Abstract
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.
Highlights
Pension funds control large capitals and represent the biggest institutional investors in many countries
Several analysis show that the funds tend to increase the portfolios risk in order to obtain higher values of the expected global asset return while many authors emphasize that pension funds have to maintain a prudent profile because the social function prevails over the speculative function
We proposed a method to quantitatively assess the risk of pension funds investments, which consists of modeling the log return series with a multifractional process with random exponent (MPRE) and the risk with the Hölder exponent H of the process
Summary
Pension funds control large capitals and represent the biggest institutional investors in many countries. Despite their social security function, their performance is usually measured in terms of returns rather than risk. The 2008 financial crisis saw the default of some of the biggest pension funds worldwide, highlighting the inadequacy of current performance measures. The case of the fund CalPERS (California Public Employees’ Retirement System) is emblematic: by focusing on high rate-of-investment-returns whilst overlooking risk levels it suffered combined losses of 67 billion in 2008 and 2009, amounting to more than a third of its capitalization being forced to impose an increase in contributions to cover the losses. Qualitative rules are used to classify the risks of individual financial products according to their typology: liquidity, bonds, stocks, derivatives, commodities etc. Following the financial crisis it has been shown how this classification can be misleading (the case of the Greek bonds is exemplary)
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