Pension strategy under volatility clustering

Abstract

This research investigates the effect of volatility clustering on optimal asset allocation in a defined benefit pension scheme. Three models of volatility clustering, GARCH, GJR and EGARCH models, are examined. Model parameters are estimated using a time series of S&P500 returns while the optimal strategy is obtained using the numerical method to solve dynamic programming. The volatility-clustering parameters of GARCH models significantly influence the decision rules of choosing optimal weight. The first parameter adjusts how much volatility in the past affects present volatility, and the second parameter captures amplitude of the uncertainty. Meanwhile, asymmetric volatility in GJR and EGARCH models, captured by an additional parameter, put a focus on high volatility in negative returns. To study the behavior of optimal strategies under different models, Monte Carlo simulation is used to obtain the distribution of optimal weights and fund values in each model. Observing the distribution from different models show that the EGARCH model yields the most reasonable strategy and, unlike GARCH and GJR models, rarely gives extreme weight on risky assets. Subsequently, the optimal strategies are backtested to see which model gives the best outcome. The three models give the similar rate of return in backtesting using S&P500 returns data, but the optimal strategy assuming the EGARCH model has most conservative strategy which will be beneficial in the presence of a financial crisis.