DOLLAR COST AVERAGING RETURNS ESTIMATION

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

International Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 01, 1-26

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.

Keywords: Dollar cost averaging; lump sum; returns estimation; geometric Brownian motion; standard and poor (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0219024923500036

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