Modeling the risk-return characteristics of the SB1 Mexican private pension fund index

Abstract

This paper analyzes the returns and variance behavior of the largest specialized private pension investment funds index in Mexico, the SIEFORE Básica 1 (or, SB1). The analysis was carried out with time series techniques to model the returns and volatility of the SB1, using publicly available historical data for SB1. Like many standard financial time series, the SB1 returns show non-normality, volatility clusters and excess kurtosis. The econometric characteristics of the series were initially modeled using three GARCH family models: GARCH (1,1), TGARCH and IGARCH. However, due to the presence of highly persistent volatility, the series modeling was extended using Fractionally Integrated GARCH (FIGARCH) methods. To that end, an extended specification: an ARFIMA (p,d,q) and a FIGARCH model were incorporated. The evidence obtained suggests the presence of long memory effects both in the returns and the volatility of the SB1. Our analysis results have important implications for the risk management of the SB1.

Keywords: Private Pension Funds, Time Series modelling, GARCH models, Long Term memory series