A notion of forecast quality is defined that is appropriate when returns forecasts are used in a simple investment decision. The relation between the conditional distribution of returns and optimal point forecasts for a risk neutral investor is characterised and it is shown that the conditional mean is a small subset of optimal forecasts. Taking into account potential model misspecification and the structure of the set of optimal forecasts, methods for developing specifically `risk neutral forecasting' models are proposed. Estimation by Empirical Risk Minimisation is shown to converge to parameters associated with optimal decisions and simulations suggest that performance in small samples is acceptable even in unfavourable circumstances. Usefulness of the proposed methods is illustrated with an empirical application in which they dominate popular alternatives.
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