Forecasting the future cashflows of a company is crucial to valuing its stock price. However, generating these forecasts is a complex task that often results in differences of opinion. Nonetheless, cashflow forecasts help investors to form conditional expectations of future cashflow growth. Comprehensive surveys by Clemen (1989) and Diebold and Lopez (1996) document that forecast combinations are superior to individual forecasts. When optimally combining multiple cashflow forecasts into an aggregate estimate, investors should assign more weight to forecasts issued by more accurate information sources.
This paper examines the optimal combination of multiple forecasts of uncertain accuracy. The investor in our model estimates the accuracy of each information source based on its past forecast errors. The cashflow forecasts are then combined into an aggregate estimate with minimal mean-squared forecast error. This aggregate estimate is the investor’s conditional expectation of a firm’s future cashflow growth. The optimal weights assigned to information sources that underly the aggregate estimate are referred to as information weights. These weights are larger for information sources with relatively superior estimated accuracies.
As additional cashflow realizations and forecast errors become available, the investor learns more about each information source’s relative accuracy. The investor gradually updates the information weights when there is sufficient evidence that re-calibrating the weights is necessary (e.g., an information source’s estimated accuracy has changed significantly). Intuitively, an information source’s true accuracy represents its unobservable “skill” at forecasting a firm’s cashflow. Investors understand the uncertainty inherent in measuring this skill. Thus, they gradually alter their assessment of each information source’s credibility.
A firm’s stock price is obtained from the aggregate cashflow estimate. We demonstrate that stock return predictability–in particular, earnings momentum and price momentumarises from gradual learning about the relative accuracy of information sources. When there is no uncertainty surrounding the forecast accuracy of information sources, stock returns are unpredictable. To focus on the ability of time-variation in the information weights to generate momentum, we assume that the individual forecasts of cashflow growth, on average, do not change over short horizons. Thus, momentum does not arise because the information sources increase (decrease) their forecasts of future cash-flow growth following positive (negative) cashflow growth realizations.
Momentum is induced solely by the dynamic updating of the weights assigned to multiple information sources as the investor learns about their relative forecast accuracy. For example, after a series of large positive cashflow growth innovations (and price increases), the estimated accuracies of optimistic information sources improve significantly, and their weights increase as the investor updates their belief regarding which information sources are more credible. The more optimistic information sources gain more influence on the subsequent aggregate cashflow estimate. This leads to higher expected cashflow growth next period (although the individual forecasts on average remain unchanged), and thus a higher stock price. Consequently, our framework predicts price drifts for recent winner (and loser) stocks. In contrast, there is no significant updating in the information weights and no momentum for stocks that are not recent winners (losers) since their past cashflow growth innovations have been less dramatic.
