Esse trabalho propõe a inserção de restrição de liquidez em um modelo de seleção de carteiras, visando aplicação no mercado brasileiro. No Brasil, a Comissão de Valores Imobiliários (CVM) expõe a importância do controle da liquidez de fundos de investimentos através de instrução publicada em 2012. A restrição proposta considera parâmetros utilizados nas normas brasileiras de controle de liquidez, como percentual do total negociado máximo, nível de liquidação e prazo para liquidação. O modelo é aplicado considerando-se diversos cenários, sendo variados parâmetros como valor da carteira formada e nível de liquidação aceitável, em diferentes intervalos de formação de carteiras. Verificam-se os níveis de liquidação das carteiras formadas e seu impacto no nível de risco das mesmas. Os resultados se mostraram consistentes, com bons níveis de percentual liquidado das carteiras formadas, próximos aos níveis de liquidação aceitáveis. Foi constatado também um aumento do nível de risco das carteiras mais restritas pela liquidez. / This work proposes the insertion of a liquidity constraint in a portfolio selection model, aiming to be applied in the Brazilian market. In Brazil, the "Comissão de Valores Imobiliários" (CVM) exposes the importance of controlling the liquidity of investment funds through the instruction published in 2012 . The constraint proposed in this work considers parameters used in the Brazilian regulatory standards of liquidity control parameters such as maximum percentage of monetary value, liquidation level and liquidation term date. The model is applied considering several scenarios, varying parameters such as the portfolio value and acceptable liquidation level, in different portfolio formation intervals. The liquidation levels of the portfolios formed and their impact on the risk of the portfolios are verified. The results were consistent, with good levels of liquidation of the portfolios formed, close to acceptable liquidation levels. There was also an increase in the risk of liquidity-restricted portfolios.

Esse trabalho propõe a inserção de restrição de liquidez em um modelo de seleção de carteiras, visando aplicação no mercado brasileiro. No Brasil, a Comissão de Valores Imobiliários (CVM) expõe a importância do controle da liquidez de fundos de investimentos através de instrução publicada em 2012. A restrição proposta considera parâmetros utilizados nas normas brasileiras de controle de liquidez, como percentual do total negociado máximo, nível de liquidação e prazo para liquidação. O modelo é aplicado considerando-se diversos cenários, sendo variados parâmetros como valor da carteira formada e nível de liquidação aceitável, em diferentes intervalos de formação de carteiras. Verificam-se os níveis de liquidação das carteiras formadas e seu impacto no nível de risco das mesmas. Os resultados se mostraram consistentes, com bons níveis de percentual liquidado das carteiras formadas, próximos aos níveis de liquidação aceitáveis. Foi constatado também um aumento do nível de risco das carteiras mais restritas pela liquidez. / This work proposes the insertion of a liquidity constraint in a portfolio selection model, aiming to be applied in the Brazilian market. In Brazil, the "Comissão de Valores Imobiliários" (CVM) exposes the importance of controlling the liquidity of investment funds through the instruction published in 2012 . The constraint proposed in this work considers parameters used in the Brazilian regulatory standards of liquidity control parameters such as maximum percentage of monetary value, liquidation level and liquidation term date. The model is applied considering several scenarios, varying parameters such as the portfolio value and acceptable liquidation level, in different portfolio formation intervals. The liquidation levels of the portfolios formed and their impact on the risk of the portfolios are verified. The results were consistent, with good levels of liquidation of the portfolios formed, close to acceptable liquidation levels. There was also an increase in the risk of liquidity-restricted portfolios.

Asset Liability Management is a current topic where accountability of asset management is of high importance. This is a result of continuously increasing investments in the stock market globally. The globalisation exposes a big part of the different markets to the same types of risk. This makes it harder to secure capital and assets through diversified investments. Further it has led to a more complex and resource demanding investment basis. The uncertainty of the future brings the focus of fund management to optimising and minimising risks, rather than trying to predict individual movements of specific assets on the market. The goal of this project has been to find, test and evaluate different investment- and portfolio selection strategies with trajectories of some chosen assets, simulated from a Economic Scenario Generator (ESG). This ESG has gratefully been provided by Willis Towers Watson, which in their daily work deal with these areas. Further the trajectories has acted as possible outcomes of asset returns. Employed portfolios intended to replicate pension foundations in placement guidelines and characteristics, with different strategies has then followed the development of the assets and has been matched against the pension liabilities of an average sized Swedish pension foundation. The outcomes of the portfolios has thereafter been assessed and compared with each other. The target has been to localise an optimal risk level in respect to the portfolios' performance and to achieve as high pension funding ratio as possible. The strategies tested have been varied. Variants such as Buy-and-Hold is an example of a simpler investment strategy. There the assets within the portfolio has initially been allocated according to given weights, then the portfolio has ran static with the initial shares over the tested period of 10 years. Other more complex, aggressive and risk taking strategies have also been tested. Here, re-allocating every year is common and the weights within the portfolios depends on the properties of the different assets and the strategy employed. The key performance indicator of the tested portfolios has been the funding ratio of pension payments. The best portfolio in this regard was the one that employed Sharpe allocation for all assets. It had a funding ratio of 91.22%. The worst portfolio due to this measurement was the buy-and-hold strategy with equal weights of the assets. It only covered 79.48% of the pension payments. Important to mention is that the initial funding ratio of all tested portfolios was set to 80%. This means that the portfolio value in time step zero was set to 80% of the value of the pension liabilities. WTW does not blindly confirm the results and this thesis should not be seen as an investment advise. The results are based on data obtained from a specific ESG and does not necessarily look the same using other scenarios or different market data. / Asset Liability Management fortsätter att vara ett aktuellt ämne och en ansvarstagande kapitalförvaltning är av hög vikt. Detta är ett resultat av kontinuerligt ökande investeringar på aktiemarknader världen över. I tillägg gör globaliseringen att de flesta människor är exponerade mot samma typ av risker vilket kan göra det svårare att säkra kapital genom diversifierade investeringar. Detta har gett upphov till alltmer komplicerade och resurskrävande investeringsunderlag. Osäkerheten framtiden för med sig gör att fokusområdet inom kapitalförvaltning framför allt handlar om att optimera och minimera risker, snarare än att försöka förutspå enstaka rörelser på aktiemarknaden. Detta projekt har gått ut på att testa och utvärdera diverse investerings- och portföljsvalsstrategier med simulerade reella tidsserier för olika tillgångar. Dessa tidsserier är simulerade ur en Ekonomisk Scenariogenerator (ESG) som tacksamt mottagits av Willis Towers Watson, som i sitt dagliga arbete sysslar med frågor rörande dessa ämnen. Vidare har tidsserierna agerat som tänkbara utfall för hur tillgångars priser kan röra sig. Antagna portföljer med olika strategier har sedan fått följa prisutvecklingen i de olika scenariona och matchas mot skuld och kassaflöden tillhörande en medelstor svensk pensionsstiftelse. Utfallen har därefter utvärderats och jämförts med varandra. Målsättningen har varit att lokalisera en optimal risknivå sett till portföljernas prestation och framför allt eftersträva en så hög pensionstäckningsgrad som möjligt. Investeringsstrategierna som har testats har varit varierande. Varianter som buy-and-hold-strategin är ett exempel på en enklare strategi. Där har tillgångarna i portföljen initialt allokerats enligt given viktning, sedan har portföljen fortlöpit statiskt med de initiala andelarna för livslängden av portföljens testperiod, vilket är 10 år. Andra mer komplexa, offensiva och risktagande strategier har också testats där innehaven i portföljen ombalanserats en gång per år. Allokeringarna inom portföljen beror av vilka egenskaper tillgångarna besitter och den använda strategin. Det tyngsta nyckeltalet kopplat till portföljernas prestation har varit täckningsgraden av pensionskostnader. Bästa portföljen i detta avseende var den som använde sig av Sharpe-allokering för alla tillgångar, den hade en täckningsgrad av 91.22%. Sämst resultat av alla testade strategier hade buy-and-hold portföljen med lika viktning av tillgångarna. Den täckte endast 79.48% av pensionsutbetalningarna. Vad som är viktigt att nämna är att fonderingsgraden för alla testade portföljer sattes till 80%. Detta betyder att portföljvärdet i tidsteg noll är 80% av pensionsskuldernas värde. WTW bekräftar inte blint resultaten och denna avhandling bör inte ses som ett investeringsråd. Resultaten är baserade på data erhållen från en specifik ESG och ser inte nödvändigtvis densamma ut baserat på andra scenarion eller annan marknadsdata.

Zugl.: Bremen, Universiẗat, Diss., 2009.

Zugl.: Augsburg, Universiẗat, Diss., 2008.

Zugl.: Bonn, Universiẗat, Diss., 2008.

Purpose: The purpose of this thesis is to address the, by scholars and managers alike, expressed need of development in the project portfolio selection. The research will aim to investigate how the selection of innovation projects portfolios could change if flexibility, and with it uncertainty, were added to the project portfolio selection. The aim is further to investigate how options value can be incorporated as additional value to a portfolio selection decision, with the goal to choose projects that maximize the goal function of the firm. Method: This thesis takes a qualitative approach as such approach is favourable when studying social science. The empirical research is carried out at a large international company conducting in an extensive amount of R&D as well working with innovation projects. The data is collected by unstructured and semi structured interviews with management at the company subjected to the study. Results: The results show, that by adapting the real options framework to a static way of selecting projects, the incorporation of flexibility to the selection process can add economic value by accounting for options value and handle uncertainty. The real options framework will substantiate a dynamic approach to the selection process of innovation projects, as flexibility is changing the selection process from individual project selection to the selection of portfolios. / Syfte: Syftet med följande uppsats är belysa och utveckla det, av forskare och chefer, uttryckta behov av utveckling av projektportföljval. Uppsatsen syftar till att undersöka hur valet av innovationsprojekt genom portföljvalsmodeller kan förändras om flexibilitet och osäkerhet adderas till beslutsprocessen. Syftet är vidare att undersöka hur ytterligare värde kan inkorporeras i ett beslut, med målet att välja den portfölj som maximerar företagets målfunktion. Metod: Denna uppsats tar en kvalitativ metodansats då ett sådant tillvägagångssätt är fördelaktigt i studier av samhällsvetenskap. Den empiriska undersökningen har bedrivits på ett stort internationellt företag vilket deltar i ett omfattande FoU arbete, samt i stor skala arbetar med innovationsprojekt. Data har samlats in genom ostrukturerade samt semistrukturerade intervjuer med ledningen på företaget. Slutsatser: Resultaten visar att genom att inkorporera reella optioner, i en statisk beslutsprocess, så kan ett bättre beslutsunderlag genereras genom inkluderandet av osäkerhet och värdet av optioner. Ett sådant beslutsunderlag genereras genom att real options adderar flexibilitet till urvalsprocessen. Genom att inkorporera flexibilitet kommer en statisk metod att välja individuella projekt på, skifta till fördel för en dynamisk metod att välja portföljer.

"Practical usage of optimal portfolio diversification using maximum entropy principle" by Ostap Chopyk Abstract This thesis enhances the investigation of the principle of maximum entropy, implied in the portfolio diversification problem, when portfolio consists of stocks. Entropy, as a measure of diversity, is used as the objective function in the optimization problem with given side constraints. The principle of maximum entropy, by the nature itself, suggests the solution for two problems; it reduces the estimation error of inputs, as it has a shrinkage interpretation and it leads to more diversified portfolio. Furthermore, improvement to the portfolio optimization is made by using design-free estimation of variance-covariance matrices of stock returns. Design-free estimation is proven to provide superior estimate of large variance-covariance matrices and for data with heavy-tailed densities. To asses and compare the performance of the portfolios, their out-of-sample Sharpe ratios are used. In nominal terms, the out-of- sample Sharpe ratios are almost always lower for the portfolios, created using maximum entropy principle, than for 'classical' Markowitz's efficient portfolio. However, this out-of-sample Sharpe ratios are not statistically different, as it was tested by constructing studentized time-series...

A crescente integração econômica e mobilidade de capital levam a uma maior exposição dos investidores a riscos externos. Com isso, ganha relevância a discussão sobre como se considerar, no cálculo do custo de capital, possíveis prêmios requeridos pelos riscos adicionais da realização de negócios em mercados emergentes. A existência de um adicional de risco é relativamente evidente, podendo ser constatada pela maior volatilidade que grande parte dos mercados acionários emergentes possuem em relação a mercados maduros, como o norte-americano. Entretanto, a existência de um prêmio requerido por esse risco adicional é menos óbvia e sua observação empírica, por dados passados, usualmente não gera resultados conclusivos. Nesse contexto, a presente pesquisa aborda o prêmio pelo risco país no mercado acionário brasileiro, apresentando as formas mais usualmente aplicadas para estimá-lo e discutindo sobre a possibilidade de eliminá-lo através da diversificação dos investimentos. A maior contribuição realizada está na aplicação do modelo de valoração de ativos AEG (Abnormal Earnings Growth) para se estimar esse prêmio. O AEG torna viável o cálculo do custo de capital implícito nas as expectativas de resultados futuros divulgadas por instituições financeiras em mídias especializadas. O prêmio pelo risco país foi, então, estimado através do diferencial entre o custo de capital das principais empresas brasileiras e o custo de capital de um grupo de empresas comparáveis norte-americanas, ambos calculados pelo AEG. Identificou-se um custo de capital maior em 2,09% (209 basis points) para as empresas brasileiras, que se mostrou estatisticamente significante. Esse resultado comprova empiricamente a existência de um prêmio específico do mercado brasileiro, indicando que ainda existem barreiras à diversificação internacional dos riscos domésticos. Adicionalmente, a estimativa ficou bastante próxima do prêmio pelo risco soberano brasileiro, o que valida a sua ampla utilização como proxy do prêmio do mercado acionário. / The increasing economic integration and capital mobility among countries lead investors to be more exposed to external risks. That grants relevance to the discussion on how to consider, in the cost of equitys estimation, premiums for additional risks of businesses performed in emergent markets. The existence of an additional risk in these markets is relatively clear, what is demonstrated by higher volatilities that the majority of emergent stock markets presents if compared to mature markets. Nevertheless, the existence of a risk premium is less obvious and its empirical observation, applying historical data, usually doesnt produce any conclusive result. Within this framework, the present research approaches the country risk premium in the Brazilian stock market, introducing the most usual means to estimate it and discussing about the potential elimination of the country risk through investment diversification. The greatest contribution of this research is the application of the Abnormal Earnings Growth Model (AEG) to estimate the country risk premium. AEG makes viable the inference of the cost of equity implied in future earnings expectations, published by financial institutions through specialized media. The country risk premium was, then, estimated through the difference between the implied cost of equity of the main Brazilian public companies and the implied cost of equity of a comparable north-American group of companies, both calculated using the AEG. Was perceived a cost of equity higher in 2,09% (209 basis points) for the Brazilian companies, what was shown statistically significant. This result proofs the existence of a country risk premium for the Brazilian market, indicating that there are still some barriers to the international diversification of domestic risks. Additionally, this result is very close to the default risk premium of the Brazilian government bonds, which validates its vast usage as a proxy of the country risk premium applied for the Brazilian stock market.

A crescente integração econômica e mobilidade de capital levam a uma maior exposição dos investidores a riscos externos. Com isso, ganha relevância a discussão sobre como se considerar, no cálculo do custo de capital, possíveis prêmios requeridos pelos riscos adicionais da realização de negócios em mercados emergentes. A existência de um adicional de risco é relativamente evidente, podendo ser constatada pela maior volatilidade que grande parte dos mercados acionários emergentes possuem em relação a mercados maduros, como o norte-americano. Entretanto, a existência de um prêmio requerido por esse risco adicional é menos óbvia e sua observação empírica, por dados passados, usualmente não gera resultados conclusivos. Nesse contexto, a presente pesquisa aborda o prêmio pelo risco país no mercado acionário brasileiro, apresentando as formas mais usualmente aplicadas para estimá-lo e discutindo sobre a possibilidade de eliminá-lo através da diversificação dos investimentos. A maior contribuição realizada está na aplicação do modelo de valoração de ativos AEG (Abnormal Earnings Growth) para se estimar esse prêmio. O AEG torna viável o cálculo do custo de capital implícito nas as expectativas de resultados futuros divulgadas por instituições financeiras em mídias especializadas. O prêmio pelo risco país foi, então, estimado através do diferencial entre o custo de capital das principais empresas brasileiras e o custo de capital de um grupo de empresas comparáveis norte-americanas, ambos calculados pelo AEG. Identificou-se um custo de capital maior em 2,09% (209 basis points) para as empresas brasileiras, que se mostrou estatisticamente significante. Esse resultado comprova empiricamente a existência de um prêmio específico do mercado brasileiro, indicando que ainda existem barreiras à diversificação internacional dos riscos domésticos. Adicionalmente, a estimativa ficou bastante próxima do prêmio pelo risco soberano brasileiro, o que valida a sua ampla utilização como proxy do prêmio do mercado acionário. / The increasing economic integration and capital mobility among countries lead investors to be more exposed to external risks. That grants relevance to the discussion on how to consider, in the cost of equitys estimation, premiums for additional risks of businesses performed in emergent markets. The existence of an additional risk in these markets is relatively clear, what is demonstrated by higher volatilities that the majority of emergent stock markets presents if compared to mature markets. Nevertheless, the existence of a risk premium is less obvious and its empirical observation, applying historical data, usually doesnt produce any conclusive result. Within this framework, the present research approaches the country risk premium in the Brazilian stock market, introducing the most usual means to estimate it and discussing about the potential elimination of the country risk through investment diversification. The greatest contribution of this research is the application of the Abnormal Earnings Growth Model (AEG) to estimate the country risk premium. AEG makes viable the inference of the cost of equity implied in future earnings expectations, published by financial institutions through specialized media. The country risk premium was, then, estimated through the difference between the implied cost of equity of the main Brazilian public companies and the implied cost of equity of a comparable north-American group of companies, both calculated using the AEG. Was perceived a cost of equity higher in 2,09% (209 basis points) for the Brazilian companies, what was shown statistically significant. This result proofs the existence of a country risk premium for the Brazilian market, indicating that there are still some barriers to the international diversification of domestic risks. Additionally, this result is very close to the default risk premium of the Brazilian government bonds, which validates its vast usage as a proxy of the country risk premium applied for the Brazilian stock market.