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EN
The results of the calculation of the Choquet integral of a monotone function on the nonnegative real line have been described. Next, the authors prepresented Choquet integral of nonmonotone functions, by constructing monotone functions from nonmonotone ones by using the increasing or decreasing rearrangement of a nonmonotone function. Finally, this paper considers some applications of these results to the continuous agregation operator OWA, and to the representation of risk measures by Choquet integral.
EN
Modern research has led to the rejection of the hypothesis of a normal distribution for financial asset returns. Under these conditions, the portfolio variance loses part of its informativity and can not serve as a good risk measure. The central aim of this work is the development and justification of a new technique of portfolio risk measure. We analyzed weekly stock returns of four largest German concerns: Deutsche Telekom, Siemens AG, Bayer AG and BMW. It is shown that asset returns are not normally distributed, but with good precision follow Laplace distribution (double exponential distribution). Using Laplace distribution function, we obtained the analytical expressions for VaR and CVaR risk measures and made calculations of risk measure using these approaches. Using modified Markowitz model the efficient frontiers of portfolios were constructed.
EN
Research background: In the literature little discussion was made about predicting state of time series in daily manner. The ability to recognize the state of a time series gives, for example, an opportunity to measure the level of risk in a state of tranquility and a state of turbulence independently, which can provide more accurate measurements of the market risk in a financial institution. Purpose of the article: The aim of article is to find an appropriate tools to predict, based on today's economic situation, the state, in which time series of financial data will be tomorrow. Methods: This paper proposes an approach to predict states (states of tranquillity and turbulence) for a current portfolio in a one-day horizon. The prediction is made using 3 different models for a binary variable (Logit, Probit, Cloglog), 4 definitions of a dependent variable (1%, 5%, 10%, 20% of worst realization of returns), 3 sets of independent variables (un-transformed data, PCA analysis and factor analysis). Additionally, an optimal cut-off point analysis is performed. The evaluation of the models was based on the LR test, Hosmer-Lemeshow test, Gini coefficient analysis and CROC criterion based on the ROC curve. The analyses were performed for 43 individual shares and 5 portfolios of shares quoted on the Warsaw Stock Exchange. The study has been conducted for the period from 1 January 2006 to 31 January 2012. Findings & Value added: Six combinations of assumptions have been chosen as appropriate (any model for a binary variable, the dependent variable defined as 5% or 10% of worst realization of returns, untransformed data, 5% or 10% cut-off point respectively). Models built on these assumptions meet all the formal requirements and have a high predictive and discriminant ability to one-day-ahead forecast of state of turbulence based on today's economic situation.
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EN
The purpose of this paper is to attempt to classify risk which can be observed when one deals with data from the metals market. Usually the general definition of risk includes two dimensions. The first one is the probability of occurrence and the second one are the associated consequences of a set of hazardous scenarios. In this research the authors try to add a new dimension: the source of risk, which can be defined in terms of the level of turnover (volatility of volume) and price (volatility of returns). One can categorize risks in terms of multidimensional ranking based on a comparative evaluation of the consequences, probability, and source of a given risk. Another dimension is the chosen risk measures, in the meaning of the risk model. In risk analysis, some selected quantile risk measures were proposed: VaR, Expected Shortfall, Median Shortfall and GlueVaR. The empirical part presents a multidimensional risk analysis of the metal market.
PL
Celem opracowania jest próba klasyfikacji ryzyka, które można zaobserwować, gdy mamy do czynienia z danymi z rynku metali. Ogólna definicja ryzyka obejmuje dwa wymiary: prawdopodobieństwo wystąpienia zdarzenia ryzykownego i związane z nim konsekwencje zestawu niebezpiecznych scenariuszy. W niniejszym badaniu staramy się dodać nowy wymiar: źródło ryzyka, które można zdefiniować w kategoriach poziomu obrotu (zmienność wolumenu) oraz ceny (zmienność stóp zwrotu). Ryzyko możemy kategoryzować według wielowymiarowego rankingu, na podstawie porównawczej oceny konsekwencji, prawdopodobieństwa i źródła danego ryzyka. Inny wymiar to wybrane miary ryzyka w rozumieniu modelu ryzyka. W analizie ryzyka wykorzystano wybrane miary kwantylowe: VaR, Expected Shortfall, Median Shortfall oraz GlueVaR. W części empirycznej przedstawiamy analizę ryzyka w ujęciu wielowymiarowym przeprowadzoną na rynku metali.
EN
The activity in conditions of credit risk has a specific place in each banks’ performance. There is no way of imagining bank’s functioning on financial services market without its stable development. Moreover, credit capacity and, related with it, credit risk mitigation must be based on trust. The questioning of this principle and its non-compliance may easily lead to credit risk increase and consequently to threat of the whole system and separate banks destabilization. The aim of proper credit risk management is to identify, measure, control and monitor. A bank, which has risk management systems implemented, presents higher value for the stockholders.
PL
Działalność w warunkach ryzyka kredytowego zajmuje specjalne miejsce w funkcjonowaniu każdego banku. Nie sposób wyobrazić sobie funkcjonowania banku na rynku usług finansowych bez jego stabilnego rozwoju. Ponadto zdolność kredytowa i związane z nią ograniczenie ryzyka kredytowego muszą być oparte na zasadzie zaufania. Podważenie tej zasady oraz jej nieprzestrzeganie z łatwością może doprowadzić do zwiększenia ryzyka kredytowego, a tym samym grozić destabilizacją całego systemu bankowego i poszczególnych banków.Celem właściwego zarządzania ryzykiem kredytowym jest jego identyfikacja, pomiar, sterowanie i monitorowanie. Bank, który posiada wdrożone systemy zarządzania ryzykiem, prezentuje wyższą wartość dla akcjonariuszy.
PL
Działalność w warunkach ryzyka kredytowego zajmuje specjalne miejsce w funkcjonowaniu każdego banku. Nie sposób wyobrazić sobie funkcjonowania banku na rynku usług finansowych bez jego stabilnego rozwoju. Ponadto zdolność kredytowa i związane z nią ograniczenie ryzyka kredytowego muszą być oparte na zasadzie zaufania. Podważenie tej zasady oraz jej nieprzestrzeganie z łatwością może doprowadzić do zwiększenia ryzyka kredytowego, a tym samym grozić destabilizacją całego systemu bankowego i poszczególnych banków.Celem właściwego zarządzania ryzykiem kredytowym jest jego identyfikacja, pomiar, sterowanie i monitorowanie. Bank, który posiada wdrożone systemy zarządzania ryzykiem, prezentuje wyższą wartość dla akcjonariuszy.
EN
The activity in conditions of credit risk has a specific place in each banks’ performance. There is no way of imagining bank’s functioning on financial services market without its stable development. Moreover, credit capacity and, related with it, credit risk mitigation must be based on trust. The questioning of this principle and its non-compliance may easily lead to credit risk increase and consequently to threat of the whole system and separate banks destabilization. The aim of proper credit risk management is to identify, measure, control and monitor. A bank, which has risk management systems implemented, presents higher value for the stockholders.
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