A Structural Accounting Framework for Estimating the Expected Rate of Return on Equity

Abstract

This paper shows how the expected rate of return (ERR) on equity may be estimated using only published accounting results, based on the information dynamics of reported earnings. As accounting‐based valuation models conditional upon financial statement articulation lead to a rank deficient system of estimating equations, the paper introduces a nonlinear constraint on the articulation that allows the information system simultaneously to produce an estimate for the ERR by iteration, together with predictions for the key clean surplus forecasts of net earnings, net dividend, and the book value of equity. Further decomposition produces estimates of expected capital gain, expected earnings, and the expected change in equity book value, and by rearrangement, the expected change in unrecorded goodwill. The clean surplus relation is maintained in the forecast variables. Exploratory data methods are used to examine the nonlinear relationship between components of the accounting‐based ERR and realized stock returns. Findings show that realized returns are higher (lower) than estimated ERR in expansionary (recessionary) periods, with evidence of a stronger returns impact in recessionary periods. For the large majority of firms, realized returns revert to the estimated ERR, and the time‐varying accounting components are strongly related to future realized stock returns, consistent with time variation in the ERR around a long‐run average. Predicted earnings and dividends provide useful additional information on short‐run variations in the ERR.