Design and evaluation of the optimal life cycle glide paths

In this paper, we figure out the framework of the optimal life cycle glide path, simulate the wealth paths and pension income under nine commonly used life cycle strategies, and evaluate the strategies with different risk and return measures.First, we build four stochastic processes for the short rate and three financial assets: an equity index and two bond funds with different time to maturities of 5 and 30 years, based on which we build a dynamic model of wealth. By optimizing the utility of pension income an investor could receive after retirement, we are able to determine the optimal life cycle glide path. We further apply the Nelson-Siegel model and Kalman filtering method, use the historical data of interest rates, bond prices and stock prices, and estimate the parameters of the asset models.The evaluation of life cycle strategies concentrates on the comparisons of pension income. Given the assumptions of salary, franchise, and premium percentage, we calculate the monthly premium an investor would pay for investment. Next we generate 1000 scenarios for short rates as well as asset returns of each month during 40 years with Monte Carlo simulation. Then we describe nine life cycle strategies that are used by pension providers and consultation companies nowadays, and formulate the wealth paths of 40 years under different strategies for each cohort.We compare the pension income that is generated under different strategies using such measures as mean, standard deviation, expected pension income per unit of risk, median, VaR and CVaR for each cohort. The results show that the pure stock plan soars on both mean and standard deviation, while the pure bond plan is just the opposite.5At last, we conduct a sensitivity analysis by changing the long run rate from 6.56% to 3%. The CVaR results show that the custom with hedge strategy performs the best on the 2.5% and 5% percentiles, and the ending with pure bond plan dominates on the 1% percentile, for an investor that starts investment at the age of 25.We also find that annuity factor does not play an important role in determining which life cycle strategy to choose, based on our assumptions.