This thesis challenges several concepts in finance. Firstly, it is the Markowitz's solution to the portfolio problem. It introduces a new method which de- noises the covariance matrix - the cornerstone of the portfolio management. Random Matrix Theory originates in particle physics and was recently intro- duced to finance as the intersection between economics and natural sciences has widened over the past couple of years. Often discussed Efficient Market Hypothesis is opposed by adopting the assumption, that financial returns are driven by Paretian distributions, in- stead of Gaussian ones, as conjured by Mandelbrot some 50 years ago. The portfolio selection is set in a framework, where Expected Shortfall replaces the standard deviation as the risk measure. Therefore, direct optimi- sation of the portfolio is implemented to be compared with the performance of the classical solution and its denoised counterpart. The results are evalu- ated in a controlled environment of Monte Carlo simulation as well as using empirical data from S&P 500 constituents. 1

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-04-18T12:06:58Z No. of bitstreams: 2 Dissertação - Alice Francener Nogueira Gonzaga - 2013.pdf: 1868045 bytes, checksum: 95be1e5827e994d97205b7e53c0c6bf6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-04-18T12:11:52Z (GMT) No. of bitstreams: 2 Dissertação - Alice Francener Nogueira Gonzaga - 2013.pdf: 1868045 bytes, checksum: 95be1e5827e994d97205b7e53c0c6bf6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-04-18T12:11:53Z (GMT). No. of bitstreams: 2 Dissertação - Alice Francener Nogueira Gonzaga - 2013.pdf: 1868045 bytes, checksum: 95be1e5827e994d97205b7e53c0c6bf6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-03-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Estimates of life on earth vary by tens of thousands and it has been claimed that there are yet a lot of species to be discovered .Taxonomy seeks to reduce this shortfall, by discovering and describing new species, but its an imperfect process that contains many types of errors. The historical pace of how the Linnean shortfall is being overcome has been temporally uneven rather than gradual. It depends on a number of factors, mainly the ones related to “who does it” (taxonomists), “how is it done” (methodologies), and “where is it done” (regions). Here we aim to point out these factors and their influences on how we have been overcoming (in time) the Linnean shortfall for bats (Chiroptera), the pace by which we do it and that of the errors that come together with it. To verify the effort in the rates of description we calculated the number of active taxonomists and the number of species described by taxonomists. To explore the completeness of bat taxonomy, we generated cumulative curves of species described per year, for both valid species and synonyms. To predict the number of species, and to see how our predictions are accurate in time and the differences between them, we adjusted the Clench function to the cumulative curve of species by regions in different periods of time. A total of 1220 species of bats are currently accepted, and of total species described 27.2% have been synonymized by now. The number of active taxonomists has been increasing exponentially through time but the number of species described per taxonomist has decreased. In the last decade, 37% of species have been described using molecular tools. The 5 total cumulative curve and most of biogeographic regions had not reached an asymptote yet and, in general, we could not make meaningful estimates of species richness. Overcoming the Linnean shortfall for bats has neither been steady in time nor has reaches an asymptote yet, evidencing that there are more species to be known. We should continue doing predictions but knowing that the factors and errors pointed here could influence the estimates. / (Sem resumo)

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-10-03T17:41:06Z No. of bitstreams: 2 Tese - Karina Dias da Silva - 2015.pdf: 4031707 bytes, checksum: a512239d28a3b06722486f8e1df40e84 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-10-04T10:45:16Z (GMT) No. of bitstreams: 2 Tese - Karina Dias da Silva - 2015.pdf: 4031707 bytes, checksum: a512239d28a3b06722486f8e1df40e84 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-10-04T10:45:16Z (GMT). No. of bitstreams: 2 Tese - Karina Dias da Silva - 2015.pdf: 4031707 bytes, checksum: a512239d28a3b06722486f8e1df40e84 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2015-02-27 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / There are large gaps in knowledge about the identity of species 21 (Linnean shortfall) and their spatial distribution (Wallacean shortfall). These gaps are 22 especially of particular concern in least developed countries in tropical regions which 23 harbor great species diversity but still lack of investments in conservation. In addition, 24 these regions are important areas for agricultural production, making the ignorance even 25 more worrying for conservation. Our objective was to analyze the temporal dynamics of 26 scientific literature on aquatic and semiaquatic Heteroptera, adressing questions related 27 to gaps of knowledge in this taxonomic group in Brazil and South America. Researches 28 focused on Heteroptera have been advancing in the last years, but much remains to 29 bedone. Especially for countries like Brazil, which lacks of satisfactory knowledge 30 about its fauna and its spatial/environmental relationships, especially in difficult access 31 areas and also in areas that have little or no one qualified researcher. / Existem grandes lacunas de conhecimento acerca de quais são as 3 espécies, (Déficit Linneano), e de suas distribuições espaciais (Déficit Wallaceano). 4 Essas lacunas são especialmente preocupantes nos países menos desenvolvidos onde o 5 investimento em conservação é reduzido, principalmente quando inseridos em regiões 6 tropicais, que tem grande diversidade de espécies. Paralelamente a falta de 7 conhecimento e importância ambiental dos países em desenvolvimento, essas regiões 8 são importantes áreas para a produção agropecuária, tornando o desconhecimento ainda 9 mais preocupante para a conservação. Assim, nosso objetivo foi analisar a dinâmica 10 temporal da produção científica sobre Heteroptera aquático e semi-aquático 11 respondendo questões relacionadas aos déficitis de conhecimento, no Brasil e na 12 América do sul. Houve um avanço nas pesquisas com Heteroptera, mas sabemos que 13 muito ainda tem de ser feito. Em especial para países como o Brasil, com grande 14 diversidade de hábitats e biológica. Ainda não conhecemos satisfatoriamente sua fauna 15 e suas relações espaciais/ambientais, e isso é mais preocupante em regiões de difícil 16 acesso geográfico e que tenham número reduzido ou inexistente de pesquisadores 17 qualificados.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-03-21T11:50:30Z No. of bitstreams: 2 Dissertação - Zander Augusto Spigoloni Vilaça - 2017.pdf: 4936242 bytes, checksum: 3e7d05bb80d2c70f737753125ee7f0c3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-03-21T12:18:52Z (GMT) No. of bitstreams: 2 Dissertação - Zander Augusto Spigoloni Vilaça - 2017.pdf: 4936242 bytes, checksum: 3e7d05bb80d2c70f737753125ee7f0c3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-03-21T12:18:52Z (GMT). No. of bitstreams: 2 Dissertação - Zander Augusto Spigoloni Vilaça - 2017.pdf: 4936242 bytes, checksum: 3e7d05bb80d2c70f737753125ee7f0c3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The distribution of biological diversity is one of the major questions for science. Several theories were proposed in attempt to understand the patterns and process that regulate the richness of extant species: species-energy theory, metabolic theory of ecology, habitat heterogeneity, and tropics as museum, cradle or casino. Terrestrial ecorregions are land units that contain similar biotic and abiotic factors, what makes them more alluring and efficient for conservation planning and land use than using geopolitical divisions, still used by several conservation institutions and governments. Odonata is one of the oldest orders of insect, belonging to the clade Paleoptera. Those insects, for being thightly related to environmental conditions and vegetation structure, are widely utilized as bioindicators and in studies of spatial patterns. In this thesis, we evaluated the lack of knowledge around Odonata geographic distribution in the Neotropical region and the way that its species composition is affected by both climate and space. / A variedade e distribuição da biodiversidade é um dos temas mais estudados na ciência. Na tentativa de compreender os padrões e processos moduladores da riqueza de espécies existente, várias teorias foram geradas: teoria espécie-energia; teoria metabólica ecológica; heterogeneidade de habitat; e trópicos como museu, berço ou cassino. Ecorregiões terrestres são unidades de terra unidas por componentes bióticos e abióticos semelhantes, tornando-as unidades mais operacionais que definições geopolíticas, utilizadas por várias instituições de conservação e governamentais para se criar planejamentos de conservação da biodiversidade e de uso de terras. Odonata é uma das ordens de insetos mais antiga ainda existente, pertencentes ao clado dos Paleoptera. Estes insetos, possuindo ótima relação com as variáveis ambientais e estrutura vegetacional, são largamente utilizados em avaliações de bioindicação e estudos de padrões espaciais. Nesta dissertação avaliamos o estado do déficit de conhecimento sobre as distribuições geográficas da Ordem Odonata no Neotrópico e como o clima e espaço afetam sua composição de espécies.

This paper analyses the impact of banking mergers on systemic risk, with in particular if internationalization prior to acquisition increases systemic risk. By using the marginal expected shortfall methodology for an international sample of mergers, a significant increase in systemic risk is found as a result of mergers in the financial sector. Moreover, if a bank is operating internationally prior to acquisition, this increases systemic risk. Additionally, there is evidence of a too-big-to-fail motive for relatively smaller banks to use mergers to become systemically important. The results confirm that consolidation in the financial sector increases fragility of the financial system.

The 2008/9 financial crisis intensified the search for realistic return models, that capture real market movements. The assumed underlying statistical distribution of financial returns plays a crucial role in the evaluation of risk measures, and pricing of financial instruments. In this dissertation, we discuss an empirical study on the evaluation of the traditional portfolio risk measures, and option pricing under the hybrid Brownian motion model, developed by Shaw and Schofield. Under this model, we derive probability density functions that have a fat-tailed property, such that “25-sigma” or worse events are more probable. We then estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using four equity stocks listed on the Johannesburg Stock Exchange, including the FTSE/JSE Top 40 index. We apply the historical method and Variance-Covariance method (VC) in the valuation of VaR. Under the VC method, we adopt the GARCH(1,1) model to deal with the volatility clustering phenomenon. We backtest the VaR results and discuss our findings for each probability density function. Furthermore, we apply the hybrid model to price European style options. We compare the pricing performance of the hybrid model to the classical Black-Scholes model. / Dissertation (MSc)--University of Pretoria, 2017. / National Research Fund (NRF), University of Pretoria Postgraduate bursary and the General Studentship bursary / Mathematics and Applied Mathematics / MSc / Unrestricted

In recent years, the question of whether Expected Shortfall is possible to backtest has been a hot topic after the findings of Gneiting in 2011 that Expected Shortfall lacks a mathematical property called elicitability. However, new research has indicated that backtesting of Expected Shortfall is in fact possible and that it does not have to be very difficult. The purpose of this thesis is to show that Expected Shortfall is in fact backtestable by providing six different examples of how a backtest could be designed without exploiting the property of elicitability. The different approaches are tested and their performances are compared against each other. The material can be seen as guidance on how to think in the initial steps of the implementation of an Expected Shortfall backtest in practice. / De senaste åren har frågan om huruvida det är möjligt att hitta backtester som validerar Expected Shortfall varit ett omdiskuterat ämne efter att Gneiting 2011 visade att Expected Shortfall saknade den matematiska egenskapen som kallas elicitabilitet. Ny forskning tyder på att det går att validera Expected Shortfall och att det inte behöver vara alltför svårt. Syftet med den här uppsatsen är att visa att det går att hitta metoder som backtestar Expected Shortfall. Vi gör det genom att visa utförandet av sex olika metoder som validerar Expected Shortfall utan att använda sig av elicitabilitet. De olika metoderna testas och deras egenskaper jämförs mot varandra. Materialet kan ses som en guide i hur man ska tänka i de första stegen i implementeringen av en metod för att backtesta Expected Shortfall.

Value-at-Risk (VaR) has long been the standard risk measure in financial risk management. However, VaR suffers from critical shortcomings as a risk measure when it comes to quantifying the most severe risks, which was made especially apparent during the financial crisis of 2007–2008. An alternative risk measure addressing the shortcomings of VaR known as expected shortfall (ES) is gaining popularity and is set to replace VaR as the standard measure of financial risk. This thesis introduces how extreme value theory can be applied in estimating ES using an unconditional peaks-over-threshold method. This includes giving an introduction to the theoretical foundations of the method. An application of this method is also performed on five different assets. These assets are chosen to serve as a proxy for the more broad asset classes of equity, fixed income, currencies, commodities and cryptocurrencies. In terms of ES, we find that cryptocurrencies is the riskiest asset and fixed income the safest.

In this work, we look into the practical applicability of three joint quantile and expected shortfall regression backtests. The strict, auxiliary, and intercept ESR backtests are applied to the historical log returns of the OMX Stockholm 30 market-weight price index. We estimate the conditional variance using GARCH models for various rolling window lengths and refitting frequencies. We are particularly interested in the rejection rates of the one-sided intercept ESR backtest as it is comparable to the current standard of backtests. The one-sided test is found to perform well when the conditional variance is estimated by either the GARCH(1,1), GJR-GARCH(1,1), or EGARCH(1,1) coupled with student’s t-innovation residuals and a rolling window size of 1000 days.

Within Central Counterparty Clearing, the Clearing House collects Initial Margin from its Clearing Members. The Initial Margin can be calculated in many ways, one of which is by applying the commonly used risk measure Value-at-Risk. However, Value-at-Risk has one major flaw, namely its inability to encapsulate Tail Risk. Due to this, there has for long been a desire to replace Value-at-Risk with Expected Shortfall, another risk measure that has shown to be much better suited to encapsulate Tail Risk. That said, Value-at-Risk is still used over Expected Shortfall, something which is mainly due to the fact that there is no consensus regarding how one should backtest Expected Shortfall. The goal of this thesis is to evaluate some of the most commonly proposed methods for backtesting Expected Shortfall. In doing this, several non-parametric backtests of Expected Shortfall are investigated using simulated data as well as market data from different types of securities. Moreover, this thesis aims to shed some light on the differences between Value-at-Risk and Expected Shortfall, highlighting why a change of risk measure is not as straightforward as one might believe. From the investigations of the thesis, several backtests are found to be sufficient for backtesting the Initial Margin with Expected Shortfall as the risk measure, the so called Minimally Biased Relative backtest showing the overall best performance of the looked at backtests. Further, the thesis visualizes how Value-at-Risk and Expected Shortfall are two risk measures that are inherently different in a real-world setting, emphasizing how one should be careful making conversions between the two based upon parametric assumptions.