https://ojs.omniscient.sg/index.php/gep/issue/feedGlobal Economic Perspectives2026-07-22T16:50:20+08:00Stellapimdt@omniscient.sgOpen Journal Systems<p><em>Global Economic Perspectives</em> （Print ISSN:2972-4813 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>https://ojs.omniscient.sg/index.php/gep/article/view/81483A Continuous-Time Framework for Time-Weighted Returns, Money-Weighted Returns, Internal Rates of Return, and Dietz Return Estimators2026-07-22T16:50:20+08:00William C. Lindseywclindsey@gmail.comGita Govahiwclindsey@gmail.com<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>2026-07-22T16:50:20+08:00Copyright (c) 2026 William C. Lindsey, Gita Govahi