This study mainly explores the declaration effect of Capital Reduction on stock price. The samples will be those listed companies which have declared the activity of Capital Reduction, and the sample period is from March 1, 2005 to August 31, 2007. We use multiple factors model (market return, stock volume variance, the net buy-and-sell ratio of foreign investment) with ADF, Ljung-Box Q and Ljung-Box Q2 to build our model, and then apply the method of event study to explain the declaration effect of Capital Reduction. As a result, this study exhibits Capital Reduction can not offer abnormal returns during the period of three days before the declaration and three days after.

nÃo hà / O presente artigo busca uma mÃtrica refinada e confiÃvel para mensurar riscos financeiros. RiskMetrics (1994) marcou o inÃcio dessa busca e desde entÃo vÃrios pesquisadores contribuÃram com inovaÃÃes e novos modelos para essa medida e aqui se apresenta mais um passo desse caminho, ao se agregar uma modelagem multivariada. Com essa modelagem à possÃvel capturar o efeito contÃgio e a interdependÃncia financeira global. O grupo de 10 paÃses presente no estudo representa 49,9% do PIB mundial e possuem representantes de 5 continentes. O modelo de volatilidade segue sugestÃo apresentada por Cappielo, Engle e Sheppard (2006) e modelos de Value-at-Risk (VaR) seguem Matos, Cruz, Macedo e Jucà (CAEN-UFC Workingpaper). AtravÃs desse procedimento à possÃvel calcular VaR levando em consideraÃÃo o efeito contÃgio e a interdependÃncia entre os mercados ao longo do tempo. Os resultados encontrados sÃo robustos contra problemas de variÃveis omitidas, heterocedasticidade e endogeneidade, alÃm de considerar quebras estruturais. De acordo com os resultados encontrados, a interdependÃncia apresenta um papel importante dentro do processo de mensuraÃÃo de risco de mercado, apesar de atà agora ter sido esquecida pelos pesquisadores. Isso se deve, principalmente, porque a integraÃÃo financeira a nÃvel global leva ao cenÃrio de dependÃncia crescente entre os mercados financeiros e, dessa forma, aumentando o contÃgio de um impacto que ocorre em um mercado nos outros. Convidamos outros pesquisadores a rever nossa metodologia, utilizando inclusive mais informaÃÃes e incluindo outros paÃses. Acredita-se que o mundo està ano a ano se tornando mais globalizado e suas economias por consequÃncia. Nesse artigo esse efeito està sendo considerado dentro da mensuraÃÃo do risco de mercado. Incorporar esse efeito leva a modelagem, legal e interna, mais acurada, que ajuda supervisores de mercado a garantirem estabilidade de longo prazo para os mercados e possuÃrem mÃtricas mais confiÃveis dentro das instituiÃÃes sob sua tutela. AlÃm disso, à de grande valia para Ãreas de GestÃo de Risco de bancos e instituiÃÃes financeiras ao ajuda-las a compreender melhor seu perfil de risco, melhorar a comunicaÃÃo com investidores institucionais internacionais e ranquear de maneira mais eficiente seus investimentos e aplicaÃÃes. Estudos anteriores possuem um aspecto comum: Apenas levam em consideraÃÃo mudanÃas de volatilidade nos mercados domÃsticos, nÃo levando em consideraÃÃo os efeitos que outros paÃses possuem neles. No presente estudo, esse efeito se provou como importante e representativo, os modelos univariados domÃsticos falharam mais e com mais severidade que os modelos multivariados. Portanto, no presente artigo, buscou-se o desafio de dar o passo de nÃo mais modelar modelos univariados domÃsticos, mas modelos 4 multivariados globais. Acredita-se que esse avanÃo metodolÃgico ajudarà a melhor mensurar e entender o comportamento do risco de mercado atravÃs do mundo. / This paper enter into the search of a refined and trustable metric for measuring financial risk. RiskMetrics (1994) marked the start of this search and since them many researches contributed with innovations and new models for that measure, and here we find a stepforward into the search, by aggregating multivariate models, with this itâs possible to capture the effect of a worldwide contagion and financial interdependence. The group of 10 countries presents in this study represents 49,9% of world GDP and has representation across 5 continents. We follow the model of volatilities suggested in Cappielo, Engle e Sheppard (2006) and Value-at-Risk follows Matos, Cruz, Macedo e Jucà (CAEN-UFC Working paper), though this procedure itâs possible to accurate VaR model, and take in count the contagion and interdependence between markets, in long term. Our results are robust to problems with omitted variable, heteroskedasticity and endogeneity. We also take into account for structural break. According to our results, the interdependence plays an important role into financial risk measure process, although its until now usually forbidden by modelers, mostly because worldâs financial integration leads the global economies to the scenario of increasing dependence among them and contagion effect that spreads the impacts that occur into one market to the others. We invite researchers to revisit this issue in order obtain evidences using larger data and other countries as well. We claim that the world is year by year more globalized, and so are the other economies, here we add this into account for measuring financial risks. This leads to model, legal and internal, more accurate that help supervisors to guarantee the long term stability across the markets, have trustable measure of the financial institutions under their responsibility. Besides, helps the Risk Management area of banks and other financial institutions to better understand their risk profile, improve communication with institutional investors worldwide and rank effiently their investments and applications into the markets. Previous studies have a common aspect: they only consider the volatilities change across the domestic market, not tanking in consider the effect of the other countries into the domestic volatility, and this effect here is proven to be important and representative, the univariate domestic risk measure fails more and harder than the multivariate model. That being said, here we take this step, the challenge of modeling no more univariate, domestic risk measures, but a worldwide multivariate. This is a methodological innovation that helps better measure and understands the financial risks behavior across the world.

In order to evaluate and manage portfolio risk, we separated this project into three sections. In the first section we constructed a portfolio with 15 different stocks and six options with different strategies. The portfolio was implemented in Interactive Brokers and rebalanced weekly through five holding periods. In the second section we modeled the loss distribution of the whole portfolio with normal and student-t distributions, we computed the Value-at-Risk and expected shortfall in detail for the portfolio loss in each holding week, and then we evaluated differences between the normal and student-t distributions. In the third section we applied the ARMA(1,1)-GARCH(1,1) model to simulate our assets and compared the polynomial tails with Gaussian and t-distribution innovations.

This report is for MA575: Market and Credit Risk Models and Management, given by Professor Marcel Blais. In this project, three different methods for estimating Value at Risk (VaR) and Expected Shortfall (ES) are used, examined, and compared to gain insightful information about the strength and weakness of each method. In the first part of this project, a portfolio of underlying assets and vanilla options were formed in an Interactive Broker paper trading account. Value at Risk was calculated and updated weekly to measure the risk of the entire portfolio. In the second part of this project, Value at Risk was calculated using semi-parametric model. Then the weekly losses of the stock portfolio and the daily losses of the entire portfolio were both fitted into ARMA(1,1)-GARCH(1,1), and the estimated parameters were used to find their conditional value at risks (CVaR) and the conditional expected shortfalls (CES).

In order to evaluate and manage portfolio risk, we separated this project into three sections. In the first section we constructed a portfolio with 15 different stocks and six options with different strategies. The portfolio was implemented in Interactive Brokers and rebalanced weekly through five holding periods. In the second section we modeled the loss distribution of the whole portfolio with normal and student-t distributions, we computed the Value-at-Risk and expected shortfall in detail for the portfolio loss in each holding week, and then we evaluated differences between the normal and student-t distributions. In the third section we applied the ARMA(1,1)-GARCH(1,1) model to simulate our assets and compared the polynomial tails with Gaussian and t-distribution innovations.

Recently, there are more and more literatures discuss on the issues of investment strategies of leveraged ETFs. In our works, we concentrate our issues on optimal leverage of ETF of S&P 500 index. Based on ARMA-GARCH model¡¦s assumption, we find out that the forecasting optimal leverage can be shown in a formula which contains return and characteristic function. In this paper, we use MA(1)-GARCH(1,1) to forecast volatility based on 1008 rolling window to forecast one day ahead¡¦s volatility; and our estimation time is start from 1954 to March 2011. In this paper, we present four dynamic leverage models (Normal, Student T, VG, and Best model¡¦s leverage) to find out the payoffs under these models. In our model, the forecasting accuracy is just about 55% which is slightly higher than SPX raise probability. But during long-term compound effect, the dynamic leverage models can out-perform than constant leverage. There may exist some important factors in these results, one of them is the crash forecasting ability. During 1980 to 2011 SPX has 14 big crashes and these models can effectively avoid 10 big crashes. In short-term investment horizon none of these five models are always outperform than others but in long-term investment horizon the strategy of best model¡¦s leverage can always earn money when investment horizon is 2400 days.

The primary purpose of this thesis was to investigate if the modern Phillips Curve is valid for ASEAN five (Indonesia, Malaysia, Thailand, Singapore and Philippines) countries using a time-varying approach in the form of an ARMA-GARCH model. The method enables us to investigate how the inflation volatility reacts to economic shocks and if its history can predict the conditional variance of inflation. This study also aimed to investigate whether financial liberalisation affects the conditional variance of inflation. Moreover, we introduce a new parameter into the Phillips Curve. We propose the inclusion of a globally decomposed financial spillover index to see how it affects the inflation dynamics. Examining the period between 1996-2020, using monthly data. We find weak results, and the Phillips Curve was only valid for Singapore. Our findings also suggest that the inflation volatility is highly time-varying, indicating the suitability of the ARMA-GARCH framework. Significant coefficients in the model allow forecasting the conditional variance of inflation. The results support the idea that financial liberalisation to be volatility augmenting in some countries, suggesting a negative relationship between the degree of financial integration and received spillover effects. The globally decomposed spillover indices demonstrated weak results. For further investigations, we, therefore, propose the usage of regionally decomposed spillover indices.

The demand for sustainable investments has seen an increase in recent years. There is considerable literature covering backtesting of the performance and risk of socially responsible investments (SRI) compared to conventional investments. However, literature that models and examines the risk characteristics of SRI compared to conventional investments is limited. This thesis seeks to model and compare the risk of mutual funds scoring in the top 10% in terms of sustainability, based on Morningstar Portfolio Sustainability Score, to those scoring in the bottom 10%. We create one portfolio consisting of the top 10% funds and one portfolio consisting of the bottom 10%, for European and global mutual funds separately, thus in total creating 4 portfolios. The analysis is based on data of the funds' returns and Morningstar Portfolio Sustainability Scores during December 2015 to August 2019. Investigating several GARCH models, we find an ARMA-GARCH model with skewed Student's t-distribution as innovation distribution to give the best fit to the daily log-returns of each portfolio. Based on the fitted ARMA-GARCH models with skewed Student's t-distribution, we use a parametric bootstrap method to compute 95% confidence intervals for the difference in long-run volatility and value at risk (VaR) between the portfolios with high and low Morningstar Portfolio Sustainability Scores. This is performed on the portfolios of European and global funds separately. We conclude that, for global and European funds respectively, no significant difference in terms of long-run volatility and VaR is found between the funds in each of the 10% ends of the Morningstar Portfolio Sustainability Score. / Efterfrågan av hållbara investeringar har ökat kraftigt de senaste åren. Det finns många studier som genomför backtesting av hållbara investeringars avkastning och risk jämfört med konventionella investeringar. Färre studier har däremot gjorts för att modellera och jämföra investeringarnas riskegenskaper. Denna uppsats syftar till att modellera risken av hållbara investeringar genom att jämföra de 10% fonder med högst Morningstar Portfolio Sustainability Score mot de 10% fonder med lägst score. Jämförelsen görs separat för globala fonder och europeiska fonder, vilket resulterar i totalt 4 portföljer. Analysen baseras på data på fondernas avkasting och Morningstar Portfolio Sustainability Score under tidsperioden december 2015 till augusti 2019. Genom att undersöka flera olika GARCH-modeller, kommer vi fram till att en ARMA-GARCH-modell med skev t-fördelning bäst beskriver den dagliga logaritmerade avkastningen för varje portfölj. Baserat på de anpassade ARMA-GARCH-modellerna, används en "parametric bootstrap"-metod för att beräkna 95%-iga konfidensintervall för skillnaden i långsiktig volatilitet och value at risk (VaR) mellan portföljerna med högt och lågt Morningstar Portfolio Sustainability Score. Detta görs separat för de europeiska och globala fonderna. Vår slutsats är att det, för globala och europeiska fonder, inte råder en signifikant skillnad i långsiktig volatilitet eller VaR mellan fonder med högt och lågt Morningstar Portfolio Sustainability Score.

Submitted by Suethene Souza (suethene.souza@ufpe.br) on 2015-03-05T17:54:19Z No. of bitstreams: 2 DISSERTAÇÃO Carolina Magda da Silva Roma.pdf: 2200454 bytes, checksum: 5284fb965bb815a50d6895a8d2342228 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-05T17:54:19Z (GMT). No. of bitstreams: 2 DISSERTAÇÃO Carolina Magda da Silva Roma.pdf: 2200454 bytes, checksum: 5284fb965bb815a50d6895a8d2342228 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2013-01-29 / FACEPE / Com a presente pesquisa se propôs a apresentar uma nova maneira de mensurar o prêmio de risco e analisar qual a melhor distribuição de probabilidade contínua que modela os dados estudados para o período completo e segmentações. Mehra e Prescott (1985) analisaram o prêmio de risco histórico por quase um século e obtiveram um resultado não suportado pela teoria econômica financeira, o qual foi denominado Equity Premium Puzzle (EPP). O prêmio de risco é estudado por diversos pesquisadores ao redor do mundo, porém, ainda hoje, não há consenso sobre como mensurá-lo, sendo classicamente entendido como o retorno de um ativo mais arriscado sobre um ativo livre de risco. Ele é uma variável integrante no cálculo do Capital Asset Pricing Model, ou Modelo de Precificação de Ativos (CAPM), comumente utilizado em finanças. Assim, buscou-se uma nova maneira de obter o prêmio de risco a partir da equação diferencial estocástica do movimento browniano geométrico (MBG). Para tanto, o prêmio foi calculado pela razão entre a diferença no retorno do índice Ibovespa (IBOV), para duas ações com maior participação no respectivo índice, baseado na última carteira de 2012, a Vale do Rio Doce (VALE5) e a Petrobrás (PETR4) e também para a empresa com maior participação no índice de consumo, a AmBev (AMBV4) e o ativo livre de risco tendo, neste caso, sido escolhido o Certificado de Depósito Interfinanceiro (CDI), com volatilidade para janeiro de 1998 a julho de 2012. As distribuições do prêmio de risco utilizadas neste trabalho foram gaussiana, Gama, T de Student, Weibull e logística. A volatilidade foi mensurada pelo software Matlab, com uma rotina que altera o modelo ARMA+ família GARCH e a distribuição do termo de erro com a gaussiana e T de Student, para que fosse escolhido aquele que melhor captura as características das séries. Os resultados apontaram um prêmio de risco pela média aritmética para os períodos completos em torno de 5,4% para o IBOV, 8,6% para a AMBV4, 7,7% para a VALE5 e 5,8% para a PETR4. Quanto à distribuição de probabilidade, predominaram, em muitos dos períodos segmentados escolhido pelos testes de aderência Anderson-Darling (A-D), Kolmogorov-Smirnov (K-S) e Qui-Quadrado ( 2  ), em primeiro lugar, a logística e, em segundo, a T de Student. Palavras

Title: Actuarial and Exposure-based Models for Hail Peril Author: Bc. Matúš Drobuliak Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: This thesis covers an introduction to catastrophe modelling and focuses on statistical methods for extreme events. This includes methods of estimating parameters of claim distribution with a focus on probability weighted moments estimation technique. Furthermore, times series modelling, skew t-distribution, and two model clustering techniques are examined as well. This is later utilised in the practical application part of this thesis, which uses real data provided by an insurance company operating in the Czech Republic. Probability distribution fitting of large claims caused by hailstorms and Monte Carlo simulation of future losses are demonstrated later. Keywords: Catastrophe modelling, Hail peril, Probability weighted moments, Extreme events, ARMA-GARCH, Monte Carlo simulation iii