Imagine a small town out west somewhere that has been living peacefully without a bank all these years. When the bank comes to town they are all happy to have a place that will protect there money AND pay them to do it! Life is hard out here and they’re a little suspicious of a free lunch, but after word gets out that you don’t have to sit through a sermon everyone piles in and is happy to be rid of Jimbob. (Jimbob owns the gun shop and used to charge a small rent to let people keep their savings in his safe.)
Let’s see what happens to the money after the bank gets a hold of it. We’ll follow the $100 that Tom deposits. Well, Tom comes in with his money and they assure him it will be safe in their big fancy vault. They show him the 10 inch thick doors and the absurdly large wheel you use to open the door. Then they tell him he can come and get his money whenever he wants, or he could just spend it with these here checks. Tom likes the sound of that and hands over his hard earned dough. As soon as Tom turns around the bank carefully places $10 of his money in the vault, and throws the other $90 in the “For Loan” pile. You see banks operate under what they call a “Fractional Reserve System”, as Jimmy Stewart famously explained in “It’s a Wonderful Life”, the bank keeps some fraction of the deposits on hand incase you as for it, in this case 10%, and loans the rest out.
Now the bank makes a $90 loan to little Billy and charges him 8% interest. They give 1% to Tom and keep the rest for all their hard work right? Well, yes, but what Jimmy didn’t explain is what the late, great Paul Harvey would call The Rest of the Story:
Now Billy spends the $90 of a new bike for his paper route. Then Sam, who owns the bike shop, deposits it in his new fangled account. At which point the banker carefully puts $9 in the vault and throws the other 81 in the “For Loan” pile. Did you catch what just happened there?
Now, where before the there was 100 dollars, there is promise of 190 dollars! They claim both Tom and Sam can come get their money whenever they want and the bank is earning 8% interest in 171 dollars! Of course that 81 dollar loan is spent as well and finds its way back to the bank who keeps a portion of it in the safe and loans the rest out at 8%. This process goes on with the money always finding its way back to the bank to be re-loaned. After awhile the situation might look like this:
And this process continues until eventually, inevitably, Toms entire real $100 is consumed as “reserves” to support $1000 in deposits and $900 in loans on which the bank is earning 8% interest. $900 x 8% = $72. 1% of this they pay to depositors, leaving $63 for the bank! That’s a 63% return for all the money the town puts in the bank!
More importantly there is now 1000 dollars in deposits that the bank claims you can come and get whenever you want. And the problem isn’t just that the money is loaned out “to support your community” as is claimed in “It’s a Wonderful Life”, it’s that 900, of the 1000 dollars does not even exist!
Talk about false advertising! Is there any other business allowed to exist, that is so premised upon a lie? It is an impossibility that your money can be both in your account at your disposal, AND loaned to someone else. It’s a scheme that would make Ponzi blush, but like all good marks were blinded by the promise of something for nothing.
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PS: If you think this is nuts wait til I tell you about the Federal Reserve!
ReplyDeleteYou can't comment on your own post!
ReplyDeleteThis is a very amusing account of a 100$ bill. It reminds me of a short story I read about a day in the life of a CO2 molecule.
ReplyDeleteHowever, your scenario is only a scheme if the bank is truly dishonest about it. Have you called and asked what their policy is on bank runs? Is it stipulated in the contracts? I bet this would be a fun conversation and I encourage you to try it and write about it :)
Assuming I derived this correctly:
ReplyDeleteLet R = a sum of money the bank will no longer lend out if deposited (for example, perhaps a bank is willing to use the fractional reserves scheme on any amount greater than a penny).
Let S = an initial sum of money deposited (in your example S = 100)
Let x = the fraction of any deposit a bank is willing to loan
Let n = the total number of loans a bank can make on an initial deposit
Then n = ceiling (log (R/S) / log X - 1)
If you pick the log base to be X the formula is even simpler!
In your example, taking S = 100, R = .01, and X = .9 we get n = 87 loans! If we take R = 1 we get 43 loans! That's 88 and 44 customers respectively (accounting for the initial customer)! Not bad for 100$...
That's somewhere between one to two customers per dollar given in the initial loan! You might, as I did, wonder if, given an R and X fixed, is there an S such that n = S? In other words, is there an initial deposit, S, which would give the bank S customers? This amounts to playing around with the parameters (R,X) of the equation:
Sx^(S+1) - R = 0
and graphically solving for the zeros. Rearranging we get:
x^(S+1) - (R/S) = 0 Unfortunately, the exponential term gets small so fast, (R/S) can't possibly catch up except for "trivial" values of S, around 1. So...no such solution.
In fact, the range of n for any reasonable S (say, from 100 to 1 trillion dollars) is only between 43 to 262 (for R = 1, x = .9), or half an order of magnitude. If you allow x or R to vary you don't get a much different result: n varies about 1/2 an order of magnitude for all possible initial deposits.
So what have we learned? Almost all our deposits, no matter how big or small, take a comparable number of trips around the market before settling into their retirement.
Interesting, no?
(Of course, I assumed only one bank exists...)
-Guy
I think the conclusion above holds even if multiple banks are included. You can run the same analysis on the Metabank (where you consider all banks as branches of one bank). Then when you're done, you get the same result, only the total number of trips made by a deposit (or loans made, or customers gained etc) is split in some way across the banks. Exactly how it's split depends on how people choose their banks, but we still retain the general (and, to me, somewhat unexpected) result:
ReplyDeleteOur deposits, no matter how big or small, take a "comparable"* number of trips around the market before settling into their retirement.
* comparable = within half an order of mag. I think this is actually sharper for the majority of loans--more like 1/4 an order of mag.
Thoughts?
Guy,
ReplyDeleteOur first string of equations. I love it!
"In fact, the range of n for any reasonable S (say, from 100 to 1 trillion dollars) is only between 43 to 262 (for R = 1, x = .9), or half an order of magnitude."
I think this is because it should take the same number of iterations to go through any order of magnitude. So from 1000 to 100 should be the same number of steps as 100 to 10. true?
"(Of course, I assumed only one bank exists...)"
I don't think this is a necessary assumption. You can allow many banks and it doesn't change the amount that money is multiplied by. It also won't change the number of round trips, so to speak.
Trisco, thanks for for your illuminating post on the one bank town. Something about "virtual money" finally makes some sense to me. I still think that the whole "fractional reserve system" is a pyramid scheme/scam, but maybe you can enlighten me. Here is why I think so.
ReplyDeleteIt seems to me that the only inherent problem with the "fractional reserve" banking system is the apparent inability of the bank to handle the relatively rare, but potentially disastrous "run on the bank" (the situation where the banks creditors recall (collectively) more than the 10% of the debt that the bank owes them. ) Any responsible bank should (by law?) to mitigate such risk by purchasing insurance from another of our favourite institutions, the insurance company.
Now I admit that I know next to nothing about how banks actually deal with insurance companies, but I can see how this relationship would have to work with the one bank town model that T described in an earlier post. The insurance company sells a service to the bank to mitigate it's vulnerability to a bank run. In order to provide this service, the insurance company must maintain at least $900 in cash (or highly liquid assets). In return, the bank pays the insurance company a fee which is probably dependent on the amount ($900), the risk of a bank run (???) and some handsome profit margin. I imagine that this fee would be at least comparable to the interest rate that the bank charges it's customers for a loan; in our little one town model that's 8%. If the rate that the insurance company charged the banks was much less than this 8%, they would be better off just lending it out themselves at 8% interest to the general public. So, it seems to me that a responsible bank wouldn't really be making as much of a killing (63% return on the initial $100 of capital with which it starts out) as it seemed. It would simply be passing the buck (he he;) to the insurance company. It seems to me that this "passing of the buck" might continue on:
Opening a one town bank requires, say, an initial capital investment of $100. Opening an insurance company to service that bank (in the way described above) takes an initial capital investment of $900. Presumably, each insurance company services several one town banks simultaneously. I imagine that the insurance companies only hold enough cash to protect against simultaneous "runs" on a small portion of its bank clients, say 10%, yet it collects fees from all of it's bank clients. Sound familiar? Basically, the insurance companies act as a big bank for the smaller banks and they make the same kind of profit margins from the smaller banks that the smaller banks make off of their individual customers.
So, there are banks, insurance companies (which I am suggesting are just meta-banks) and possibly even meta-meta-banks. Anyone with the least bit of appreciation for the concept of exponential growth knows that this structure can only go so high, indeed, I suspect that there is no such thing as a meta-meta-bank.
(How) do the insurance companies handle a simultaneous "run" on several of their client banks?
dan
Hi Dan,
ReplyDeleteFirst one minor point, I think there is another big problem with the fractional reserve system, which is the inflationary effect. So whenever they get a hold of a new dollar, they essentially print 9 more. They and the first people they lend it too get the benefit of that created money before prices have adjusted.
As to the rest of it, your reasoning is quite correct. Insurance against this sort of thing would be prudent, and as long as you were talking about protecting against runs on individual banks, as opposed to the whole system, it could probably be written profitably, though it would certainly eat into banks profits. But your thinking suffers from a malady I am also often afflicted with. I haven’t quite nailed it down, but its something like the assumption, “if this is so obviously the way the world ought to work, it must be that way.”
Sadly, its not.
Banks have come up with a much better solution, from their point of view. In the event that they need more cash then they have, they have the Federal Reserve print it. It essentially comes out of all of our pockets through inflation. Now I’m about three books ahead of you in understanding this mess, so I’m no expert either, but here is roughly how it works. If a particular bank is in need of cash, due to withdrawals, they simply borrow it from other banks. If other banks don’t have it to spare, there is one Meta-bank. That bank is the Federal Reserve, which is tasked with being the lender of last resort. Since the FED, simply prints money it can lend all the banks need, completing the counterfeiting cycle by finally printing the cash we’ve all been pretending existed. Of course, as soon as people calm back down, and put their money back in the bank, this new money is considered excess reserves, promptly lent out, and ends up itself multiplied by ten.
[I ran into some kind of space limitation for comments, so I've broken the comment up. ]
Hi Dan: Part II
ReplyDeleteNow in the event that a bank is technically bankrupt, that is its assets are less then its liabilities, as opposed to simply being short cash on hand, then it is taken over by the Federal Deposit Insurance Corporation or FDIC. This would be like, if half the loans went bad, so there wasn’t even loans supporting deposits. “A ha! So there is insurance.”
Well sort of. It works a lot like an insurance company, but is not insurance. Banks pay a premium of sorts, that is a fixed percentage of their deposit base. The difference between this and insurance is in the utter lack of even an attempt to avoid moral hazard. As Apos, could explain better than I, its important in any insurance contract that the insured retains some motivation to avoid the catastrophe being insured. For example with car insurance, not only would I hate to get in an accident, but I don’t even want to risk a speeding ticket, for fear that my premium will go through the roof. But with premiums depending only on the size of deposits, banks are encouraged to push risk to the limit to get their moneys worth. It would be like if my car insurance only depended on what the car cost… lets just stay I’d get places faster! If the FDIC insurance were instead allowed to be replaced with an insurance industry trying to earn a profit, risk in banking would be largely reduced, since lower risk would be reflected in higher profits, from lower premiums.
[Uh... ok same problem... continue for Part III!]
Hi Dan! Part III!!
ReplyDeleteThere is another important sense in which the FDIC is different from an insurance company. When the “premiums” are paid to the FDIC, they are deposited in the FDIC’s account at the Treasury. The government then spends the money and replaces it the IOU’s. I know I know sounds crazy! But here is it from the former FDIC Chairman William Isaac(Despite this being comment part3, this is to funny to leave out!):
“When I became Chairman of the FDIC in 1981, the FDIC’s financial statement showed a balance at the U.S. Treasury of some $11 billion. I decided it would be a real treat to see all of that money, so I placed a call to Treasury Secretary Don Regan:
Isaac: Don, I’d like to come over to look at the money.
Regan: What money?
Isaac: You know ... the $11 billion the FDIC has in the vault at Treasury.
Regan: Uh, well you see Bill, ah, that’s a bit of a problem.
Isaac: I know you’re busy. I don’t need to do it right away.
Regan: Well ... it’s not a question of timing ... I don’t know quite how to put this, but we don’t have the money.
Isaac: Right ... ha ha.
Regan: No, really. The banks have been paying money to the FDIC, the FDIC has been turning the money over to the Treasury, and the Treasury has been spending it on missiles, school lunches, water projects, and the like. The moneyvs gone.
Isaac: But it says right here on this financial statement that we have over $11 billion at the Treasury.
Regan: In a sense, you do. You see, we owe that money to the FDIC, and we pay interest on it.
Isaac: I know this might sound pretty far-fetched, but what would happen if we should need a few billion to handle a bank failure?
Regan: That’s easy — we’d go right out and borrow it. You’d have the money in no time ... same day service most days.
Isaac: Let me see if I’ve got this straight. The money the banks thought they were storing up for the past half century — sort of saving it for a rainy day — is gone. If a storm begins brewing and we need the money, Treasury will have to borrow it. Is that about it?
Regan: Yep.
Isaac: Just one more thing, while I’ve got you. Why do we bother pretending there’s a fund?
Regan: I’m sorry, Bill, but the President’s on the other line. I’ll have to get back to you on that.
Once upon a time, there was indeed a segregated FDIC fund. During the Johnson Administration, someone had the bright idea to put the FDIC into the federal budget as a way to reduce the deficit. This was in the good old days when the FDIC always produced a surplus. Putting the FDIC on budget reduced the deficits being created by spending on the Great Society programs in tandem with the war in Vietnam.
The reality is that there is no FDIC fund. Anything the FDIC lays out to handle a bank failure must be borrowed by the Treasury, which adds to the federal deficit. The total amount of the current outlay is charged against the federal budget even if recoveries are expected in the future, as problem assets are collected by the FDIC. That’s the case whether the FDIC’s nominal balance at the Treasury is positive or negative.”
So at the end of the day the FDIC also gets its funds from the Federal Reserve, or in other words from the rest of us through inflation.
[Ok we made. I'll try to work the above comments into a post with links and such]
I'm sorry Trisco, but this dialog just screams internet urban legend. Can you please provide a reputable source for it?
ReplyDeleteHi Dependable, no apologies necessary! Sounds to crazy to be true right. Unfortunately, I'm convinced it is. The only way I can see this being false, is if 1)someone broke into former head of the FDIC William Isaac's consulting company's website, and posted it under his name. Then 2) several reputable people believed it, and wrote about it and 3) no has bothered to debunk it including William Isaac himself. I find this chain of events highly unlikely but within the realm of possibility.
ReplyDeleteUnfortunately, Isaac has removed the article from his sight. I'm not sure if this happened when his former company, Secura group switch to LECG of which he if currently Chairman or if he was asked to remove it or what.
Here is the original link to the article, which will bounce you to LEGC of which Isaac is chairman. :
http://www.securagroup.com/news/archives/articles/2008/AB080827.pdf
Here is the Article by Vernon Hill, founder and former CEO of Commerce Bancorp, co-founder of Commerce Bank/Harrisburg (soon to be Metro Bank, Philadelphia), and chairman and founder of Hill-Townsend Capital, LLC of Chevy Chase, Maryland, which originally pointed me to the article.:
http://www.bankstocks.com/ArticleViewer.aspx?ArticleID=5350&ArticleTypeID=2
Also on Seeking alpha:
http://seekingalpha.com/article/95129-fdic-insurance-fund-it-doesn-t-actually-exist
I was unable to find the full text of the article online, so if you run across is please let me know. I have a paper printout somewhere, but don't have the patience to search through the ~6 unorganized boxes of papers to find it. If I run across it in the future though I'll scan it and put it up. If I recall, his point was that its silly to raise the "premium" on banks in bad times. Since the money is just borrowed when its needed anyway, might as well wait and raise the premiums to make up for the losses when banks are doing better.
Hope this is helpful.
Trisco