Financial crisis: a new measure for risk of pension fund portfolios

It has been argued 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 the log 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 mixture of beta distribution. We prove the efficacy of the methodology by
implementing it on different risk level financial instruments and portfolios.