Analytic Methods in Finance with Applications to Portfolio and Risk Management

Khanthaporn, Rewat
Wichitaksorn, Nuttanan
Cao, Jiling
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Doctor of Philosophy
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Auckland University of Technology

The thesis studies and develops an investment portfolio strategy using a regular-vine-based forecasting model in period of the recent COVID-19 crisis. The model parameter estimation technique uses families of Bayesian inference and variational Bayes inference. The optimisation model uses family of machine learning algorithms. Overall, the thesis comprises three papers in which the ultimate outcome in paper three is the solution of dynamic portfolio allocation. Prior to that, the first two papers develop the multivariate asset returns forecasting models using the inference function of margins method and then apply it to the third paper in a portfolio optimisation model. The full details of each paper are provided in their abstracts: Chapter 3 for paper one, Chapter 4 for paper two and Chapter 5 for paper three. A brief outline of the three papers can be stated as follows.

The first paper studies a univariate forecasting model using the hybrid of asymmetric generalised autoregressive conditional heteroskedasticity and intertemporal capital asset pricing, with the following innovations: (1) a mixture of two generalised Pareto distributions and a Gaussian distribution; and (2) generalised error distribution. The Griddy Gibbs sampling algorithm in the Bayesian Markov chain Monte Carlo with parallel computing is used for the model parameter estimation. The study demonstrates the proposed model and estimation method through both simulation and empirical experiments among the benchmarks. It proves that the proposed model statistically outperforms competing models in the return forecasting under the conditions of market turmoil during the COVID-19 period.

The second paper extends the first paper from the univariate forecasting model to a multivariate forecasting model using high dimensional data and up to 100 dimensions where the comovement model is a regular vine model. The paper initiates a magnitude 13 bivariate copula candidate for the pair structure well-known in the literature of quantitative risk management. While the estimation techniques for the current paper explore another Bayesian Markov chain Monte Carlo, which is random-walk Metropolis-Hasting sampling, and, in Bayesian machine learning, variational Bayes with (and without) latent variables and data augmentation. Both simulation results and empirical results show satisfactory outcomes, since the proposed model and its estimation can outperform the traditional model.

The third paper extends multivariate regular vine forecasting model to the problem of dynamic optimal asset allocation in variate optimisation models. The study introduces evolutionary optimisation algorithms, including a genetic algorithm and a clonal selection algorithm, to optimisation problems. There are two main scenarios in optimisation problems which correspond to three model performance indicators: (1) the reward-risk indicator, (2) the diversity indicator, and (3) the convergence indicator. In addition, stock selection analysis is also applied to the optimisation problem. The empirical studies show that the proposed vine-copula-based forecasting model performs well in optimisation problems in terms of performance measures. Furthermore, based on the scenario experiment, the paper mathematically reveals that the financial market dependence structure has been disrupted as if a new normal has been established since the impact of the COVID-19 pandemic.

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