Fractional dynamics in financial indexes

The goal of this study is the analysis of the dynamical properties of financial data series from 32 worldwide stock market indices during the period 2000–2009 at a daily time horizon. Stock market indices are examples of complex interacting systems for which a huge amount of data exists. The methods and algorithms that have been explored for the description of physical phenomena become an effective background in the analysis of economical data. In this perspective are applied the classical concepts of signal analysis, Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional dynamical systems.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Persistence characteristics in financial prices: evidence from the portuguese stock market returns

The objective of this article is to provide additional knowledge to the discussion of long-term memory, leaning over the behavior of the main Portuguese stock index. The first four moments are calculated using time windows of increasing size and sliding time windows of fixed size equal to 50 days and suggest that daily returns are non-ergodic and non-stationary. Seeming that the series is best described by a fractional Brownian motion approach, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA). The findings indicate evidence of long term memory in the form of persistence. This evidence of fractal structure suggests that the market is subject to greater predictability and contradicts the efficient market hypothesis in its weak form. This raises issues regarding theoretical modeling of asset pricing. In addition, we carried out a more localized (in time) study to identify the evolution of the degree of long-term dependency over time using windows 200-days and 400-days. The results show a switching feature in the index, from persistent to anti-persistent, quite evident from 2010.

Long-term dependence in financial prices: evidence from the Belgian stock market returns

This article aims to contribute to the discussion of long-term dependence, focusing on the behavior of the main Belgian stock index. Non-parametric analyzes of the general characteristics of temporal frequency show that daily returns are non-ergodic and non-stationary. Therefore, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA), under the fractional Brownian motion approach, and we found slight evidence of long-term dependence. These results refute the random walk hypothesis with i.i.d. increments, which is the basis of the EMH in its weak form, and call into question some theoretical modeling of asset pricing. Other more localized complementary study, to identify the evolution of the degree of dependence over time windows, showed that the index has become less persistent from 2010. This may mean a maturing market by the extension of the effects of current financial crisis.

The impact of the 2008 and 2010 financial crises on international stock markets : contagion and long memory

Nesta tese estudamos os efeitos de contágio financeiro e de memória longa causados pelas crises financeiras de 2008 e 2010 em alguns mercados acionistas internacionais. A tese é composta por três ensaios interligados. No Ensaio 1, recorremos à teoria das cópulas para testar a existência de contágio e revelar os canais “investor induced” de transmissão da crise de 2008 aos mercados da Bélgica, França, Holanda e Portugal (grupo NYSE Euronext). Concluímos que existe contágio nestes mercados, que o canal “portfolio rebalancing” é o mecanismo mais importante de transmissão da crise, e que o fenómeno “flight to quality” está presente nos mercados. No Ensaio 2, usando novamente modelos de cópulas, avaliamos os efeitos de contágio provocados pelo mercado acionista grego nos mercados do grupo NYSE Euronext, no contexto da crise de 2010. Os resultados obtidos sugerem que durante a crise de 2010 apenas o mercado português foi objeto de contágio; além disso, conclui-se que os efeitos de contágio provocados pela crise de 2008 são claramente superiores aos efeitos provocados pela crise de 2010. No Ensaio 3, abordamos o tema da memória longa através do estudo do expoente de Hurst dos mercados acionistas da Bélgica, E.U.A., França, Grécia, Holanda, Japão, Reino Unido e Portugal. Verificamos que as propriedades de memória longa dos mercados foram afetadas pelas crises, especialmente a de 2008 – que aumentou a memória longa dos mercados e tornou-os mais persistentes. Finalmente, usando cópulas mais uma vez, verificamos que as crises provocaram, em geral, um aumento na correlação entre os expoentes de Hurst locais dos mercados foco das crises (E.U.A. e Grécia) e os expoentes de Hurst locais dos outros mercados da amostra, sugerindo que o expoente de Hurst pode ser utilizado para detetar efeitos de contágio financeiro. Em síntese, os resultados desta tese sugerem que comparativamente com períodos de acalmia, os períodos de crises financeiras tendem a provocar ineficiência nos mercados acionistas e a conduzi-los na direção da persistência e do contágio financeiro.

Long-term memory in financial prices: evidence from the Dutch stock market returns

Prepared for presentation at the Portuguese Finance Network International Conference 2014, Vilamoura, Portugal, June 18-20

Spanish society's perceptions about socially responsible investing

The debate surrounding the financial needs of investors and the impact on society of investment is considered to be an important research topic due to the growth of socially responsible financial markets. The objective of this research is to study the perception of the Spanish public about socially responsible investing (SRI) criteria and real-life investment needs. To examine the Spanish perception of SRI, we conducted a field survey. The results show that SRI is in an early stage and Spanish investors need more exact information regarding social, environmental, and governance criteria in order to invest in socially responsible companies and products.

Long-run consumption risk with durable goods : UK evidence for equity and bond markets

"It is a widely accepted fact that the consumption-based capital asset pricing model (CCAPM) fails to provide a good explanation of many important features of the behaviour of financial market returns in a large range of countries over a long period of time. However, within a representative consumer/investor model, it is hard to see how the basic structure of the consumption based model can be safely abandoned." [introdução]

100 Años de desarrollo de la teoría financiera : situación actual y previsible evolución tras la crisis : resumen de la ponencia

"Las Finanzas, como disciplina académica, nacen a caballo entre los siglos XIX y XX. Sin duda el importante desarrollo industrial de la época y la necesidad de empresas de mayores dimensiones llevaron a un creciente interés por las concentraciones empresariales como fusiones y adquisiciones. También aumentó el interés por los mercados donde se financiaban estas empresas cada vez mayores. Y esto, aunque sucedía en diversas partes del mundo, estaba ocurriendo de forma especial en Estados Unidos, de manera que allí fue donde nacieron las finanzas, y donde se han seguido desarrollando. De esta manera, desde un comienzo, las finanzas tienen un claro sello anglosajón." [introdução]

Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

A fractional perspective to financial indices

The application of mathematical methods and computer algorithms in the analysis of economic and financial data series aims to give empirical descriptions of the hidden relations between many complex or unknown variables and systems. This strategy overcomes the requirement for building models based on a set of ‘fundamental laws’, which is the paradigm for studying phenomena usual in physics and engineering. In spite of this shortcut, the fact is that financial series demonstrate to be hard to tackle, involving complex memory effects and a apparently chaotic behaviour. Several measures for describing these objects were adopted by market agents, but, due to their simplicity, they are not capable to cope with the diversity and complexity embedded in the data. Therefore, it is important to propose new measures that, on one hand, are highly interpretable by standard personal but, on the other hand, are capable of capturing a significant part of the dynamical effects.

Changing representations and practices in school mathematics: the case of Modern Math in Portugal

The curricular movement known as Modern Mathematics aimed at the transformation of representations and practices in school mathematics. Its study provides us with ways of understanding how these changes came about. The purpose of this paper is to contribute to the understanding of the ways in which representations of school mathematics gradually were influenced by ideas from the Modern Mathematics movement, how these new ideas merged into local educational traditions, and how they were transformed into meaningful practice. This work is centred on the Portuguese context from the middle 1950s to the middle 1960s, and builds on Chervel’s notion of school culture and Gruzinski’s discussion of connected histories.

Multi-Objective and Financial Portfolio Optimization of Carrier-Sense Multiple Access Protocols with Cooperative Diversity

8th International Workshop on Multiple Access Communications (MACOM2015), Helsinki, Finland.

Ensino direto da matemática funcional: estudo de caso

Neste estudo, focado na aprendizagem do manuseio do dinheiro, pretendeu-se que os alunos adquirissem competências que os habilitasse a um maior grau de independência e participação na vida em sociedade, desempenhando tarefas de cariz financeiro de forma mais independente, por exemplo, compra de produtos, pagamento de serviços e gestão do dinheiro. Para alcançar o pretendido, utilizou-se a metodologia do ensino direto, com tarefas estruturadas. Numa fase inicial o investigador prestava apoio constante aos alunos, que foi diminuindo gradualmente à medida que atingiam as competências relacionadas com o dinheiro. Na fase final, os alunos realizaram as tarefas propostas de forma autónoma. Construído como um estudo de caso, os dados foram recolhidos através de observação direta e de provas de monitorização. Os alunos começaram por realizar uma avaliação inicial para delinear a linha de base da intervenção. Posteriormente, foi realizada a intervenção baseada no ensino direto, com recurso ao computador, à calculadora, a provas de monitorização e ao manuseio de dinheiro. O computador foi utilizado na intervenção como tecnologia de apoio à aprendizagem, permitindo a realização de jogos interativos e consulta de materiais. No final da intervenção os alunos revelaram autonomia na resolução das tarefas, pois já tinham automatizado os processos matemáticas para saber manusear corretamente a moeda euro. O ensino direto auxiliou os alunos a reterem as competências matemáticas essenciais de manuseamento do dinheiro, compondo quantias, efetuando pagamentos e conferindo trocos, que muito podem contribuir para terem uma participação independente na vida em sociedade

E-assessment in mathematics courses with multiple-choice questions tests

With the implementation of the Bologna Process several challenges have been posed to higher education institution, particularly in Portugal. One of the main implications is related to the change of the paradigm of a teacher centered education, to a paradigm that is student centered. This change implies the change of the way to assess courses in higher education institutions. Continuous and formative assessments emerged as the focus, catalyzed by electronic assessment, or e-assessment. This paper presents a case of the implementation of an e-assessment strategy, implemented in order to allow continuous, formative assessment in numerous mathematics classes using multiple-choice questions tests implement in Moodle open-source learning management system. The implementation can be considered a success.