From Discrete Trailing Returns to a Continuous Graphical Profile: Return-to-Present Curves
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.
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BibTeX
@misc{liu2026from,
title = {{From Discrete Trailing Returns to a Continuous Graphical Profile: Return-to-Present Curves}},
author = {Lei Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06267},
eprint = {2609.06267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06267},
}
RIS
TY - UNPB
TI - From Discrete Trailing Returns to a Continuous Graphical Profile: Return-to-Present Curves
AU - Lei Liu
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06267
UR - https://arxiv.org/abs/2609.06267
AB - 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.
ER -