Financial forecasts in the presence of asymmetric loss aversion, skewness and excess kurtosis

We present closed-form results for the out-of-sample forecasts under the joint presence of asymmetric loss and non-normality, extending the results of Granger [1969. Operations Research Quarterly 20, 199–207; 1999. Spanish Economic Review 1, 161–173] and Christoffersen and Diebold [1997. Econometric Theory 13, 808–817]. We consider the LinEx and Double LinEx loss functions and non-normal distributions in the form of the Gram–Charlier class. We show how the preference asymmetries interact with the distribution asymmetries to determine optimal forecasts which contain the optimal predictors under symmetry and normality as special cases. We also examine the implications of our results for the development of forecast rationality tests, extending the work of Batchelor and Peel [1998. Economics Letters 61, 49–54]. Our results are relevant for the design of efficient investment and risk management policies.