We propose a method to classify banks as profit-makers, loss-makers or neither by randomising Thompson-Thrall s linked-cone (LC) profit ratios with assurance-regions (AR) in data envelopment analysis (DEA). Thompson et al. (1995) addressed profitability of banks with the introduction of LC-AR profit ratios. We randomise LC-AR and show that randomised profit ratios uncover more profit-makers than Thompson-Thrall s profit ratios. In an application to banks from four South Asian nations, we demonstrate how to do this classification. Then, using cluster analysis with financial ratios and randomised profit ratios, we strengthen the classification of profit-makers and do a comparative study across nations.