DOLLAR COST AVERAGING RETURNS ESTIMATION

Given a geometric Brownian motion wealth process, log-Normal lower bound is constructed for the returns of regular investing schedule. The distribution parameters this are computed recursively. For dollar cost averaging (equal amounts in equal time intervals), closed form. A lump sum (single amount at 0) schedule described which achieves terminal that matches indicated by bound. Results applied to annual S&P Composite Index from last 150 years. Among data analysis results, probability negative less than 2.5% when lasts over 40