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Since Markowitz presented the mean-variance model as a way of putting together a financial portfolio, variance has been the established measure of risk. Even though the measures of downside risk hasn’t gained the same attention as variance, it has been used in research for some time. Semivariance, best described as the risk of a portfolio’s return falling below a set target, was introduced as a ri
In this paper we consider the distribution of the product of a Wishart random matrix and a Gaussian random vector. We derive a stochastic representation for the elements of the product. Using this result, the exact joint density for an arbitrary linear combination of the elements of the product is obtained. Furthermore, the derived stochastic representation allows us to simulate samples of arbitra
In this paper we study the distribution of the product of an inverse Wishart random matrix and a Gaussian random vector. We derive its asymptotic distribution as well as its approximate density function formula which is based on the Gaussian integral and the third order Taylor expansion. Furthermore, we compare obtained asymptotic and approximate density functions with the exact density which is o
Expected Shortfall has become a prominent risk measure after the global financial crisis which hit the economy in 2007. This master thesis examines whether Expected Shortfall (ES) estimation gives better estimates when we incorporate skewness and the impact during turbulent versus tranquil period. This specific analysis scrutinized daily total returns (TR) of three Indexes: Standard & Poor 500
In this paper we study the distribution of the product of an inverse Wishart random matrix and a Gaussian random vector. We derive its asymptotic distribution as well as a formula for its approximate density function which is based on the Gaussian integral and the third order Taylor expansion. Furthermore, we compare the asymptotic and approximate density functions with the exact density obtained
Oil is the most traded commodity in the world and is an important part in the global economy. The change in the price of oil has an effect on all sectors of the economy, and the ability to capture its risk is an important research topic. This study calculates the risk of one benchmark crude oil (West Texas Intermediate) over the period 1986-2015 by estimating the Value-at-Risk (VaR) and the Expect
With the implementation of the Fundamental Review of the Trading Book in January of 2022, financial institutions will be obligated to implement Expected Shortfall as a means of determining market risk capital. With the transition from Value at Risk to Expected Shortfall, the question of how to accurately forecast Expected Shortfall arises. This paper investigates the forecasting ability of non-par
Purpose: The purpose of this paper is to empirically evaluate the performance of seven different methods that are used when estimating Value-at-Risk for a portfolio of Swedish index-bonds with different maturities. As a supplementary objective, the paper tries to determine the history that one needs to account for when calculating VaR. Methodology: In order to calculate the VaR, a portfolio consi
The deteriorating European economic situation has suggested the necessity of risk management in the exchange rate of EUR for governments and corporations, but there is few researches studying in this field. In this thesis, by choosing USD/EUR, JPY/EUR and GBP/EUR as subjects, with a focus on the availability of different methods to the estimation of exchange rate risk of EUR, we aim to calculate t
This thesis investigates the volatility structures found in forward-looking fundamental valuations of the Swedish stock index OMXS30. The evaluated data constitutes daily observations of P/E ratios based on twelve months earnings estimates during the period 2009-01-02 until 2018-10-18. The analysis is conducted by applying a GARCH modelling framework to a log-return transformed return series deriv
Following spinal cord injury (SCI) a series of anatomical and functional plastic changes occur in the spinal cord, including reorganization of the spinal neuronal network, alteration of properties of interneurons and motoneurons as well as up- or down-regulation of different neurotransmitter receptors. In mammalian spinal cord, one of the important neurotransmitters, serotonin (5-HT), plays an ess
This thesis aims to understand copula theory and its application in measuring dependence, particularly in the context of the paper "Multivariate conditional versions of Spearman’s rho and related measures of tail dependence" by Schmid and Schmidt. We clarify certain statements and formulas in Schmid and Schmidt's work, explore the potential of the conditional version of Spearman'
Arid mountainous regions are vulnerable to extreme hydrological events such as floods and droughts. Providing accurate and continuous rainfall records with no gaps is crucial for effective flood mitigation and water resource management in these and downstream areas. Satellite data and geospatial interpolation can be employed for this purpose and to provide continuous data series. However, it is es
The sum of a random number of independent and identically distributed random vectors has a distribution which is not analytically tractable, in the general case. The problem has been addressed by means of asymptotic approximations embedding the number of summands in a stochastically increasing sequence. Another approach relies on fitting flexible and tractable parametric, multivariate distributionThe sum of a random number of independent and identically distributed random vectors has a distribution which is not analytically tractable, in the general case. The problem has been addressed by means of asymptotic approximations embedding the number of summands in a stochastically increasing sequence. Another approach relies on fitting flexible and tractable parametric, multivariate distribution
This thesis explores the parametric and nonparametric approaches for estimating Value at Risk and Expected Shortfall through foreign exchange exposure. The data for this study was provided by Trelleborg Group. We look at the translational risk on the balance sheet when translating the Groups investments in foreign subsidiaries to SEK. In the parametric approach we make the assumption that the po
Renewable energy is gaining increasing importance in the generation of power due to the finite existence of fossil fuels and concerns about climate change. As its demand grows financial interest from investors’ increases, thus it is important to find the most effective way of quantifying the risk of the renewable energy market. Furthermore as renewable energy can be viewed as an economic substitut
