On Monday, October 22, at 3:30 in Math Building 357, Dr. Bob Henderson will be talking about Bounded Bootstrap Estimation and Simulation of Primary Factors Utilized in Retirement Planning.
Abstract: In previous work, a bounded approach to simulating four of the primary variables utilized in retirement planning – annual return rates on equity, fixed income, and cash investments, as well as the annual inflation rate – was proposed and shown to provide much more realistic distributions of possible outcomes for simulations of up to 65 years into the future. The bounded simulation approach used in that work assumed normal (or log normal) distributions for the error distributions after fitting appropriate time series models to the historical data for each variable. While examination of model residuals suggested that this assumption was reasonable for three of the four variables (equity, cash returns, and inflation); there was one extreme result for the variable (fixed income returns) that suggested perhaps heavier tailed error distributions might be more appropriate for at least this variable. In order to investigate the impact (if any) distributional assumptions for the model errors on simulation efforts, simulations for the same four variables were conducted with no distributional assumption being made by simulating potential future model errors using a bootstrap approach (Efron, 1979 or Efron and Tibshirani, 1993) rather than drawing random deviates from any assumed distribution. Perhaps unsurprising is that an unbounded bootstrap simulation generated extremely unrealistic future distributions for these variables, similar to those observed in the 2013 work using unbounded simulations from specified distributions. However, a bounded bootstrap simulation approach produced results similar to those obtained with the bounded distributional simulations completed in 2013. However, specific issues that arise in the bootstrap simulation of future model errors do not occur when simulations use specific error distributions. Simulation results will be used in example cases to evaluate investment strategies for those nearing retirement, someone just entering retirement, and someone just entering the work force. (flyer in PDF form)