In a Black-Scholes-Merton model of single name default, instability could be seen as the level of volatility that would trigger default, everything else equal. At a portfolio level, for instance comprising all credit liabilities of the corporate sector, potential for instability could be measured by a credit portfolio loss distribution. For such a loss distribution, it should then be possible to define a level of volatility that would trigger instability, for instance by producing credit losses in excess of the aggregate capital of the banking system. This paper analyses the potential for instability in the Euro area by looking at both aggregate and name-level data for the corporate sector. Loss distributions are computed under plausible hypotheses for the underlying default, loss and correlation parameters, and our conclusion is that aggregate bank capital could cover losses at a very high confidence level; in other words, the likelihood of financial instability is negligible. However, we identify a sizable degree of concentration in the aggregate liabilities of Euro zone non-financial corporations. Significant concentration, even at investment grade, augments potential credit losses (measured as Credit Value at Risk) in a similar way to a substantial increase in the aggregate average default probability or the average asset return correlation. Further analysis is warranted in order to assess the level of volatility that could trigger default of a 'concentrated exposure' and to better understand under which conditions this could lead to instability.