This empirical study has shown that optimal portfolios need approximately 10 securities to diversify away the unsystematic risk. This challenges previous studies of randomly chosen portfolios which states that at least 30 securities are needed. The result of this study sheds light upon the difference in risk diversification between random portfolios and optimal portfolios and is a valuable contribution for investors. The study suggests that a major part of the unsystematic risk in a portfolio can be diversified away with fewer securities by using portfolio optimization. Individual investors especially, who usually have portfolios consisting of few securities, benefit from these results. There are today multiple user-friendly software applications that can perform the computations of portfolio optimization without the user having to know the mathematics behind the program. Microsoft Excel’s solver function is an example of a well-used software for portfolio optimization. In this study however, MATLAB was used to perform all the optimizations. The study was executed on data of 140 stocks on NASDAQ Stockholm during 2000-2014. Multiple optimizations were done with varying input in order to yield a result that only depended on the investigated variable, that is, how many different stocks that are needed in order to diversify away the unsystematic risk in a portfolio. / <p>Osäker på examinatorns namn, tog namnet på den person som skickade mejl om betyg.</p>

This report deals with detecting object position using sensor datausing three different types of sensors held at four corners of a givendimensional plate; two sensors of URM09 Analog, 1 of URM09 Ultrasonic and 1 of VL6180X ToF sensor. The accuracy of the sensors performance is investigated using relative standard deviation. The results show that the proposed solution allows to estimate the objectposition and size without significant error.

To investigate the relationship between the structural characteristics of rough single fracturesand the electrical properties of the rock. In this study, a series of physical models of roughand smooth single fractures were established using the finite element method and Ohm's lawto test the electrical conductivity. By varying the distance between the fracture surfaces, arange of individual fractures with different surface roughness characterized by the relativestandard deviation (RSD) was generated using COMSOL Multiphysics software.Subsequently, the intensity of current passing through the fractures and the influence of roughsurfaces on rock electrical properties were monitored. Numerical simulations demonstrated anon-linear relationship between the current intensity through the models and the RSDroughness, with the equivalent resistivity of the fractured rock increasing with higher RSDvalues. As the RSD roughness increased, the difference in equivalent resistivity betweenrough and smooth fractures also increased, indicating a greater impact of rough surfaces onelectrical properties. The equivalent resistivity of the rock model was 1.05-1.45 times that ofthe parallel plate model with same average aperture. The novelty of this study lies in directlyinvestigating the relationship between roughness of single fractures and rock electricalproperties in three-dimensional, providing insights for understanding the electrical behaviorof rock fractures. / För att undersöka sambandet mellan strukturella egenskaper hos ojämna enkelstrålar och deelektriska egenskaperna hos bergarten. I denna studie etablerades en serie fysiska modeller avojämna och jämna enkelstrålar genom att använda finita elementmetoden och Ohms lag föratt testa elektrisk ledningsförmåga. Genom att variera avståndet mellan strålytornagenererades en rad individuella strålar med olika ytjämnhet som karakteriseras av relativstandardavvikelse (RSD) med hjälp av COMSOL Multiphysics-programvara. Därefterövervakades intensiteten av ström som passerade genom strålarna och inflytandet av ojämnaytor på bergens elektriska egenskaper. Numeriska simuleringar visade på ett icke-linjärtsamband mellan strömintensiteten genom modellerna och RSD-ytjämnheten, där denekvivalenta resistiviteten hos den spruckna bergarten ökade med högre RSD-värden. NärRSD-ytjämnheten ökade, ökade även skillnaden i ekvivalent resistivitet mellan ojämna ochjämna strålar, vilket indikerar en större påverkan av ojämna ytor på de elektriskaegenskaperna. Den ekvivalenta resistiviteten hos bergmodellen var 1,05–1,45 gånger högreän den hos parallellplattanmodellen med samma genomsnittliga apertur. Nyheten i dennastudie ligger i att direkt undersöka sambandet mellan ytjämnheten hos enkelstrålar ochbergens elektriska egenskaper på en tredimensionell skala, vilket ger värdefulla insikter föratt förstå det elektriska beteendet hos bergstrålar och ytterligare förbättra modeller.