Â© 2014 IEEE. In this article we introduce a new strategy for optimal diversification which combines elements of Diversified Risk Parity ,  and Diversification Ratio , with emphasis on positive risk premiums. The Uncorrelated Positive Bets strategy involves the identification of reliable, independent sources of randomness and the quantification of their positive risk premium. We use principal component analysis to identify the most significant sources of randomness contributing to the market and then apply the Randomness Deficiency Coefficient metric  and principal portfolio positivity to identify a set of reliable uncorrelated positive bets. Portfolios are then optimized by maximizing their diversified positive risk premium. We contrast the performance of a range of diversification strategies for a portfolio held for a two-year out-of-sample period with a 30 stock constraint. In particular, we introduce the notion of diversification inefficiency to explain why diversification strategies might outperform the market.