<p>The statistical analysis of a sample estimator for the Sharpe ratio of the minimum Value-at-Risk (<i>VaR</i>) portfolio is provided. The asymptotic distribution of this estimator is found under two assumptions regarding the behavior of the vector of portfolio asset returns: it either follows a multivariate elliptic distribution with nonautocorrelated realizations or behaves as a weakly stationary Gaussian process. A simulation study shows that the standard sample estimator exhibits a significant bias. To address this, an adjusted estimator is developed that mitigates the bias. In addition, it is shown that a historical sample size of 1000 observations provides a good approximation for variances. These findings are used to examine the significance of the difference between the Sharpe ratio for the minimum <i>VaR</i> portfolio and zero with a confidence level of 0.95. Throughout the observation period, the Sharpe ratio remains equivalent to zero. The maximum confidence level for <i>VaR</i> such that the Sharpe ratio for the minimum <i>VaR</i> portfolio is definitely different from zero is determined.</p>