A Convex Collaborative Filtering Framework for Global Market Return Prediction

Abstract

A new convex collaborative filtering framework for global market return prediction is presented. The prediction problem is first phrased as a matrix completion problem assuming that the matrix of market returns is low rank. Using historical data, we examine the experimental conditions of the matrix of market returns that lends to a low rank matrix and low value for subspace incoherence in view of convex matrix completion theory. The method then uses convex nuclear norm minimization to predict returns for the missing future markets based on this analysis. We evaluate prediction performance of the technique for global market return prediction through several simulation experiments and compare performance against user based collaborative filtering and singular value decomposition impute. We also conduct several trading experiments to assess the practical value of the predictions using basic momentum, reverse momentum, naive random and minimum variance trading strategies. Our experiments demonstrate that collaborative filtering via nuclear norm minimization consistently achieves better prediction performance compared with the two other collaborative filtering techniques tested. Furthermore, the trading experiments that incorporate these predictions demonstrate improvement in average return by 0.41%.