Before revision: The relation between volatility and the predicted average returns of portfolios in excess of market returnsis investigated using four risk measures: 1) Tsallis q-Gaussian relative entropy, 2) Kullback-Leibler relative entropy, 3) the parameter 'beta' of the Capital Asset Pricing Model (CAPM), and 4) relative standard deviation.
After 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. The results are compared with those from three other risk measures: 1) Tsallis q-Gaussian relative entropy, 2) Kullback-Leibler relative entropy, 3) the parameter 'beta' of the Capital Asset Pricing Model (CAPM), and 4) relative standard deviation.