The Paradox Between Correlations and Sign Predictability

This paper uncovers a paradoxical disconnect between two widely used metrics for forecast evaluation: Mean Directional Accuracy (MDA) and the correlation between the forecast and the target variable. We show that a forecast that is more strongly correlated with the target may deliver poorer sign predictions than a less correlated alternative. Within a Gaussian framework, we derive analytical expressions showing that directional accuracy depends not only on correlation but also on the standardized means of both the forecast and the target variable. As a consequence, higher correlation does not guarantee superior sign predictability. We illustrate this paradox through analytical examples and derive formal conditions under which it cannot arise. Interestingly, we show that when forecasts are efficient, the MDA Paradox is impossible. Finally, we present an empirical application from the exchange rate literature that demonstrates the practical relevance of our results.