Beyond CAGR: Sum-Matching CAGR for Uneven Growth Series

CAGR is a simple and useful way to compress a growth history into a single endpoint-to-endpoint rate. However, it can represent uneven windows poorly because it does not use the observations between the first and last dates. This paper defines Sum-Matching CAGR (SM-CAGR), a cumulative-equivalent annualized growth summary. Given a positive starting observation and an equally spaced series, SM-CAGR is the constant annual rate whose smooth compounding path reproduces the same cumulative or weighted cumulative exposure as the observed path. SM-CAGR retains CAGR's compound annual-rate format while changing the matching object from terminal value to full-window cumulative exposure. If CAGR summarizes the change from starting value to terminal value, SM-CAGR summarizes the cumulative exposure realized over the selected window. Discounted SM-CAGR matches present-value exposure instead of raw cumulative exposure, making timing differences visible. The statistic is especially suited to level or flow variables for which cumulative exposure over time is meaningful, such as market forecasts, subscribers or users, shipments, capacity, revenue, earnings, free cash flow, and dividends. For ratio-type variables, the unweighted statistic is a path-exposure summary unless an explicit exposure base is used; when an economic denominator such as revenue, invested capital, principal, or market size is available, weighted SM-CAGR can express that exposure directly. Illustrations using Burford Capital, Meta Platforms, and Netflix show how CAGR, SM-CAGR, and discounted SM-CAGR can be read together to distinguish endpoint dependence, cumulative full-window delivery, and timing.