This paper is motivated by recent concerns, prompted by the recent financial crisis, that regulatory capital guidelines on loan loss reserves can generate dysfunctional outcomes and, moreover, by the fact that the Greek bonds held by the banks have an important impact on the risk level of the bank portfolio. The purpose of this paper is to incorporate risk into bank efficiency and to provide a snapshot of the efficiency profile of the Greek banking industry. Efficiency is measured by means of a satisficing data envelopment analysis (DEA) model in which the financial risk is proxied by credit risk provisions and by the participation of banks in the Private Sector Involvement (PSI), a controllable and an uncontrollable factor by the bank management, respectively. The results of the proposed probabilistic DEA model derived through the Monte-Carlo simulation are compared with the results of the respective deterministic model. As the constructed stochastic frontier screens further some of the 'best-in-class' banks, the merit of the proposed metric is evident.