The Percent-Change Extension to the DuPont Identity

From the DuPont Identity, this paper derives a formula relating the percent changes in the return on equity (ROE) to the percent changes in the DuPont components. This formula is useful in determining the primary reasons why the ROE changed from one period to the next. While the periodic percent change relationship is nonlinear, a simple and intuitive additive formula is an approximation, albeit at times a poor approximation. We also convert the periodic percent changes in the ROE and its DuPont components into their equivalent instantaneous rates of change. These instantaneous rates of changes in the DuPont components do precisely sum to the instantaneous rate of change in the ROE, providing a method for analysts to both intuitively and accurately present their analysis.