Avkastningen från privata och publika fastighetsinvesteringar är något som undersökts extensivt, med slutsatsen att noterade fastighetsinvesteringar uppvisat en högre avkastning jämfört med onoterade fastighetsinvesteringar på kort sikt. Denna uppsats avser att analysera historiska direktavkastningar i syfte av att upptäcka eventuella diskrepanser i värdering mellan noterade och onoterade fastighetsinvesteringar. Utöver det, avser denna uppsats att diskutera huruvida det föreligger fördelar med att äga onoterade fastigheter som skulle motivera en högre värdering, trots historiskt lägre totalavkastning. Den underliggande datan är hämtad från MSCI Sweden Annual Property Index och Refinitiv Worldscope Fundamentals-databasen som säkerställts med årsredovisningar för de noterade fastighetsföretagen. Med hjälp av denna data skapades två direktavkastningsserier för perioden mellan 2000 - 2019. Dessa jämfördes sedan med varandra och påvisade diskrepanser i form av högre direktavkastning på den noterade marknaden under större delar av 00-talet medan den onoterade marknaden uppvisade en högre direktavkastning mellan 2011 - 2016. Sedan dess har direktavkastningen för båda noteringsformerna sjunkit till historiskt låga nivåer. Vad gäller onoterade fastighetsinvesteringar återfinns fördelar i form av målstyrning och genomförandet av långsiktiga utvecklingsprojekt, ofta som en del av en långsiktig och värdeskapande ägarstrategi. / The return of private and public real estate is a matter that has been studied extensively and has often proved the outperformance of securitized real estate over direct property in the short term. This paper will analyze historical capitalization rates in order to locate any value discrepancies between the direct and indirect property market in Sweden. Furthermore, the paper aims to understand whether there are any benefits to holding direct property, otherwise not justified by higher returns, that would explain its high valuation. The underlying data collection relies on MSCI Sweden Annual Property Index as well as financial reports and profile data from the Refinitiv Worldscope Fundamentals database for the listed real estate companies. Using the collected data, net operating income yields were built for the direct and indirect property market for the period between 2000 - 2019. These historical capitalization rate series were then compared to each other and showed some discrepancy in favor of securitized real estate which demonstrated higher capitalization rates during most of the 2000s. However, the direct real estate market was shown to outperform the indirect one between 2011 - 2016. Ever since, public and private real estate on the Swedish market has shown similar valuations and the capitalization rates are now historically low, (as at December 2019). As for holding direct property, advantages include the ability to carry out development projects, which are often part of a long-term and value-adding ownership strategy.

This thesis analyzes the mean variance optimization problem with respect to cardinalityconstraints. The aim of this thesis is to figure out how much of an impact transactionchanges has on the profit and risk of a portfolio. We solve the problem by implementingmixed integer programming (MIP) and solving the problem by using the Gurobi solver.In doing this, we create a mathematical model that enforces the amount of transactionchanges from the initial portfolio. Our results is later showed in an Efficient Frontier,to see how the profit and risk are changing depending on the transaction changes.Overall, this thesis demonstrates that the application of MIP is an effective approachto solve the mean variance optimization problem and can lead to improved investmentoutcomes.

Thesis (MBA.) -- University of Limpopo, 2015 / The Department of Economic Development, Environment and Tourism is mandated to focus on growing the provincial economy, empowering women and youth, on supporting small businesses and co-operatives and improving the lives of the people of the province for the better as indicated in the Limpopo Economic Development, Environment and Tourism Province Budget Vote (2015/16). Economic growth and social wellbeing are closely tied to the ability to protect the natural environment. Mining, electricity generation and agriculture are among the economic activities that have a direct impact on the environment and need to be carried out in a sustainable and responsible manner. Towards this vision, the assets which are furniture, transport, computer hardware and other machinery and equipment need to be managed efficiently and effectively in order to fulfil the needs of society and the departments. These assets represent an enormous value for the owner which is LEDET and for society at large. To grasp the full potential of these assets, a deep and thorough understanding of an asset’s complete lifetime is needed. However, the assets especially physical assets, public buildings and infrastructures are not managed properly and that results in numerous challenges and audit queries that are raised by the Auditor General. The purpose of this study was to investigate the challenges that are facing the asset management unit of Limpopo Department of Economic Development & Tourism (LEDET). Asset Management has been hailed as important in order to enable government to deliver proper services to the citizens of the country. This has encouraged the researcher to undertake the study in order to add more knowledge on the asset management process of the government, looking at the challenges and possible solutions. The need for this study was considered relevant and necessary as government departments and other private sectors face numerous challenges in implementing the asset management. Limpopo Department of Economic Development, Environment and Tourism, as a case study, faces challenges in fulfilling some of its mandate due to lack of support from asset management activities. In terms of its strategic plan, the department seeks to address issues relating to economic growth, the promotion and development of tourism and using environmental management to guide and monitor sustainable development in the province. These challenges have negative implications on the delivery of services to the communities it serves. In this study, the researcher investigated the following: demographic profile of respondents, challenges facing asset management, the impact of asset management on service delivery and lastly the best practice on the implementation of asset management. Data were analysed into themes and revealed communication, training, interpretation of relevant prescripts, limited resources, proper allocation of resources and effective participation of relevant stakeholders as, amongst others, challenges to the process. The study concluded by providing recommendations to management of the Limpopo Department of Economic Development, Environment and Tourism on how to improve the asset management activities to achieve the strategic goals of the department. The recommendations proposed are improved communications with stakeholders, development of asset plan, skills capacity of asset management officials and sourcing the asset information system that integrates with the financial system to provide a reliable asset register. / LEDET (Limpopo Department of Economic Development & Tourism)

Portfolio rebalancing has become a popular tool for institutional investors the last decade. Adaptive asset allocation, an approach suggest by William Sharpe is a new approach to portfolio rebalancing taking market capitalization of asset classes into consideration when setting the normal portfolio and adapting it to a risk profile. The purpose of this thesis is to evaluate the traditional approach of portfolio rebalancing with the adaptive one. The comparison will consist of backtesting and two simulation methods which will be compared computationally measuring time and memory usage (Monte Carlo and Latin Hypercube Sampling). The comparison was done in Excel and in R respectively. It was found that both of the asset allocation approaches gave similar result in terms of the relevant risk measurements mentioned but that the traditional was a cheaper and easier alternative to implement and therefore might be more preferable over the adaptive approach from a practical perspective. The sampling methods were found to have no difference in memory usage but Monte Carlo sampling had around 50% less average running time while at the same time being easier to implement. / Portfölj rebalansering har blivit ett populärt verktyg för institutionella investerare det senaste årtiondet . Adaptiv tillgångsallokering, en taktik föreslagen av William Sharpe är en typ av rebalansering där hänsyn tas till marknadsvärdet av tillgångsklasserna samtidigt som man anpassar det efter en riskprofil. Syftet med detta arbete är att evaluera den traditionella strategin kontra den adaptiva strategin där jämförelsen kommer bestå av backtesting (tillämpa strategin på historisk data) samt två simulationsmetoder(Monte Carlo och LHS). Simulationernas implementering kommer jämföras med avseende på tid och minnesanvändning. Jämförelserna gjordes i Excel och i R respektivt. Resultatet av studien visar att att båda strategierna gav liknande resultat med avseende på de riskmått som finns med men att den traditionella strategin var billigare och enklare att implementera och kan därför vara den strategi att föredra från ett praktiskt perspektiv. Simulationsmetoderna visade ingen skillnad i minnesanvänding men däremot att Monte Carlo var både lättare att implementera samt hade ca 50% mindre körtid i genomsnitt.

Financial advisory services currently face many challenges such as adapting to regulations, competing against robot advisors and offering qualitative advice. We use a utility function based on the clients' risk preferences and investigated the value added by advisory services. The data represents real clients that received financial advisory services from an advisory firm, which gives this thesis a unique accuracy. For the calculations we simulated outcomes of the portfolios and computed key values pertaining to the investors' financial positions. Our calculations show that investors on average gain corresponding 1.66 % per year in risk free return on their investments from advisory services. In addition, we show that the client's value of advisory service increased with respect to the investor's risk level and time horizon of investment. / Aktörerna inom finansiell rådgivning står för närvarande inför flera utmaningar, att anpassas efter regleringar, konkurrera mot robotrådgivare och erbjuda hög kvalitet i rådgivningen. Vi har använt en nyttofunktion baserad på kunders riskpreferenser och utrett vilket värde som finansiell rådgivning tillför. De data som använts representerar verklig kunddata från ett rådgivningsföretag, vilket ger denna studie en unik träffsäkerhet. Beräkningarna av nyckeltal för investerarnas finansiella position har gjorts genom simulering av portföljer. Våra beräkningar visar att finansiell rådgivning ger investerare i genomsnitt motsvarande 1.66 % i ökad riskfri avkastning per år efter avgifter och skatter. Dessutom vi visa att rådgivarnas tillförda värde ökar med avseende på investerarnas risknivå och tidshorisont.

In 2023, the topic of ongoing inflation is being discussed almost daily as it has become inevitable. The global economy is facing significant uncertainty and downward pressure as several leading developed nations adopted expansionary fiscal policies and quantitative easing monetary policies during the pandemic. Those action has lead to an unprecedented level of inflation today. The purpose of this report is to investigate different portfolio strategies and evaluate how various asset classes perform under varying inflationary conditions. Using regression analysis, the study assesses the performance of different assets during high and low inflation regimes. Additionally, two different portfolio strategies are implemented and compared against the 60/40 portfolio strategy, which is considered a benchmark approach among investors. The first strategy involves a modified version of the Markowitz optimization method, which determines the optimal weights of the portfolio during high and low inflationary environments. The second strategy entails identifying a signal and then dynamically adjusting the portfolio's weights based on the signal's value. The findings indicate that during high inflation periods, oil, gold, energy, basic materials, and technology sectors exhibit strong performance. Furthermore, the results reveal that the first strategy is more effective than the second strategy and the 60/40 benchmark. An interesting topic for further investigation is exploring the impact of short selling on portfolio allocation and strategy, which was not addressed in this report. / Under år 2023 är ämnet om pågående inflation nästan oundvikligt. Den globala ekonomin har stått inför betydande osäkerhet och nedåtgående tryck då flera ledande utvecklade nationer antagit expansiva finanspolitiska åtgärder och kvantitativa lättnadsmonetära åtgärder under pandemin. Dessa åtgärder har lett till en enastående nivå av inflation idag. Syftet med denna rapport är att undersöka olika portföljstrategier och hur olika tillgångsslag presterar under olika inflationsregimer. Med hjälp av regressionsanalys undersöks hur olika tillgångar presterar under hög respektive låg inflation. Därefter genomförs två olika portföljstrategier som sedan jämförs mot en 60/40 portföljstrategi, som anses vara en standardstrategi bland investerare. Den första strategin som genomförs är en modifierad version av Markowitz optimeringsmetod. Metoden används för att identifiera de optimala vikterna av portföljen under hög respektive låg inflationsmiljö. Den andra strategin som undersöks innebär att identifiera en signal och sedan dynamiskt justera portföljens vikter baserat på signalens värde. Resultaten visar att olja, guld, energi-, basmaterial- samt teknologisektorn presterar bra under hög inflation. Resultaten påvisar även att den första strategin är den mest effektiva i jämförelse med den andra strategin och 60/40 portföljstrategin. En aspekt som inte inkluderades i denna rapport är att undersöka hur blankning påverkar portföljallokeringen och strategin. Detta kan vara ett intressant ämne för vidare forskning.\\\\

With an increasingly globalised market and growing asset universe, estimating the market covariance matrix becomes even more challenging. In recent years, there has been an extensive development of methods aimed at mitigating these issues. This thesis takes its starting point in the recently developed Hierarchical Principal Component Analysis, in which a priori known information is taken into account when modelling the market correlation matrix. However, while showing promising results, the current framework only allows for fairly simple hierarchies with a depth of one. In this thesis, we introduce a generalisation of the framework that allows for an arbitrary hierarchical depth. We also evaluate the method in a risk-based portfolio allocation setting with Futures contracts.  Furthermore, we introduce a shrinkage method called Hierarchical Shrinkage, which uses the hierarchical structure to further regularise the matrix. The proposed models are evaluated with respect to how well-conditioned they are, how well they predict eigenportfolio risk and portfolio performance when they are used to form the Minimum Variance Portfolio. We show that the proposed models result in sparse and easy-to-interpret eigenvector structures, improved risk prediction, lower condition numbers and longer holding periods while achieving Sharpe ratios that are at par with our benchmarks. / Med en allt mer globaliserad marknad och växande tillgångsuniversum blir det alltmer utmanande att uppskatta marknadskovariansmatrisen. Under senare år har det skett en omfattande utveckling av metoder som syftar till att mildra dessa problem. Detta examensarbete tar sin utgångspunkt i det nyligen utvecklade ramverket Hierarkisk Principalkomponentanalys, där kunskap känd sedan innan används för att modellera marknadskorrelationerna. Även om det visar lovande resultat så tillåter det nuvarande ramverket endast enkla hierarkier med ett djup på ett. I detta examensarbete introduceras en generalisering av detta ramverk, som tillåter ett godtyckligt hierarkiskt djup. Vi utvärderar också metoden i en riskbaserad portföljallokeringsmiljö med terminskontrakt.  Vidare introducerar vi en krympningsmetod som vi kallar Hierarkisk Krympning. Hierarkisk krympning använder den hierarkiska strukturen för att ytterligare regularisera matrisen. De föreslagna modellerna av korrelationsmatrisen utvärderas med avseende på hur välkonditionerade de är, hur väl de förutsäger egenportföljrisk samt hur de presterar i portföljallokeringssyfte i en Minimum Variance portfölj. Vi visar att de introducerade modellerna resulterar i en gles och lätttolkad egenvektorstruktur, förbättrad riskprediktion, lägre konditionstal och längre hållperiod, samtidigt som portföljerna uppnår Sharpe-kvoter i linje med benchmarkmodellerna.

[pt] Nesta tese buscamos fornecer duas diferentes abordagens para a otimização de carteiras de ativos sob incerteza. Demonstramos como a incerteza acerca da distribuição dos retornos esperados pode ser incorporada nas decisões de alocação de ativos, utilizando as seguintes ferramentas: (1) uma extensão da metodologia Bayesiana proposta por Black e Litterman através de uma estratégia de negociação dinâmica construída sobre um modelo de aprendizagem com base na análise fundamentalista, (2 ) uma abordagem adaptativa baseada em técnicas de otimização robusta. Esta última abordagem é apresentada em duas diferentes especificações: uma modelagem robusta com base em uma análise puramente empírica e uma extensão da modelagem robusta proposta por Bertsimas e Sim em 2004. Para avaliar a importância dos modelos propostos no tratamento da incerteza na distribuição dos retornos examinamos a extensão das mudanças nas carteiras ótimas geradas. As principais conclusões são: (a ) é possível obter carteiras ótimas menos influenciadas por erros de estimação, ( b ) tais carteiras são capazes de gerar retornos estatisticamente superiores com perdas bem controladas, quando comparadas com carteiras ótimas de Markowitz e índices de referência selecionados. / [en] In this thesis we provide two different approaches for determining optimal asset allocation portfolios under uncertainty. We show how uncertainty about expected returns distribution can be incorporated in asset allocation decisions by using the following alternative frameworks: (1) an extension of the Bayesian methodology proposed by Black and Litterman through a dynamic trading strategy built on a learning model based on fundamental analysis; (2) an adaptive dynamic approach, based on robust optimization techniques. This latter approach is presented in two different specifications: an empirical robust loss model and a covariancebased robust loss model based on Bertsimas and Sim approach to model uncertainty sets. To evaluate the importance of the proposed models for distribution uncertainty, the extent of changes in the prior optimal asset allocations of investors who embody uncertainty in their portfolio is examined. The key findings are: (a) it is possible to achieve optimal portfolios less influenced by estimation errors; (b) portfolio strategies of such investors generate statistically higher returns with controlled losses when compared to the classical mean-variance optimized portfolios and selected benchmarks.

Modern portfolio theory has its attractive characteristics of promoting diversification in a portfolio and can be seen as an easy alternative for setting optimal weights for portfolio managers. Furthermore, as portfolio managers try to beat a defined benchmark for their portfolio the Black-Litterman model allows them to include their own prospects on the future return of markets and securities. This thesis examines how the practical use of the Black-Litterman model can affect portfolios' performance. The analysis was done by calculating historical portfolio weights with investor views, without investor views, and with perfect investor views in the Black-Litterman model. Thereafter, calculating historical return and volatility for six multi-asset portfolios between 2017-09-25 and 2021-01-31. This was then compared with benchmark portfolios, which reflect the practical use. These portfolios included historically used investor views and constraints in the mean-variance optimization. The results showed that investor views had a negative effect on total return (lower return) and a positive effect on volatility (lower risk), however, an increased Sharpe ratio. The constraints in the mean-variance optimization used in the benchmark portfolios resulted in a lower total return. In conclusion, the Black-Litterman model showed robustness and did not generate unintuitive or unreasonable portfolios, and it has great potential with increasing accuracy in the investor views. / Modern portföljteori har attraktiva egenskaper vad gäller att främja diversifiering i en portfölj och kan ses som ett enkelt alternativ för att välja optimala vikter för portföljförvaltare. Eftersom portföljförvaltare försöker slå ett definierat benchmark för sin portfölj tillåter dessutom Black-Litterman modellen dem att inkludera sina egna åsikter angående förväntade avkastningar på marknader och värdepapper. Detta examensarbete undersöker hur den praktiska användningen av Black-Litterman modellen kan påverka portföljernas prestation. Analysen gjordes genom att beräkna historiska portföljvikter med Black-Litterman modellen med och utan invetserarens egna åsikter angående förväntade avkastningar, och med perfekta förväntade avkastningar. Därefter beräknades historiska avkastningar och volatiliteter för sex investeringsportföljer mellan 2017-09-25 och 2020-01-31. Detta jämfördes med benchmarkportföljer, vilka återspeglade den praktiska användningen. Dessa portföljer inkluderade historiskt använda förväntade avkastningar och restriktioner i mean-variance optimeringen. Resultaten visade att investerares åsikter angående förväntade avkastningar hade en negativ effekt på avkastningen (lägre avkastning), positiv effekt på volatiliteten (lägre risk), vilket resulterade i en högre Sharpe kvot. Restriktionerna i mean-variance optimeringen som användes i benchmarkportföjerna resulterade i en lägre totalavkastning. Sammanfattningsvis visade Black-Litterman modellen robusthet och genererade inte ointuitiva eller olämpliga portföljer, och modellen har stor potential med ökad träffsäkerhet i investerarens åsikter angående förväntade avkastningar.

This project investigates the applicability of the originalversion of Markowitz’s mean-variance model for portfoliooptimization to real-world modern actively managed portfolios.The method measures the mean-variance model’s capability toaccurately capture the riskiness of given portfolios, by invertingthe mathematical formulation of the model. The inversion of themodel is carried out both for fabricated data and real-world dataand shows that in the cases of real-world data the model lackscertain accuracy for estimating risk averseness. The method hascertain errors which both originate from the proposed estimationmethods of input variables and invalid assumptions of investors. / Projektet undersöker lämpligheten att använda den ursprungliga versionen av Markowitzs ”Mean-Variance model” för portföljoptimering för moderna aktivt förvaltade portföljer. Metoden mäter modellens förmåga att tillförlitligt beräkna risken för givna portföljer genom att invert-era den matematiska formuleringen av modellen. Inversionen av modellen utförs både för simulerad data och verklig data och visar att i fallet med verkliga data saknar modellen viss noggrannhet för att uppskatta riskpreferens. Metoden har vissa fel som både uppstår från de föreslagna uppskattningsmetoderna för inputvariabler och ogiltiga antaganden för investerare. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm