<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>

Some financial problems as minimizing the shortfall risk when hedging in incomplete markets lead to problems belonging to test theory. This paper considers a generalization of the Neyman-Pearson lemma. With methods of convex duality we deduce the structure of an optimal randomized test when testing a compound hypothesis against a simple alternative. We give necessary and sufficient optimality conditions for the problem.

In insurance risk theory, the surplus of an insurance company is modelled to monitor and quantify its risks. With the outgo of claims and inflow of premiums, the insurer needs to determine what financial portfolio ensures the soundness of the company’s future while satisfying the shareholders’ interests. It is usually assumed that the net profit condition (i.e. the expectation of the process is positive) is satisfied, which then implies that this process would drift towards infinity. To correct this unrealistic behaviour, the surplus process was modified to include the payout of dividends until the time of ruin. Under this more realistic surplus process, a topic of growing interest is determining which dividend strategy is optimal, where optimality is in the sense of maximizing the expected present value of dividend payments. This problem dates back to the work of Bruno De Finetti (1957) where it was shown that if the surplus process is modelled as a random walk with ± 1 step sizes, the optimal dividend payment strategy is a barrier strategy. Such a strategy pays as dividends any excess of the surplus above some threshold. Since then, other examples where a barrier strategy is optimal include the Brownian motion model (Gerber and Shiu (2004)) and the compound Poisson process model with exponential claims (Gerber and Shiu (2006)). In this thesis, we focus on the optimality of a barrier strategy in the more general Lévy risk models. The risk process will be formulated as a spectrally negative Lévy process, a continuous-time stochastic process with stationary increments which provides an extension of the classical Cramér-Lundberg model. This includes the Brownian and the compound Poisson risk processes as special cases. In this setting, results are expressed in terms of “scale functions”, a family of functions known only through their Laplace transform. In Loeffen (2008), we can find a sufficient condition on the jump distribution of the process for a barrier strategy to be optimal. This condition was then improved upon by Loeffen and Renaud (2010) while considering a more general control problem. The first chapter provides a brief review of theory of spectrally negative Lévy processes and scale functions. In chapter 2, we define the optimal dividends problem and provide existing results in the literature. When the surplus process is given by the Cramér-Lundberg process with a Brownian motion component, we provide a sufficient condition on the parameters of this process for the optimality of a dividend barrier strategy. Chapter 3 focuses on the case when the claims distribution is given by a univariate mixture of Erlang distributions with a common scale parameter. Analytical results for the Value-at-Risk and Tail-Value-at-Risk, and the Euler risk contribution to the Conditional Tail Expectation are provided. Additionally, we give some results for the scale function and the optimal dividends problem. In the final chapter, we propose an expectation maximization (EM) algorithm similar to that in Lee and Lin (2009) for fitting the univariate distribution to data. This algorithm is implemented and numerical results on the goodness of fit to sample data and on the optimal dividends problem are presented.

Neste trabalho, aprofundamos o estudo sobre risco sistêmico via funções de agregação. Consideramos três carteiras diferentes como proxy para um sistema econômico, estas carteiras são consistidas por duas funções de agregação, baseadas em todos as ações do E.U.A, e um índice de mercado. As medidas de risco aplicadas são Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR), elas são previstas através do modelo GARCH clássico unido com nove funções de distribuição de probabilidade diferentes e mais por um método não paramétrico. As previsões são avaliadas por funções de perda e backtests de violação. Os resultados indicam que nossa abordagem pode gerar uma função de agregação adequada para processar o risco de um sistema previamente selecionado. / In this work, we deepen the study of systemic risk measurement via aggregation functions. We consider three different portfolios as a proxy for an economic system, these portfolios are consisted in two aggregation functions, based on all U.S. stocks and a market index. The risk measures applied are Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR), they are forecasted via the classical GARCH model along with nine distribution probability functions and also by a nonparametric approach. The forecasts are evaluated by loss functions and violation backtests. Results indicate that our approach can generate an adequate aggregation function to process the risk of a system previously selected.

Neste trabalho, aprofundamos o estudo sobre risco sistêmico via funções de agregação. Consideramos três carteiras diferentes como proxy para um sistema econômico, estas carteiras são consistidas por duas funções de agregação, baseadas em todos as ações do E.U.A, e um índice de mercado. As medidas de risco aplicadas são Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR), elas são previstas através do modelo GARCH clássico unido com nove funções de distribuição de probabilidade diferentes e mais por um método não paramétrico. As previsões são avaliadas por funções de perda e backtests de violação. Os resultados indicam que nossa abordagem pode gerar uma função de agregação adequada para processar o risco de um sistema previamente selecionado. / In this work, we deepen the study of systemic risk measurement via aggregation functions. We consider three different portfolios as a proxy for an economic system, these portfolios are consisted in two aggregation functions, based on all U.S. stocks and a market index. The risk measures applied are Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR), they are forecasted via the classical GARCH model along with nine distribution probability functions and also by a nonparametric approach. The forecasts are evaluated by loss functions and violation backtests. Results indicate that our approach can generate an adequate aggregation function to process the risk of a system previously selected.

[pt] Atualmente, o mundo tem se voltado à promoção do desenvolvimento da energia proveniente de fontes renováveis, pois estas aparecem como uma alternativa para a redução do aquecimento global. No Brasil, as principais fontes de geração renováveis de energia são: geração de cogeração à bagaço de cana-deaçúcar (biomassa), eólica e pequenas centrais hidrelétricas (PCH). Atualmente, o grande desafio enfrentado por elas é comercialização de contratos lastreados em perfis de geração que, apesar de exibirem um baixo fator de emissões, são extremamente sazonais e incertos. Contudo, sabe-se que existe uma relevante complementaridade entre a disponibilidade dos seus recursos (colheita da cana, vento e hidrologia), que como consequência, promove a possibilidade de um ganho sinérgico com a formação de um portfolio contendo tais fontes. A sinergia entre os perfis de geração de uma biomassa e uma PCH foi recentemente estudada através de um modelo de otimização de portfolio com aversão a risco. Esta dissertação tem dois objetivos: (i) estender o modelo de comercialização integrada de fontes renováveis para considerar também a fonte de geração eólica, e (ii) utilizá-lo para definir a estratégia ótima de oferta (compra) da comercializadora em um leilão de compra de contratos de fontes renováveis no ACL. Dois formatos de leilão serão testados e comparados tanto em termos de benefício para a comercializadora, como em termos de participação final de cada fonte. Por fim, o objetivo (ii) preenche uma lacuna na literatura correspondente a ausência de modelos de oferta estratégica avessa a risco em leilões de contratos por parte da demanda. / [en] Nowadays, the world has turned to promoting the development of energy from renewable sources, because they appear as an alternative to reducing global warming. In Brazil, the main renewable energy sources are the thermoelectric cogeneration of sugarcane bagasse (biomass), wind power and small hydro resources. Besides, the major challenge faced by them is the contracts trade guaranteed by generation profiles that, despite exhibiting a low emission factor, are highly seasonal and uncertain. However, it is known that there is an important complementarity between the availability of resources (sugar cane harvesting, wind and hydrology), which as a consequence, promotes the ability to gain a synergistic effect with the formation of a portfolio containing such sources. The synergy between the resources availability profile of biomass and a small hydro was recently studied by a model of portfolio optimization with risk aversion. This work has two objectives: (i) extend the portfolio trade model of renewable sources to consider also the a wind generation power plant, and (ii) define an optimal strategic bidding (demand side) for a trading company on a contract auction for renewable sources. Two auction formats will be tested and compared in terms of benefit to the energy trading company. Finally, the objective (ii) fills a gap in the literature corresponding to the absence of risk-averse bidding models for contract auctions on the demand side.

This study investigates and evaluates how different portfolio optimization methods perform when varying assets and financial market scenarios. Methods included are mean variance, Conditional Value-at-Risk, utility based, risk factor based and Monte Carlo optimization. Market scenarios are represented by stagnating, bull and bear market data from the Bloomberg database. In order to perform robust optimizations resampling of the Bloomberg data has been done hundred times. The evaluation of the methods has been done with respect to selected ratios and two benchmark portfolios. Namely an equally weighted portfolio and an equally weighted risk contributions portfolio. The study found that mean variance and Conditional Value-at-Risk optimization performed best when using linear assets in all the investigated cases. Considering non-linear assets such as options an equally weighted portfolio performs best. / Den här studien undersöker och utvärderar hur olika portföljoptimeringsmetoder presterar med varierande finansiella tillgångsslag och marknadsscenarion. De metoder som har undersökts är: väntevärde-varians, villkorligt-värde-av-risk, nyttjande- och Monte Carlo baserad optimering. De marknadsscenarion som valts är: stagnerande, uppåt- samt nedåtgående scenarion där marknadsdata hämtats från Bloomberg för respektive tillgång. För att erhålla robusta optimeringsresultat har data omsamplats hundra gånger. Utvärderingen av metoderna har gjorts med avseende på utvalda indikatorer och två jämförelseportföljer, en likaviktad portfölj och en likariskviktad portfölj. Studien fann att portföljer genererade av väntevärde-varians och villkorligt-värde-av-risk optimering visade bäst prestanda, när linjära tillgångar använts i samtliga scenarion. När ickelinjära tillgångar såsom optioner har använts gav den likaviktade jämförelseportföljen bäst resultat i samtliga scenarion.

This thesis aims to fill this gap between static and dynamic risk measures. It presents a theory of dynamic risk measures based directly on classical, static risk measures. This allows for a direct connection of the static, the discrete time as well as the continuous time setting. Unlike the existing literature this approach leads to a interpretable pendant to the well-understood static risk measures. As a key concept the notion of divisible families of risk measures is introduced. These families of risk measures admit a dynamic version in continuous time. Moreover, divisibility allows the definition of the risk generator, a nonlinear extension of the classical infinitesimal generator. Based on this extension we derive a nonlinear version of Dynkins lemma as well as risk-averse Hamilton–Jacobi–Bellman equations.

With the world becoming more conscious about achieving 1.5-degree scenario as promisedby the most powerful economies of the world, much needed push was received by the renewable energy technology providers.  This has led to an increased a share of energy production from renewables and a decrease in the fossil-based energy production with the overall energy production.  As a result, a large share of inertia of the system is lost and a big challenge in the name of flexibility is presented to the world of energy.  Virtual Power Plant is quite a novel and new concept to address the new generation challenge of flexibility and can offer various other benefits like competitivity,reliability, accessibility etc.  In this thesis, a commercial virtual power plant is studied by developing a mixed integer linear model to emulate the trading for short term markets with the risk mea- sures in a Nordic Electricity Framework.  Further, the developed model is implemented in a quite a new mathematical programming language known as “Julia”.  The model is implemented using a hypothetical portfolio consisting of a dispatchable unit, a battery system and a wind farm in the SE3 bidding zone of Sweden.  An investigation on varia- tion of imbalance costs in three different modes also has been carried out, to demonstratethe advantage of such a virtual power plant concept in reducing the imbalance costs. / För att uppfylla 1,5-gradersmålet som beslutats av världens ledande ekonomier har olika‌typer av förnybar energiproduktion fått ett stort uppsving. Detta har lett till ökad energiproduktion från förnybara källor och minskad energiproduktion från fossila källor. För elsystemen innebär en högre andel förnybar produktion minskad svängmassa ochökat behov av flexibilitet för att kompensera för variationen hos förnybara energikällor. Virtuella kraftverk är ett nytt koncept för att tillgodose behovet av flexibilitet och kanäven ge andra fördelar som konkurrenskraft och tillförlitlighet. I denna uppsats studeras ett virtuellt kraftverk genom att utveckla en optimeringsmodell för att emulera handeln i elmarknader med riskmått inom ett ramverk för den nordiska elmarknaden. Modellen implementeras i det nya programmeringsspråket Julia. Modellen innehåller en hypotetisk blandning av resurser bestående av ett planerbart kraftverk, ett batterisystem och en vindpark i elområdet SE3 i Sverige. Balanseringskostnaderna i tre olika modeller undersöks för att visa potentialen hos det virtuella kraftverket att minska dessa kostnader.

Seit der Nahrungsmittelpreiskrise 2007/08 ist die Volatilität von Nahrungsmittelpreisen wieder als wichtiges Thema in der politischen Diskussion aufgetaucht. Nicht nur die Beobachtung eines steigenden Preisniveaus, sondern auch der scheinbare Anstieg der Volatilität auf Schlüsselmärkten (vor allem Getreide) hat viele Studien sowohl auf konzeptioneller als auch auf empirischer Ebene ausgelöst. Da Menschen, insbesondere in Entwicklungsländern, unter hohen und instabilen Preisen leiden, ist diese Entwicklung als globales Problem und ein Haupthindernis zur Bekämpfung von Hunger und Mangelernährung erkannt worden. Diese Doktorarbeit hat das Ziel, zu der Debatte beizutragen, wie am besten mit Preisvolatilität auf Agrarmärkten umzugehen ist. Um einen umfassenden Überblick über Agrarpreisvolatilität, ihre Ursachen und die Möglichkeiten, betroffenen Marktteilnehmern sinnvoll zu helfen, zu geben, konzentriert sich diese Arbeit auf drei bedeutende Aspekte, welche die drei Hauptkapitel dieser kumulativen Dissertation bilden: Kapitel 2 hat das Ziel, die Frage, wie sich Volatilität seit der Nahrungsmittelpreiskrise 2007/08 entwickelt hat, robust zu beantworten. Generelle Unterschiede im Volatilitätslevel, der Volatilität der Volatilität und der Persistenz der Volatilität werden für ein Set von realisierten, GARCH-Modell basierten und impliziten Volatilitäten auf drei Agrarmärkten – Weizen, Mais und Sojabohnen – betrachtet. Darüber hinaus werden verbreitete Aussagen bezüglich des Anstiegs der Volatilität seit der Nahrungsmittelpreiskrise 2007/08 und weitere relevante Aspekte wie die Veränderung der Persistenz der Volatilität und die Quantifizierung des Anstiegs hinsichtlich einer robusten Schlussfolgerung geprüft. Kapitel 3 identifiziert die Treiber von Volatilität für verschiedene Ölsaaten und pflanzliche Ölmärkte. Das Kapitel liefert eine Untersuchung der gemeinsamen Effekte von fundamentalen Volatilitätstreibern und der Übertragungseffekte zwischen verwandten Märkten. Kapitel 4 stellt ein Set von verwandten Risikomaßen vor, um die detaillierte Struktur der Volatilität in Agrarmärkten zu charakterisieren. Diese Maße erlauben die Zerlegung einer allgemeinen Preisbewegung in „große“ Veränderungen mit möglicherweise schwerwiegenden ökonomischen Konsequenzen und „normale“ Veränderungen. Es werden zukunftsgerichtete Schätzer der Risikomaße abgeleitet, die die Erwartungen des Marktes über zukünftige Bewegungen der Rohwarenpreise aus aktuellen Optionspreisen extrahieren. Eine empirische Studie für wichtige Getreidemärkte demonstriert die Vorhersagekraft der impliziten Schätzer. Insgesamt zeigt die Doktorarbeit, dass Risikomanagement und die Abmilderung der Effekte erhöhter Preisvolatilität nur dann wirkungsvoll ist, wenn man sich bewusst ist, welche Agrarmärkte betroffen sind, mit welcher genauen Art von Preisrisiko man konfrontiert ist und somit welche Gruppe von Marktteilnehmern Schutz benötigt und wenn das Risiko frühzeitig erkannt wird, um hilfreiche Maßnahmen zu unternehmen.