Pension funds rules: Paradoxes in risk control

•In current pension funds investment rules, risk is based on assets typology or origin.•We define the risk of an asset as the roughness of series of return.•Model the series with a multifractional Brownian motion with random exponent H(t).•Use H(t) to measure risk and model it with a combination of two beta distributions.•We find that current pension funds investment rules lead to paradoxes.

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.