My screed on "Mark To Market" brought the tinfoil brigade out of the woodwork in spades, and one of their most common "attack points" is that "reserve banking is fraud."

Simply put, "no its not."

Let's prove it.

We'll set our temporal transporter to a world called "TimmyLand", where there are no banks but there is a very trusting government.

We show up and decide to establish a bank, being the only bank in the land.  Since the government is very trusting, it does not require us to post any capital to do this - it simply takes our word for it that this is a good, safe and sound business.

Ok, so on the first day I open my doors to the world with no capital and nothing in my empty vault.

Joe walks in and being the trusting man he is, he deposits $100,000.

I now have a balance sheet that looks like this:

Note that I have $100,000 in cash in the vault, and Joe has a piece of paper - a note - that makes him a creditor of my bank for $100,000 with no time-certainty (he didn't take a CD, he just deposited the money into a demand account.) 

Now while this government is very trusting, they're not totally stupid.  They demand that I keep a 10% reserve - that is, that I fractionally reserve at 10%.

So a few minutes after Joe comes in, Jane walks in and wants to buy a house.  She has her eye on a nice $120,000 home and has $30,000 to put down, but doesn't have the rest.

That's no problem, says I.  I do some investigation of Jane and find that she has a very good job, and its a very nice house.  The one right down the street of the same size sold a month ago for $150,000, so the valuation looks pretty conservative.  Jane must be a good negotiator besides.  I make the loan @ 6%.  Now my balance sheet looks like this:

Notice that my net balance sheet has not changed. Yet.

But the seller of that house, Rich, doesn't want to sit on $90,000; someone might rob him! He comes into the bank and deposits it. Now my balance sheet looks like this:

Now wait a minute, you protest! How the hell can you take $100,000 and turn it into $190,000? That's fraud you scream.

Uh, I didn't take $100,000 and turn it into $190,000. I took $100,000 and cycled it through my bank twice, leaving $100,000 cash in the bank and for the other $90,000 worth of liabilities, there is an equal value in assets.  Both Joe and Rich loaned the bank their money which the bank in turn used in the first case to make a loan to Jane (and still has $81,000 in additional loan capacity which it will use to make another loan to someone else.)

Nor are Joe and Rich's loans to the bank "unsecured"; in fact if you examine banking laws you will find that depositors have a senior claim on all of the bank's assets, behind only the government's interest in redemption for circulation (that is, if the bank has a loan outstanding for currency to cash checks and the like.)  The bondholders and others with interest in the bank are subordinate to depositors; the only get paid once the depositors do.

But, you protest, if Joe and Rich both come in and want their money at the same time, the bank doesn't have it!

True.

Does it matter?

No, and here's why.

Jane's mortgage has value. Provided I properly underwrote it, that paper is actually worth more than $90,000 - it is in fact likely worth 102 or 103% of "par", because there's a discounted cash flow in the form of interest payments and so long as the interest charged is higher than the inflation rate (or alternatively, the risk-free return I can obtain in, for example, Treasury bonds of equivalent duration) and the collateral protects against default that paper is in fact more valuable than its $90,000 face value.

So if Joe and Rich both come in at the same time and demand their money, I can sell Jane's mortgage to someone for the $90,000 face value plus a profit, pay both Joe and Rich, and (since I now have no money left in my bank) close my doors. No harm, no foul and no fraud.

(In reality if both Joe and Rich come in and want their cash at the same time I'm more likely to borrow against Jane's mortgage than sell it, but the fact remains that so long as Jane's mortgage plus my vault cash exceeds the value of deposit liabilities, the bank is fine - and there is no fraud.)

Can we dispense with the "fraud" claim now?  I think so.

Ok, on to the meat of this thing - fractional reserve banking in general.  We've established that it's not fraud to lend money, take a deposit of the money you lend after its spent, and lend part of that again.  But wouldn't we have a "safer" economy if there was no fractional reserve banking? 

Maybe.  But would you want that system?

Let's go back to TimmyLand, the land with no banks, and set one up.

We're going to need a building; let's assume we can lease 3,000 square feet (a small bank) for $20/ft all-in (its not Class-A space, but it's reasonably decent.)  That's $60,000 a year in leases.

We need three tellers, one branch manager and one loan officer.  Figure $40,000 (all-in cost, including taxes, health insurance, etc) for the tellers, $60,000 for the branch manager and loan officer (heh, we're cheapskates!); that's $250,000 a year in labor.

We need computer gear to keep track of our books, and we need a long-term lease on a vault, since we're not open 24x7, utilities, and other sundries.  Call that another $40,000 a year all-in.

We've got a gross operating cost of $350,000 a year.

Now let's assume we capitalize this bank with $5 million dollars of our hard-earned money (heh, I've got some cash, I'm gonna open a bank!)

What's a reasonable "return on investment" for those funds?

I would argue that 10% is reasonable.  After all, if I invest in this business I could lose everything.  I can get 5% tax-free in Munis, which on $5 million is somewhere around 8% or so taxable.  Add a small premium for working 14 hour days (as opposed to the munis that leave me sipping Mai Tais by the pool all day) and 10% is actually quite low.

But this means I need to make $500,000 pretax, and I start with a deficit of $350,000 in operating expenses; ergo, I need to be able to gross $850,000 annually for this business venture to make sense.

Now let's assume I cannot fractionally reserve.  That is, I can't loan out deposited funds (I must reserve them all), only those funds that I have as paid-in capital.

So I can loan out, at best, my $5 million dollars.  Once.

I thus must make on that $5 million dollars $850,000 in interest charges to make this enterprise worthwhile.

That means that on average I must charge 17% interest, and this assumes that I never make a bad loan!  If there's a bad loan here and there in the mix then the average interest rate must of course be high enough to cover that too.  In all probability I need to charge an average rate of around 20%, net-on-net.

This means your mortgage rate is about 15%, car loans are 20% interest, credit cards are 30% (and not only when you don't pay either), and on and on and on.

That sucks, to be blunt.  With those sorts of interest rates nobody's going to be borrowing anything, because they simply can't afford to.

But what if I can fractionally reserve?

Then it gets much better.

Let's take the $5 million and run it "to extinction" on a 10% fractional reserve system.  In this case I can have around $50 million in loans outstanding at the maximum, but note that I still only need to make the same $850,000, because my capital at-risk is $5 million, not $50 million.

Now my average "net interest margin" must only be 1.7% to make a reasonable amount of money after charge-offs and similar events.

Heh, that's not so bad! 

Now I can pay interest on deposits such as savings accounts and CDs, I can offer 6% home mortgages and 7 or 8% car loans.  I can offer 10% credit cards.  If I pay 2% in interest for the deposits that people place with me, my net interest margin on that mortgage is 4% - well into the safe zone - and this means that I can have a few loans go bad without going bust.  I can thus take a bit more risk and do loans with 20% down instead of 30%, and perhaps not force you to prove six or 12 months of segregated cash reserves - just in case you lose your job.

In fact, if you think about this you'll quickly realize that banking in a fractional reserve system is a nicely profitable business - without doing anything dangerous at all. 

Without using unreasonable leverage, without gaming the system, without any sort of nonsense I can make a very nice chunk of money.

But you know there is never a free lunch, right?

There is a cost to fractional reserve banking, and it comes from the law of exponents.

See, nobody will loan you money at less than the expected growth rate in the economy.  They'd be nuts to; the law of basic business balance says that you can't get something for nothing.  Remember, the banker has to pay his operating costs, and that money must come from you, the borrower.

So let's assume that the average economic growth is 3% annually.  Let's further assume that the average loan is made at 6% annually.

Well, now we've got a problem; over 30 years $100 in "base economic output" turns into $243.

But over that same 30 years $100 in "interest expense" turns into $574!

It doesn't start out all that different.  After five years its $116 for growth and $134 for interest.  That's a difference of 16%.  But over 30 years its nearly a double.

What this means is that over time the net percentage of output required to cover debt increases, all things being equal.

This is the mathematical principle of exponents, otherwise known as "compounding" in the investing and banking world.

Not all loans are productive.  Some are made to do things like buy a machine that makes car parts, and as such the output gain from the machine grossly exceeds the interest cost.  That productive investment, financed with debt, doesn't get the person who takes it out in trouble, because his personal growth in productivity exceeds the interest cost.

But some loans are made to finance consumption; the person who borrows to buy a bigscreen TV or a vacation as just two examples.  There is no particular productivity increase in such a purchase.

As the "spread" between production and net interest expense rises, the economy falters.  A higher and higher percentage of the loans ultimately cannot be paid back, even productive loans, because the net interest expense over time exceeds the productive gain of the person who takes them out.  The presence of this ever-widening spread, which is inherently part and parcel of fractional reserve banking, means that recessions are necessary and more importantly, some people who have taken out loans and some people who made loans must, during those recessions, go bankrupt.

That is the purpose of a recession - to clear out the excess indebtedness along with excess capacity, resetting downward the "spread" between net interest expense and gross output (GDP).

This is mathematically necessary for any monetary system to remain stable in which fractional reserve lending is used.  Should government attempt to prevent (or shorten) recessions by manipulating liquidity (that is, "make it better Joe!" when times get tough), or worse, try to "spend its way out" of a recession, preventing the imprudent or simply unlucky from going broke all that happens is that the system becomes more and more "backloaded" with excessive debt carrying costs that have not been cleared.

Eventually these costs overwhelm the ability of government - or anyone else - to paper them over and you get the sort of collapse we are seeing now.

The math always wins, and the more you stretch the rubber band the worse the snapback hurts.

Does this mean that we should get rid of fractional reserve banking?

Not necessarily. 

There is nothing particularly wrong with it; it comes with both costs and benefits.  Certainly, the ability of a farmer to borrow at 5% to plant his field, instead of at 20% (which he could not afford, and thus he would not plant all of his acreage) is tremendously to the weal and wealth of society.  Certainly, the manufacturer who buys a machine with debt that produces toasters contributes to the benefit of society.  And we, of course, like being able to buy houses and cars at reasonable interest rates.

But we must recognize that just as fractional reserve banking contributes to booms, it brings the necessity of busts.

Proper regulation of leverage and prudential standards for lending prevent those booms from getting out of control, and thus limit the ugliness of the busts - but make them inevitable at an earlier date.

That is, the benefit of reserve banking (the availability of credit on reasonable terms for a wide variety of purposes) comes with the cost that those who use credit to finance consumption ("pulling forward demand") or engage in speculation are likely to go broke during the inevitable busts; they are those who are in effect gambling with their use of credit and when the cyclicality catches up with them, they (and those who loaned to them) will be the ones who go under.

Our failure over the last 20 years is not found in the principle of reserve banking.  It is, rather, found in the complete and utter refusal to accept the cyclicality that is a necessary component of reserve banking systems - to accept the costs that come with the benefits.

Instead of accepting these facts we have gamed the system in an attempt to prevent the inevitable costs from coming to fruition with actions such as:

• Gramm-Leach-Bliley, which repealed Glass-Steagall, allowing banking leverage to cross into investment services, where it should have remained tightly regulated.
• Sweep account exemptions put into effect for banks that made reserve requirements nearly meaningless, allowing more leverage expansion than was lawful under a proper reserve implementation.
• Removal of leverage limits from investment banks.
• Refusal to regulate both sellers and buyers of leveraged derivatives, such as the CDS that AIG sold, then providing "back door bailouts" to the counterparties for the demonstrably-unsound paper they wrote.
• Granting of "23A Exemptions", which circumvented limits on related-party capital tie-ups by banking entities.
• The recent authority granted to The Fed to set reserve requirements on banks anywhere, including to zero.
• The continued levering up of The Fed's and Government's balance sheets, essentially without limit, in an attempt to prevent the unwinding of the excesses of the previous 20 years (since mid 2007)

All of these actions and more are simply attempts to forestall what mathematics tells us is an inevitable process, and one that gets far worse the longer we delay it.

Our problems today are no different than they were in 1929 or 1873.  We have once again refused to accept the mathematical inevitability that comes with the system of finance and banking we (and the rest of the world) have chosen for hundreds of years, and instead of enforcing prudent regulation up and down the line, including in our government itself, we have once again tried to game the outcome.

Unfortunately you can't game mathematics - no matter what you decree, 2 + 2 will always equal 4.