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1

Fundamental Portfolio Construction Based on Semi-Variance

100%

Rutkowska-Ziarko A.

Olsztyn Economic Journal

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2013

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vol. 8

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issue 2

151-162

EN

In models for creating a fundamental portfolio, based on the classical Markowitz model, the variance is usually used as a risk measure. However, equal treatment of negative and positive deviations from the expected rate of return is a slight shortcoming of variance as the risk measure. Markowitz defined semi-variance to measure the negative deviations only. However, finding the fundamental portfolio with minimum semi-variance is not possible with the existing methods.The aim of the article is to propose and verify a method which allows to find a fundamental portfolio with the minimum semi-variance. A synthetic indicator is constructed for each company, describing its economic and financial situation. The method of constructing fundamental portfolios using semi-variance as the risk measure is presented. The differences between the semi-variance fundamental portfolios and variance fundamental portfolios are analysed on example of companies listed on the Warsaw Stock Exchange.

2

Power generalization of Chebyshev’s inequality – multivariate case

100%

Budny K.

Statistics in Transition new series

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2019

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vol. 20

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issue 3

155-170

EN

In the paper some multivariate power generalizations of Chebyshev’s inequality and their improvements will be presented with extension to a random vector with singular covariance matrix. Moreover, for these generalizations, the cases of the multivariate normal and the multivariate t distributions will be considered. Additionally, some financial application will be presented.

3

Identification of multivariate outliers – problems and challenges of visualization methods

63%

Majewska J.

Studia Ekonomiczne

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2015

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vol. 247

69-83

EN

The identification of outliers is often thought of as a means to eliminate observations from a data set to avoid disturbance in further analyses. But outliers may as well be the interesting observations in themselves, because they can give us hints about certain structures in the data or about special events during the sampling period. Therefore, appropriate methods for the detection of outliers are needed. Literature is abundant with procedures for detection and testing of single outliers in sample data. The difficulty of detection increases with the number of outliers and the dimension of the data because the outliers can be extreme in any growing number of directions. An overview of multivariate outlier detection methods that are provided in this study because of its growing importance in a wide variety of practical situations. We focus on methods that can be visually presented.

PL

Proces identyfikacji obserwacji odstających jest często rozważany jako wstęp do eliminacji obserwacji nietypowych ze zbiorów danych w celu uniknięcia jakichkolwiek problemów w dalszej analizie danych. Tymczasem obserwacje nietypowe dostarczają niejednokrotnie istotnych informacji o strukturze danych lub wyjątkowych zdarzeniach podczas badanego okresu. Dlatego potrzebne są właściwe metody identyfikacji tychże obserwacji. Literatura jest bogata w metody wykrywania obserwacji nietypowych w jednowymiarowych przypadkach. W wielowymiarowej przestrzeni proces ten znacznie się komplikuje. W artykule prezentujemy wybrane metody wizualizacyjne wykrywania wielowymiarowych obserwacji nietypowych.

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1 Olsztyn Economic Journal

1 Statistics in Transition new series

1 Studia Ekonomiczne

1 Budny K.

1 Majewska J.

1 Rutkowska-Ziarko A.

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1 2013

Fundamental Portfolio Construction Based on Semi-Variance

Power generalization of Chebyshev’s inequality – multivariate case

Identification of multivariate outliers – problems and challenges of visualization methods