In this paper, we investigate the role played by the TCR and LCR among determinants of banks' profitability. To this end, using Random Forest regressions and a large dataset of banks' balance sheet variables, we assess the impact and predicting power of Basel III capital and liquidity ratios. Our results confirm the trade-off theory of the capital structure: banks have an optimal capital ratio below which the relation between capital and profitability is positive. On average, this optimum falls between 15% and 20%. Furthermore, we show that LCR has a positive, but weak, effect on profitability. Overall, our findings illustrate the fact that regulatory ratios do not constitute binding conditions for banks' performance.