‘Optimal’ probabilistic and directional predictions of financial returns

This paper examines the probability of returns exceeding a threshold, extending earlier work of Christoffersen and Diebold (2006) on volatility dynamics and sign predictability. We find that the choice of the threshold matters and that a zero threshold (leading to sign predictions) does not lead to the largest probability response to changes in volatility dynamics. Under certain conditions there is a threshold that has maximum responsiveness to changes in volatility dynamics that leads to ‘optimal’ probabilistic predictions. We connect the evolution of volatility to probabilistic predictions and show that the volatility ratio is the crucial variable in this context. The overall results strengthen the arguments in favor of accurate volatility measurement and prediction, as volatility dynamics are integrated into the ‘optimal’ threshold. We illustrate our findings using daily and monthly data for the S&P500 index.