Are Banks Too Big to Fail or Too Big to Save?

Assets, or the log of bank assets in millions of US dollars, are our measure of absolute bank size. This variable can affect a bank's market-to-book ratio on account of any technological or managerial economies of scale and potentially through a TBTF effect, if the bank is so large that a bank failure would create unacceptably high negative externalities to the economy. A bank's TBTF status affects the risk profile of its liabilities, and therefore potentially is priced into CDS spreads as well.  

A bank that is large relative to its national economy stands to create large negative externalities relative to its economy, if it fails. Thus, systemic size, as proxied by the Liabilities variable and the various Big variables, also potentially bestows a bank with TBTF status, leading to higher share prices and a lower CDS spread. Conversely, systemic size can make it too expensive for a country to bail out a bank, rendering a bank 'too big to save' (TBTS). If so, systemic size leads to lower bank valuation and higher CDS spreads. Thus the relationships between systemic size on the one hand and bank valuation and CDS spreads on the other are a priori ambiguous and potentially non-monotonic.  

A country's ability to bail out its systemically large banks should depend on the health of its public finances, as proxied by the central government debt and fiscal balance ratios. The government debt and deficit ratios are expected to negatively affect bank valuation, as higher government debt signals higher taxes in the future to service the debt and lower capacity to support banks through the financial safety net. Bank profitability tends to reflect economic rents so that expected future corporate income taxation may well be capitalized into lower share prices. A reduced ability on the part of governments to bail out banks affects the risk profile of bank liabilities, and hence potentially is priced into higher CDS spreads.   

A restricted government ability to bail out banks on account of distressed public finances should especially affect systemically important banks. To test this, we can include an interaction variable of, say, the public debt ratio and a categorical indicator of systemic size in our empirical specifications. A negative estimated coefficient on such an interaction variable suggests that systemically large banks can expect fewer subsidies from the financial safety net in highly indebted countries, indicating that they have become 'too big to save'. Similarly, such an interaction term may positively affect the CDS spread, signaling larger expected losses on bank liabilities for systemically sizeable banks in countries laden with public debt. 

Banks are commonly taken to be subject to moral hazard as increased bank risk potentially increases expected benefits from the financial safety net, thereby increasing bank valuation. This can explain a positive relationship between bank valuation and an indicator of bank risk such as the annualized standard deviation of weekly bank stock return. The relationship between bank valuation and bank risk may be even more positive for systemically large banks if especially these banks are TBTF, and it can be less positive if there is an offsetting negative effect in case these banks are TBTS. To test the relative importance of TBTF and TBTS effects for systemic banks, we can include an interaction term of bank risk and an indicator of systemic size in the empirical specification. 

Bank risk can be expected to imply larger losses on bank liabilities in the presence of an imperfect financial safety net. Thus, bank risk should lead to higher CDS spreads. The relationship between the CDS spread and bank risk may be more muted for systemic banks if TBTF is relatively more important, while can be more pronounced if TBTS is relatively more important. To test this, we can include an interaction variable of bank risk and bank systemic size in an empirical specification for estimating the CDS spread.