Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-10T13:05:15Z No. of bitstreams: 1 marciamariaazzibolotari.pdf: 27501408 bytes, checksum: 314d77eeb433504c0d6b58bba7b93fbd (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-15T13:11:42Z (GMT) No. of bitstreams: 1 marciamariaazzibolotari.pdf: 27501408 bytes, checksum: 314d77eeb433504c0d6b58bba7b93fbd (MD5) / Made available in DSpace on 2016-06-15T13:11:42Z (GMT). No. of bitstreams: 1 marciamariaazzibolotari.pdf: 27501408 bytes, checksum: 314d77eeb433504c0d6b58bba7b93fbd (MD5) Previous issue date: 2015-07-31 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, apresenta-se uma proposta para o ensino do componente curricular Matemática Financeira na Educação Básica tendo como base as sugestões curriculares dos Parâmetros Curriculares Nacionais (PCNs) e do Conteúdo Básico Comum do Estado de Minas Gerais para o Ensino Médio (CBC-MG). O objetivo é a conscientização do aluno quanto ao fato de que os conceitos da Matemática Financeira são um instrumento poderoso para o entendimento das relações existentes no mundo econômico e financeiro, bem como para o desenvolvimento da cidadania. Como meta principal se objetiva a exploração e o desenvolvimento de competências que tornem os discentes mais participativos e críticos quanto ao modo como a Matemática Financeira atua em suas vidas. Mais importante do que decorar fórmulas ou aprender técnicas matemáticas ou ainda desenvolver a capacidade de cálculo é desenvolver uma visão contextualizada da importância da matemática financeira na formação social contemporânea, partindo do estudo de seu desenvolvimento histórico. Através de reportagens e textos relevantes que ressaltam a importância da matemática financeira no cotidiano, apresentam-se conteúdos que se alicerçam em situações do dia a dia, em acontecimentos reais presentes na vida do aluno, de seus amigos e parentes. Usando ferramentas tecnológicas como facilitadores, transforma-se a aula, tornando-a mais atrativa e próxima da realidade, explorando sugestões interdisciplinares que abordam a economia doméstica e o consumo consciente. / This paper presents a proposal for curriculum component Financial Mathematics in Primary teaching based on the curriculum suggestions of the National Education Curriculum Parameters (PCNs – Parâmetros Curriculares Nacionais) and the Common Basic Contents of Minas Gerais for Secondary Education (CBC-MG). The objective is student awareness about the fact that the concepts of financial mathematics are a powerful tool for the understanding of the relationship in economic and financial world, as well as for the development of citizenship. The main goal is objective exploration and the development of skills that make them more participatory and students critical of the way the Financial Mathematics acts in their lives. More important than decorating formulas or learn mathematical techniques or develop the capacity of calculation is to develop a contextualized view of the importance of financial mathematics in contemporary social formation, starting from the study of its historical development. Through reports and relevant texts that highlight the importance of financial mathematics in everyday life, we present contents that are rooted in everyday situations, actual events present in the lives of the students, their friends and relatives. Using technological tools as facilitators, the lesson becomes, making it more attractive and closer to reality, exploring interdisciplinary suggestions that address the domestic economy and consumer awareness.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-02T12:06:21Z No. of bitstreams: 1 lucianopecorarocosta.pdf: 3438112 bytes, checksum: 3896600479f38ac7e056d633475793f4 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-28T14:35:07Z (GMT) No. of bitstreams: 1 lucianopecorarocosta.pdf: 3438112 bytes, checksum: 3896600479f38ac7e056d633475793f4 (MD5) / Made available in DSpace on 2016-06-28T14:35:07Z (GMT). No. of bitstreams: 1 lucianopecorarocosta.pdf: 3438112 bytes, checksum: 3896600479f38ac7e056d633475793f4 (MD5) Previous issue date: 2012-10-03 / Este trabalho é fruto de reflexões acerca dos questionamentos inerentes ao dia a dia de uma sala de aula, de estudantes jovens e adultos. A disciplina Matemática não necessita, exclusivamente, trabalhar conteúdos explícitos, contemplando “resolva” e “calcule”. Tendo como intenção, proporcionar aos estudantes, além de trazer os conteúdos pertinentes à disciplina, mas também, a emersão, em caráter reflexivo. Um aluno terá condições de apoderar-se de seus conhecimentos advindos do meio escolar e de mundo, a fim de conjecturar sobre possíveis caminhos, em tomadas de decisão. Diante da intenção de incorporar debate de cunho crítico às aulas, tomamos como prerrogativa, as características da Educação Matemática Crítica, de Ole Skovsmose, em que consequentemente acarretam reflexões de cunho social, perante questões relacionadas à Cidadania, descritas nas obras de Nilson José Machado. A pesquisa foi desenvolvida num colégio público estadual da cidade de Miguel Pereira/RJ, cujo pré-teste ocorrera em uma turma de 9° ano do Ensino Fundamental, sendo o pós-teste, aplicado no 3° ano do Ensino Médio, ambos na modalidade da Educação de Jovens e Adultos – EJA. A fim de aglutinar aos aspectos de criticidade e cidadania, foram incorporadas ferramentas tecnológicas – calculadora e computador – como meio de intencionar a inclusão digital, e paralelamente, como instrumento auxiliador diante de tomadas de decisão. Diante da escassez de materiais destinados ao público da EJA, seja no âmbito editorial quanto por meio de publicações no meio acadêmico, forçou-nos a planejar aulas, tanto quanto materiais, destinados a esta modalidade de ensino. As atividades aplicadas tanto no pré-teste quanto no pós-teste converteram-se em produto educacional, os quais aduziram neste trabalho. / This work is the reflections result on the questions about everyday life of a classroom of young and adult students. The mathematics course does not require exclusively working explicit content, contemplating "settle" and "calculate". The intention is to provide students, in addition to bring in relevant content to the discipline, but also the emergence, in reflective nature. A student will be able to seize his knowledge from the school and the world in order to speculate on possible paths indecision making. Faced with the intention of incorporating critical debate of nature classes, we take the prerogative, the characteristics of Critical Mathematics Education, Ole Skovsmose, which consequently cause reflections of social; faces issues related to citizenship, described in the works of José Nilson Machado. The research was conducted in a public state school in Miguel Pereira/RJ, whose pre test occurred in a class of 9th grade of elementary school and the post-test, applied in the 3rd year of high school, both in the form Education of Youth and Adults-EJA. In order to unite the aspects of criticality and citizenship were incorporated technological tools-calculator and computer-as means of intending digital inclusion, and in parallel, as a tool helper before making decisions. Given the scarcity of materials intended for EJA public, is under editorial and through publications in academic, forced us to plan lessons as well as material intended for this type of education. The activities implemented both pretest and post-test have become educational product, which did this work.

The main aim of the study was (1) to identify errors committed by learners in financial mathematics and (2) to understand why learners continue to make such errors so that mechanisms to avoid such errors could be devised. The following has been hypothesised; (1) errors committed by learners are not impact upon by language difficulties, (2) errors committed by learners in financial mathematics are not due to prerequisite skills, facts and concepts, (3) errors committed by learners in financial mathematics are not due to the application of irrelevant rules and strategies. Having used Polya’s problem-solving techniques, Threshold Concept and Newman’s Error Analysis as the theoretical frameworks for the study, a four-point Likert scale and three content-based structured-interview questionnaires were developed to address the research questions. The study was conducted by means of a case study guided by the positivists’ paradigm where the research sample comprised of 105 Grade-10 Mathematics Literacy learners as respondents. Four sets of structured-interview questionnaires were used for collecting data, aimed at addressing the main objective of the study. In order to test the reliability and consistency of the questionnaires for this study, Cronbach’s Alpha was calculated for standardised items (α = 0.705). Content analysis and correlation analysis were employed to analyse the data. The three hypotheses of this study were tested using the ANOVA test and hence revealed that, (1) errors committed by learners in financial mathematics are not due to language difficulties, as all the variables illustrated a statistical non-significance (2) errors committed by learners in financial mathematics are not due to prerequisite skills, facts and concepts, as the majority of the variables showed non-significance and (3) errors committed by learners in financial mathematics were due to the application of irrelevant rules and strategies, as 66.7% of the variables illustrated a statistical significance to the related research question.

The purpose of this thesis is to compare option pricing models. We have investigated the constant volatility models Black-Scholes-Merton (BSM) and Merton’s Jump Diffusion (MJD) as well as the stochastic volatility models Heston and Bates. The data used were option prices from Microsoft, Advanced Micro Devices Inc, Walt Disney Company, and the S&P 500 index. The data was then divided into training and testing sets, where the training data was used for parameter calibration for each model, and the testing data was used for testing the model prices against prices observed on the market. Calibration of the parameters for each model were carried out using the nonlinear least-squares method. By using the calibrated parameters the price was calculated using the method of Carr and Madan. Generally it was found that the stochastic volatility models, Heston and Bates, replicated the market option prices better than both the constant volatility models, MJD and BSM for most data sets. The mean average relative percentage error for Heston and Bates was found to be 2.26% and 2.17%, respectively. Merton and BSM had a mean average relative percentage error of 6.90% and 5.45%, respectively. We therefore suggest that a stochastic volatility model is to be preferred over a constant volatility model for pricing options. / Syftet med denna tes är att jämföra prissättningsmodeller för optioner. Vi har undersökt de konstanta volatilitetsmodellerna Black-Scholes-Merton (BSM) och Merton’s Jump Diffusion (MJD) samt de stokastiska volatilitetsmodellerna Heston och Bates. Datat vi använt är optionspriser från Microsoft, Advanced Micro Devices Inc, Walt Disney Company och S&P 500 indexet. Datat delades upp i en träningsmängd och en test- mängd. Träningsdatat användes för parameterkalibrering med hänsyn till varje modell. Testdatat användes för att jämföra modellpriser med priser som observerats på mark- naden. Parameterkalibreringen för varje modell utfördes genom att använda den icke- linjära minsta-kvadratmetoden. Med hjälp av de kalibrerade parametrarna kunde priset räknas ut genom att använda Carr och Madan-metoden. Vi kunde se att de stokastiska volatilitetsmodellerna, Heston och Bates, replikerade marknadens optionspriser bättre än båda de konstanta volatilitetsmodellerna, MJD och BSM för de flesta dataseten. Medelvärdet av det relativa medelvärdesfelet i procent för Heston och Bates beräknades till 2.26% respektive 2.17%. För Merton och BSM beräknades medelvärdet av det relativa medelvärdesfelet i procent till 6.90% respektive 5.45%. Vi anser därför att en stokastisk volatilitetsmodell är att föredra framför en konstant volatilitetsmodell för att prissätta optioner.

The equity trading of today is fragmented across regulated markets (RMs) and multilateral trading facilities (MTFs). Despite being legally very similar Busch (2017), market participants have reported that they attract different types of traders. Market dynamics arise from the interactions between all market participants (agents) Kyle (1985). Price impact is an important part of these dynamics which, for the most part, can be explained by the competition between liquidity takers and liquidity providers Bouchaud et al. (2009). Hence, this thesis studies whether price impact is venue dependent by using the transient impact model, developed by Bouchaud et al. (2004), on Nordic stocks listed at Nasdaq but also traded on London based MTFs. Furthermore, MiFID II and entailing legislation introduced a considerable amount of changes to the financial markets, the effects of which on price impact will also be subject to investigation here. The findings indicate that price impact is indeed venue dependent, where RMs show less price impact than the MTFs. The effects of MiFID II are vague but seems to have lowered the temporal aspect of price impact for the MTFs, while the effects on the RMs are less evident. / Dagens aktiehandel är fragmenterad över reglerade marknader och multilaterala handelsplattformar (MTF-plattformar), trots att de är juridiskt väldigt lika Busch (2017), så har marknadsaktörerna rapporterat att de attraherar olika typer av aktörer. Marknadens dynamik uppstår ur interaktionen mellan dess aktörer Kyle (1985). Prispåverkan är en viktig del av denna dynamik som, för det mesta, kan förklaras av konkurrensen mellan likviditetstagare och likviditetsgivare (Bouchaud et al. 2009). Således undersöker denna uppsats om prispåverkan skiljer sig mellan handelsplatser genom att använda en transient prispåverkansmodell, utvecklad av Bouchaud et al. (2004), på handelsdatat från nordiska aktier listade på Nasdaq, men som även handlas på MTF-platformar i London. Introduktionen av MiFID II och tillhörande lagstiftning har inneburit betydande förändringar för den finansiella marknaden, vilkas effekter på prispåverkan vid aktiehandel också kommer att undersökas här. Fynden i denna studie indikerar att prispåverkan är handelsplatsberoende, där priset påverkas mindre på reglerade marknader än på MTF-plattformar. Effekterna av MiFID II är vaga men verkar ha sänkt den temporala aspekten av prispåverkan och då främst för MTF-plattformarna, medan effekterna på de reglerade marknaderna är mindre framträdande.

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.

The investment and financing instrument AT1, or Contingent Convertible bond, has become popular in the post-crisis capital markets, prompting interest and research in the academic world. The instrument's debt definition but equity boosting properties makes it rather extraordinary, and its stochastic features makes multiple mathematical valuation methodologies relevant, especially with regard to the risk of extending the call date of the instrument. With investors still relying on screening tools for valuation, there is an absence of applications using existing mathematical approaches. This report therefore aims to narrow the gap between academia and industry by evaluating the use of such mathematical approaches in a practical investment setting, in particular the Improved Credit Derivative approach and the Extension Premium Relative Value approach shall be examined. Both models strive to account for the extension risk, a commonly disregarded yet critical risk, adding computational challenges to the implementation. Besides from discovering necessary practical adjustments, and their effects, the two pricing approaches are compared in an attempt to confirm their joint purpose of accounting for extension risk. Ending up with varying results consisting of evident offsets for the improved credit derivative model but significant correlations in the case of the extension premium model, their individual performance was diverse while the hypothesis of joint behaviour could be dismissed. / Investerings- och finansieringsinstrumentet AT1, eller Contingent Convertible bond, har blivit populärt i kapitalmarknaderna efter finanskrisen, vilket lett till intresse och forskning i den akademiska världen. Instrumentets grund som skuld men egenskaper för att tillskjuta eget kapital gör det extraordinärt, och dess stokastiska funktioner öppar upp för flertalet värderingsmetoder, speciellt gällande förlängningsrisken hos datumet för kallning. Eftersom att investerare fortfarande använder sig utav screening-verktyg för värdering finns det endast begränsad forskning rörande användande av matematiska metoder. Denna rapport har därför som mål att minska avståndet mellan den akademiska världen och industrin genom att utvärdera användandet av sådana matematiska metoder för praktiska investeringar, särskillt skall Improved Credit Derivative och Extension Premium Relative Value metoderna användas. Båda modellerna strävar efter att ta hänsyn till förlängningsrisken, en risk vanligtvis bortsedd ifrån men trots det kritisk, vilket tillägger ytterligare beräkningsutmaningar vid implementationen. Bortsätt ifrån att upptäcka praktiska justeringar och dess effekter jämförs de två värderingsmetoderna i ett försök att bekräfta deras gemensamma syfte, att ta hänsyn till förlängningsrisken. Att i slutändan nå blandade resultat besående av uppenbara avvikelser för improved credit derivative modellen men starka korrelationer i fallet av extension premium modellen gjorde att man kunde dra slutsatsen att deras individuella prestanda skilde sig medan hypotesen om gemensamt beteende kunde avfärdas.

Contingent convertible bonds (often referred to as CoCo bonds, or simply CoCos) are a relatively new financial instrument designed to absorb unexpected losses. This instrument became increasingly more common after the financial crisis of 2008, as a way to decrease the risk of insolvency among banks and other financial institutions. In this thesis, we will investigate two mathematical models for valuation of CoCo bonds, known as the credit derivative approach and the equity derivative approach, previously developed by De Spiegeleer and Schoutens [1]. We will investigate how these models can be modified in order to be applied to a large set of bonds available on the market. The effect of parameter alterations will also be studied, in order to determine which parameters that influence the pricing accuracy the most. We reach the conclusion that by estimating market triggers, conversion prices and by computing a continuous interest rate from a discrete rates table, the models are indeed executable on a large set of bonds available on the market. However, these parameter estimations come at the cost of reduced accuracy. In general, both investigated models produces prices which follows the overall movements of the market prices quite well, but at the same time with a relatively large absolute distance from the market prices. In other words, the correlation with the market is often high, but the absolute error (measure by root mean square error) is often large. The sensitivity analysis of the parameters shows that the market trigger is the most influential parameter in both investigated models. The fact that we had to estimate the market trigger in order to be able to price a large number of bonds is believed to be the main cause of reduced accuracy. By utilizing a more bond-specific parameter estimation, the accuracy of the investigated models could most likely be improved. We can conclude that there is a trade-off between being able to price a large set of bonds with a mediocre accuracy, or being able to price a few bonds with high accuracy. / Det finansiella instrumentet contingent convertible bond (ofta benämnt CoCo bond, eller endast CoCo) är en relativt ny obligationstyp som används av banker och andra finansiella institutioner för att absorbera oväntade förluster. Instrumentet blev mer vanligt förekommande efter finanskrisen 2008, som ett sätt att minska risken för insolvens. I detta examensarbete undersöker vi två matematiska modeller för värdering av CoCo bonds, nämligen den så kallade credit derivative approach och equity derivative approach, som tidigare har utvecklats av De Spiegeleer och Schoutens [1]. Vi kommer att undersöka hur dessa modeller kan modifieras för att bli applicerbara på ett stort antal obligationer tillgängliga på marknaden. En omfattande parameterstudie kommer att genomföras, för att dra slutsatser kring de mest betydelsefulla parametrarna för prissättningen. Genom att skatta så kallade market triggers, conversion prices och en kontinuerlig ränta är det möjligt att exekvera de undersökta modellerna på ett stort antal obligationer. Dessa skattningar medför dock en viss försämrad noggrannhet. Generellt sett följer priserna från modellerna marknadens rörelser ganska väl, men är samtidigt ganska långt ifrån marknadspriset. Med andra ord är korrelationen hög, men absolutfelet är relativt stort. Parameterstudien visar att parametern som kallas market trigger är mest betydelsefull för prissättningen. Faktumet att vi måste skatta market triggers för att kunna prissätta ett stort antal obligationer tros vara den största anledningen till försämrad noggrannhet. Genom att använda en mer ”obligationsspecifik” skattning av parametrar bör noggrannheten kunna förbättras. I dessa modeller är det en tydlig avvägning mellan att kunna prissätta många obligationer med relativt låg noggrannhet, och att kunna prissätta få obligationer med hög noggrannhet.

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 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.\\\\