On goal reaching time distributions estimated from DAX stock index investments

Abstract

This research paper analyzes the distributional properties of stock index time series data from a new perspective, that is, time optimal decision making building on the conceptual foundation of the time optimal approach to portfolio selection introduced by Burkhardt. In this approach, the investor's goal is to reach a predefined level of wealth as soon as possible. We investigate the empirical properties of the goal reaching times for DAX stock index investments for various levels of aspired wealth, compare the observed properties to those expected by the Inverse Gaussian distributional model, investigate the use of overlapping instead of independent goal reaching times, and highlight some methodological issues involved in the empirical analysis. The results are of immediate interest to investors.