{"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/long-term-returns-estimation-of-leveraged","title":"Long-Term Returns Estimation of Leveraged Indexes and ETFs","arxiv_id":"2301.03186","date":"2023-01-09","proceeding":null,"authors":["Hayden Brown"],"abstract":"Daily leveraged exchange traded funds amplify gains and losses of their underlying benchmark indexes on a daily basis. The result of going long in a daily leveraged ETF for more than one day is less clear. Here, bounds are given for the log-returns of a leveraged ETF when going long for more than just one day. The bounds are quadratic in the daily log-returns of the underlying benchmark index, and they are used to find sufficient conditions for outperformance and underperformance of a leveraged ETF in relation to its underlying benchmark index. Results show that if the underlying benchmark index drops 10+\\% over the course of 63 consecutive trading days, and the standard deviation of the benchmark index's daily log-returns is no more than .015, then going long in a -3x leveraged ETF during that period gives a log-return of at least 1.5 times the log-return of a short position in the underlying benchmark index. Results also show promise for a 2x daily leveraged S&P 500 ETF. If the average annual log-return of the S&P 500 index continues to be at least .0658, as it has been in the past, and the standard deviation of daily S&P 500 log-returns is under .0125, then a 2x daily leveraged S&P 500 ETF will perform at least as well as the S&P 500 index in the long-run.","url_abs":"https://arxiv.org/abs/2301.03186v1","url_pdf":"https://arxiv.org/pdf/2301.03186v1.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":"long-term-returns-estimation-of-leveraged","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}