{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/dollar-cost-averaging-returns-estimation","title":"Dollar Cost Averaging Returns Estimation","arxiv_id":"2112.09807","date":"2021-12-17","proceeding":null,"authors":["Hayden Brown"],"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.","url_abs":"https://arxiv.org/abs/2112.09807v1","url_pdf":"https://arxiv.org/pdf/2112.09807v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"dollar-cost-averaging-returns-estimation","repo_url":"https://github.com/haydenbrown/investing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}