Joint distribution of forecasts and outcomes: Impact of non-normality on the measurement of forecasting skill, with applications to analysts' target prices

The purpose of this paper is to provide a detailed analysis of the joint distribution of forecasts and outcomes in the context of financial forecasting. We use Edgeworth expansions to model this joint distribution. In turn this allows us to assess the impact of non-normality, either in forecasts, or outcomes or both. This leads to multiple results; we can deduce the distribution of the forecast error; we can analyse the properties of the hit rate (H), as a statistical concept in its own right, and also in its relation to the information coefficient (IC); two tools that are used in the assessment of forecasting ability by active fund managers and financial analysts. Our paper contributes to the recent econometric literature on directional forecasting as well as the empirical literature that examines analyst performance. We find that the close link between H and IC under normality breaks down in the more general case. We provide further evidence on the richness of this approach by looking at simulation and empirical evidence.