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What Do Banks Do With Your Money Anyway? Jon Stewart Almost Gets It Right…

April 29th, 2010 · 11 Comments
Finance · Fun With Math · Macroeconomics

Go to about 0:13 in the clip:


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If you’re like me, you think that when you deposit money in a bank, the bank takes that money, puts it in a mattress with your name on it, and has a fat guy sleep on top of the mattress so that nobody can take it. Not true. It turns out, when you give your money to a bank, uh, what they, uh, do with it is, uh, anything they want.

Hm. Now while that’s not technically true, the real answer is much further toward the “anything they want” end of the spectrum than the “fat guy on mattress” end. Here’s how it works: when you deposit money in, say, a checking account, that money becomes both an asset and a liability for the bank. (For those of you scoring at home, the net worth of a company is the value of its assets – things it holds – minus the value of its liabilities – things it owes to others. It shouldn’t then be surprising that the money deposited counts in both categories, since it’s not like the money in and of itself adds to the net worth of the bank.) The money goes in the assets column because, well, the bank has the cash in its vault for the time being. It goes in the liabilities column because the bank owes you the money back when you ask for it, since it’s still your money.

If your deposit doesn’t directly add to the bank’s net worth, then how does the bank make money? (While the real answer is likely “from exorbitant overdraft fees,” that’s not where I’m going here.) Banks make money by lending your money out to others and charging a higher interest rate to them for their loan than they are paying to you on your deposit. Think about it…if you could borrow money from me at basically a zero interest rate and lend it to some other guy who will pay 5% interest, you’d be sitting pretty, right? Well, that situation is not far from reality. From E*Trade Bank:

On the surface, this is quite possibly the best business model I’ve ever heard- maybe that’s why banks make so much money. =P Think about it- some guy deposits $100, you loan out the $100, the borrower buys something with it, the person that the borrower paid needs to put the money somewhere, so he…wait for it…deposits it in your bank! So you loaned out $100 and got $100 as a result…and that’s before even considering that the borrower has yet to pay back the loan!

Ok, maybe there’s a catch. Actually, there are two of them. First, as a checking account owner, I don’t have to commit to only withdrawing my money at particular points in time, I can instead have it whenever I want. In this way, if I want my money back before the guy that ultimately borrowed it from the bank has to return it, the bank is stuck in the lurch. Also, there’s no guarantee that the borrower will actually pay the money back on time, or at all for that matter. (This should be obvious to anyone who hasn’t been living in a cave for the last two years.) Luckily, the fact that banks have a whole lot of customers, most of whom won’t default on the loans or conspire to all demand the money in their checking accounts at the same time, and this alleviates most of the potential problem.

As an added precaution (intended or not), the Federal Reserve sets what is called the reserve ratio. This ratio is the percentage of any deposit that is required to be held within the bank. For example, if the reserve ratio is 10% and I deposit $100 in my checking account, only $90 of that is available to loan out because $10 of it required to stay in the bank vault. How does this affect the bank’s profitability?

Well, in the cycle I initially mentioned, the bank could keep loaning out the same $100 indefinitely (and earning interest on each iteration), as long as all of the money was eventually deposited into a bank account (i.e. not hidden under a mattress with a fat guy on top) and the bank was the only game in town for depositing money. What happens instead when the reserve ratio is greater than 0%? Let’s walk through the cycle…again, I’m assuming that there is no money under mattresses and only one bank in town, mainly for simplicity:

Step 1: $100 deposit
Step 2: $10 in vault, $90 loaned out
Step 3: $90 deposit
Step 4: $9 in vault, $81 loaned out
Step 5: $81 deposit
Step 6: $8.10 in vault, $72.90 loaned out
Step 7: $72.90 deposit
Step 8: $7.29 in vault, $65.61 loaned out
Step 9: $65.61 deposit

Okay, I’ll stop here because I am just not that good at arithmetic. You see in this case that the amount available for lending gets smaller with each iteration, so the cycle will eventually stop when there is less than one penny or whatever to be lent out. This is in contrast to the original cycle that would just keep the $100 going around and around.

So what do the totals for the bank look like in terms of deposits and holdings? Well, if we apply some math (Google infinite summation if you are curious), we get that the total amount of deposits is $1000 and the total amount of holdings, or reserves, is $100. In general, the total amount of deposits is going to equal the initial deposit divided by the reserve ratio (10%, or 0.1, in this case) and the total amount of reserves is going to equal the initial reserve contribution divided by the reserve ratio. (Note that $1000=$100/0.1 and $100=$10/0.1.)

Because we are dividing by the reserve ratio here, it is the case that if the Fed were to increase the reserve ratio, the total amount of deposits would go down…but the total amount of reserves would still be $100. Why is this? Let’s think about what would happen if the reserve requirement were to be increased to 20%. The initial deposit is still $100, so the total amount of deposits is $100/0.2, or $500. The total reserves, on the other hand, stays the same since we are starting with an initial contribution of $20 now rather than the original $10, and $20/0.2 still equals $100.

Why is the reserve ratio important? Given our above conversation about the uncertainty of loan paybacks and account withdrawals, it stands to reason that a higher reserve ratio makes it less likely that the bank would have to get bailed out in some fashion (borrowing to cover withdrawals, going to the FDIC, whatever) if an unusually high fraction of people want their money back. So higher reserve ratios make banks safer, but they also make banks less profitable because higher reserve ratios mean that they can’t make as many loans. The reserve ratio is sometimes also used as a monetary policy instrument, since, by the same reasoning as above, lower reserve ratios increase the money supply and vice versa. In reality, however, this doesn’t happen very often, since the Fed mainly relies on open market operations to implement monetary policy.

In case you were wondering, the “fat guy on mattress” approach would correspond to a reserve ratio of 100%.

Tags: Finance · Fun With Math · Macroeconomics

11 responses so far ↓

  • 1 Michael // Apr 29, 2010 at 7:13 pm

    There are a bunch of “borrow” in your article which should be “borrower”. Check it :P

  • 2 Indianagreg // Apr 29, 2010 at 8:12 pm

    It’s probably fair to point out that some countries, like the UK and Canada, don’t have a reserve requirement, and that US banks regularly “game” the reserve requirement system.

    http://moneyterms.co.uk/reserve-requirement/

  • 3 econgirl // Apr 29, 2010 at 9:48 pm

    @ Michael: Thanks. *sheepish*

  • 4 RiteshAroa // May 1, 2010 at 6:11 pm

    I think reserve ratio is in place to tell Humans, but not Econs, that fed is doing its job by minimizing the risk. Its just an image building tool, since any layman would think of very basic and intrinsic risk of borrower not paying back and will keep some kind of safeguard in place.

  • 5 Kurt Streich // May 10, 2010 at 12:27 pm

    But if the reserve ratio were not existent or even at an extremely low percentage, the multiplier would be huge. A reserve ratio of 0.1% would mean that the open market operation of purchasing $100 dollars worth of securities would increase the money supply by a whopping $100,000 $(100/.001) . And if there weren’t any reserve ratio a deposit would create an unlimited amount of money, making the Fed’s ability to set nominal interest rates impossible through open market operations.

  • 6 Dave // May 10, 2010 at 11:49 pm

    Remember, Kurt, that a reserve ratio of zero (or even something approaching very close to zero) is only a theoretical possibility. In practice, people will occasionally be accessing their demand deposits for real, host-to-goodness cash (they are, after all, DEMAND deposits), which means that the banks will occasionally have to produce real, host-to-goodness cash, which means that, even in the absence of reserve ratio regulation, banks will still be forced to keep some cash on hand, giving the economy some sort of effective non-zero reserve ratio.

  • 7 Dave // May 11, 2010 at 5:06 pm

    So just read the preceding post, which I wrote, and it appears that the spell-checker on my Mac consistently converted “honest-to-goodness” to “host-to-goodness”. Anyway, just in case there was confusion, I’ll try posting this from a Winders box and see what happens.

  • 8 Ben // Jul 9, 2010 at 5:14 pm

    Well Dave that is true for traditional banks but bank like institutions (when I say bank like I’m using the Krugman definition: anything that borrows short and lends long is in some sense a bank.) such as hedge funds who have less liquid liabilities and aren’t restricted by fed regulation of traditional banks do actually run reserve ratios around zero. That’s how they’re able to take such huge positions on things like currency speculation. To be a clear i don’t disagree with th point in general just though it was an interesting exception.

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