We study the impact of the Basel III liquidity constraints, represented by the liquidity coverage ratio (LCR) and the net stable funding ratio (NSFR), on bank profitability, by employing the simultaneous quantile regression framework with time fixed effects. We find a positive and significant relationship between the LCR and profitability and the NSFR and profitability over most quantiles. However, the small magnitudes of the coefficients on LCR and NSFR across all quantiles of profitability suggest that LCR and NSFR have a minor quantitative impact on bank profitability. We then test and find that the Basel III liquidity constraints have a significantly different impact on banks with very low profits compared to banks who enjoy high profitability, emphasizing the need to use a quantile approach. We plot the coefficients to illustrate the impact of liquidity constraints across different conditional profitability spectrums. Lastly, we find that small banks are more vulnerable to short term liquidity risks (LCR) and big banks are more susceptible to medium to long term liquidity risks (NSFR). This suggests that considerations should be given to tailoring liquidity regulations based on the bank size and the relative bank profitability. The quantitatively small impact of the constraints suggest that Basel III has successfully set liquidity requirements to minimize the impact on bank profitability and the likelihood of an industry-wide liquidity crisis.