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

Taras Zabolotskyy, Orest Bilyy

Abstract


Purpose and subject of research

The 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 methodology

We 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 results

Using 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).

Conclusions

Finally, 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.


Keywords


Value-at-Risk; financial assets portfolio; return level

References


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