<p><strong>Problem</strong></p><p>When choosing topic for this study the economy was on the brink of a recession. Many experts made varying statements regarding this fact, and further readings in this area led us to question: can an in- clusion of gold enhance the performance in an index portfolio dur- ing recessions? And if so, how much should be allocated to gold?</p><p><strong>Purpose</strong></p><p>The purpose of this thesis is to look back at the historical price de- velopment of gold and DJIA during recessions in order to find out whether an inclusion of gold can improve a DJIA index portfolio held in today’s recession. In addition, by analyzing the risks and pos- sibilities with gold, the optimal allocation of gold in a DJIA portfolio will be investigated in.</p><p> </p><p><strong>Method</strong></p><p>The methodological approach will be of a quantitative data analysis approach. By using historical data, new empirical findings will be found by using the deductive approach. This method has been cho- sen due to the nature of the purpose and in order to best give a gen- eral answer to our research questions.</p><p><strong>Conclusion</strong></p><p>The gold price is strongly influenced by uncertainty, and even though an optimal allocation of gold in each recession could be found, no general optimal allocation applicable in today’s recession could be found. Gold has higher risk (higher variance) than DJIA, but is compensated with higher return as well.</p>

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

To θέμα της συγκεκριμένης διπλωματικής εργασίας είναι η βέλτιστη επιλογή χαρτοφυλακίου, η οποία μπορεί να επιτευχθεί μέσω του προσδιορισμού του βέλτιστου μεγέθους του χαρτοφυλακίου. Στo πρώτο κεφάλαιο, που αποτελεί και την εισαγωγή, διατυπώνεται ο αντικειμενικός σκοπός της διπλωματικής εργασίας και αναφέρεται η δομή της εργασίας. Στο δεύτερο κεφάλαιο αναφέρονται συνοπτικά η σύγχρονη θεωρία χαρτοφυλακίου και το Υπόδειγμα της Αποτίμησης Κεφαλαιακών Στοιχείων (CAPM). Στο τρίτο κεφάλαιο αναφέρονται συνοπτικά 4 μελέτες σχετικά με τον προσδιορισμό του βέλτιστου μεγέθους χαρτοφυλακίου. Στο τέταρτο κεφάλαιο παρουσιάζεται η εμπειρική εφαρμογή. Στο πέμπτο κεφάλαιο παρουσιάζονται τα εμπειρικά αποτελέσματα της ανάλυσης. Στο έκτο κεφάλαιο διατυπώνονται τα συμπεράσματα που προκύπτουν από την ανάλυση και, επιπλέον, αναφέρεται η δυνατότητα για μελλοντική περαιτέρω έρευνα. / The subject of this diploma thesis is the optimal portfolio allocation, which can be achieved through the assignment of the optimal portfolio size. In the first chapter, which consists the introduction, the subjective purpose and the structure of the thesis are given. In the second chapter, the Modern Portfolio Theory and the Capital Asset Pricing Model are referred in brief. In the third chapter, 4 studies relative to the assignment of the optimal portfolio size are referred briefly. In the fourth chapter, the empirical application is presented. In the fifth chapter, the empirical results of the analysis are also presented. Finally, in the sixth chapter, the conclusions are given and, additionally, the possibility for future further research is referred.

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This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

This paper considers dynamic optimal portfolio strategies of utility maximizing investors in the presence of risk constraints. In particular, we investigate the optimization problem with an additional constraint modeling bounded shortfall risk measured by Value at Risk or Expected Loss. Using the Black-Scholes model of a complete financial market and applying martingale methods we give analytic expressions for the optimal terminal wealth and the optimal portfolio strategies and present some numerical results.

Divestitures have grown in importance and popularity over the years, rivaling other strategic transactions in mergers and acquisitions. The dominating opinion in academic research is that divestitures overall generate an abnormal return for the parent company stock. This thesis will focus on how Swedish companies perform in the short-term around the announcement of a divestiture. A multiple linear regression analysis finds significance for divestiture gains being attributed to companies focusing on core competencies and to companies with low returns on assets and high returns on equity. However, no significance is found for the size of the companies or financial distress. / Avknoppningar är idag en populär företagstransaktion. Den dominerade åsikten i den globala forskningen kring avknoppningar gör gällande att de generar en överavkastning för företaget i förhållande till marknaden. Denna kandidatuppsats ämnar undersöka vilka faktorer som kan påverka denna överavkastning genom att studera svenska företag på Nasdaq Stockholm. En multipel regressionsanalys visar att företag som säger sig utföra avknoppningar för att fokusera på kärnverksamheten generar en överavkastning. Vidare blir det en överavkastning på företag som har låg avkastning på totalt kapital och hög avkastning på eget kapital. Ingen verkan hittas dock för att storleken på företaget eller skuldstrukturen har en inverkan på överavkastningen.

My thesis will focus on optimal investment decisions, especially those that are planned for longer investment horizon. I will review the literature, showing that changes in investment opportunities can alter the risk-return tradeoff over time and that asset return predictability has an important effect on the variance and correlation structure of returns on bonds, stocks and T bills across investment horizons. The main attention will be given to pension funds, which are institutional investors with relatively long investment horizon. I will find the term structure of risk-return tradeoff in the empirical part of this paper. Later on I will add some variables into the model and investigate whether it can improve the results. Finally the optimal investment strategies will be constructed for various levels of risk tolerance and the results will be compared with strategies of Czech pension funds. I am going to use data from Thomson Reuters Datastream, Wharton Research Data Services and additionally from some other sources.

[pt] O novo Modelo Energético Brasileiro trouxe um mundo de novos desafios para as Distribuidoras de Energia Elétrica. Elas têm que atender a carga através de contratos de longo prazo (cinco a quinze anos). As incertezas são enormes, desde a evolução da carga até a disponibilidade de energia, com seus preços associados. As restrições se encontram próximas a seus limites, sendo a sobrecontratação severamente punida - apenas 3% de excesso pode ser contratado na tarifa regulada e recuperado no preço ao consumidor. As distribuidoras devem então criar um portfólio de contratos sob incertezas, minimizar os custos (visando um preço competitivo) e os riscos (visando garantias a longo prazo). Este trabalho tem como objetivo ajudar o agente a construir seu portfólio ótimo, que corresponde a um problema não-linear, inteiro, misto, de larga escala, a princípio de difícil solução através de modelos atualmente disponíveis (tanto modelos econômicos como algoritmos de otimização). Neste trabalho, combinase técnicas econômicas e de otimização, num novo modelo capaz de analisar um portfólio possível e/ou encontrar um conjunto de soluções ótimas. O modelo pode ser adaptado para acomodar diferentes funções- objetivo, tais como risco mínimo, custo mínimo, VaR (Value-at-Risk), etc. Espera-se que o modelo possa oferecer uma ferramenta eficiente e flexível, além de precisa, capaz de ajudar a encontrar uma comercialização justa, mitigando riscos e minimizando custos, levando a um melhor uso da energia e a um preço melhor para toda a sociedade. / [en] The new Brazilian Energy Model brought a whole new world of challenges to Distribution Companies (DISCOS). They have to meet the load through longterm contracts (five to fifteen years). Uncertainties are enormous, from load evolution to energy availability and associated prices. Restrictions are tight - for instance overcontracting is punished - only a mere 3% excess may be included in the regulated tariff and thus recovered by consumer´s prices. DISCOS must therefore build a contract portfolio under uncertainties, minimize costs (searching for a competitive price) and risks (searching for long-term guarantees). The objective of this work is to help the agent constructing its optimum portfolio - which corresponds to a large-scale non-linear mixed integer problem, in principle difficult to solve by available models (from economic to optimization algorithms). In this model economic and optimization techniques have been combined into a new model able to both analyze a possible portfolio and/or find a set of optimal solutions. The model may be adapted to accommodate different objective functions, such as minimum risk, minimum cost, VaR (Value- at-risk), etc. This model may offer an efficient and flexible, yet precise tool, able to help finding a fair trade, mitigating risks and minimizing costs, leading to a better use of energy and a better price for whole society.

The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the Expected Utility Loss. We generalize the findings our previous papers to this case. Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.