Fractional Reserve Banking

There is an old erroneous view of fractional reserve banking.

“Naturally, all fractionally reserved banks are de facto insolvent at all times…”

The Acting Man blog is usually very good, but it published an article by Pater Tenebrarum containing this comment (http://www.acting-man.com/?p=6781).  If there is a weakness in Austrian School thinking surely fractional reserve banking is it.

The myth goes something like this.  Banks take in $100 of deposits, and make $1000 of loans, creating the “money” ex nihilo out of thin air.  Mr. Tenebrarum does not make this argument in the article, nor have I read him make it previously.  But I cannot think of what the statement I quoted above means, if not that.

Think about the bank’s balance sheet for a moment.  The following examples are presented as being for one bank, but could as easily represent the consolidated balance sheet of the entire banking sector.  Ignoring shareholder equity and other complicating factors that would make this analysis harder to follow, the bank takes the deposit:

Assets                                               Liabilities

Cash $100                                        Depositor account $100

Now assuming they could lend $1000, what would this look like?

Assets                                               Liabilities

Cash $0                                            Depositor account $100

Loan Portfolio $1000

I am not an accountant, but I don’t know how you could make this work!

The first error we must correct is that fractional reserve lending is when the bank lends out *less* than it takes in via deposits (but more than zero).  Lending more than it takes in via deposits does not exist.

Mr. Tenebrarum does not give his logic, but we can assume that he is referring to the fact that aggregate deposits in the banking system (and thus bank debt) exceed the amount of “base money” in the system.  Let’s look at what it would be in a gold standard with fractional reserves, to make it simpler and clearer.  First, someone deposits some gold coin into a bank.

Assets                                               Liabilities

Cash 100 oz                          Depositor account 100 oz

 

So far, so good.  Next, the bank makes a loan of more than zero but less than the total deposited.

 

Assets                                               Liabilities

Cash 10 oz                                        Depositor account 100 oz

Loan Portfolio 90 oz

It’s still solvent, and “total money supply” has not grown yet.  But now let’s say that the borrower pays the 90 oz to a contractor to build a new house and the contractor deposits the money in the same bank.

Assets                                               Liabilities

Cash 100 oz                          Depositor accounts 190 oz

Loan Portfolio 90 oz

So what just happened here?  First, the size of the balance sheet increased as did the total “money supply” in the system (we will come back to this below).  But the balance sheet shows assets to match the liabilities; there is no evidence of insolvency yet.  The bank may or may not be insolvent.

To drill down further, we need to introduce the idea of duration.  Every deposit has a duration (a demand deposit effectively has zero duration), and every loan of course has a maturity date or a duration also.

So let’s go back to the original depositor.  He put in 100 oz of gold, asking the bank to keep 10 oz for withdrawal on demand, 15 oz to be withdrawn in 1 year, and 75 oz to be withdrawn in 5 years.

Assets                                               Liabilities

Cash 100 oz                          Demand deposit account 10 oz

1-year deposit account 15 oz

5-year deposit account 75 oz

Now the bank makes two loans, a 1-year loan of 15 oz and a 5-year loan of 75 oz.

 

Assets                                               Liabilities

Cash 10 oz                                        Demand deposit account 10 oz

1-year loan portfolio 15 oz 1-year deposit account 15 oz

 

5-year loan portfolio 75 oz            5-year deposit account 75 oz

This is still a good balance sheet and the bank is solvent.  Now let’s say the borrowers of those loans pay people who deposit the 90 oz of gold back into the bank as demand deposits.

Assets                                               Liabilities

Cash 100 oz                          Demand deposit accounts 100 oz

1-year loan portfolio 15 oz 1-year deposit account 15 oz

5-year loan portfolio 75 oz            5-year deposit account 75 oz

There is still no problem.  The maturities of the bank’s assets match its liabilities.  This bank is perfectly solvent.  (In the real world, the bank would set aside loan loss reserves out of its own capital to cover the credit risk, and of course it would charge interest at a much higher rate than the default rate.)

Before proceeding to duration mismatch, which is the real fraud and source of insolvency, I want to address the fact that the balance sheet has expanded.  Some would argue that the bank has just expanded the “money supply”.  The answer is that this is, of course, nonsense.  The same 100 oz of gold is still in the system.  The difference is that credit has been extended.  One side of credit is the asset on the books.  To the bank, the loans it extended are assets.  These assets have real value based on the expectation to be repaid, and they can be sold to other banks, etc.  And to the bank, a deposit is a liability.  The depositor will have to be paid.

So what has happened is that the bank has increased both its assets and its liabilities by the same amount.

OK, now let’s look at borrowing short to lend long, otherwise known as duration mismatch.  Let’s say the depositor specified 10 oz on demand, and 90 oz to be withdrawn in 1 year.  This balance sheet is:

Assets                                               Liabilities

Cash 100 oz                          Demand deposit account 10 oz

1-year deposit account 90 oz

Up until this point, the bank is OK.  Its assets are of zero duration (i.e. gold in the vault) and it has a portion of its liabilities of zero duration (i.e. demand deposit) and a portion that it must be able to pay in one year.  The gold in the vault is obviously good for this (not counting that the gold is earning no interest, and the deposit must be paid back with interest).  But let’s say the bank lends 90 ounces for 30 years, perhaps for a mortgage.

Assets                                               Liabilities

Cash 10 oz                                        Demand deposit account 10 oz

30-year mortgage 90 oz                1-year deposit account 90 oz

This bank has, at the very least, a liquidity problem.  In 1 year, the depositor will come back asking for his 100 oz of gold.  The bank has only 10.  The other 90 oz worth is locked into a long-term mortgage.  The bank will have to do something in order to be able to pay the depositor and avoid bankruptcy.  I’ll discuss that further, below.

This gets back to the point I mentioned earlier about the “money supply”.  As the bank discovers when the depositor demands his money back, a mortgage is not money that can be used to pay expenses.  The depositor wants his gold back, not a paper instrument.

Something that cannot be overstated or overemphasized is that one cannot simply add up the “money” in the banking system.  Just as one cannot add up 1/2 + 3/8 + 5/19 = 8/29, one cannot add up demand deposits + 1-year time deposits + … 30-year time deposits.

So what does the bank do when presented by the demand from the depositor for his money?  They find another depositor.  This is one form of “rolling” the loan (from the first depositor to the bank) by borrowing from a second depositor.  And most of the time it “works”.  That is (usually) the banks can borrow fresh money to pay off loans that are due.  There are many forms of “rolling” expiring loans, not necessarily involving depositors but all have the same problem.

It is a confidence game, and of course it doesn’t work when there is stress in the system.  Let people start to question the bank’s solvency, or solvency in general in the banking system, and depositors on net will withdraw their gold from the system and refuse to re-deposit it until they feel more comfortable.  And the irony is that duration mismatch will necessarily cause depositors to lose confidence sooner or later.

This is basically a glorified check-kiting scheme (Wikipedia describes it under “circular kiting” in the Check Kiting record: http://en.wikipedia.org/wiki/Check_kiting), and is fraud.  The issue is not merely that the bank is taking a “risk”.  It is not the proper place of government to dictate by force to every party, in every kind of transaction including those yet to be conceived, how much risk to take. The issue is that the bank is contractually obligated to its depositors and yet it is conducting its business such that it will, sooner or later, be unable to honor such obligations.  This is a mathematical inevitability.  It is made much worse by FDIC, bailouts, and the “Too Big to Fail” doctrine that let banks push the inevitable losses onto the taxpayer.  But even without central banking and moral hazard insurance, this problem remains.  It is a major factor contributing to the so-called “business cycle”, which is actually a credit cycle of credit-expansion boom followed by credit-contraction bust.

One of the mechanisms of credit contraction is driven by banks that need to raise cash to pay down liabilities which cannot be “rolled over”.  They must sell assets (i.e. bonds and loans in their portfolio).  But one of the universal principles of markets is that in times of stress, the bid disappears.  This is no mere matter of banks bring more “supply” to the market and thus “equilibrium” prices fall.  This is the general unwillingness to buy such assets at any price, in the extreme case.

So asset prices fall, putting more stress on banks because their liabilities do not decline, only their assets.  So they must sell more assets, forcing values to fall further.  Credit availability in this environment falls.  Businesses cannot expand, or even finance manufacturing, and the vicious cycle begins.

Another fraud is that a duration-mismatched bank would probably have to misrepresent its financial condition to its investors.  Balance sheets like the first set of examples conceal this duration mismatch and thus give the false sense that everything balances.  I will concede that this fraud is not necessarily part of duration mismatch per se, but I doubt that many investors would buy the equity (shares) of a bank if they knew the bank was only able to remain solvent in sunny weather and it was inevitable that the bank would take big losses in the future.  (Long before the depositors lose a penny, the equity investors are wiped out.)

So what have we concluded?  First, fractional reserve lending is about lending less than the bank takes in via deposits.  The only party capable of creating money out of thin air is a central bank (which should be abolished).

Second, fractional reserves do not necessarily cause any problems to the bank.  If a depositor wants to liquidate a time deposit before maturity, the bank will seek the best bid in the market—and hand the loss off to the depositor.

Third, one cannot simply add up the various kinds and durations of banking deposits to come up with a simple (scalar) total.  A demand deposit is money; a time deposit will mature into money next year or in 2041 but is not money today.  Thus banks can expand credit in the system (which is not necessarily bad) but not money.

Fourth, borrowing short to lend long, aka duration mismatch, inevitably implodes.  This is not a matter of odds or probability.  Like a geological fault line, one can try to assess probability of a destructive event in any given year, but sooner or later catastrophe is certain.  When a business knowingly engages in an activity that is guaranteed to cause it to dishonor its obligations, that is acting in bad faith.  Such a business has no intention of honoring its obligations over the long term, only in the short term when it is expedient.

Finally, fractional reserve banking is one of those issues where there is a deep misunderstanding in Austrian circles.  This is compounded by the dearth of information about duration mismatch (I am only aware of Professor Antal Fekete writing about it, and of course some of his students such as myself) and the proliferation of misinformation about it.  I strongly encourage anyone interested in this topic (which should be all students of the Austrian School) to read the works of Fekete (http://professorfekete.com/) which go deeper than I could in this one essay.