Optimal portfolios have historically been computed using standard deviation as a risk measure.However, extreme market events have become the rule rather than the exception. To capturetail risk, investors have started to look for alternative risk measures such as Value-at-Risk andConditional Value-at-Risk. This research analyzes the financial model referred to as Markowitz 2.0 and provides historical context and perspective to the model and makes a mathematicalformulation. Moreover, practical implementation is presented and an optimizer that capturesthe risk of non-extreme events is constructed, which meets the needs of more customized investment decisions, based on investment preferences. Optimal portfolios are generated and anefficient frontier is made. The results obtained are then compared with those obtained throughthe mean-variance optimization framework. As concluded from the data, the optimal portfoliowith the optimal weights generated performs better regarding expected portfolio return relativeto the risk level for the investment.

This thesis aims to investigate different types of optimization methods that can be used when optimizing fund of fund portfolios. Moreover, the thesis investigates which funds that should be included and what their respective portfolio weights should be, in order to outperform the Swedish SIX Portfolio Return Index. The funds considered for the particular fund of funds in this thesis are all managed by a particular company. The optimization frameworks applied include traditional mean variance optimization, min conditional value at risk optimization, as well as optimization methods studying alpha in combination with the risk measures tracking error and maximum drawdown, respectively. All four optimization methods were applied on a ten years data period as well as on a five years data period. It was found that while the funds have different strengths and weaknesses, four of the funds were considered most appropriate for the fund of funds. Geography and sector constraints were also taken into account and it was found that, in this particular case, the healthcare sector constraint affected the allocated portfolio weights the most. / Syftet med detta masterexamensarbete är att undersöka olika typer av optimeringsmetoder som kan användas vid optimering av en fond i fond. Vidare är syftet med optimeringen att utvärdera vilka fonder som bör inkluderas och vilka deras respektive portföljvikter bör vara för att prestera bättre än det svenska SIX Portfolio Return Indexet. Optimeringsmetoderna inkluderar traditionell modern portföljteori, minimering av conditional Value at Risk och optimeringsmetoder som studerar alpha i kombination med riskmåtten tracking error respektive maximum drawdown. Alla fyra optimeringsmetoder applicerades på en tio år lång respektive fem år lång dataperiod. Det visade sig att även om fonderna har olika styrkor och svagheter kunde fyra av fonderna anses vara mest lämpliga att inkluderas i fond i fonden. Geografiska och sektoriella begränsningar beaktades och det konstaterades att sektorbegränsningen för hälsovårdssektorn hade störst påverkan på resultatet.

In traditional investment decision making, one tool commonly used is the mean variance model, also known as an expected-value variance (EV) model, which evaluates the anticipated payout of different assets with respect to uncertainty where portfolios with higher risk demand higher expected returns from an individual. This thesis adapts this framework to a cost setting where decision makers are evaluating alternative physical assets that carry lifetime cost uncertainty for maintenance. Specifically, this paper examines homeowner choices for their home plumbing systems in the event of a pinhole leak, a tiny pin-sized hole that forms in copper, drinking-water pipes. These leaks can cause substantial damage and cost homeowners thousands of dollars in repairs. Since pinhole leaks are not related to the age of pipe material, a homeowner is subject to the risk of additional costs if a pinhole leak occurs again despite their repair efforts. The EV cost model in this paper defines two discrete choices for the homeowner in the event of a leak; to apply a simple repair at lower cost and higher future cost uncertainty, or to replace their plumbing with new pipe material, usually made of plastic, at a higher upfront cost but lower likelihood of future expenses. The risk preference of homeowners are demonstrated by their repair strategy selection, as well as the level of cost they incur to reduce uncertainty. Risk neutral individuals will select the repair strategy with the lowest lifetime expected cost and high variance, while risk averse homeowners will prefer to replace their plumbing with higher cost but lower variance. Risk averse individuals are also exposed to indirect costs, which is an additional unobserved cost in the form of a risk premium the homeowner is willing to pay to remove all uncertainty of future pinhole leak expense. Expected costs and variances are also higher for regions in the U.S. that experience elevated leak incident rates, known as hotspots. Using this mean variance cost framework, indirect cost can be quantified for homeowners in hotspot regions and compared to the rest of the U.S. to evaluate the magnitude of pinhole leak risk. The EV cost model estimates risk premiums on pinhole leaks to be $442 for homeowners in hotspots and $305 for those in the rest of the U.S. Finally, this paper examines the impact of pinhole leak cost uncertainty on the U.S. economy. Of an estimated $692 million in annual pinhole leak costs to homeowners, this study estimates a lower bound cost of $54 million per year (7.8% of estimated national annual cost) in risk premium that homeowners would be willing to pay to avoid pinhole leak cost uncertainty. Information in this study on the role of risk in home plumbing decisions and indirect costs would be helpful to policymakers and water utility managers as they deal with infrastructure management decisions. Furthermore, the EV cost methodology established in this paper demonstrates an effective use of mean variance modeling under cost uncertainty. / Master of Science

In this study within quantitative portfolio optimization, stochastic programming is investigated as an investment decision tool. This research takes the direction of scenario based Mean-Absolute Deviation and is compared with the traditional Mean-Variance model and widely used Risk Parity portfolio. Furthermore, this thesis is done in collaboration with the First Swedish National Pension Fund, AP1, and the implemented multi-asset portfolios are thus tailored to match their investment style. The models are evaluated on two different fund management levels, in order to study if the portfolio performance benefits from a more restricted feasible domain. This research concludes that stochastic programming over the investigated time period is inferior to Risk Parity, but outperforms the Mean-Variance Model. The biggest aw of the model is its poor performance during periods of market stress. However, the model showed superior results during normal market conditions. / I denna studie inom kvantitativ portföljoptimering undersöks stokastisk programmering som ett investeringsbeslutsverktyg. Denna studie tar riktningen för scenariobaserad Mean-Absolute Deviation och jämförs med den traditionella Mean-Variance-modellen samt den utbrett använda Risk Parity-portföljen. Avhandlingen görs i samarbete med Första AP-fonden, och de implementerade portföljerna, med era tillgångsslag, är därför skräddarsydda för att matcha deras investeringsstil. Modellerna utvärderas på två olika fondhanteringsnivåer för att studera om portföljens prestanda drar nytta av en mer restrektiv optimeringsmodell. Den här undersökningen visar att stokastisk programmering under undersökta tidsperioder presterar något sämre än Risk Parity, men överträffar Mean-Variance. Modellens största brist är dess prestanda under perioder av marknadsstress. Modellen visade dock något bättre resultat under normala marknadsförhållanden.

此篇論文利用馬可夫狀態轉換模型實證出在歐元區的股票市場中，以規模溢酬、價值溢酬以及市場溢酬建構的投資組合存在兩個不同的情境狀態。以歐元區市場溢酬和規模溢酬建構的投資組合(SMB portfolios)在牛市存在較高的平均報酬，另一方面以價值溢酬建構的投資組合(HML portfolios)則在熊市有較高的平均報酬。而以規模溢酬、價值溢酬以及歐元區市場溢酬建構的投資組合，其報酬率變異數在熊市皆比牛市來得高。由於此篇論文實證出不論在樣本內或樣本外的測試中，以規模溢酬以及價值溢酬建構的投資組合，其特色反轉投資策略皆優於買入並持有的投資策略，因此本篇論文建議，在歐元區以規模因素（size factor）及帳面價值與市價比因素（book-to-market factor）為考量建構投資組合時，考慮規模溢酬以及價值溢酬在不同情境狀態下的反轉異常現象是重要且不可忽視的課題。 / This paper documents the presence of two regimes in the joint distribution of stock returns on European market premium portfolio and portfolios tracking size- and value effects in the Euro area. The mean returns of the EMU market portfolio and SMB portfolios are higher in the bull state while the mean return of the HML portfolio is larger in the bear state. Volatilities of the EMU market portfolio, SMB portfolio and the HML portfolio are all larger in the bear state compared to the bull state. This paper uses the Markov regime-switching model to generate the switching signal of market, size and value portfolios in the stock market and reallocates the market, size and value portfolios in the stock market by the mean-variance approach. Since both in the in-sample and out-sample test, the performance of the style rotation strategy outperforms style consistent strategy of the SMB portfolio and HML portfolio, this paper proposes that when analyzing investments in returns of size and value portfolios in the European market, it is important for us to account for anomalies for size and value effects in European market under different regimes. In the regime-switching VAR(1) model to account for the net capital flow predictability on the stock returns of EMU market, SMB and HML portfolios and the interrelationships among these variables. The result shows that adding the European Union net capital flow in relation to the economy's size as the predictor variable to the regime switching VAR(1) model, it improves the asset allocation outcomes both in the in-sample and out-sample test. Furthermore, this paper has found that both in the bull and bear states, the impulse response function shows that a shock of one standard deviation of net capital inflows last month will reduce the EMU market return up to near three months. Besides, the net capital inflow shock in European stock market will generates appreciation of companies with low book-to-market ratios (growth stocks) and large-sized firms in the bull state, while it generates appreciation of companies with high book-to-market ratios (value stocks) in the bear state.

資產配置乃是將資金分散投資到主要的資產類別中，諸如股票、債券、現金等。傳統的均數/變異數方法在資產配置上早已被廣泛的運用。但是，現今的金融情勢多變，多期配置的需求提高，傳統均數/變異數方法只處理單一期間的資產配置，且反應未來的能力不佳，顯然已經不適用。 本論文提供一種多期動態的資產配置，可以改良過去單點估計值的缺點，同時能夠將未來情境納入考量，使多期資產配置更富策略性。並實證在兩期的情況下，期中調整資產組合與不調整的差異性。從而瞭解持續的動態規劃，方能提升資產配置的效率性。 / Asset allocation is the process of dividing an investment fund among major asset classes such as equities, bonds, cash, etc. Traditional mean-variance portfolio selection is widely used for asset allocation. However, as time goes by, the financial condition changes rapidly. The method of mean-variance analysis has some limitations. It not only can’t deal with multiperiod asset allocation, but also cannot reflect future economic circumstances, especially for long-term investments. This research tries to use the method of multi-stage dynamic programming for asset allocation. This method can improve the pits of single estimate in using mean-variance analysis, and take future scenarios into account so that the model will become more useful in practice. The two-period empirical results have shown that using continuous dynamic programming to build strategic asset allocation decision can improve the efficiency of asset allocation.

Cette thèse s’attèle à déterminer les conséquences théoriques et empiriques de la considération d’indicateurs socialement responsables dans la sélection de portefeuille traditionnelle. Le premier chapitre étudie la significativité de la perte d’efficience moyenne-variance d’un portefeuille d’obligations souveraines lorsque l’on introduit une contrainte sur la notation socialement responsable moyenne des Etats. En utilisant un échantillon d’obligations d’Etats développés sur la période 1995-2008, nous montrons qu’il est possible d’augmenter sensiblement la notation socialement responsable moyenne sans perdre significativement en termes de diversification. Le second chapitre propose une analyse théorique de l’effet sur la frontière efficiente d’une contrainte sur la notation socialement responsable du portefeuille. Nous mettons en évidence les différents cas de figure pouvant se produire en fonction de la corrélation entre les rendements attendus et les notations socialement responsables et de l’aversion au risque de l’investisseur. Enfin, puisque la question de l’efficience des portefeuilles investis en fonction de critères socialement responsables fait débat dans la littérature financière, un dernier chapitre propose un nouveau test d’efficience moyenne-variance dans le cas réaliste où aucun actif sans risque n’est disponible. / This thesis aims at determining the theoretical and empirical consequences of the consideration of socially responsible indicators in the traditional portfolio selection. The first chapter studies the significance of the mean-variance efficiency loss of a sovereign bond portfolio when introducing a constraint on the average socially responsible ratings of the governments. By using a sample of developed sovereign bonds on the period 1995-2008, we show that it is possible to increase sensibly the average socially responsible rating without significantly losing in terms of diversification. The second chapter proposes a theoretical analysis of the impact on the efficient frontier of a constraint on the socially responsible ratings of the portfolio. We highlight that different cases may arise depending on the correlation between the expected returns and the socially responsible ratings and on the investor’s risk aversion. Lastly, as the issue of the efficiency of socially responsible portfolios is a central point in the financial literature, the last chapter proposes a new mean-variance efficiency test in the realistic case where there is no available risk-free asset.

Submitted by Diego de Carvalho Martins (diego.cmartins@gmail.com) on 2015-03-03T17:37:26Z No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717457 bytes, checksum: 7b47eb855a437b18798c842352f083b8 (MD5) / Rejected by Renata de Souza Nascimento (renata.souza@fgv.br), reason: Prezado Diego, Encaminharei por e-mail o que deve ser alterado, para que possamos aceita-lo junto à biblioteca. Att Renata on 2015-03-03T21:33:00Z (GMT) / Submitted by Diego de Carvalho Martins (diego.cmartins@gmail.com) on 2015-03-03T22:13:33Z No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717977 bytes, checksum: 446abdc648b62abddb519b99648b6a3a (MD5) / Approved for entry into archive by Renata de Souza Nascimento (renata.souza@fgv.br) on 2015-03-04T17:27:29Z (GMT) No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717977 bytes, checksum: 446abdc648b62abddb519b99648b6a3a (MD5) / Made available in DSpace on 2015-03-04T18:27:00Z (GMT). No. of bitstreams: 1 Dissertação Diego Martins Vf.pdf: 5717977 bytes, checksum: 446abdc648b62abddb519b99648b6a3a (MD5) Previous issue date: 2015-02-06 / This work aims to analyze the performance of regularized mean-variance portfolios, employing financial assets available in Brazilian markets. In particular, regularized portfolios are obtained by restricting the norm of the portfolio-weights vector, following DeMiguel et al. (2009). Additionally, we analyze the performance of portfolios that take into account information about the group structure of assets with similar characteristics, as proposed by Fernandes, Rocha and Souza (2011). While the covariance matrix employed is the sample one, the expected returns are obtained by reverse optimization of market equilibrium portfolio proposed by Black and Litterman (1992). The empirical analysis out of the sample for the period between January 2010 and October 2014 indicates that, in line with previous studies, penalizing the norm of weights can (depending on the chosen standard and intensity of the restriction) lead to portfolios having best performances in terms of return and Sharpe, when compared to portfolios obtained via Markowitz models. In addition, the inclusion of group information can also be beneficial in order to calculate optimal portfolios, when compared to both Markowitz portfolios or without using group information. / Este trabalho se dedica a analisar o desempenho de modelos de otimização de carteiras regularizadas, empregando ativos financeiros do mercado brasileiro. Em particular, regularizamos as carteiras através do uso de restrições sobre a norma dos pesos dos ativos, assim como DeMiguel et al. (2009). Adicionalmente, também analisamos o desempenho de carteiras que levam em consideração informações sobre a estrutura de grupos de ativos com características semelhantes, conforme proposto por Fernandes, Rocha e Souza (2011). Enquanto a matriz de covariância empregada nas análises é a estimada através dos dados amostrais, os retornos esperados são obtidos através da otimização reversa da carteira de equilíbrio de mercado proposta por Black e Litterman (1992). A análise empírica fora da amostra para o período entre janeiro de 2010 e outubro de 2014 sinaliza-nos que, em linha com estudos anteriores, a penalização das normas dos pesos pode levar (dependendo da norma escolhida e da intensidade da restrição) a melhores performances em termos de Sharpe e retorno médio, em relação a carteiras obtidas via o modelo tradicional de Markowitz. Além disso, a inclusão de informações sobre os grupos de ativos também pode trazer benefícios ao cálculo de portfolios ótimos, tanto em relação aos métodos tradicionais quanto em relação aos casos sem uso da estrutura de grupos.

This thesis aims at determining the theoretical and empirical consequences of the consideration of socially responsible indicators in the traditional portfolio selection. The first chapter studies the significance of the mean-variance efficiency loss of a sovereign bond portfolio when introducing a constraint on the average socially responsible ratings of the governments. By using a sample of developed sovereign bonds on the period 1995-2008, we show that it is possible to increase sensibly the average socially responsible rating without significantly losing in terms of diversification. The second chapter proposes a theoretical analysis of the impact on the efficient frontier of a constraint on the socially responsible ratings of the portfolio. We highlight that different cases may arise depending on the correlation between the expected returns and the socially responsible ratings and on the investor’s risk aversion. Lastly, as the issue of the efficiency of socially responsible portfolios is a central point in the financial literature, the last chapter proposes a new mean-variance efficiency test in the realistic case where there is no available risk-free asset. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit. / This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit.