The optimal portfolio in respect to Expected Shortfall: a comparative study

• Autorzy: Gurgul H. , Machno A. , Syrek R.

Identyfikatory

DOI

10.7494/manage.2013.14.17

Warianty tytułu

PL

Optymalny portfel na podstawie Expected Shortfall: badania porównawcze

• Języki publikacji: EN

Abstrakty

EN

Value at Risk plays a crucial role in the risk management. However, this risk measure has some drawbacks. The alternative risk measure is Expected Shortfall, which is rarely used, but exhibits desirable properties. In the paper, the estimation of both risk measures has been conducted, for pairs of index returns (DJIA, DAX, ATX), based on Markowitz model, the regime switching copula model and the multivariate GARCH model. The results suggest that a misspecification can cause many errors. Incorrect models cause bias of mean, especially models which do not assume dynamic structure of the market Both an underestimation and an overestimation of a risk has been observed. In the paper, it is shown that the measure of change in Expected Shortfall as a function of the expected return is strongly underestimated under the normal distribution assumption.

PL

Value at Risk jest kluczową wielkością w zarządzaniu ryzykiem. Jako miara ryzyka nie ma ona jednak pożądanych własności. Alternatywną miarą jest Expected Shorfall, która jest mniej używana w praktyce, za to ma własności, które są oczekiwane przez użytkowników modeli. W artykule zostały oszacowane obie miary, dla par stóp zwrotu z indeksów DJIA, DAX i ATX, na podstawie modeli Markowitza, kopuli przełącznikowych oraz wielowymiarowego GARCH. Otrzymane wyniki pokazują, iż zły dobór modelu może powodować wiele błędów. Modele, które nie uwzględniają dynamicznego charakteru badanych szeregów czasowych błędnie oceniają średnią. Obie badane miary ryzyka mogą być przeszacowane oraz niedoszacowane. Szczególnie błędne okazało się oszacowanie zmiany Expected Shortfall wraz ze wzrostem oczekiwanej stopy zwrotu przy założeniu rozkładu normalnego.

Słowa kluczowe

EN

value at risk; Expected Shortfall; interdependency; regime switching copulas; risk management

PL

Expected Shortfall; wpółzależność; model przełącznikowy; kopula; zarządzanie ryzykiem

• Wydawca: Wydawnictwa AGH
• Czasopismo: Managerial Economics
• Rocznik: 2013
• Tom: nr 14
• Strony: 17--38
• Opis fizyczny: Bibliogr. 38 poz., tab., wykr.

Twórcy

autor

Gurgul H.

• AGH University of Science and Technology in Cracow, Department of Applications of Mathematics in Economics

autor

Machno A.

• AGH University of Science and Technology in Cracow, Department of Applications of Mathematics in Economics

autor

Syrek R.

• Jagiellonian University, Institute of Economics and Management

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