Before revision: Tsallis relative entropy , which is the generalization of Kullback-Leibler relative entropy  to non-extensive systems, is investigated as a possible risk measure in constructing risk optimal portfolios whose returns beat market returns.
After revision: Earlier studies have shown that stock market distributions can be well described by distributions derived from Tsallis entropy, which is a generalization of Shannon entropy to non-extensive systems. In this paper, Tsallis relative entropy (TRE) , which is the generalization of Kullback-Leibler relative entropy to non-extensive systems, is investigated as a possible risk measure in constructing risk optimal portfolios whose returns beat market returns.