Calculation of the Value at Risk (VaR) measure, of a portfolio, can be done using Monte Carlo simulations of that portfolio's potential losses over a specified period of time. Regulators, such as the US Securities and Exchange Commission, and Exchanges, such as the New York Stock Exchange, establish regulatory capital requirements for firms. These regulations set the amount of capital that firms are required to have on hand to safeguard against market loses that can occur. VaR gives us this specific monetary value set by Regulators and Exchanges. The specific amount of capital on hand must satisfy that, for a given confidence level, a portfolio's loses over a certain period of time, will likely be no greater than the capital required a firm must have on hand. The scenario used will be one of a Risk Manager position in which this manager inherited a portfolio that was set up for a client beginning in April 1992. The portfolio will have to meet certain parameters. The initial portfolio is worth $61,543,328.00. The risk manager will be responsible for the calculation of the Value at Risk measure, at five percent, with a confidence level of 95% and 20 days out from each of the 24 business quarters, over a six year period, starting in 1992 and ending in 1996.

This master thesis aims to describe and apply in practice solutions of basic tasks in portfolio management- portfolio optimization, portfolio modelling and risk management. As value of financial assets in future is a random variable, it is necessary to use mathematic tools resulting from probability theory and statistics. Basic terms from this area are for example stochastic Wiener process or geometric Brownian motion, which are described in first part of this thesis. Next parts of thesis describe the Markowitz model or method Value at Risk. In the last part of thesis is application of calculation VaR using Monte Carlo simulation for stock portfolio constructed as optimal portfolio according to Markowitz model from real data.

The thesis covers a wide range of topics from the credit risk modeling with the emphasis put on pricing of the claims subject to the default risk. Starting with a separate general contingent claim pricing framework the key topics are classified into three fundamental parts: firm-value models, reduced-form models, portfolio problems, with a possible finer sub-classification. Every part provides a theoretical discussion, proposal of self-developed methodologies and related applications that are designed so as to be close to the real-world problems. The text also reveals several new findings from various fields of credit risk modeling. In particular, it is shown (i) that the stock option market is a good source of credit information, (ii) how the reduced-form modeling framework can be extended to capture more complicated problems, (iii) that the double t copula together with a self-developed portfolio modeling framework outperforms the classical Gaussian copula approaches. Many other, partial findings are presented in the relevant chapters and some other results are also discussed in the Appendix.

Cryptocurrencies have since the creation in 2008 constituted a unique and modern addition tothe financial setting throughout the world. Such assets are commonly known to be associatedwith great risk but also the possibility of great reward. The corresponding research field hasadapted to the evolution of cryptocurrencies and has for over a decade undergone a constantexpansion. Despite this, there is still plenty of unexplored territory within the particular researcharea and this report seeks to examine a part of it. The central topic of this paper concernscryptocurrencies in relation to Swedish retail investors’ different demographic factors and theeffect those have on investment strategy and behavior. To examine this, the report centersaround two main aspects, the investment purpose which cryptocurrency investors associatetheir investments with and investors’ exposure to herd behavior. Additionally, both aspectswere put in relation to various demographic factors to allow an analysis of whether demographicfactors affect the investors’ strategy and behavior. A quantitative method was used for theprocess of collecting data whereby a survey was constructed and replied to by Swedish retailinvestors active in the cryptocurrency market. The primary data obtained was analyzed andpresented through descriptive statistics, t-Tests, and regression models. By interpreting theresults, it was evident that demographic factors were found to not influence the investmentpurpose or the herd behavior of investors. This contradicts previous findings regardingtraditional markets e.g., the stock market where demographic factors are established as factorsaffecting both aspects. Hence, this report suggests that there are differences between thecryptocurrency market and traditional markets. Further, the research conducted in this paperindicates that a majority of investors associate cryptocurrency investments with speculativetrading and there is also a strong bias toward herd behavior among Swedish retail investorsactive in the cryptocurrency market.

This research study examines the risk-adjusted performance and portfolio risk of 60 large cap equity funds - mutual funds - under Swedish management. These funds apply environmental, social and governance criteria in their investment strategies. The empirical context concerns the COVID-19 situation and the context is divided into three periods, before, during and after the COVID-19 crisis. The ESG concept, modern portfolio and stakeholder theories are used to develop a theoretical base for the study on which the hypotheses are based which are summarized in a conceptual model. Secondary data regarding ESG and risk-adjusted returns are collected for each fund based on which the sharpe ratios and standard deviations (total or portfolio risk) for each fund are calculated. While there are associations between ESG and portfolio risk, no associations are found between ESG and sharpe ratios. As a result, this confirms the fact that ESG could be characterized as a mechanism to protect against downside risk in poor economic times but no association was established that ESG could also be used as a mechanism to determine efficiency in terms of risk-adjusted performance

Risk measurement of mortgage-backed security portfolios presents a very involved task for analysts and portfolio managers of such investments. A strong predictive econometric model that can account for the variability of these securities in the future would prove a very useful tool for anyone in this financial market sector due to the difficulty of evaluating the risk of mortgage cash flows and prepayment options at the same time. This project presents two linear regression methods that attempt to explain the risk within these portfolios. The first study involves a principal components analysis on absolute changes in market data to form new sets of uncorrelated variables based on the variability of original data. These principal components then serve as the predictor variables in a principal components regression, where the response variables are the day-to-day changes in the net asset values of three agency mortgage-backed security mutual funds. The independence of each principal component would allow an analyst to reduce the number of observable sets in capturing the risk of these portfolios of fixed income instruments. The second idea revolves around a simple ordinary least squares regression of the three mortgage funds on the sets of the changes in original daily, weekly and monthly variables. While the correlation among such predictor variables may be very high, the simplicity of utilizing observable market variables is a clear advantage. The goal of either method was to capture the largest amount of variance in the mortgage-backed portfolios through these econometric models. The main purpose was to reduce the residual variance to less than 10 percent, or to produce at least 90 percent explanatory power of the original fund variances. The remaining risk could then be attributed to the nonlinear dependence in the changes in these net asset values on the explanatory variables. The primary cause of this nonlinearity is due to the prepayment put option inherent in these securities.

Bakgrund Människor måste alltid fundera över risk och avkastning. Att omkring 80% av svenskarna äger någon form av fond skapar ett stort beroende av hur en extern aktör, portföljförvaltare, ser på begreppet och hur de hanterar portföljrisken mer precist. Det är därför intressant för alla investerare att förstå om och hur portföljrisk används och ses på utifrån förvaltarna som styr över vårt sparande. Är deras synsätt speglat i de befintliga teorierna och används den ofta kritiserade riskvariabeln beta i praktiken. Syfte: Syftet med magisteruppsatsen är att förklara och analysera hur institutionella investerare använder risk i portföljförvaltning, illustrera hur de i praktiken använder riskvariabler och om risk är nära relaterat till avkastning. Metod: Den här uppsatsen har sin utgångspunkt i den kvalitativa forskningsmetodiken för att kunna analysera hur portföljförvaltare ser på portföljrisk. Ett slumpmässigt urval av nio portföljförvaltare, oberoende av storlek och strategi, valde att ställa upp på intervjuer. De intervjuade fick fritt besvara frågorna för att skapa en så heltäckande bild som möjligt av de olika uppfattningarna inom portföljrisk. Slutsats: Analysen av det empiriska materialet visar att det är svårt att frambringa en enhetlig syn på portföljrisk och definition av densamma. De intervjuade skiljer sig åt i de flesta frågor förutom i kritiken mot betas värde som riskvariabel. Ingen använder beta som främsta riskmått, istället används riskvariabler som Value at Risk, tracking error och/eller variansen av avkastning. De statligt ägda fonderna använder sig av strategier där riskhantering kommer i främsta rummet och de ser även en stark koppling mellan risk och avkastning. Värdet av riskhantering skiljer sig åt bland de privata portföljförvaltarna eftersom några aktivt justerar och övervakar risknivån medan andra inte använder sig av risktänkande alls. Korrelationen mellan risk och avkastning är inte heller uppenbar då några anser att sambandet inte alltid är positivt eller linjärt. / Background: Humans have to constantly consider risk- and return tradeoffs. The fact that about 80% of the Swedish population owns some kind of mutual fund creates a great dependency on how an external part, a portfolio manager, views this tradeoff and especially how the concept of portfolio risk is looked upon. It becomes interesting for all investors to understand if and how portfolio risk is utilized and looked upon through the eyes of the mangers in charge over our savings. Do their view of risk and return translate to available theories and is the theoretically popular and much criticized beta measure used at all in practice. Purpose: The purpose of this master thesis is to describe and analyze how institutional investors apply the concepts of risk in portfolio management, to illustrate how they work with risk variables in practice and if risk is closely linked to return. Methodology: To be able to thoroughly analyze a few selected portfolio managers’ view on portfolio risk, this thesis has its foundation in the qualitative research approach. A random sample of nine mutual funds’ portfolio managers, independent of size and investment strategies, agreed to participate in face-to-face inter-views. The interviewees were allowed to answer freely in order to get the full picture of the different views of portfolio risk. Conclusion: The analysis of the empirical findings makes it clear that it is hard to find a unified view nor a unified definition of portfolio risk. The respondents differ a lot in their opinions in most issues except that they doubt beta being a good risk measure. No one is using beta as its main risk variable, instead risk variables such as Value at Risk, tracking error and variance of returns are used. The government operated funds have strategies putting risk management on the frontline and sees a strong connection between risk and return. The importance of risk management show a large divergence amongst the private portfolio managers since some respondents actively adjust and monitor the level of risk while other employ strategies that do not incorporate risk thinking at all. The correlation between risk and return is not apparent since some respondents do not believe the relation to be linear or positive at all times.

<p>Bakgrund Människor måste alltid fundera över risk och avkastning. Att omkring 80% av svenskarna äger någon form av fond skapar ett stort beroende av hur en extern aktör, portföljförvaltare, ser på begreppet och hur de hanterar portföljrisken mer precist. Det är därför intressant för alla investerare att förstå om och hur portföljrisk används och ses på utifrån förvaltarna som styr över vårt sparande. Är deras synsätt speglat i de befintliga teorierna och används den ofta kritiserade riskvariabeln beta i praktiken.</p><p>Syfte: Syftet med magisteruppsatsen är att förklara och analysera hur institutionella investerare använder risk i portföljförvaltning, illustrera hur de i praktiken använder riskvariabler och om risk är nära relaterat till avkastning.</p><p>Metod: Den här uppsatsen har sin utgångspunkt i den kvalitativa forskningsmetodiken för att kunna analysera hur portföljförvaltare ser på portföljrisk. Ett slumpmässigt urval av nio portföljförvaltare, oberoende av storlek och strategi, valde att ställa upp på intervjuer. De intervjuade fick fritt besvara frågorna för att skapa en så heltäckande bild som möjligt av de olika uppfattningarna inom portföljrisk.</p><p>Slutsats: Analysen av det empiriska materialet visar att det är svårt att frambringa en enhetlig syn på portföljrisk och definition av densamma. De intervjuade skiljer sig åt i de flesta frågor förutom i kritiken mot betas värde som riskvariabel. Ingen använder beta som främsta riskmått, istället används riskvariabler som Value at Risk, tracking error och/eller variansen av avkastning.</p><p>De statligt ägda fonderna använder sig av strategier där riskhantering kommer i främsta rummet och de ser även en stark koppling mellan risk och avkastning. Värdet av riskhantering skiljer sig åt bland de privata portföljförvaltarna eftersom några aktivt justerar och övervakar risknivån medan andra inte använder sig av risktänkande alls. Korrelationen mellan risk och avkastning är inte heller uppenbar då några anser att sambandet inte alltid är positivt eller linjärt.</p> / <p>Background: Humans have to constantly consider risk- and return tradeoffs. The fact that about 80% of the Swedish population owns some kind of mutual fund creates a great dependency on how an external part, a portfolio manager, views this tradeoff and especially how the concept of portfolio risk is looked upon. It becomes interesting for all investors to understand if and how portfolio risk is utilized and looked upon through the eyes of the mangers in charge over our savings. Do their view of risk and return translate to available theories and is the theoretically popular and much criticized beta measure used at all in practice.</p><p>Purpose: The purpose of this master thesis is to describe and analyze how institutional investors apply the concepts of risk in portfolio management, to illustrate how they work with risk variables in practice and if risk is closely linked to return.</p><p>Methodology: To be able to thoroughly analyze a few selected portfolio managers’ view on portfolio risk, this thesis has its foundation in the qualitative research approach. A random sample of nine mutual funds’ portfolio managers, independent of size and investment strategies, agreed to participate in face-to-face inter-views. The interviewees were allowed to answer freely in order to get the full picture of the different views of portfolio risk.</p><p>Conclusion: The analysis of the empirical findings makes it clear that it is hard to find a unified view nor a unified definition of portfolio risk. The respondents differ a lot in their opinions in most issues except that they doubt beta being a good risk measure. No one is using beta as its main risk variable, instead risk variables such as Value at Risk, tracking error and variance of returns are used.</p><p>The government operated funds have strategies putting risk management on the frontline and sees a strong connection between risk and return. The importance of risk management show a large divergence amongst the private portfolio managers since some respondents actively adjust and monitor the level of risk while other employ strategies that do not incorporate risk thinking at all. The correlation between risk and return is not apparent since some respondents do not believe the relation to be linear or positive at all times.</p>

This thesis is focused on a theoretical explanation of some models for the optimization stock portfolios with different risk measure. The theory of the nonlinear programming is detailed developed and also basic Markowitz`s model with another optimization models as Konno -- Yamazaki`s model, Roy`s model, semivariance approach and Value at Risk approach, which are based on alternative risk measure. For all models the assumptions of their applications are highlighted and the comparation of these models is made too. Analytical part is concerned in the construction of the effecient portfolios according to the described models is made on the historical market prices of 13 companies traded on Prague Stock Exchange in SPAD.

This thesis addresses the problems associated with security of the electricity supply in the UK. The British electricity supply industry has experienced a significant structural change. Competition has been brought into the electricity industry and a single wholesale electricity market of Great Britain has been established. The evolution of the British electricity market raises new challenges, such as improving the liquidity of wholesale markets and developing clean energy. The wholesale electricity prices are less transparent and trading arrangements are very complex in the British electricity market. In this thesis a fundamental model, called a stack model, has been developed in order to forecast wholesale electricity prices. The objective of the stack model is to identify the marginal cost of power output based on the fuel prices, carbon prices, and availability of power plants. The stack model provides a reasonable marginal cost curve for the industry which can be used as an indicator for the wholesale electricity price. In addition, the government's targets for climate change and renewable energy bring new opportunities for wind energy. Under the large wind energy penetration scenario the security of the energy supply will be essential. We have modelled the correlations between wind speed data for a set of wind farms. The correlation can be used to measure the portfolio risk of the wind farms. Electricity companies should build their portfolio of wind farms with low or negative correlations in order to hedge the risk from the intermittency of wind. We found that the VAR(1) model is superior to other statistic models for modelling correlations between wind speeds of a wind farm portfolio.