Transition matrix and stochastic kernel for repeatability assessment of performance of Polish open pension funds

Abstract

This study focuses on the issue of repeatability and reversal of performance achieved by Polish open pension funds. For the choice of the fund investing the contributions of the future pensioner, the phenomenon of repeatability and reversal of its performance is essential. Otherwise, historical rates of return cannot be used to predict future ones, and in that case the only rational method of choosing a pension fund is a pure random selection. Contrarily to the other studies taking into account numerous variables describing open pension funds, the author analyzes the only one variable interesting from a future pensioner’s viewpoint: rate of return. As a consequence the formulated conclusions are not flawed due to considering factors having no influence on future pensioners’ wealth. The analysis of these phenomena was carried out by adopting the dynamics of distribution testing methods. The estimated Markovian transition matrix and the conditional density function allowed us to formulate the conclusion about the weak performance repeatability of pension funds.