Abstract In this paper, we consider the sample estimators for the expected return, the variance, the value-at-risk (VaR), and the conditional VaR (CVaR) of the minimum VaR and the minimum CVaR portfolio. Their exact distributions are derived. These expressions are used for studying the...

In the paper, we derive an unbiased estimator of the efficient frontier. It is shown that the suggested estimator corrects the overoptimism of the sample efficient frontier documented in Siegel and Woodgate (2007). Moreover, an exact F-test on the efficient frontier is presented.

The efficient frontier is a parabola in the mean-variance space which is uniquely determined by three characteristics. Assuming that the portfolio asset returns are independent and multivariate normally distributed, we derive tests and confidence sets for all possible arrangements of these...