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Dollar Cost Averaging Returns Estimation

Author

Listed:
  • HAYDEN BROWN

    (Department of Mathematics and Statistics, University of Nevada, Reno, 1664 N. Virginia Street, Reno, NV 89557, USA)

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.

Suggested Citation

  • Hayden Brown, 2023. "Dollar Cost Averaging Returns Estimation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 1-26, February.
    • Handle: RePEc:wsi:ijtafx:v:26:y:2023:i:01:n:s0219024923500036
    DOI: 10.1142/S0219024923500036
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