Wyniki wyszukiwania - Biblioteka Nauki

1

Pomiar ryzyka finansowego w warunkach niepewności

100%

Trzpiot G.

Badania Operacyjne i Decyzje

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2006

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tom nr 2

81-88

EN

Coping with the uncertainties of future outcomes is a fundamental theme in finance in a stochastic environment. In the field of stochastic programming, which has grown from the traditions of linear and quadratic programming, constrains on future outcomes have commonly been relaxed to the penalty expressions. Probabilistic constrains, requiring that a condition only to be satisfied up to a given probability. Objectives have usually taken the form of maximizing expected utility or minimizing expected cost. In financial optimization, where uncertainties are likewise unavoidable, approaches of stochastic programming have prevailed. An important example is constraint and objective based notion of the value-at-risk, which is closely related to probabilistic one; unfortunately it suffers from similar mathematical shortcomings. Value-at-risk suffers from financial inconsistencies, which have led to axiomatic development of coherent risk measures, so we also add the robust alternative called conditional value-at-risk. We also cope with some connection between CVaR and stochastic dominance.

PL

Zarządzanie losowymi przyszłymi stopami zwrotu jest podstawowym zadaniem finansów w otoczeniu, które ma charakter stochastyczny. W metodologii programowania stochastycznego, które wyrosło z tradycji programowania liniowego i kwadratowego, ograniczenia, co do przyszłych wartości, są często zamieniane na funkcję kary. Probabilistyczne ograniczenia w zadaniu wymagają jedynie, aby zdarzenia zachodziły z pewnym prawdopodobieństwem. Funkcja celu zazwyczaj maksymalizuje oczekiwaną użyteczność albo minimalizuje koszty. W finansach zadania optymalizacji stochastycznej mają, zatem uprzywilejowane miejsce. Ważne są zadania bazujące na optymalizacji VaR, które są podejściem probabilistycznym do zagadnienia. Rozwój aksjomatycznej teorii związanej z koherentnymi miarami ryzyka, wskazał na odporny odpowiednik VaR nazywany CVaR. W pracy omówiono związek tej miary z dominacjami stochastycznymi.

2

Computing the portfolio conditional value-at-risk in the α-stable case

99%

Stoyanov S. , Samorodnitsky G. , Rachev S. T. , Ortobelli S.

Probability and Mathematical Statistics

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2006

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tom Vol. 26, Fasc. 1

1--22

EN

The class of α-stable distributions is an attractive probabilistic model of asset returns distribution in the field of finance. When dealing with real issues, such as optimal portfolio selection, it is important that we can compute the Conditional Value-at-Risk (CVaR) accurately. The CVaR is also known as the expected tail loss (ETL) proposed in literature as a coherent risk measure. In our paper we propose an integral expression for the calculation of the CVaR of a stable law. We compare the current approach to some existing method and we demonstrate how to relate the derived result to some common multivariate distributional assumptions.

3

Assessing the Efficiency of Investment Fund Management Using Quantile Risk Measures

99%

Rutkowska-Ziarko A. , Garsztka P.

Olsztyn Economic Journal

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2016

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tom 11

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nr 3

277-298

EN

The aim of the research is to compare the efficiency of managing selected Polish investment funds in various phases of stock market condition. The Value at Risk (VaR) and Conditional Value at Risk (CVaR) is used to construct efficiency ratios of fund management. Those funds investing in financial instruments have the most stable expected rate of return and the lowest risk, in all the analysed periods which made them highly effective. The article also discusses the alternative methods to VaR and CVaR estimation which are used in the study. It is noted VaR and CVaR estimates obtained using backtesting and using APARCH models give similar results.

4

A bi-objective portfolio optimization with conditional value-at-risk

99%

Sawik B.

Decision Making in Manufacturing and Services

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2010

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tom Vol. 4, no. 1-2

47-69

EN

This paper presents a bi-objective portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a bi-objective linear program. Numerical examples based on 1000, 3500 and 4020 historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that the proposed linear programming approach provides the decision maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.

5

Conditional value-at-risk and value-at-risk for portfolio optimization model with weighting approach

85%

Sawik B.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2011

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tom T. 15, z. 2

429-434

EN

This paper presents a multi-objective portfolio models with the expected return as a performance measure and the expected worst-case return as a risk measure. The problem objective is to allocate the wealth on different securities to optimize the portfolio expected return. This portfolio approach has allowed the two popular in financial engineering percentile measures of risk, value-at-risk (VaR) and conditional value-at-risk (CVaR) to be applied. Numerical examples based on historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided.

PL

W artykule przedstawiono model wielokryterialnej optymalizacji portfelowej z ważoną funkcją celu. Celem optymalizacji jest wyznaczenie portfela o maksymalnej oczekiwanej stopie zwrotu przy ryzyku wyznaczonym za pomocą miar CVaR oraz VaR. Przedstawiono wyniki eksperymentów obliczeniowych z użyciem danych z GPW w Warszawie.

6

On measuring sensitivity of the optimal portfolio allocation

85%

Konarzewska I.

Badania Operacyjne i Decyzje

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2008

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tom nr 2

55-73

EN

In this paper we consider the sensitivity problem connected with portfolio optimization results when different measures of risk such as: portfolio rates of return standard deviation, portfolio VaR, CVaR are minimized. Conditioning the data (represented by spectral condition index of the rates of return correlation matrix) plays, as it is shown, crucial role in describing the properties of the optimization model when portfolio variance is minimized. Quadratic programming problem becomes ill-conditioned and there is a problem of alternate optima which can be located far from each other taking into account the optimal portfolio structure. Minimizing CVaR when the data are interdependent we can identify many distant structures with similar values of minimal risk although global minimum exists. Strong interdependence of series of the rates of return enlarges problem of identifying portfolio structure minimizing VaR – the surface which is always rough with many local extrema becomes much more difficult to analyze with heuristic search methods. We report on the research carried out for 13 largest firms on theWarsaw Stock Exchange. We have found that series of rates of return on the real stock exchange market are strongly interdependent. We illustrate how much this fact influences the sensitivity of optimal portfolio structure when two different measures of risk are taken into account – portfolio variance and CVaR. The question is how much the structures differ when we change the assumptions of model parameters. We propose two measures of distance between vectors of portfolio weights: angular distance and scaled Euclidean distance. Minimum variance portfolios were not sensitive on even not so small changes in data matrices. Minimum CVaR portfolios exhibited more visible sensitivity on changes in data series.

PL

W artykule podjęto rozważania na temat wrażliwości rozwiązań problemu optymalizacji portfeli akcji, gdy brane są pod uwagę różne miary ryzyka: odchylenie standardowe stóp zwrotu, VaR portfela, CVaR portfela. Uwarunkowanie danych, mierzone za pomocą stopnia uwarunkowania macierzy korelacji stóp zwrotu z akcji, odgrywa, jak pokazano, zasadniczą rolę dla własności rozwiązań modelu minimalizacji wariancji portfela. Model, który jest modelem programowania kwadratowego, jest źle uwarunkowany i pojawia się problem niejednoznaczności rozwiązania optymalnego – wielu strukturom portfeli, nawet bardzo odległym, odpowiada podobna, bliska minimalnej wartości wariancji. Minimalizując CVaR w warunkach współzależności, napotykamy na podobny problem, choć nie występuje on z taką samą siłą. Silna współzależność szeregów stóp zwrotu zwiększa również problemy minimalizacji VaR – nasila się problem występowania wielu lokalnych ekstremów, co powoduje znaczne trudności w stosowaniumetod heurystycznych. Przeprowadzono badanie empiryczne, biorące pod uwagę 13 największych spółek na GPW w Warszawie. Stwierdzono silną współzależność stóp zwrotu. Zbadano siłę wrażliwości rozwiązań modeli minimalizujących wariancję i CVaR z wykorzystaniem miary odległości kątowej oraz skalowanej odległości euklidesowej. W efekcie badań stwierdzono, że portfele znalezione przy kryterium minimalizacji wariancji nie wykazały dużej wrażliwości na zmiany w macierzy danych. Portfele minimalizujące CVaR okazały się bardziej wrażliwe.

7

Optimal scheduling of Virtual Power Plant with risk management

57%

Xia Y. , Liu J.

Journal of Power Technologies

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2016

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tom Vol. 96, nr 1

49--56

EN

Due to intense electricity consumption, environmental concerns and technological development, a great number of renewable distributed resources have been widely installed in the distributed network. However, the reality that renewable distributed resources frequently fluctuate under high penetration makes effective use a challenge. Fortunately, with improved communication architecture and control techniques, this could be achieved by a Virtual Power Plant (VPP). VPP can aggregate various resources in a distributed generation portfolio, by creating one single operating profile. The aim of this paper is mainly to analyze optimal scheduling of VPP to maximize its profit, with due consideration given to the uncertainty of renewable energy output, such as wind power, and to make the energy mix respond to system need. A risk quantization method (CVaR) is introduced to deal with uncertainty. This paper presents a VPP scheduling model, which takes VPP total operation cost, traded electricity cost, unit earnings, supply-demand balancing and other constraints into account, with a CVaR assessment method embedded into this model. According to the scenarios generated by uncertainty of wind power output, numerical results for a proposed case are discussed. These results show the expected profit of VPP scheduling is closely associated with different degrees of confidence , which is a great help for VPP operators when making the tradeoff between risk and profit.