https://ojs.omniscient.sg/index.php/gep <p><em>Global Economic Perspectives</em> （Print ISSN:2972-4813&nbsp; Online ISSN:2972-4821）is an open access, international academic journal dedicated to promoting academic research and knowledge exchange in the global economic field. This journal aims to provide an open platform for economists, scholars, and decision-makers to explore and discuss various aspects of global economic development. We welcome original and high-quality research papers, reviews, and review articles covering various fields of economic theory, methods, and applications.</p> Omniscient Pte. Ltd. en-US Global Economic Perspectives 2972-4813 <p>Copyright on any open access article in a journal published by Omniscient Pte. Ltd. is retained by the authors.&nbsp;Authors grant Omniscient Pte. Ltd. a license to publish the article and identify itself as the original publisher.&nbsp;Authors also grant any third party the right to use the article freely as long as its integrity is maintained and its original authors, citation details and publisher are identified.&nbsp;The <a href="https://creativecommons.org/licenses/by/4.0/"><u>Creative Commons Attribution-NonCommercial 4.0 International License</u></a>&nbsp;formalizes these and other terms and conditions of publishing articles.</p> https://ojs.omniscient.sg/index.php/gep/article/view/81483 <p>This paper develops a unified continuous-time framework for portfolio return measurement in the presence of external cash flows. Beginning with a stochastic differential equation describing portfolio value dynamics, we demonstrate how several widely used return measures—including the Time-Weighted Return (TWR), Simple Dietz Return, Modified Dietz Return, and Internal Rate of Return (IRR), also known as the Money-Weighted Return (MWR) or Dollar-Weighted Return (DWR)—may be interpreted as alternative reductions or approximations of a common portfolio evolution process.</p> <p>The framework clarifies the relationships among these methodologies and identifies the role of invested-capital approximation in performance measurement. In particular, the Modified Dietz Return denominator is interpreted as a first-order approximation to average invested capital within a continuous-time setting, providing a theoretical explanation for its practical effectiveness. The analysis further examines the sources of divergence among return measures and demonstrates how differences arise from cash-flow timing, cash-flow magnitude, valuation frequency, and portfolio volatility.</p> <p>The framework is subsequently extended to AUM fee arrangements, establishing a direct relationship between fee revenue and average invested capital through time. Numerical examples illustrate both the convergence and divergence of the major return measures under alternative cash-flow scenarios.</p> <p>The principal contribution of this paper is the development of a unified continuous-time interpretation of portfolio return measurement. By identifying average invested capital as a common underlying quantity, the framework clarifies the mathematical and economic relationships among Time-Weighted Returns, Money-Weighted Returns, Internal Rates of Return, Dietz Return estimators, and AUM fee economics.</p> William C. Lindsey Gita Govahi Copyright (c) 2026 William C. Lindsey, Gita Govahi https://creativecommons.org/licenses/by-nc/4.0 2026-07-22 2026-07-22 4 3