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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.

Bakgrund och problemformulering: Investmentbolag är ett bolag vars affärsidé är att äga andra bolag. De har en betydande roll i samhället genom att bidra med kapital och att hjälpa driva etablerade företag framåt. I tidigare forskningssammanhang har andra liknande typer av bolag varit i fokus vilket orsakar ett gap i forskningen kring investmentbolag och riskhantering. Det här blir särskilt intressant att studera då investmentbolag har blivit en allt mer vanlig investering samtidigt som de beskrivs ha liknande riskspridning som en aktiefond. För att få en bredare förståelse om hur det skiljer sig mellan olika bolag och länder jämförs svenska investmentbolag med brittiska samt amerikanska investmentbolag.   Syfte: Syftet med denna uppsats är att analysera om investmentbolagens portföljer är effektiva.   Metod: Utgångspunkten i studien är den moderna portföljvalsteorin som utgår ifrån Markowitz tankar och menar att en effektiv portfölj inte enbart består av en lång rad med aktier. Det är i stället korrelationen mellan tillgångarna som är viktiga att ha i åtanke och den optimala portföljen är den mest effektiva samt har den högsta sharpekvoten. För att besvara studiens syfte jämförs den optimala portföljen men den faktiska portföljen och de bolag som har det minsta avståndet anses vara effektivast i sin riskhantering och vice versa.    Resultat: Resultaten visar att det finns förbättringar att göra för de allra flesta investmentbolag och det är ytterst få som håller en portfölj som är lika effektiv som den optimala portföljen. Det finns även skillnader mellan hur de olika investmentbolagen hanterar risker i portföljen och vilka typer av bolag som de investerar i, vilket främst är de brittiska investmentbolagen som främst skiljer sig från mängden. / Background and problematization: An investment company is a firm which business idea is to own other companies. It has a significant role in the society by contributing with capital and help already established companies forward. Within a research context other kind of companies with similar business ideas has been in focus which causes a gap in the research area regarding investment companies and risk management. This is especially interesting to study because investment companies have become a more common investment, meanwhile investment companies are described to have a similar risk diversification as an equity fund. To get a broader understanding on how it differs between different companies and countries a comparison is made between Swedish, British and American investment companies.   Purpose: The purpose of this paper is to analyze if investment companies manage an efficient portfolio.    Method: The main theory of this study is the modern portfolio theory which is based on Markowitz´s ideas of an efficient portfolio that does not only contain a long list of assets but instead consider the correlation between assets. According to this theory the optimal portfolio is the most efficient and has the highest sharperatio. To be able to achieve the purpose of this study the optimal portfolio will be compared to the investment companies’ actual portfolio. The companies with the smallest difference between these portfolios will be considered the most efficient regarding risk management and vice-versa.   Conclusion: The results show that there are room for improvements for most investment companies and there are extremely few that holds a portfolio that is as effective as the optimal portfolio. There are also differences between the companies regarding how they manage their portfolio risk and which types of companies they invest in. The British investment companies are those who stands out in this study.

In this thesis, an optimal investment problem is studied for an investor who can only invest in a financial market modelled by an Itô-Lévy process; with one risk free (bond) and one risky (stock) investment possibility. We present the dynamic programming method and the associated Hamilton-Jacobi-Bellman (HJB) equation to explicitly solve this problem. It is shown that with purification and simplification to the standard jump diffusion process, closed form solutions for the optimal investment strategy and for the value function are attainable. It is also shown that, an explicit solution can be obtained via a finite training of a neural network using Stochastic gradient descent (SGD) for a specific case.

This thesis aims to investigate the benefits of international diversification from a Swedish perspective. It presents a comparative study of the performance of different portfolios based on their degree of international diversification with a focus on Swedish investors frame of reference. Such a study is motivated by the contradictory literature about portfolio diversification and information portfolio theory that advocate for a more concentrated portfolio. It focuses solely on comparing portfolios constituted with major indices of a representative sample including countries from different parts of the world. The different scales of those portfolios start from a divided part of the Swedish economy to end with a global portfolio. We observed that international diversification can outperform the domestic portfolios when considering risk and return. In addition, we observed that the best performing portfolios over the periods are systematically concentrated on emerging countries and that the high return of those emerging countries is often not associated with a correspondingly high standard deviation as it should be expected. The best levers of performance that we identified as a result of this comparative study are, first, the strategy consisting in focusing on the most concentrated portfolios in order to maximize the return and then trying to time the market, thanks to a specialized information collection strategy, but this bear a high undiversifiable risk. Or second, adopting an intentionally diversified portfolio and collecting information about the most promising emerging markets that will be then over weighted in the portfolio to lower the risk and higher the return. Lastly, the study recommend that home-biased investors should change their behavior and consider international investments when building a portfolio.