Theory suggests that competition tends to equalize profit rates through the process of capital reallocation, and numerous studies have confirmed that profit rates are indeed persistent and mean-reverting. Recent empirical evidence further shows that fluctuations in the profitability of surviving corporations are well approximated by a stationary Laplace distribution. Here we show that a parsimonious diffusion process of corporate profitability that accounts for all three features of the data achieves better out-of-sample forecasting performance across different time horizons than previously suggested time series and panel data models. As a consequence of replicating the empirical distribution of profit rate fluctuations, the model prescribes a particular strength or speed for the mean-reversion of all profit rates, which leads to superior forecasts of individual time series when we exploit information from the cross-sectional collection of firms. The new model should appeal to managers, analysts, investors and other groups of corporate stakeholders who are interested in accurate forecasts of profitability. To the extent that mean-reversion in profitability is the source of predictable variation in earnings, our approach can also be used in forecasts of earnings and is thus useful for firm valuation.