In this thesis, portfolio optimisation is used to evaluate if a specific sample of portfolios have a higher risk level or lower expected return, compared to what may be obtained through optimisation. It also compares the return of optimised portfolios with the return of the original portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for the optimisations. With the expected return and risk level used in this thesis, all portfolios can obtain a higher expected return and a lower risk. Over a six-month period, the optimised portfolios do not consistently outperform the original portfolios and therefore it seems as though the optimisation do not improve the return of the portfolios. This might be due to the uncertainty of the expected returns used in this thesis.

Stabilieji skirstiniai yra plati tikimybinių skirstinių klasė. Atsitiktiniai dydžiai, pasiskirstę pagal stabiliuosius skirstinius, pasižymi savybe – jų suma taip pat yra stabili. Šie pasižymi sunkiomis uodegomis ir, kai kuriais atvejais, asimetriškumu. Taigi jie gerai aprašo duomenis. Pagrindinis šių skirstinių trūkumas yra tas, kad nežinomos tikslios pasiskirstymo ir tankio funkcijų išraiškos (išskyrus kelis atvejus: normalusis, Koši ir Levi skirstiniai). Darbo pradžioje pateikta stabiliųjų skirtinių apžvalga bei jų pritaikymas finansų rinkose. Aprašytos pagrindinės stabiliųjų skirstinių savybės, įverčių skaičiavimo algoritmai bei optimalaus portfelio sudarymas ir jo vertės pokyčio rizikos mato (VaR) skaičiavimas. Antroje darbo dalyje nagrinėjamas optimaliojo investicinio portfelio „normalioje“ ir „stabilioje“ rinkoje sudarymas. Rizikos matu laikomas sklaidos parametras (stabiliuoju atveju) arba standartinis nuokrypis, padalintas iš kvaratinės šaknies iš 2, (normaliuoju atveju). Palyginami portfeliai, sudaryti iš septyniolikos lietuviškų akcijų, gauti pagal skirtingas tikimybines prielaidas. Parodyta, kad optimalieji portfeliai skiriasi, kuomet duomenys yra pasiskirstę pagal stabilųjį ir normalųjį skirstinius. / Stable distributions are a rich class of probability distributions that allow skewness and heavy tails. The lack of closed formulas for densities and distribution functions for all distributions (except Gaussian, Cauchy and Levy distributions) is the major drawback. There is an overview of the stable distributions and their applications in finance markets at the beginning of this paper. There are described basic properties of stable distributions, estimation algorithms and optimal asset allocation and stable computation of Value at Risk in the first part of the work. We analyze an investment allocation problems in this work. We consider as the risk measure the estimate of scale parameter (in the stable case) or the expected value of absolute deviation divided by square root of 2 (in Gaussian case). We examine the optimal allocation between seventeen risky assets with normal or stable distributed returns and then we compare the allocation obtained under the Gaussian and stable distributional assumptions. We show that there are differences in the allocation when the data follow the stable non-Gaussian and the normal distribution.

This paper examines data for 12,868 individuals from the National Longitudinal Survey of Youth (NLSY79) from 1979 through 2010 to explore certain financial incentives of marriage. In particular, this paper focuses on identifying the combination of occupations that decreases idiosyncratic income volatility to the greatest extent. For the sake of this paper, marriage is defined as the combination of two separate assets into a single portfolio. With such, I derive the efficient frontier for each occupation and gender. In the process, reward-to-volatility and mean-variance utility maximization techniques are introduced. Ultimately, applying modern portfolio theory to the marriage market allows one to examine the economic incentives of marriage in a way that has not previously been done. On the whole, the analysis confirms previous literature on marriage dynamics, while offering a new framework for analysis.

This thesis will focus on the creation of a portfolio. The first part of this paper describes how to get the efficient frontier of a portfolio. The thesis explains things such as the diversification and international diversification of the portfolio. It also explains how the investor can use it for his profit. In the second part of this paper, these methods are tested and evaluated in the condition of today's globalized world.

This diploma thesis deals with optimization models of financial risks. The first part, which is devoted to the theoretical background, introduces the basic concepts of optimization, modern portfolio theory, fundamental and technical analysis and statistical background. The basic principles of operation of modern portfolio theory are presented. The methods for analysis and selection of assets called Growth at A Reasonable Price and portfolio optimization approach according to Harry Markowitz were used with selected methods. The practical part is focused on the data analysis, selection of assets and design of a portfolio optimization model according to selected conditions with an emphasis on minimizing investment risk. The used models examine the selected data and are solved using the MS Excel add-in Solver version.

The efficient portfolios for the period 1993 – 2010 based on IPD data have a major portfolio weight in residential properties in the three largest regions Stockholm, Gothenburg and Malmo. The portfolio with the highest risk adjusted return (measured as the highest Sharpe-ratio) combines a large portfolio weight in residential properties with a small weight in industrial properties. During the time period of 2005 – 2010 a majority of the listed real estate companies held a real estate portfolio far below the efficient frontier based on the corresponding IPD data. These companies can increase their total return without taking on any more risk by using the concept of diversification. When including all available diversification categories two out of seven companies can be said to have an efficient real estate portfolio. When we excluded the outperforming residential asset class, however, none of the companies’ portfolios were in fact efficient. The real estate market is inefficient and thus results in the IPD data being less useful as it is based on transactions occurring in this inefficient market. Investors can, in this market, easily find properties with another risk and return profile than what IPD indicates is the market risk and return for a particular property type in a certain region. The inefficiency of the market, together with the IPD data being less useful, thus makes it difficult for the companies to focus on diversification in their investment strategy. Moreover, there are several reasons that explain the discrepancy between the actually held listed real estate portfolios and the optimal portfolio based on IPD data. Since each property is heterogeneous and possesses unique risks, investors are not able to accurately quantify the risk of each investment and thus rely more on their gut feeling. This also results in investors focusing on single investment opportunities rather than looking at all investments from a portfolio perspective.

This thesis investigates how ESG ratings for Nordic companies vary between two ESG providers, and how the risk and expected return differs between two highly rated ESG portfolios according to the two providers. In doing so, we aim to contribute to research on the topic of ESG divergence as it is of great importance for investors that this subject is studied further. To achieve the purpose of this thesis, secondary data was gathered in terms of ESG ratings from two chosen providers, S&P Global and Refinitiv. Based on the collected data, a Spearman correlation analysis was performed as well as statistical investigations in Excel in order to examine the rating divergence between the two providers. Additionally, efficient frontier values of the two provider dependent portfolios were calculated using R Studio. The results found suggests that there is an evident ESG rating divergence amongst all companies examined, regardless of origin and industry. Furthermore, it was concluded that Refinitiv consistently rated companies higher than S&P Global. The comparison between the two provider dependent portfolios illustrates that relying on ESG ratings from different providers will result in different portfolio composition. In turn, this has an impact on investors seeking to implement ESG as a part of their investment strategy. The results indicate that the composition differences affects portfolio performance. This led to the conclusion that it is of great importance for investors to be aware of the existing divergence in order to make accurate investment decisions.

The State of Mississippi wants to manage its oyster resource to increase production, quality, ecological, and economic benefits. In this study, we employ modern portfolio theory (MPT) to test if there are potential gains to hold multiple oyster resources for multiple benefits to aid the state's effort in achieving its goal. Using a Delphi approach, we elicit complete sets of data on ecosystem services (on oxygen, nutrients, sedimentation, and salinity) across multiple oyster resources (traditional plantings, off-bottom farms, and restored reefs). A benefit transfer method is used later to assigned money-metric value to each service estimate. The multiple service values are then aggregated into net service value. We compute the means, standard deviations, and correlations of benefits across all resources using the net service values, and generate efficient frontiers from that information. Results indicate that Mississippi could benefit from holding multiple oyster resources while focusing more on off-bottom oyster farms.

An asset manager's goal is to provide a high return relative the risk taken, and thus faces the challenge of how to choose an optimal portfolio. Many mathematical methods have been developed to achieve a good balance between these attributes and using di erent risk measures. In thisthesis, we test the use of a relatively simple and common approach: the Markowitz mean-variance method, and a more quantitatively demanding approach: the tail optimization method. Using active portfolio based on data provided by the Swedish fund management company Enter Fonderwe implement these approaches and compare the results. We analyze how each method weighs theunderlying assets in order to get an optimal portfolio.

I och med pensionsreformen vid sekelskiftet lades ett större ansvar på den individuelle pensionsspararen då man nu själv ska besluta hur en del av den allmänna pensionen ska placeras. Syftet med denna uppsats är att analysera huruvida det hade varit möjligt för en pensionssparare att uppnå en högre riskjusterad avkastning för sin premiepension genom att göra ett aktivt val i form av en egen sammansatt portfölj, än att låta staten förvalta pensionen i förvalsalternativet AP7 Såfa. Analysen är baserad på Harry Markowitz etablerade moderna portföljteori där han uppmärksammade hur sparare genom diversifiering kan reducera risken i sin placering genom att välja tillgångar som inte fullt samvarierar. Genom användning av tillgänglig data för tidsperioden 2000 – 2014 över de fonder som finns valbara i PPM-systemet har vi beräknat de optimala portföljer med samma risknivå som förvalsalternativet. Därefter har dessa jämförts med försvarsalternativet med avseende på risk och avkastning. Dessutom har tre teoretiska portföljer satts samman över en period på tio år, som placerats som dessa optimala portföljer och omallokerats efter Markowitz rekommendation att se över sitt sparande en gång om året. Analysen visar att det har gått att uppnå en högre riskjusterad avkastning genom att själv göra ett aktivt val av portfölj i sitt sparande. Problemet ligger i att det är svårt att identifiera dessa portföljer i förtid. De tre teoretiska portföljerna har samtliga presterat väsentligt mycket sämre än vad förvalsalternativet har gjort under samma tidsperiod. Resultatet visar att förvalsalternativet inte är fullt riskjusterat, man har alltså inte fullt fått betalt för den risk man tagit i sitt sparande. Vi drar ändå slutsatsen att förvalsalternativet är ett fullgott alternativ. / The Swedish premium pension reform at the turn of the century resulted in a greater responsibility for the individual saver. The decision concerning how the premium pension should be invested now lies with the investor. The purpose of this thesis is to analyze whether it had been profitable for a saver to achieve a higher risk-adjusted return for its premium pension money contributions by making an active choice by a self-composed portfolio, rather than to allow the State to invest the capital in the Seventh AP Fund (AP7 Såfa) which is the default option. The analysis is based on Harry Markowitz’s established Modern Portfolio Theory by which he drew attention to how investors through diversification can reduce risk in its investment by choosing assets that are not fully correlated. By using the available data of the funds that were selectable in the Swedish Premium Pension system by the time period 2000 – 2014, we have calculated the optimized portfolios with the same risk level as the default option. Subsequently, a comparison of these optimized portfolios and the default option are made in terms of risk and return. Furthermore, three theoretical portfolios are put together over a period of ten years and are invested as these optimized portfolios and reallocated after Markowitz's recommendation to review their savings once a year. The analysis shows that it has been possible to achieve higher risk-adjusted returns by making an active choice of portfolio. The problem though is that it is difficult to identify these portfolios in advance. The three theoretical portfolios have all generated a lower return than the default option did during the same period. The result shows that the default option is not fully risk-adjusted. Nonetheless, we conclude that the default fund is a good alternative.