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.

The traditional way to analyze stocks and portfolios within the area of finance have been restricted to Sharpe and Markovitz. The Omega function and its properties enlighten the field of finance and differs from the traditional ways when it comes to the volatility of the stocks. The Omega function, the Sharpe performance criteria and mean-variance model by Markovitz will be used. All calculations are done in Matlab and the data sheets are excel tables. The aim of this thesis is to investigate the nordic small cap market by using the Omega function, Sharpe performance criteria and the mean variance model by Markovitz. In order to to see how the purposed methods differs.

Global bond market capitalization amounts to approximately $100 trillion, compared to $60 trillion in the equity markets. Despite debt financing being a large part of the global financial market, the measurements and greenhouse gas reduction investment strategies to date are not nearly as thorough as for equity financing. More recently, the problem has been brought into light by the World Bank, expressing concerns about the crucial role of debt financing activities in the current and upcoming threats caused by climate change. A commonly used credit derivative in debt financing is credit default swaps (CDS), which is an agreement between two parties to exchange the credit risk of a reference entity. The buyer of the contract makes fixed periodic payments to the seller of the contract, who collects the premiums in exchange for making the protection buyer whole in the case of a defaulting reference entity. This thesis aims to minimize the greenhouse gas emission exposure for two CDS indices, iTraxx Main and CDX.IG, each consisting of 125 equally weighted constituents, or companies. The CDS indices are widely used high liquid fixed income instruments. In 2017, iTraxx Main had a monthly trading volume of $330-440 billion notional, and CDX.IG a corresponding volume of $200-275 billion. In order to rate the greenhouse gas emissions of the constituents, the ECOBAR model was used. The model utilizes a discrete ranking score system, where the aim is to obtain as low score as possible. To minimize the ECOBAR score for the baskets, Markowitz Modern Portfolio Theory was used, implemented by using a quadratic programming algorithm. By optimizing the portfolios while retaining a low tracking error and high correlation toward the CDS indices, underlying investment properties were retained. We show that one can construct replicated portfolios of the CDS indices that have significantly lower ECOBAR scores than the indices themselves, whilst still maintaining a low tracking error and high correlation with the actual indices. When constructing baskets of fewer constituents, one can replicate the indices with merely 10-30 constituents, without worsening the tracking error or correlation substantially, and obtain an even lower ECOBAR score for the respective portfolios.

Submitted by Ricardo Porto (ricardoporto@bancobbm.com.br) on 2010-08-23T15:32:21Z No. of bitstreams: 1 DISSERTAÇÃO RICARDO PORTO.pdf: 454076 bytes, checksum: 66bba39f53ab22d9842749c2713ec606 (MD5) / Approved for entry into archive by Vitor Souza(vitor.souza@fgv.br) on 2010-08-23T15:34:47Z (GMT) No. of bitstreams: 1 DISSERTAÇÃO RICARDO PORTO.pdf: 454076 bytes, checksum: 66bba39f53ab22d9842749c2713ec606 (MD5) / Made available in DSpace on 2010-08-23T17:42:59Z (GMT). No. of bitstreams: 1 DISSERTAÇÃO RICARDO PORTO.pdf: 454076 bytes, checksum: 66bba39f53ab22d9842749c2713ec606 (MD5) Previous issue date: 2010-05-26 / The Black-Litterman model calculates the expected market returns as a combination of a set of investor views and a neutral reference point. The model uses Bayesian approach to blend both sources of information. The results from the Black-Litterman model, in contrast to the traditional approach, are quite intuitive, stable and consistent with the investors views. The purpose of this thesis is to provide a detailed analysis of each component of the Black-Litterman model and verify if the use of the Black-Litterman model, introducing the views of the market based on the Central Bank report, FOCUS, outperforms brasilians Hegde Funds. / O modelo Black-Litterman calcula os retornos esperados de mercado como uma combinação de um conjunto de expectativas específicas de cada investidor e um ponto de referência neutro. A combinação dessas duas fontes de informações são feitas pelo modelo utilizando a abordagem bayesiana. Os resultados obtidos a partir do modelo Black-Litterman, ao contrário da abordagem tradicional, são bastante intuitivos, estáveis e consistentes em relação as expectativas dos investidores. O objetivo dessa dissertação é fazer uma análise detalhada de cada um dos componentes do modelo Black-Litterman e verificar se a utilização o modelo de Black-Litterman, introduzindo as opiniões de mercado com base no relatório FOCUS do Banco Central, supera o retorno dos fundos multimercados brasileiros.

Made available in DSpace on 2014-06-12T17:16:09Z (GMT). No. of bitstreams: 1 license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / O objetivo principal desta dissertação foi avaliar a alocação dos ativos dos fundos de pensão brasileiros considerando quatro cenários factíveis dentre eles um que pressupõe estabilidade econômica com taxas de juros reais em torno de 4% ao ano. O modelo utilizado foi o da teoria de carteiras proposto por Harry Markowitz. Os resultados da pesquisa mostraram que no cenário com taxas de juros reais de 4% ao ano, o retorno esperado para o mesmo risco de uma carteira atual, hipoteticamente representativa da carteira dos fundos de pensão brasileiros, foi de 4,53% ao ano, já com os ativos domésticos de maior risco na carteira. Por outro lado, incluindo investimentos no exterior esse retorno ficou na faixa de 4,78% a 5,41% ao ano, mesmo considerando o risco cambial. A pesquisa explorou também os limites para alocação e os resultados mostraram que a imposição de limites provocou um aumento do risco, deslocando a fronteira eficiente para a direita. Assim, o trabalho apresenta elementos que contribuem de maneira significativa para o debate desse importante tema, subsidiando a gestão dos fundos de pensão e o órgão regulador na revisão do normativo que disciplina o assunto. O trabalho concluiu, tecnicamente, que em qualquer cenário os fundos de pensão brasileiros podem melhorar ainda mais a eficiência na alocação dos recursos e no cenário de estabilidade com taxas de juros reais em torno de 4% ao ano é imprescindível a alocação em ativos alternativos incluindo investimentos no exterior

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 thesis is focused on a theoretical explanation of some models for the optimization stock portfolios with different risk measure. The theory of the nonlinear programming is detailed developed and also basic Markowitz`s model with another optimization models as Konno -- Yamazaki`s model, Roy`s model, semivariance approach and Value at Risk approach, which are based on alternative risk measure. For all models the assumptions of their applications are highlighted and the comparation of these models is made too. Analytical part is concerned in the construction of the effecient portfolios according to the described models is made on the historical market prices of 13 companies traded on Prague Stock Exchange in SPAD.

This thesis presents two Models of portfolio optimization, namely the Markowitz Mean Variance Optimization Model and the Rockefeller and Uryasev CVaR Optimization Model. It then presents an application of these models to a portfolio of clean energy assets for optimal allocation of financial resources in terms of maximum returns and low risk. This is done by writing GAMS programs for these optimization problems. An in-depth analysis of the results is conducted, and we see that the difference between both models is not very significant even though these results are data-specific.

Die Arbeit gibt einen Überblick über den aktuellen Stand der Industrialisierungsbestrebungen der Banken. Darauf aufbauend erfolgt eine Analyse der Wertschöpfungspotentiale entlang des Leistungserstellungsprozesses (Transformation, Abwicklung und Vertrieb). Um die Wirkungsweise und Effizienzpotentiale von Industrialisierungsfaktoren einzuschätzen wird mittels eines Simulationsmodells zum einen das Verhalten von unterschiedlichen Entscheidern (Markowitz-Entscheider, CVaR-Entscheider) und zum anderen die strategische Ausrichtung der Bank mit ihrer Struktur (Geschäftsfelder, Prozesse) und der sie umgebenden Umwelt simuliert. Daraus werden für unterschiedliche Marktumfelder Implikationen zur Effizienz im Sinne einer Nutzenüberlegung oder auch RAROC-Betrachtung für Banken abgeleitet und Aussagen zur Zyklusverstärkung der Märkte durch die Bank getroffen.:ABBILDUNGSVERZEICHNIS TABELLENVERZEICHNIS ANLAGENVERZEICHNIS ABKÜRZUNGS- UND SYMBOLVERZEICHNIS 1 EINLEITUNG UND PROBLEMSTELLUNG 2 GRUNDLAGEN ZUR INDUSTRIALISIERUNG IN BANKEN 3 AUFBAU DES SIMULATIONSMODELLS 4 AUSWERTUNG DER WIRKUNGSWEISEN DER INDUSTRIALISIERUNG 5 SCHLUSSBETRACHTUNG ANHANG LITERATURVERZEICHNIS

Leaders of nonprofits businesses adopt revenue diversification strategies to create innovative program services, creative ways to source materials, utilize volunteers and community partnerships, and identify business solutions related to solving societal problems. To continue providing services, it is crucial for nonprofit leaders to maintain adequate financial resources. The purpose of this single-case study was to explore revenue diversification strategies used by 3 leaders of a nonprofit organization in western California of the United States using Markowitz's modern portfolio theory as the conceptual lens. Data were collected through in-depth semistructured interviews and examination of organizational documents, internal archival data, and online databases. Through thematic analysis, 8 revenue diversification themes emerged: adding income streams; establishing practical financial performance measures; establishing operating reserve; achieving financial health, sustainability, and resilience; building organizational capacity; adopting transparency; achieving efficiency and effectiveness; and conducting active surveys. Additionally, 10 recommendations were identified: developing written procedurals, developing a process improvement strategy, engaging in contingency planning, increasing transparency and governance, using metrics for donor attrition and retention, developing and upgrading technology, increasing staff capacity, creating an employee handbook, conducting active surveys to reinforce additional services, establishing performance measures. These findings may have implications for positive social change, including the potential to contribute to nonprofit leaders' models of effective strategies with processes to grow income sources to support organizational sustainability and support a leader's ability to improve and maintain service offerings, while avoiding dependence on single source of revenue.