Dollar Cost Averaging Returns Estimation

TL;DR

This paper develops a probabilistic lower bound for returns of dollar cost averaging strategies using geometric Brownian motion models, providing insights into long-term investment risks and outcomes.

Contribution

It introduces a new log-Normal lower bound for DCA returns and derives closed-form parameters, linking continuous and lump sum investment strategies.

Findings

Probability of negative returns is less than 2.5% over 40 years of DCA.

The lower bound provides a conservative estimate for long-term DCA performance.

Results are validated using 150 years of S&P index data.

Abstract

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