Improving Asset Price Prediction when All Models are False

Abstract

Abstract This study considers three alternative sources of information about volatility potentially useful in predicting daily asset returns: past daily returns, past intraday returns, and a volatility index based on observed option prices. For each source of information the study begins with several alternative models, and then works from the premise that all of these models are false to construct a single improved predictive distribution for daily S&P 500 index returns. The criterion for improvement is the log predictive score, equivalent to the average probability ascribed ex ante to observed returns. The first implication of the premise is that conventional models within each class can be improved. The paper accomplishes this by introducing flexibility in the conditional distribution of returns, in volatility dynamics, and in the relationship between observed and latent volatility. The second implication of the premise is that model pooling will provide prediction superior to the best of the improved models. The paper accomplishes this by constructing ex ante optimal pools, which place a premium on diversification in much the same way as optimal portfolios. All procedures are strictly out-of-sample, recapitulating one-step-ahead predictive distributions that could have been constructed for daily returns beginning January 2, 1992, and ending March 31, 2010. The prediction probabilities of the optimal pool exceed those of the conventional models by as much as 7.75%. The optimal pools place substantial weight on models using each of the three sources of information about volatility