying the analysis and interpretation of the portfolios’ dependence structure and their sectors’ dependence risk dynamics. The average model convergence provides an alternative avenue to identify stocks with large weight allocations and high return relative to risk. The research findings and empirical results are interesting in terms of theory and practical financial applications. Portfolio managers, risk managers, hedging practitioners, financial market analysts, systemic risk and capital requirement agents, who follow the trends of the Australian mining, energy, retail and manufacturing sectors, may find the obtained results useful to design investment risk and dependence risk-adjusted optimization algorithms, risk management frameworks and dynamic hedging strategies that best account for the downside risk the mining and energy sectors face during crisis periods

Functional Estimator Selection Techniques for Production Functions and Frontiers

This dissertation provides frameworks to select production function estimators in both the state-contingent and the general monotonic and concave cases. It first presents a Birth-Death Markov Chain Monte Carlo (BDMCMC) Bayesian algorithm to endogenously estimate the number of previously unobserved states of nature for a state-contingent frontier. Secondly, it contains a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm to determine a parsimonious piecewise linear description of a multiplicative monotonic and concave production frontier. The RJMCMC based algorithm is the first computationally efficient one-stage estimator of production frontiers with potentially heteroscedastic inefficiency distribution and environmental variables. Thirdly, it provides general framework, based on machine learning concepts, repeated learning-testing and parametric bootstrapping techniques, to select the best monotonic and concave functional estimator for a production function from a pool of functional estimators. This framework is the first to test potentially nonlinear production function estimators on actual datasets, rather than extrapolation of Monte Carlo simulation results

Optimal risk minimization of Australian energy and mining portfolios under multiple measures of risk

Australia’s 2000’s decade saw the sharpest rise in mining investments arising from developing Asian emerging economies’ high demand for commodities like coal, iron ore, nickel, oil and gas which drove up prices to a historic level (Connolly & Orsmond, 2011). As of December 2012, 39 % and 9 % of the Australian Securities Exchange’s stocks were of the mining (coal and uranium stocks are included in this category) and energy (e.g. oil, gas and renewable energy stocks) sectors respectively, and investors recently have been considering separate portfolio positions in energy and mining stocks (Jennings, 2010). Facts of these nature set the stage for the task of selecting an optimal portfolio of stock securities where the fundamental questions faced by every investor, individual or institutional, are: a) what is the optimal point in time to go long in the investment position?, b) what are the optimal amounts to invest in every asset of a portfolio? and, c) when is the optimal time to short the portfolio investment position? The focus of the present study is on b) within a one period ahead forecast scenario. Understanding the price and volatility movements of stock securities taking as a basis of study their own dynamics and co-dynamics is a complex task that may be better addressed through a multilateral modelling approach. This paper, in this regard, departs from a single model application by fitting multiple risk measures to the optimization of four portfolios each consisting of 20 ASX’s stocks from the gold, iron ore-nickel, uranium-coal and oil-gas sectors. The five risk measures compared are: the variance, mean absolute deviation (MAD), minimizing regret (Minimax), conditional value at risk (CVaR), and conditional drawdown at risk (CDaR), where the last two are threshold based measures. The risk measure parameters are input into meanvariance quadratic (QP) and differential evolution (DE) portfolio problem specifications. Accurate estimations of the underlying interaction of stocks return series is a crucial element in portfolio allocation and portfolio risk management and frequentist traditional measures of dependence are rather inadequate. Here, with the objective of achieving more accuracy in the estimation of the dependence matrix, a Gaussian pair c-vine copula (PC), the regular graphical lasso (RL) and adaptive graphical lasso (AL) are fitted. Possible advantages from using these recently proposed and sophisticated techniques under model specifications where the covariance matrix is the measure of risk are indicated. The main objectives of the present study are to calculate the optimal weights to be invested in every stock of the portfolios making use of linear and nonlinear model specifications and the risk measures suggested, analyse the weight allocation differences and seek portfolio optimization advantages from using pair vine copulas and the graphical lasso in the estimation of dependence. The present multimodal approach is, therefore, expected to be more robust and as a consequence, provide more complete information that could serve for improved decision making on portfolio selection, allocation and rebalancing. Research questions are answered based on the analysis of gold portfolio outcome values, only. Findings indicate that CDaR is an important risk measure to be considered, along with other measures of risk when optimizing portfolios of stocks and no single measure of risk is suggested alone. The Gaussian pair cvine copula through the use of one different parameter in the modelling of every pair of variables’ joint distribution appears to be more sensitive in capturing data’s distribution characteristics. The adaptive graphical lasso also appears to be more perceptive when grasping the signal of the underlying interaction of the stocks. Therefore, valuable information could be drawn and inferred from applying multiple risk measures and sophisticated statistical techniques for their estimation. The weight allocation from threshold risk measures such as CVar and DaR and Minimax clearly differs from the rest. The models identified stocks with high return relative to risk and vice versa. The originality of the present study lies on the sectors of application and its multi-model nature

Dependence estimation and controlled CVaR portfolio optimization of a highly kurtotic Australian mining sample of stocks

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

Functional Estimator Selection Techniques for Production Functions and Frontiers

This dissertation provides frameworks to select production function estimators in both the state-contingent and the general monotonic and concave cases. It first presents a Birth-Death Markov Chain Monte Carlo (BDMCMC) Bayesian algorithm to endogenously estimate the number of previously unobserved states of nature for a state-contingent frontier. Secondly, it contains a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm to determine a parsimonious piecewise linear description of a multiplicative monotonic and concave production frontier. The RJMCMC based algorithm is the first computationally efficient one-stage estimator of production frontiers with potentially heteroscedastic inefficiency distribution and environmental variables. Thirdly, it provides general framework, based on machine learning concepts, repeated learning-testing and parametric bootstrapping techniques, to select the best monotonic and concave functional estimator for a production function from a pool of functional estimators. This framework is the first to test potentially nonlinear production function estimators on actual datasets, rather than extrapolation of Monte Carlo simulation results

Quantitative Analysis of the Voltage-dependent Gating of Mouse Parotid ClC-2 Chloride Channel

Various ClC-type voltage-gated chloride channel isoforms display a double barrel topology, and their gating mechanisms are thought to be similar. However, we demonstrate in this work that the nearly ubiquitous ClC-2 shows significant differences in gating when compared with ClC-0 and ClC-1. To delineate the gating of ClC-2 in quantitative terms, we have determined the voltage (Vm) and time dependence of the protopore (Pf) and common (Ps) gates that control the opening and closing of the double barrel. mClC-2 was cloned from mouse salivary glands, expressed in HEK 293 cells, and the resulting chloride currents (ICl) were measured using whole cell patch clamp. WT channels had ICl that showed inward rectification and biexponential time course. Time constants of fast and slow components were ∼10-fold different at negative Vm and corresponded to Pf and Ps, respectively. Pf and Ps were ∼1 at −200 mV, while at Vm ≥ 0 mV, Pf ∼ 0 and Ps ∼ 0.6. Hence, Pf dominated open kinetics at moderately negative Vm, while at very negative Vm both gates contributed to gating. At Vm ≥ 0 mV, mClC-2 closes by shutting off Pf. Three- and two-state models described the open-to-closed transitions of Pf and Ps, respectively. To test these models, we mutated conserved residues that had been previously shown to eliminate or alter Pf or Ps in other ClC channels. Based on the time and Vm dependence of the two gates in WT and mutant channels, we constructed a model to explain the gating of mClC-2. In this model the E213 residue contributes to Pf, the dominant regulator of gating, while the C258 residue alters the Vm dependence of Pf, probably by interacting with residue E213. These data provide a new perspective on ClC-2 gating, suggesting that the protopore gate contributes to both fast and slow gating and that gating relies strongly on the E213 residue

Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios

We propose a model for optimizing structured portfolios with liquidity-adjusted Value-at-Risk (LVaR) constraints, whereby linear correlations between assets are replaced by the multivariate nonlinear dependence structure based on Dynamic Conditional Correlation t-copula modeling. Our portfolio optimization algorithm minimizes the LVaR function under adverse market circumstances and multiple operational and financial constraints. When we consider a diversified portfolio of international stock and commodity market indices under multiple realistic portfolio optimization scenarios, the obtained results consistently show the superiority of our approach relative to other competing portfolio strategies including the minimum-variance, risk-parity and equally weighted portfolio allocations

Estado de México y democracia en los albores del siglo XXI

De acuerdo con su título, este libro, compuesto por seis capítulos y dos anexos, reúne textos relativos a la democracia y al Estado de México, una de las principales entidades federativas de la República Mexicana. La importancia del Estado de México en el contexto nacional es indiscutible: de las 32 entidades que integran el país, es la que tiene más habitantes y electores (el segundo y el tercer lugares en ambos sentidos son ocupados, respectivamente, por el Distrito Federal y Veracruz), en tanto que está en el segundo lugar por el tamaño de su economía (en el primero se ubica el Distrito Federal y en el tercero, Nuevo León)

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

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