Working Papers No 308 from BIS talks about this subject, which is one of the important things we need to understand in order to fix the Too Big to Fail type of banking regulation.

This aim is to require important banks, those that because of their size will likely take others down with them when they fail, to be more careful in how they run their business. It will not be easy to get everyone to agree on how this should be done.

This paper attribute the importance of a bank to several factors:

• The number of banks
• The banks' relative sizes
• The exposure of banks to common risk factor
• Banks' probabilities of default

I have not read through the paper yet, but here are a few paragraph and a nice set of charts.

we investigate the joint impact of system lumpiness and banks’ exposure to the common factor on systemic tail risk. The results are portrayed in Graph 1, left-hand panel. In this panel, lumpiness is captured solely by the number of homogeneous banks in a hypothetical system and is held fixed (at one of three levels) in order to plot systemic risk as a function of the common-factor exposure.

A key message of the graph is that a decrease in the lumpiness of the system depresses systemic risk by more (the distance between the lines is greater) when banks’ exposure to the common risk factor is smaller. To see why, note that lower exposure to the common factor means greater importance of idiosyncratic risks. In turn, idiosyncratic risks are those that are diversified away at the level of the system when its lumpiness decreases (in this case, as the number of banks increases). In the limit case, in which all banks are exposed only to the common risk factor (i.e. when the asset-return correlations equal unity), changes in the lumpiness of the system are inconsequential.

The flipside of this intuitive result reveals an important insight regarding the consequences of measurement error. The different slopes of the three lines in the left-hand panel of Graph 1 indicate that systemic risk tends to increase faster in the exposure to the common factor when there are more banks in the system. Thus, a given error in the estimate of banks’ exposures to the common factor is likely to result in a larger error in the measurement of systemic tail risk when the system is less lumpy.