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Alternatywne względem ujęcia Markowitza podejście do szacowania stopy zwrotu z portfela

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Stachura M., Wodecka B.
Studia Ekonomiczne
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2013
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vol. 154
92-101
EN
In the study, two approaches of rate-of-return estimation are compared. One of them, that predominates in practice and that is called by the authors heterogeneous, refers to a separate rate-of-return estimation for every individual asset, and then to an interpolation of obtained values in order to asses rate of return for any portfolio with priorly given proportions of assets. The heterogeneous approach is based on premises concerning a proper method of rate-of-return estimation for individual assets, and a specific method of interpolating estimates for any portfolio as well. In contrast, the other approach, called homogeneous, refers to uniform treatment of all portfolios without exceptions, which leads to a direct rate-of-return estimation for any portfolio with priorly given proportions of assets. The essence of both approaches and discrepancies between them are illustrated with use of properly chosen examples (arbitrary and empirical). Examples' analysis indicates some advantage of the homogeneous approach over the heterogeneous one.
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Optymalizacja portfela z zastosowaniem kopuli niesymetrycznych

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Stachura M., Wodecka B.
Studia Ekonomiczne
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2013
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vol. 154
135-143
EN
This paper is some kind of a discussion about both the necessity and possibility of asymmetric copula applications. Presented deliberation is settled in the context of financial portfolio analysis that, in a specific way, requires taking the correlations of the component assets into consideration, which creates an opportunity for asymmetric copula implementation. Mentioned issues are exemplified by real two-asset portfolio optimization.
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k-th record estimator of the scale parameter of the α-stable distribution

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Stachura M., Wodecka B.
Statistics in Transition new series
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2022
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vol. 23
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issue 4
203-215
EN
Various techniques of scale parameter estimation have been proposed in the case of alpha stable distributions. In the paper, the authors present an estimation technique that involves the k-th record theory. Although this theory is over 40 years old, its implementation in the classical extreme value theory – being the other cornerstone of the presented approach – is quite new, and tempting. Several theoretical properties of the introduced scale parameter estimators are presented. With the use of Monte Carlo methods, a comparative analysis is performed between the approach based on k-th records and approaches based on Hill’s and Pickands’ estimators. Additionally, the paper uses a real-life data set to illustrate how to effectively apply the k-th record estimator of the scale parameter. The research indicates several advantages of the k-th record approach over its other counterparts, especially when dealing with incomplete information about the underlying sample.
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