Thursday, April 29, 2010

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.






Anonymous said...

Speaking of extend and pretend,.. and the troubles from modern day Greek society structure and how it eventually affected their banks ....

Shorting shares of First Solar -FSLR,... Can you tells us of the pain of having ones head removed?

Tide rolls out. Someone's naked. ;-)



Robert in Chicago said...

A zero-percent rate for an "extended period" takes wealth from net creditors and gives it to net debtors, including highly imprudent net debtors, including those whose imprudence is what _caused_ them to become net debtors (such as the bank in your example). You can say it's not a "subsidy," but that is just semantics. Whatever you call it, it is one more facet of the enormous moral hazard that the government has created over the past year.

Charles Butler said...


Are you sure about all this? All of the short term, real cheap funding for Spanish banks came from the ECB, not the guv. When that tap began to be turned off, the Spanish financials resorted to, among other things, covered bonds which were linked to Spanish government borrowing costs only if they carried a government guarantee. I believe that neither BBV or Santander, for example, ever availed themselves of this support.

This week's BDE auctions, by the way, gave:

6 mths - 0.736%
12 mths - 0.904%
18 mths - 1.18%

All are higher than they were a couple of weeks ago.

Longer dated stuff like the ten-year remains firmly entrenched within the range that, with the exception of the May 2009 panic, has been in effect for at least 14 months. Greek events and the S&P downgrade nudged the yield on the 10 to the top of the channel. Today, for what it is worth, it has settles back down to a bit over 4%.

Then again, I may be missing your point.

Wee Kang said...

In other words banks make rate r + spread s on their assets A and pay r on their liabilities L. Hence their cashflow is (r+s)A - rL = r(A-L) + sA, which is just r times equity plus s times assets. Which may explain why banks always want to balloon their asset base if they can especially if spreads are good. So if equity is negative, holding r at 0 is good for them while if they have positive equity, higher interest rates would benefit their cashflow.

Don said...

"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."

That's the point of a LOLR and Guarantee in combating Debt-Deflation. To induce investors like yourself to invest. In my view, an Explicit Guarantee would have been even better.

Don the libertarian Democrat

Jonathan said...

Paul Krugman, bah, I'll never listen to that man. His Keynesian economics is what got us into this crap that we're in now!

Banks are profitable right now because they're using taxpayers money from the private federal reserve system.

I agree with Huffington that we should boycott the big banks and start to use local financial firms.

The financial reform is a big break for the banks as they'll stand to make even more billions of dollars and they will also have a permanent bailout fund!

Anonymous said...

Looks like I picked the wrong week to stop sniffing glue!

Looks like I picked the wrong month to stop gargling silica.

-Steve McCroskey

Jim Glass said...

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.

It won't work in America either, come 2025 or so.

Anonymous said...

Inflation. Deflation.

Creditors. Debtors.

Better know what side you are on at a particular time in history.

Does not one or the one end up favoring different strategists?



Anonymous said...

John, so what is your current opinion of Fannie? Is there hope they can turn the corner and become profitable in 2012 if we assume housing goes slightly up from here and foreclosures clear out by the end of 2011. Thoughts please!

Scott said...

Mr Hempton,

Can you clarify what you mean by sovereign solvency, especially as it relates to the US?

狂猪 said...


I have a different take on why banks are so profitable in the last 30 years from Krugman.

In the last 30 years, the whole world has gotten a lot wealthier due to the triumph of capitalism in large developing countries. Given the role of banks in the global economy, there is simply a lot more wealth that needed various banking services. For example, the so call savings glut is just one of the many symptoms of this massive increase in global wealth. Speaking of which, according to IMF, the savings glut is now much larger than its pre-crisis level.

The growth of large developing countries still have a few more decades to go. In deed, almost half of the world's population still live in poverty. As such I think the whole global banking sector will continue to be very profitable. Yes, more competitions and stricter regulations are looming ahead. However the pie is so much bigger and it is still growing rapidly.

I think the affect mentioned by Krugman is really insignificant in comparison to the ever increasing global wealth.

Anonymous said...

Isn't it more correct to say that 'in a fiat money system ever bank sooner or later gets their finances entwined with their central bank'?

Anonymous said...

There might be a problem once people start asking themselves what the shares in your bank should be worth: after all, it will barely break even over the next 20 years.

Anonymous said...

The problem is not that spanish bank would become suddenly unprofitable.

It is that, being highly leveraged an increase in their funding cost (while at the same time their credits are indexed to 1-year euribor)would mean that for banks REDUCING their balance would be priority number 1.

This has ominous macro implications (if deposits must fall more than credit, banks must restrain credit in order to reduce their leverage).

狂猪 said...

Hi John,

I think recent events may have changed the calculation for European banks. Please let me know if my understanding is correct.

The $1 trillion intervention and the $145bn Greece aid may have made your analysis above not applicable in the next two years for European banks holding government bonds from the PIGS countries. With these packages, the PIGS governments will be able to continue to make interest payments on their government bonds. Therefore, 100% of these type of bank assets will continue to generate yield. As a result the European banks, including Spanish banks, are now a lot healthier, at least for now?

With the aid packages, sovereign default does not make economic senses in the near term. If Greece defaults now, it will immediately have to make a hard stop on all government expenditures that are financed by debt. Whereas with the $145bn aid, Greece has 2+ years to more gradually adjust it's fiscal situation. The 2 year adjustment will still be painful but it should be a lot less painful than a full hard stop.

Interestingly, after 2 years Greece may want to default. If, by that time, Greece no longer needed to issue new debt to finance government spending, than it could make sense for Greece to default. Since it doesn't need to access the debt market, it can choose to just walk away from a debt that has grown to 150% of GDP (more reason to default later on a larger amount). It is a sovereign strategic default!

The economic interest of European banks, the PIGS countries, the Eurozone and the ECB all seemed align. Everyone wants to avoid a near term sovereign default. With the ECB's printing press, I'd bet there won't be a sovereign default in the near term.

Anyway, please let me know what you think.

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