Maximization of the Sharpe ratio of an asset portfolio in the context of risk minimization

Economic Annals-XXI: Volume 135, Issue 11-12(1), Pages: 110-113

Citation information:
Bodnar, T., & Zabolotskyy, T. (2013). Maximization of the Sharpe ratio of an asset portfolio in the context of risk minimization. Economic Annals-XXI, 11-12(1), 110-113.

Taras Bodnar
Dr. Hab. in Statistics and Econometrics,
PhD (Physical and Mathematical Sciences),
Humboldt University of Berlin
6 Unter den Linden, Berlin, 10099, Germany

Taras Zabolotskyy
PhD (Economics),
Lviv Banking Institute of University of Banking of the National Bank of Ukraine
9 T. Shevchenko Ave, Lviv, 79005, Ukraine

Maximization of the Sharpe ratio of an asset portfolio in the context of risk minimization

Abstract. The authors investigate the problem of optimal portfolio selection based on the Sharpe ratio of portfolio maximizing by usage the principle of Value-at-Risk minimization. We derive the confidence level for the Value-at-Risk under which the portfolio with the maximum Sharpe ratio coincides with the portfolio that minimizes the Value-at-Risk. Using historical data of five monthly MSCI indices, it is shown that the sample estimator of this confidence level is very accurate even for a small sample size (n=60), and it sufficiently quickly converges to the true value as the sample size increases. Finally, we prove that the problem of the Sharpe ratio maximizing in practice can be replaced by more universal one, which is the Value-at-Risk minimizing.

Keywords: Portfolio Selection Problem; Sharpe Ratio; Value-at-Risk; Variance; Sample Estimator; Risk Measure

JEL Classification: G11; G17; C13


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Received 25.10.2013