Bibliographic Record JÍLEK, Jiří. European Real Estate Investment Trusts: Analyzing Correlation with a DCC- GARCH Model. Prague, 2012. 50 p. Master thesis (Mgr.) Charles University in Prague, Faculty of Social Sciences, Institute of Economic Studies. Supervisor: Tomáš Jandík MA MSc MRICS. Abstract The main goal of this thesis is to study the interdependencies between returns of European real estate investment trusts (REITs) and other investment asset classes such as European equities, government bonds and commodities. The thesis is divided into two parts: in the first part, we describe the necessary background that led to the emergence of first REIT structures and also provide an overview of the European REITs market. In the second part, we apply the Dynamic Conditional Correlation GARCH (DCC-GARCH) model to examine correlations between the above mentioned asset classes. The general understanding of real estate is that it provides diversification benefits to a diversified portfolio. However, our results suggest that returns of European REITs and stocks show a relatively high correlation and more importantly, the correlation increases in time. These findings have significant implications for investors and portfolio managers who seek protection for their portfolios in time of market downturns. Our results...

The correlation between stock market returns and changes in bond market yields are of big interest among investors because this indicator helps them allocate their assets and diversify investment risk more effectively. An in- vestor should keep track of development of the economies of individual coun- tries, understand the causes of dissimilarities in the correlations among them and take these differences into account for successful international financial investment. The current author contributes to the existing researches by the modeling of stock-bond market co-movements using the updated datasets with focus on Central European countries and differences in public debt levels. The paper contains the empirical analysis of stock and bond market returns condi- tional correlations, modeled by the use of the Asymmetric Generalized Dynamic Conditional Correlation (AG-DCC) Generalized Autoregressive Conditional Het- eroskedasticity (GARCH) specification, for nine Western and Central European countries (the United Kingdom, Germany, France, Spain, Portugal, Italy, Czech Republic, Poland and Hungary) that differ both by their geographic locations and economic development. The main distinctions in the correlations are ob- served during the European sovereign debt crisis. The three types of develop- ment are...

This master thesis is focused on analysis and forecasting of hourly and daily electricity price on the deregulated Czech daily electricity market. The methods used for estimating and forecasting hourly and daily prices are picked from the ARIMA-GARCH family of models and Neural Networks. For daily price data, the Redundant Haar Wavelet Transform decomposition of the time series is used in combination with ARIMA and Neural Networks models for forecasting. For hourly data, ARIMA and Neural Network models are considered. The forecasting results of daily data indicate that simpler models such as seasonal ARIMA outperform all other methods. Also the wavelet decomposi- tion of the daily series didn't prove useful in enhancing the forecast precision. For hourly data, the Multilayer Perceptron architecture of the neural network outperformed the ARIMA forecast. JEL Classification C20, C22, C45, C53, C65 Keywords Forecasting, Time Series, ARIMA, GARCH, Neural Net- works, Wavelet Transform Author's e-mail krystof.cerny@gmail.com Supervisor's e-mail lebovicm@gmail.com 1

The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models, which have many advantages. Nevertheless, an issue which has been raised is whether there exist other models that can explain and forecast real data better than linear ones. In this thesis, new nonlinear time series models are suggested, which consist of a nonlinear conditional mean model, such as an ExpAR or an Extended ExpAR, and a nonlinear conditional variance model, such as an ARCH or a GARCH. Since new models are introduced, simulated series of the new models are presented, as it is important in order to see what characteristics real data which could be explained by them should have. In addition, the models are applied to various stationary and nonstationary economic and financial time series and are compared to the classic AR-ARCH and AR-GARCH models, in terms of fitting and forecasting. It is shown that, although it is difficult to beat the AR-ARCH and AR-GARCH models, the ExpAR and Extended ExpAR models and their special cases, combined with conditional heteroscedastic errors, can be useful tools in fitting, describing and forecasting nonlinear behaviour in financial and economic time series, and can provide some improvement in terms of both fitting and forecasting compared to the AR-ARCH and AR-GARCH models.

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.

Since the introduction univariate GARCH models number of available models have grown rapidly and has been extended to the multivariate area. This paper compares three different multivariate GARCH models and they are evaluated using out of sample Value at Risk of dif- ferent portfolios. Sector portfolios are used with different market capitalization. The models compared are the DCC,CCC and the GO-Garch model. The forecast horizon is 1-day, 5-day and 10-day ahead forecast of the estimated VaR limit. The DCC performs best with regards to both conditional anc unconditional violations of the VaR estimates.

O objetivo principal deste trabalho foi o de explorar a possibilidade de usar uma metodologia capaz de decompor uma série temporal via ondaletas, conjuntamente com os modelos econométricos e de redes neurais já existentes de previsão e comparar a qualidade de previsões obtidas para sucessões cronológicas não lineares simuladas. A proposta foi alcançada principalmente pela elaboração de um fluxograma para tratamento das previsões de sucessões cronológicas para colocar um rigor quantitativo mais adequado. O diferencial deste trabalho esteve na realização das previsões dentro das sub-séries decompostas por uma ondaleta em até dois níveis, e obtendo-se a previsão da série original via reconstrução da série para modelos construídos por processos geradores de dados de sucessões cronológicas não-lineares. Foram simulados séries de um processo ARIMA-GARCH, um processo ARIMA, um processo bilinear e uma série de um movimento browniano. O trabalho principal constituiu-se na elaboração da fase de pré-processamento e das previsões estática em separado para cada uma das sub-séries encontradas sendo feitas para 10 e 200 observações futuras. Além das previsões pontuais foi verificada também o envelopamento dos dados, que consiste em comparar o modelo de previsão através de um intervalo de confiança para os valores previstos em mil séries simuladas pela mesma semente. Os resultados apontaram que para um modelo ARIMA(1,0,0)-GARCH(1,1), pode-se observar que o pré-processamento pela ondaleta foi melhor para apenas uma etapa de separação de altas e baixas freqüências tanto pela correlação quanto pelos critérios do TIC sendo este reduzido e pelo MAPE menor para as previsões de curto prazo. Já para os modelos de redes neurais uma diferença importante que deve ser ressaltada entre as redes neurais recorrentes e as redes com algoritmo de retropropagação é a capacidade de previsão das redes recorrentes para dados não-lineares com 2 níveis de pré-processamento e para previsões de curto prazo. Todavia, já para o critério do envelopamento, os melhores resultados foram para as redes recorrentes na previsão do processo ARIMA-GARCH e bilinear e pré-processamento com 1 nível. Todos os dados também foram comparados com as previsões feitas sem pré-processamento, as quais se mostraram impróprias com MAPE perto de 100% para previsões de longo prazo. Também checou-se neste trabalho as alterações que a mudança da escolha de uma ondaleta por outra, poderia impactar nos resultados das previsões futuras. Constatou-se que a troca da forma de onda no pré-processamento que se pareça mais visualmente com a forma dos dados da série, reduz as medidas de acurácia em 48%, deixando evidências que possa haver melhoras nos resultados. Na análise prática para o IBOVESPA, os resultados não foram satisfatórios, visto que os melhores resultados ficam para redes recorrentes com 1 nível de pré-processamento. Outrossim, da análise deste trabalho, emerge a importância dada ao fluxograma implementado para as previsões e o papel das previsões em separado por ondaletas como redutores dos erros nos processos estocásticos, e da implementação das bandas de previsões para redes recorrentes para sucessões cronológicas não-lineares. / The main objective of this work was it of exploring the possibility to use a methodology capable to decompose a temporary series through ondaletas, jointly with the econometrics models and of neural network already existent of forecast and to compare the quality of forecasts obtained for chronological successions no lineal simulated. The proposal was reached mainly by the elaboration of a flowchart for treatment of the forecasts of chronological successions to put a more appropriate quantitative rigidity. The differential of this work was in the accomplishment of the forecasts inside of the sub-series decomposed by an ondaleta in up to two levels, and being obtained the forecast of the original series through reconstruction of the series for models built by generating processes of data of no-lineal chronological successions. They were simulated series of a process ARIMA-GARCH, a process ARIMA, a process bilinear and a series of a movement browniano. The main work was constituted in the elaboration of the pré-processing phase and of the forecasts static in separate for each one of the found sub-series being done for 10 and 200 future observations. Besides the punctual forecasts it was also verified the envelopamento of the data, that it consists of comparing the forecast model through a trust interval for the values foreseen in a thousand simulated series by the same seed. The results appeared that for a model ARIMA(1,0,0)-GARCH(1,1), it can be observed that the pré-processing for the ondaleta went better so much for just a stage of separation of discharges and low frequencies for the correlation as for the criteria of TIC being this reduced and for smaller MAPE for the forecasts of short period. Already for the models of nets neurais an important difference that it should be emphasized between the nets appealing neurais and the nets with retropropagação algorithm is the capacity of forecast of the appealing nets for no-lineal data with 2 pré-processing levels and for forecasts of short period. Though, already for the criterion of the envelopamento, the best results went to the appealing nets in the forecast of the process ARIMA-GARCH and bilinear and pré-processing with 1 level. All the data were also compared with the forecasts done without pré-processing, which were shown inappropriate with MAPE close to 100% for forecasts of long period. It was also checked in this work the alterations that the change of the choice of an ondaleta for other, was able to impactar in the results of the future forecasts. It was verified that the change in the wave way in the pré-processing that if it seems more visually with the form of the data of the series, it reduces the acurácia measures in 48%, leaving evidences that it can have improvements in the results. In the practical analysis for IBOVESPA, the results were not satisfactory, because the best results are for appealing nets with 1 pré-processing level. Likewise, of the analysis of this work, the importance emerges given to the flowchart implemented for the forecasts and the paper of the forecasts in separate for ondaletas as reducers of the mistakes in the processes estocásticos, and of the implementation of the bands of forecasts for appealing nets for no-lineal chronological successions.

Mais do que uma ferramenta para gestão do risco de preços para produtores e consumidores, os contratos futuros agropecuários tem se tornado uma importante opção de investimento principalmente em períodos de crise quando os riscos no mercado de ações aumentam. No Brasil, a participação de investidores no mercado futuro agropecuário ainda é pequena, mas há um considerável potencial de crescimento, posto que o país é um importante player no mercado internacional das principais commodities agropecuárias como café, soja, milho, açúcar, etanol e carne. Neste contexto, será analisada neste trabalho a relação entre os retornos resultantes de posições compradas em contratos futuros agropecuários negociados na BM&FBOVESPA e o retorno apresentado pelo mercado de ações, representado pelo Índice Bovespa com atenção especial aos períodos de crise. Para isso, utilizou-se uma metodologia similar a desenvolvida por Baur e Lucey (2009) buscando identificar em qual categoria porto seguro, hedge ou diversificador - os dois principais contratos futuros negociados na BM&FBOVESPA - boi gordo e café arábica se encaixam. Os comportamentos de tais contratos foram analisados de forma isolada e também considerando carteiras formadas pelo ponto de mínimo risco da teoria do portfólio de Markowitz. Como resultado identifcou-se que o contrato futuro do boi gordo atua como hedge em relação ao mercado de ações, já o contrato futuro do café arábica, por apresentar correlação positiva, mas não perfeita, atua como diversificador. Combinando os dois contratos em posição comprada durante todo o período obteve-se uma carteira cuja variância média foi inferior a variância do boi gordo e do café arábica, no entanto esta carteira apresenta correlação positiva em relação ao mercado de ações, o que a coloca na categoria de diversificador. Outra combinação entre os contratos foi feita utilizando uma estratégia dinâmica de negociação, ou seja, a posição adotada pelo investidor se altera no decorrer do tempo. Esta carteira apresentou uma variância média inferior à carteira estática e a correlação com o mercado de ações reduziu ainda mais, porém continuou positiva. Sendo assim, o boi gordo mostrou ser o contrato que melhor protege o investidor, mas seu retorno médio é inferior se comparado às demais opções, já a carteira dinâmica apresenta a segunda menor correlação e um retorno superior. Vale destacar que, apesar de nenhum contrato ter se mostrado como porto seguro em relação ao mercado de ações, todos podem ser utilizados com a finalidade de redução do risco. / More than a tool for managing price risk, commodity futures contracts have become an important investment option especially in times of crisis when the risk in the stock market increases. In Brazil, the participation of investors in the agricultural futures market is still small, but there is a huge potential for growth, given that the country is an important player in the international market of agricultural commodities such as coffee, soybeans, corn, sugar, ethanol and meat. In this context, this study aims to examine the relationship between returns resulting from long positions in the two major futures contracts traded at BM&FBOVESPA live cattle and arabica coffee - and returns made with an investment in the Brazilian stock market, with special attention to crisis periods. For this, a methodology similar to that developed by Baur and Lucey (2009) was used in order to identify in which category - safe haven, hedge or diversifier - the futures contracts fit. The behaviours of these two contracts were analysed separately and also considering portfolios formed using the Markowitz theory of portfolio. As a result, it was identified that the live cattle futures contract can be considered as a hedge against the stock market. The arabica coffee, for presenting a positive correlation, but not perfect, serves as a diversifier. Combining the two contracts considering long position throughout the period was obtained a portfolio whose average variance was lower than the variance of the live cattle as well as the arabica coffee, however the returns of this portfolio presents a positive correlation against the stock market which places it in the diversifier category. Another combination of the contracts was made using a dynamic trading strategy, ie, the position adopted by the investor changes over time. This portfolio presented an average variance lower than the static portfolio (long position) and the correlation with the stock market was even lower than the static portfolio, but still positive. Thus, the live cattle contract proved to be the one that best protects the investor when added into a stock portfolio, but its average return is lower than all the others arabica coffee, static portfolio and dynamic portfolio). It is worth noting that although no contract had been shown as a safe haven compared to the stock market, all of them can be used for the purpose of reducing risk.