The relation between Value-at-Risk minimization and the return level of financial assets portfolio

  • Taras Zabolotskyy Lviv Institute of Banking
  • Orest Bilyy Lviv Institute of Banking Ukraine
Keywords: Value-at-Risk, financial assets portfolio, return level

Abstract

Purpose and subject of researchThe paper investigates the problem of optimal portfolio selection based on Value-at-Risk minimization with the preselected level of expected return by using the principle of unconditional (concerning expected return) Value-at-Risk minimization.Research methodologyWe show that the optimal portfolio with the minimum level of Value-at-Risk and preselected level of expected return is efficient by Markowitz. We derive the confidence level for the Value-at-Risk under which the expected return of optimal portfolio with the minimum level of Value-at-Risk is equal to the preselected level of expected return.Value resultsUsing historical monthly data of seven assets from Dow Jones Index it is analyzed the relationship between expected return level and confidence level and it is shown that the sample estimator of this confidence level is very accurate even for a small sample size (n=60).ConclusionsFinally, we prove that the problem of Value-at-Risk minimization with the preselected level of expected return in practice can be replaced by more universal one of unconditional (concerning expected return) Value-at-Risk minimization.

Author Biographies

Taras Zabolotskyy, Lviv Institute of Banking
Zabolotskyy Taras Nikolaevichcandidate of economic sciences, computer technologies department,Lviv Institute of Banking the University of Banking of the National Bank of Ukraine(Lviv, Ukraine)
Orest Bilyy, Lviv Institute of Banking Ukraine
Bilyy Orest Vasyliovychlecturer, computer technologies department,Lviv Institute of Banking the University of Banking of the National Bank of Ukraine(Lviv, Ukraine)

References

Markowitz H. Portfolio selection / H. Markowitz // Journal of finance. – 1952. – No 7. – P. 77–91.

Merton R. C. An analytical derivation of the efficient frontier / R. C. Merton // Journal of financial and quantitative analysis. – 1972. – No 7. – P. 1851–1872.

Jorion P. Value at Risk: the new benchmark for managing financial risk / P. Jorion. – New York: McGraw-Hill Professional, 2002. – 544 p.

Duffie D. An overview of Value-at-Risk / D. Duffie, J. Pan // Journal of derivatives. – 1997. – P. 7-49.

Вітлінський В.В. Комплексний підхід застосування методології Value-at-Risk / В.В. Вітлінський, А.Б. Камінський // Економічна кібернетика. – 2004. – № 5-6. – С. 4-14.

Камінський А.Б. Моделювання ставлення до ризику при застосуванні методології Value-at-Risk / А.Б. Камінський // Теоретичні та прикладні питання економіки: Зб. наук. пр. – К.: Київський національний університет імені Тараса Шевченка, 2005. – Випуск 6. – С. 145-154.

Alexander G. J. Economic implication of using a mean-VaR model for portfolio selection: a comparison with mean-variance analysis / G. J. Alexander, M. A. Baptista // Journal of economic dynamics & control. – 2002. – No 26. – P. 1159–1193.

Bodnar T. Minimum VaR and Minimum CVaR optimal portfolios: estimators, confidence regions, and tests / T. Bodnar, W. Schmid, T. Zabolotskyy // Statistics & risk modeling. – 2012. – No 29. – P. 281-314.

Bodnar T. Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data / T. Bodnar, W. Schmid, T. Zabolotskyy // Metrica. – 2013. – №76. – P. 1105–1134.

Боднар Т.Д. Максимізація відношення Шарпа портфеля фінансових активів у контексті мінімізації ризику /Т.Д. Боднар, Т.М. Заболоцький // Економічний часопис – ХХІ. – 2013. – No 11-12(1). – C. 110-113.

Fama E.F. Foundations of finance / E.F. Fama. – New York: Basic Books. 1976. – 391 p.

Заболоцький Т.М. Portfolio choice problem with the Value-at-Risk utility function under general linear constraints / Т.М. Заболоцький, Т.Д. Боднар, В.В. Вітлінський // Економічна кібернетика. – 2012. – No 4-6(76-78). – С. 4-11.

Mori H. Finite sample properties of estimators for the optimal portfolio weights / H. Mori // Journal of the Japan statistical society. – 2004. – 35. – P. 27-46.

Published
2014-07-04
Section
Decision-making