Evaluating the risk of pension funds by statistical procedures

The adoption of pension funds in the social security policy constitutes an important transformation in the social life; in fact, workers have a pension based on an investment fund and not a pre-determined amount. Investment funds have different degrees of risk, varying their asset composition. In front of Governments which have adopted this policy from several years (for example, U.S.A.), other Nations have experimented this policy only recently (for example, Italy). In the 2006 annual report on the condition of public and private welfare, the Italian Agency which evaluates the social security expenditure, stresses the social rather than the speculative function of such funds, evaluating the maximum risk profile in function of the liability for pension payments. This evaluation is based on simple and obvious criteria (essentially the composition of the fund in terms of bonds and stocks). But different stocks (bonds) have different behaviors and different degrees of risk. Furthermore the investors would like to have a global measure of the riskiness of each fund. In this work we propose a purely statistical procedure to classify the funds in different clusters of risk; for this purpose we deal with a time series framework and we use the conditional variance, investigated with GARCH models, as a proxy of the risk. We distinguish between two kinds of risk, the constant risk and the time-varying risk, and, developing a set of tests on the GARCH parameters, we are able to obtain groups of funds with similar risk. The procedure is applied to a set of Italian pension funds.