My dissertation considers solving of linear programming problems with p-order conic constraints that are related to a class of stochastic optimization models with risk objective or constraints that involve higher moments of loss distributions. The general proposed approach is based on construction of polyhedral approximations for p-order cones, thereby approximating the non-linear convex p-order conic programming problems using linear programming models. It is shown that the resulting LP problems possess a special structure that makes them amenable to efficient decomposition techniques. The developed algorithms are tested on the example of portfolio optimization problem with higher moment coherent risk measures that reduces to a p-order conic programming problem. The conducted case studies on real financial data demonstrate that the proposed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.

[pt] Black e Litterman propuseram um modelo de otimização de portfólio que combina visões do investidor sobre retornos esperados de ativos com o equilíbrio neutro de mercado. No entanto, especificar visões sobre uma carteira de investimentos é uma tarefa difícil, especialmente quando os investidores têm opiniões conflitantes sobre o mesmo ativo. Neste trabalho, é proposto uma nova formulação para otimização de carteiras, que é robusta diferentes à visões do investidor. A nossa abordagem foi testada em dados sintéticos e dados reais disponíveis em uma plataforma do Banco Central do Brasil. Esta plataforma consolida projeções macroeconômicas de mais de uma centena de analistas profissionais e disponibiliza para o mercado numa base semanal. Por fim, é comparado o desempenho desta formulação robusta com o modelo Black-Litterman tradicional frequentemente utilizado na indústria financeira. Os resultados mostram que a metodologia robusta pode providenciar melhor desempenho ajustado ao risco em comparação com o modelo orignial e são menos sensíveis às visões do investor. / [en] Black and Litterman proposed a portfolio optimization model that combines investor s views on future asset s returns with neutral market equilibrium. However, specifying portfolio views is a challenging task, specially when investors have conflicting opinions on the same asset. In this thesis, we suggest a new portfolio optimization formulation that is robust for investor s views. Our approach was tested on synthetic and real data available on a framework developed by Central Bank of Brazil. This online framework collects projections on main macroeconomics variables from more than a hundred professional forecasters and provides public online access on a weekly basis. The performance of this new robust formulation is compared with the traditional Black-Litterman model. The result show that our robust methodology can provide better risk adjusted performance compared to the orignial model and are less sensitive to incorrect inverstor views.

<p>The purpose of the thesis has been to explore the use of hedge fund styles when constructing portfolios of hedge funds (i.e. funds of hedge funds). The central question is if the use of hedge fund styles can significantly explain and improve risk adjusted returns (characterized by Sharpe ratios). The study has been done in collaboration with Optimized Portfolio Management AB who desire further knowledge and evaluation of hedge fund styles for their fund of hedge funds.</p><p>To be able to create successful ex ante portfolios we have explored various prediction models for both risk and return. Our findings indicate that return prediction is problematic using simple models such as regression since the risk exposure of the indices appear to change significantly over time. One can however using exponentially weighted moving averages (EWMA) achieve relatively promising estimations of future returns. </p><p>Covariance matrix estimation seems to be more straightforward. We have achieved promising results using both traditional EWMA models as well as improved estimators using principal component analysis.Covariance prediction models were evaluated separately using a minimum-variance portfolio optimization technique and provided a significant risk reduction compared to the aggregated hedge fund universe (represented by a naively diversified portfolio). Combinations of risk and return prediction models were evaluated using traditional mean-variance portfolio construction methods, which were optimized for Sharpe ratios. These provided a significant increase in risk adjusted returns relative to the aggregated hedge fund universe. The allocation is however discouraging due to serious instability over time.</p><p>Our findings indicate that there indeed is an advantage of taking hedge fund styles into consideration when constructing funds of hedge funds in a risk adjusted perspective. However, further research into return prediction needs to be done in order to stabilize portfolio allocation. An alternative seems to be tactical style allocation on a more fundamental analysis basis.</p>

<p><strong>Bakgrund:</strong> Sedan introduktionen i början av 1990-talet har utvecklingen av volymen nyemitterade aktieindexobligationerna totalt sett varit positiv vilket tyder på att produkten blivit en populär sparform hos svenskar. Detta tillsammans med det faktum att det finns få studier gjorda kring aktieindexobligationer som sparform där ett större perspektiv tas i beaktande gör ämnet intressant att studera.</p><p><strong>Syfte:</strong> Uppsatsens syfte är att kartlägga och analysera för vilka privata investerare aktieindexobligationer passar som sparform ur ett livscykelperspektiv med utgångspunkt i (i) bransch- och rådgivningspraxis, (ii) finansiell riskhanteringsteori med fokus på portföljvalsteori och (iii) historisk data avseende risk och avkastning.</p><p><strong>Genomförande:</strong> Studien har genomförts med hjälp av att intervjua privatrådgivare, kapitalrådgivare och personer som arbetar med strukturerade produkter på storbanker och hos mindre finansiella aktörer. Fem stereotyper har använts som diskussionsunderlag vid intervjuerna. För att kunna föra en djupare analys kring produkten som sparform för privata investerare har en portföljoptimering genomförts för att ta historisk data gällande risk och avkastning i beaktande.</p><p><strong>Slutsats:</strong> Studien fastställer att produkten passar privata investerare som befinner sig i den senare delen av konsolideringsfasen och inte är de mest riskbenägna. Studien visar att det främst är kredit- och marknadsrisken som är kopplade till aktieindexobligationer samtidigt som risken i produkten bedöms som låg. Studien visar även på att egenskaper som tillförs investerares portföljer är låg risk samt en potentialaspekt.</p> / <p><strong>Background:</strong> Since the introduction in the early 1990s, the volume of newly issued equity index bonds overall had a positive development. This increase indicates that the product has become a popular form of savings among Swedes. Together with the fact that there are few studies done on equity index bonds as a savings product. A wider perspective has been taken into account which makes the subject interesting to study.</p><p><strong>Aim: </strong>Purpose of this study is to identify and analyze for who private investors equity index bonds fit as a savings product on lifecycle thought based on (i) professional and consulting practices, (ii) financial risk management theory, focusing on portfolio theory, and (iii) historical data on risk and return.</p><p><strong>Completion: </strong>The study was completed using interviews with private consultants, capital advisors and people working with structured products at major banks and of small players. In addition, five stereotypes were used as a basis for discussion during the interviews. In order to conduct a deeper analysis of the product as a form of saving for private investors, a portfolio optimization carried out taking the historical data on risk and return into account.</p><p><strong>Conclusion:</strong> The study determines that the product is suitable for private investors who are in the latter part of the consolidation phase and mainly not prone to risk. The study suggests that equity index bonds primarily are associated with credit- and market risk, while the risk of the product is assessed as low. The study also indicates that the properties that are added to investors’ portfolios are low risk and a potential aspect.</p>

The purpose of the thesis has been to explore the use of hedge fund styles when constructing portfolios of hedge funds (i.e. funds of hedge funds). The central question is if the use of hedge fund styles can significantly explain and improve risk adjusted returns (characterized by Sharpe ratios). The study has been done in collaboration with Optimized Portfolio Management AB who desire further knowledge and evaluation of hedge fund styles for their fund of hedge funds. To be able to create successful ex ante portfolios we have explored various prediction models for both risk and return. Our findings indicate that return prediction is problematic using simple models such as regression since the risk exposure of the indices appear to change significantly over time. One can however using exponentially weighted moving averages (EWMA) achieve relatively promising estimations of future returns. Covariance matrix estimation seems to be more straightforward. We have achieved promising results using both traditional EWMA models as well as improved estimators using principal component analysis.Covariance prediction models were evaluated separately using a minimum-variance portfolio optimization technique and provided a significant risk reduction compared to the aggregated hedge fund universe (represented by a naively diversified portfolio). Combinations of risk and return prediction models were evaluated using traditional mean-variance portfolio construction methods, which were optimized for Sharpe ratios. These provided a significant increase in risk adjusted returns relative to the aggregated hedge fund universe. The allocation is however discouraging due to serious instability over time. Our findings indicate that there indeed is an advantage of taking hedge fund styles into consideration when constructing funds of hedge funds in a risk adjusted perspective. However, further research into return prediction needs to be done in order to stabilize portfolio allocation. An alternative seems to be tactical style allocation on a more fundamental analysis basis.

Bakgrund: Sedan introduktionen i början av 1990-talet har utvecklingen av volymen nyemitterade aktieindexobligationerna totalt sett varit positiv vilket tyder på att produkten blivit en populär sparform hos svenskar. Detta tillsammans med det faktum att det finns få studier gjorda kring aktieindexobligationer som sparform där ett större perspektiv tas i beaktande gör ämnet intressant att studera. Syfte: Uppsatsens syfte är att kartlägga och analysera för vilka privata investerare aktieindexobligationer passar som sparform ur ett livscykelperspektiv med utgångspunkt i (i) bransch- och rådgivningspraxis, (ii) finansiell riskhanteringsteori med fokus på portföljvalsteori och (iii) historisk data avseende risk och avkastning. Genomförande: Studien har genomförts med hjälp av att intervjua privatrådgivare, kapitalrådgivare och personer som arbetar med strukturerade produkter på storbanker och hos mindre finansiella aktörer. Fem stereotyper har använts som diskussionsunderlag vid intervjuerna. För att kunna föra en djupare analys kring produkten som sparform för privata investerare har en portföljoptimering genomförts för att ta historisk data gällande risk och avkastning i beaktande. Slutsats: Studien fastställer att produkten passar privata investerare som befinner sig i den senare delen av konsolideringsfasen och inte är de mest riskbenägna. Studien visar att det främst är kredit- och marknadsrisken som är kopplade till aktieindexobligationer samtidigt som risken i produkten bedöms som låg. Studien visar även på att egenskaper som tillförs investerares portföljer är låg risk samt en potentialaspekt. / Background: Since the introduction in the early 1990s, the volume of newly issued equity index bonds overall had a positive development. This increase indicates that the product has become a popular form of savings among Swedes. Together with the fact that there are few studies done on equity index bonds as a savings product. A wider perspective has been taken into account which makes the subject interesting to study. Aim: Purpose of this study is to identify and analyze for who private investors equity index bonds fit as a savings product on lifecycle thought based on (i) professional and consulting practices, (ii) financial risk management theory, focusing on portfolio theory, and (iii) historical data on risk and return. Completion: The study was completed using interviews with private consultants, capital advisors and people working with structured products at major banks and of small players. In addition, five stereotypes were used as a basis for discussion during the interviews. In order to conduct a deeper analysis of the product as a form of saving for private investors, a portfolio optimization carried out taking the historical data on risk and return into account. Conclusion: The study determines that the product is suitable for private investors who are in the latter part of the consolidation phase and mainly not prone to risk. The study suggests that equity index bonds primarily are associated with credit- and market risk, while the risk of the product is assessed as low. The study also indicates that the properties that are added to investors’ portfolios are low risk and a potential aspect.

A guaranteed minimum income benefit (GMIB) is a long-dated option that can be embedded in a deferred variable annuity. The GMIB is attractive because, for policyholders who plan to annuitize, it offers protection against poor market performance during the accumulation phase, and adverse interest rate experience at annuitization. The GMIB also provides an upside equity guarantee that resembles the benefit provided by a lookback option. We price the GMIB, and determine the fair fee rate that should be charged. Due to the long dated nature of the option, conventional hedging methods, such as delta hedging, will only be partially successful. Therefore, we are motivated to find alternative hedging methods which are practicable for long-dated options. First, we measure the effectiveness of static hedging strategies for the GMIB. Static hedging portfolios are constructed based on minimizing the Conditional Tail Expectation of the hedging loss distribution, or minimizing the mean squared hedging loss. Next, we measure the performance of semi-static hedging strategies for the GMIB. We present a practical method for testing semi-static strategies applied to long term options, which employs nested Monte Carlo simulations and standard optimization methods. The semi-static strategies involve periodically rebalancing the hedging portfolio at certain time intervals during the accumulation phase, such that, at the option maturity date, the hedging portfolio payoff is equal to or exceeds the option value, subject to an acceptable level of risk. While we focus on the GMIB as a case study, the methods we utilize are extendable to other types of long-dated options with similar features.

Current global efforts for energy conservation and optimization are focused on improvements in energy supply and production systems, and on encouraging the adoption of energy-efficient devices and equipment. However, systematic assessments of economic and technical implications when adopting energy-efficient alternative systems in buildings have not yet been explored thoroughly. The uncertainty about the consequences of investing in alternative energy-efficient systems has led to a prolonged utilization of obsolete building systems (underperforming HVAC systems, inefficient lighting systems, badly maintained and equipment, and so forth). This has led to overall poor energy efficiency, creating considerable burden on the building operation budget. This research discusses the procedure for formulating an investment strategy to improve existing building energy performance. The approach is suitable for large building portfolios where a plethora of potential refurbishment interventions can be considered. This makes our approach especially suited for use on university campuses and most of this report will focus on that particular application utilization protocols especially for use on campuses. This investment model only looks at the energy related savings versus investments; it is well understood that the ultimate selection of the optimal set of improvement options of a portfolio will be determined by additional considerations, such as overall value, occupant satisfaction, productivity improvements, aesthetics, etc. Nevertheless, many campus managers are confronted with the question how much energy they can save with a given investment amount. This is exactly what our approach helps to answer. The investment optimization strategy is implemented in software "InvEnergy," which systematically calculates the costs and benefits of all possible building-technology pairings, taking uncertainties in the saving/investment calculations and estimates into account. This tool empowers decision makers in facility management to make complex investment decisions during continuous building commissioning.

In this study, general geometric Levy market models are considered. Since these models are, in general, incomplete, that is, all contingent claims cannot be replicated by a self-financing portfolio consisting of investments in a risk-free bond and in the stock, it is suggested that the market should be enlarged by artificial assets based on the power-jump processes of the underlying Levy process. Then it is shown that the enlarged market is complete and the explicit hedging portfolios for claims whose payoff function depends on the prices of the stock and the artificial assets at maturity are derived. Furthermore, the portfolio optimization problem is considered in the enlarged market. The problem consists of choosing an optimal portfolio in such a way that the largest expected utility of the terminal wealth is obtained. It is shown that for particular choices of the equivalent martingale measure in the market, the optimal portfolio only consists of bonds and stocks. This corresponds to completing the market with additional assets in such a way that they are superfluous in the sense that the terminal expected utility is not improved by including these assets in the portfolio.

The most popular and fundamental portfolio optimization problem is Markowitz&#039 / s one period mean-variance portfolio selection problem. However, it is criticized because of its one period static nature. Further, the estimation of the stock price expected return is a particularly hard problem. For this purpose, there are a lot of studies solving the mean-variance portfolio optimization problem in continuous time. To solve the estimation problem of the stock price expected return, in 1992, Black and Litterman proposed the Bayesian asset allocation method in discrete time. Later on, Lindberg has introduced a new way of parameterizing the price dynamics in the standard Black-Scholes and solved the continuous time mean-variance portfolio optimization problem. In this thesis, firstly we take up the Lindberg&#039 / s approach, we generalize the results to a jump-diffusion market setting and we correct the proof of the main result. Further, we demonstrate the implications of the Lindberg parameterization for the stock price drift vector in different market settings, we analyze the dependence of the optimal portfolio from jump and diffusion risk, and we indicate how to use the method. Secondly, we present the Lagrangian function approach of Korn and Trautmann and we derive some new results for this approach, in particular explicit representations for the optimal portfolio process. In addition, we present the L2-projection approach of Schweizer for the continuous time mean-variance portfolio optimization problem and derive the optimal portfolio and the optimal wealth processes for this approach. While, deriving these results as the underlying model, the market parameterization of Lindberg is chosen. Lastly, we compare these three different optimization frameworks in detail and their attractive and not so attractive features are highlighted by numerical examples.