The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty, an important component of model risk. Using a robust approach, we introduce a portfolio rule for investors who wish to invest in the global minimum...

This paper proposes a new duration-based backtesting procedure for value-at-risk (VaR) forecasts. The GMM test framework proposed by Bontemps (2006) to test for the distributional assumption (i.e., the geometric distribution) is applied to the case of the VaR forecasts validity. Using simple...

This paper proposes an original procedure which allows for testing of Granger-causality for multiple risk levels across tail distributions, hence extending the procedure proposed by Hong et al. (2009). Asymptotic and finite sample properties of the test are considered. This new Granger-causality...