The Value-at-Risk (V@R) is an important and widely used measure of the extent to which a given portfolio is subject to risk inherent in financial markets. In this paper, we present a method of calculating the portfolio which gives the smallest V@R among those, which yield at least some specified expected return. Using this approach, the complete mean-V@R efficient frontier may be calculated. The method is based on approximating the historic V@R by a smoothed V@R (SV@R) which filters out local irregularities. Moreover, we compare V@R as a risk measure to other well known measures of risk such as the Conditional Value-at-Risk (CV@R) and the standard deviation.It is shown that the resulting efficient frontiers are quite different. An investor, who wants to control his V@R should not look at portfolios lying on other than the V@R efficient frontier, although the calculation of this frontier is algorithmically more complex. We support these findings by presenting results of a large scale experiment with a representative selection of stock and bond indices from developed and emerging markets which involved the computation of many thousands of V@R-optimal portfolios.

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