A Mixed-Stable Approach to the Management of the Portfolio Using High-Frequency Financial Data

This paper considers the problem of portfolio selection using high-frequency financial time series. Such time series often exhibit the stagnation effect when the assets' returns are not changing. This effect causes a lot of unusual difficulties in the analysis and modelling of such series. In classical statistics, when the distributional law has two first moments, i.e. mean and variance, the relationship between the two random variables is described by the covariance or correlation. However, if the financial data follow the stable law, and empirical studies often support this assumption, covariance and especially correlation often cannot be calculated. In this work, alternative relation measures are applied to deal with the portfolio selection problem using the mixed-stable modelling. The modelling is applied to the high-frequency financial time series obtained from the German DAX index intra-daily data. The performance of the mixed-stable model is compared with alternative approaches. The portfolio selection problem is formulated as the optimization problem, with covariances replaced by the generalized power-correlations. The results of the portfolio selection strategy without the relationship coefficients matrix are also presented.