We provide an assessment of the IMF suggestion, based on Severo (2012), to use an index of systemic liquidity risk (SLRI) that could help to estimate a Pigouvian tax on large banks for the externality on the international banking system out of their risk exposure. To this end we compute a parsimonious and fully documented SLRI and investigate its statistical significance in explaining level and variability of stock returns for a group of large international banks during the subprime financial and the Eurozone sovereign debt crises. The empirical investigation consistently fails to detect, within and across the two crises, a core group among the systemically important banks listed by the Financial Stability Board and thus supports a sceptical assessment of the proposal
