The arithmetic of bank solvency – part 1

This is a post driven by Krugman’s many debates on  bank profitability.  In particular, a post from Krugman – about why banks are suddenly profitable – and the debates it engendered amongst my friends is the origin of this post.  Long-time readers of my blog will know I have explored these ideas before.

First observation: at zero interest rates almost any bank can recapitalize and become solvent if it has enough time. 

Imagine a bank which has 100 in assets and 90 in liabilities.  Shareholder equity is 10. The only problem with this bank is that 30 percent of its assets are actually worthless and will never yield a penny.  [This is considerably worse than any major US bank got or for that matter any major Japanese bank in their crisis.]

Now what the bank really has is 70 in assets, 90 in liabilities and a shareholder deficit of 20.  However that is not what is shown in their accounts – they are playing the game of “extend and pretend”.

Now suppose the cost of borrowing is 0 percent and the yield on the assets is 2 percent.  [We will ignore operating costs here though we could reintroduce them and make the spread wider.]

This bank will earn 1.4 in interest (2 percent of 70) and pay 0 in funding cost (0 percent of 90).  It will be cash-flow-positive to the tune of 1.4 per annum and in will slowly recapitalize.  Moreover provided it can maintain even the existing level of funding it will be cash-flow-positive and will have no liquidity event.  (It does however need to be protected from runs by a credible government guarantee.)

Now lets put the same bank in a high interest rate environment.  Assume funding costs are 10 percent and loans yield 12 percent.

In this case the bank earns 8.4 per year in interest (12 percent of 70) and pays 9 per year in funding (10 percent of 90).  The same bank with the same spread is cash flow negative.  

This is an important observation – because – absent another wave of credit losses – a marginally insolvent bank with a government guarantee will certainly recapitalize over time provided its funding costs are pinned somewhere near zero.  The pinning of the funding costs near zero is not a subsidy (except in-as-much-as the government guarantee is a subsidy).  Both these banks have the same spread and have the same profitability.  The answer depends criticially on whether you can pin the funding to a low interest rate. 

Banks and sovereign solvency

All banks more or less anywhere get their finances entwined with the finances of the sovereign.  No sovereign will (or in my opinion should) allow a mass run on banks but they can only stop such a run if their own credit is good.  But this link between sovereign solvency and bank-system solvency means that bank funding costs at a minimum are bounded at the lower end by sovereign borrowing costs.

It was pretty clear in the crisis where the US Sovereign borrowing costs were pinned.  I barely cared whether BofA was solvent when I purchased it (but I was pretty sure it was).  I cared that the US government was going to pin its funding costs.  Buying BofA at low single digits was – in the end – a bet on US Government solvency.

On the same token Spanish banks may go the way of Greek banks.  They can’t control their funding costs because the Spanish sovereign cannot control their funding costs.  The idea that European sovereigns can default is now front-and-center.  And the Spanish banks can’t control that either.

Extend-and-pretend (what Felix Salmon crudely deigned to be the Hempton plan) worked well in America.  It won’t work in Spain because you can’t pin rates at zero even with a government guarantee.  The scale of financial restraint needed to solve this problem is enormous.  But the alternatives are worse.

 

 

 

John