In this paper we derive the asymptotic distributions of the estimated weights and of estimated performance measures of the minimum value-at-risk portfolio and of the minimum conditional value-at-risk portfolio assuming that the asset returns follow a strictly stationary process. It is proved...

Abstract In this paper we consider the portfolio weights obtained by maximizing the expected quadratic utility function. The unknown parameters of the return process, the mean vector and the covariance matrix, are estimated by their sample counterparts. Assuming independent and multivariate...

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 this paper, we derive an exact test for a column of the covariance matrix. The test statistic is calculated by using a single observation. The exact distributions of the test statistic are derived under both the null and alternative hypotheses. We also obtain an analytical expression of the...

In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The...

In the present paper, we propose an exact test on the structure of the covariance matrix. In its development the properties of the Wishart distribution are used. Unlike the classical likelihood-ratio type tests and the tests based on the empirical distance, whose statistics depend on the total...

In the paper, a finite sample test is suggested for detecting changes in the composition of the global minimum variance portfolio. The exact density of the test statistic is calculated. It appears that under the null hypothesis of no change, it is independent of the parameters of the asset...