{
  "abstract": "Investment performance is commonly presented either as a conventional cumulative-return chart, which fixes a historical starting date and traces performance forward, or as a trailing-return table, which fixes the current endpoint but reports only a small set of prespecified horizons. These two displays have complementary limitations: fixed-start comparisons are conditional on the selected origin, whereas trailing returns provide only discrete snapshots of the underlying fixed-endpoint return function. We present the Return-to-Present (RTP) curve as a continuous fixed-endpoint representation that brings these perspectives together by holding the evaluation date fixed while allowing the hypothetical historical purchase date to vary over the available history. Familiar 1-month, 3-month, 6-month, 1-year, and longer trailing returns therefore become selected points on a continuous curve. When multiple investments are overlaid, RTP directly displays entry-date sensitivity, persistent relative advantage, crossings, and the timing and magnitude of separation without requiring selection of a single historical origin. The same endpoint-based construction naturally accommodates investments with unequal inception dates, recurring purchases, and retrospective portfolio rotation decisions in which sale and replacement-purchase dates may differ. We illustrate these uses with real investment data and discuss its relationship to momentum. RTP does not define a new return measure; its contribution is a simple graphical organization of familiar realized returns for historical comparison and decision support rather than prediction or statistical inference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06267",
  "author_total": 1,
  "authors": [
    {
      "name": "Lei Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cq8w6xwd4tvp5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06267",
  "fulltext_url": null,
  "id": "cq8w6xwd4tvp5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06267",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "q-fin.ST"
    ],
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "openalex",
      "2003|Financial Markets and Investment Strategies"
    ]
  ],
  "openalex": "W7212078799",
  "pdf_url": "https://arxiv.org/pdf/2609.06267",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cq8w6xwd4tvp5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.06267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06267"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "From Discrete Trailing Returns to a Continuous Graphical Profile: Return-to-Present Curves",
  "title_text": "From Discrete Trailing Returns to a Continuous Graphical Profile: Return-to-Present Curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/cq8w6xwd4tvp5",
  "venue": "arXiv",
  "versions": []
}