Pension funds rules: Paradoxes in risk control

Pension funds are financial institutions that invest retirement savings from workers to provide pension benefits. Due to this social security function, each country enforces laws to regulate investments. Usually regulations identify pension portfolio's risk level based on the nature of its financial products. After the latest financial crisis, it became evident that such approach may not be sufficient to control the risk. In this paper we measure risk level with a multifractional Brownian motion with random exponent. We show how current rules can lead to paradoxes, where portfolios which comply with the laws are riskier than those that do not.