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

Taras Zabolotskyy; Orest Bilyy

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)

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