# Why do banks charge a spread on credit?

According to the doctrine of the money multiplier (https://en.wikipedia.org/wiki/Money_multiplier), a positive reserve ratio means a bank has LESS loans than deposits. See the table in the link. Therefore, if a bank gets a loan of 100, it can lend, say 80. Here I understand that the interest rate on loans must be higher than the interest rate on deposits, so that the bank can make a profit.

HOWEVER, there are other theories like endogenous money theory which state that actually, if a bank has 100 in deposits, it creates 900 of bank money (see https://en.wikipedia.org/wiki/Reserve_requirement). In this case, there is no need for the bank to charge a spread!

Can you guide me on this? I am confused!

Is this a proof that the money multiplier is correct?

You're getting two quite different concepts mixed up:

1. Banks earn a spread on loans for serving as an intermediary between savers and borrowers and for holding credit risk.
2. The process of borrowing and lending, of banking, leads people in an economy to have more liquid assets (money in a broader sense), than there is underlying cash.

When economists say banks "create money" they don't mean they're printing money off the presses and giving it to themselves as profits.

### How banking expands the money supply

To understand banking clearly, its helpful (perhaps 100% required) to understand and use the fundamental equation of accounting:

$$\mathrm{Assets} = \mathrm{Liabilities} + \mathrm{Shareholders Equity}$$

Let's say Warren Buffet decides to start a bank. He puts in \$10 billion of his own money. The balance sheet of the bank would look like: $$\begin{array}{r|rr}\text{Assets} & \text{Liabilities} & \text{Equity} \\ \hline \10 \text{ cash}& & \10\end{array}$$ Let's say he now collects \$90 billion worth of deposits from people. These bank deposits are assets for the people, but they are liabilities to the bank (the bank owes the depositors \$90 billion). $$\begin{array}{r|rr}\text{Assets} & \text{Liabilities} & \text{Equity} \\ \hline \100 \text{ cash}& \90 \text{ deposits} & \10\end{array}$$ Now let's imagine that the bank lends out$80 billion. The balance sheet would then look like:

$$\begin{array}{r|rr}\text{Assets} & \text{Liabilities} & \text{Equity} \\ \hline \20 \text{ cash}& \90 \text{ deposits} & \10 \\ \80 \text{ loans}\end{array}$$

Depositors have \$90 billion in deposits, and the borrowers have \$80 billion in cash. So the economy now has \$170 billion in money where there previously was only \$90 billion.

### A key point to realize...

Across the whole economy, all these assets and liabilities cancel out! Borrowing and lending (on its own) is not creating any real wealth. The expansion of the banking system's balance sheet is simply creating more entries on the assets and liabilities side that cancel out. To the extent though that the liabilities of the banking system, deposits etc... are easily tradeable, this does create more money in the economy. More people have liquid assets in the form of bank deposits etc... (which are liabilities of the bank).

The money supply expansion mechanics are interesting, but do not affect loan pricing.

Let’s assume that the only assets a bank invests in are loans it extended, and required reserves at the central bank. Furthermore, assume that the rate of interest on required reserves is 0%.

We will assume that bank equity is extremely small (close to the truth), and the bank only funds itself with deposits. For simplicity, assume that deposits are equal to 100% of the right hand side of the balance sheet.

In order to break even, the total interest rate on assets has to equal the amount of interest paid on deposits.

Denote:

• $r$is the percentage of the balance sheet held as reserves;
• $D$ is the amount of deposits,
• $i_d$ ($i_l$) is the average interest rate on deposits (loans).

Then, interest received is equal to $(1-r)D i_l$, and interest paid is $D i_d$. Therefore, for the bank to not lose money, $$(1-r) i_l \geq i_d.$$

In other words, the average interest rate on loans has to be greater than the average interest rate on deposits (assuming non-zero reserve holdings). This is going to be true regardless of the size of the bank’s balance sheet (the amount of the money multiplier).

If balance sheets get more complicated, the equation needs additional terms. However, the basic principle remains: by forcing banks to hold an asset that yields 0%, they have to increase lending spreads to remain profitable. This makes banks less competitive versus non-bank financial firms, creating an incentive to move towards less regulated entities. This perverse incentive explains why many countries (such as Canada) have abolished reserve requirements. (I am unsure which developed countries still have reserve requirements, other than the United States.)

Amongst central bankers there is no controversy, the money multiplier is plain wrong, see this definitive paper from the Bank of England here.

So assuming that loans create deposits...

Imagine a bank lends (i.e. creates) 1000 dollars for person A to buy second hand car from person B (for simplicity imagine they both are customers of the same bank). Person B stores the 1000 dollars in their bank account, expecting interest to be paid on their savings. The bank then makes its profit on the difference between the interest A is paying to the bank and what the bank pays in interest to the saver B.

Note that as A repays the principal on the loan the money disappears back out of existence. The bank only gets to keep the interest.

• Your answer seems to contradict the others... Why is this not an entirely self-evident, settled issue? Ultimately, the banking sector has been opperating for centuries! – user928172 Nov 20 '17 at 12:01
• @user928172 it is a settled issue. It's just that Mick has taken a very technical document, read one bit out of context, and misinterpreted it. – 410 gone Nov 20 '17 at 12:07
• @EnergyNumbers: I disagree. I would invite anyone to read the document from start to finish and then decide who is right. – Mick Nov 20 '17 at 12:28
• The paper is modern, comes from the most impeccable source possible, is aimed at bankers and has over 430 citations. Critics are going to be hard pressed to find any description of the monetary system that is more authoritative. – Mick Nov 20 '17 at 12:40
• The paper is called "Money creation in the modern economy" and as the title suggests, it explains how our monetary system works. It states "The reality of how money is created today differs from the description found in some economics textbooks" and is therefore an extremely important paper. – Mick Nov 20 '17 at 13:07

You may have misunderstood the endogenous money-creation argument. The endogenous money growth theory is a useful explanation of how monetary expansion works: but note that it describes the aggregate effect across the whole banking system; not the effect within a single bank.

When a bank takes deposits of 100, it can't lend more than that. Indeed, because of the capital requirements placed on banks, it can only lend strictly less than that. That's because the money the bank lends, is going to leave the bank shortly after being loaned: it will get spent on something, and the seller is unlikely to use the same bank as the buyer.

So, because a balance sheet always has to balance, banks can't lend out more than they borrow from savers (plus the amount they borrow from the markets or the Central Bank, plus any equity).

There are differences between a bank's lending rates and its borrowing rates, for several reasons.

1. The bank has to make a surplus (profit), as well as costs such as staff salaries, building maintenance, and so on. So in general, the average lending rate has to be above the average saving rate by an amount to cover all this.

2. The bank can only lend out part of the deposits, so the average lending rate has to be even further above the average saving rate, to cover that too.

3. Although the bank will pay back all of its savers in full, when they ask for their money, not all of its borrowers will repay their full loans: some will go bankrupt, others will default in other ways. So the average lending rate has to be even further above the average savings rate, to cover that too.

4. Banks lend out money on different terms to those on which they accept savings. For example, savings accounts can often be emptied at a moment's notice, or with 90 days notice, or 1 year of notice. So in effect, the bank is borrowing short-term money. Whereas loans and mortgages aren't repaid in such short intervals: they get repaid over months to decades. And usually, the yield curve (yields vs loan duration) curves upwards, which means that longer-term loans carry higher interest rates than shorter-term loans.

• But do banks operate as this? the money multiplier view is that banks create loans from deposits. The endogenous money theory says it does not. What banks do instead is simply to put in assets X for the loan, and then put in their liabilities X for the deposits (which is the money the individual is entitled to, as part of the loan). – user928172 Nov 20 '17 at 13:39
• Those are two ways of looking at the same thing, because a bank's balance sheet always has to balance; and because money - once lent - tends to leave the bank. – 410 gone Nov 20 '17 at 13:42

There are two topics mixed up here and they aren't really "doctrine":

1. On one hand, there's a reserve requirement. This ubiquitous regulation comes from the fact that banks are by their very nature illiquid: if they make a profit by lending other people's money then they can't give all that money back immediately. A minimum of liquid reserves may (or may not!) be established, by the central bank and/or the bank itself, to safeguard deposits.

2. On the other hand, consider that the bank lends all the money he's allowed. The borrowers won't have immediate use of that money, so they store it in the bank once again as deposits. Now, the bank can get those new deposits, fulfill their reserve requirement and lend that money once again. Repeat this to infinity, that is, until 100% of the original money is reserve requirement. Suppose you have 10% of R.R.: $$C_1=100\%-(100*{10\over 100})=90\%\\ C_2=90\%-(90*{10\over 100})=81\%\\ ...\\ C_n=0.9^n\\ \sum_{n=1}^\infty C_n={0.9\over{1-0.9}}=900\%$$ What this means is that, even though the economy has a certain amount of cash, it may behave as if there's more, with an upper bound on 900%. The bank isn't benefiting with money creation except that it's lending more money than at first sight.

The spread neither influence the reserve requirement nor the money supply expansion argument seen above.

• I am confused. If the RR is 100%, the bank cannot lend. Therefore, it cannot pay an interest on deposits, as it has no revenues. The lower RR is, the more the bank can lend, and hence , for a given level of profits, the smaller the spread needs to be? – user928172 Nov 17 '17 at 21:22
• If the RR is 100%, then the bank doesn't have incentives to accept deposits. It can still lend, though: instead of using deposits, it uses its own capital, obtained through some other mean like stock selling, a cheaper loan or past profits. – one_teach_wonder Nov 17 '17 at 21:49
• As for the second part, you are back on track: given an initial amount of money available and a desired profit, there's a spread that solves for that. – one_teach_wonder Nov 17 '17 at 22:01
• There are advocates of 100% reserves. Bank lending has to be funded by instruments other than deposits. The most likely outcome would be that banks would issue money market instruments, and people would buy them via money market funds. Those fund holdings would end up acting like bank deposits now do, other than deposit insurance. – Brian Romanchuk Nov 17 '17 at 23:27