Financial Crisis: a new measure for risk of pension funds assets

It has been debated that pension funds should have limitations on their asset
allocation, based on the risk profile of the different financial instruments available
on the financial markets. This issue proves to be highly relevant at times of market
crisis, when a regulation establishing limits to risk taking for pension funds could
prevent defaults. In this paper we present a framework for evaluating the risk level
of a single financial instrument or a portfolio. By assuming that asset returns can be
described by a multifractional Brownian motion, we evaluate the risk using the time
dependent Hurst parameter H(t) which models volatility. To provide a measure of
the risk, we model the Hurst parameter with a random variable with beta
distribution. We prove the efficacy of the methodology by implementing it on
different risk level financial instruments and portfolios.