The Banking System Made Simple

One of the most popular discussions on the web is banking. Numerous commentators have been commenting on how banks work or how we perceive that they work. These views are occasionally correct while they are also occasionally wrong. In addition, a relative confusion on how bank loans are created or why deposits are needed by the banks appears to exist. What follows are three simple examples intending to indicate how banking really works, how deposits and loans are created and how the Central Bank functions in a financial system.

In all examples, we assume (for simplicity) a closed economy where banks face a mandatory reserve requirement of 10% and a Tier 1 ratio which cannot fall under 10%. It is also assumed that the money needed in the economy for transactions is on average a fixed amount M (already existing in the economy) and all loans have a fixed risk weight of 40%. 

Note: all of the above assumptions can be altered with no change to the conclusions reached.

Example 1:One-Bank Economy

In this economy we have a bank which has in its balance sheet deposits of 100 units of currency with its equity being 10. In period 1 it decides, according to the regulations imposed above, to lend out 90 units. These units, we have just one bank in the economy will be deposited in the banks' accounts. A simple balance sheet would indicate the following:

Then, the bank would continue to operate under the same way until it reached the limit of 10%. This limit is nevertheless not the one imposed by the reserve requirements but by the Tier 1 needs. The reserve requirements would, under these assumptions, allow the amount of loans available in the economy to reach 1000 units had there not been for the Tier 1 ratio which essentially forces the bank to stop at 250 (for more details about the money multiplier see this). The "final" balance sheet would look like this:

Example 2: Two-Bank Economy

Now let's suppose that 2 banks exist in the economy, both having a 50% share of the market. Their equity values would be 5 each and their starting deposits would be 50.

In the first period of time, each bank will lend 45 units to the public. Each bank knows that it controls only 50% of the market thus it makes sense to expect 22.5 of those units to be deposited in its rival. Yet, the total amount of loans in the economy has not been altered even though the banks are now more and lending less individually. Total loans will still be 90 and they will be divided equally between each bank. Thus, each bank now knows that if the other bank lends as much as it will they will both get back in the form of deposits as much currency as they have provided as loans. In addition, the number of banks is irrelevant to the conclusion, as is their market share. If we had 10 or 200 banks in the economy total loans would still be 90 and the market share would have been the same after the lending as it was before. More still, the situation would not have been altered even if market shares were unequal. 

With some frictions, this is what most commonly occurs in real life: as banks do not have the same amount of loan applications or do not grant the same amount of loans in each period of time, market shares are continuously changing. Thus, although banks (usually) want to lend until their Tier 1 limit is reached, they cannot do this as easily (either because of lower demand or because applications do not match the perceived risk-reward profile needed) thus making market shares and loans growing at different paces in every bank. In addition, reputation makes a great difference; banks who were leading the market once are now mere followers as clients view others as better alternatives.

Example 3: Two-Bank Economy with a Central Bank Providing Liquidity

Assuming that the previous initial conditions hold, the situation should theoretically be the same. Yet, reality is different. Since the Central Bank can provide liquidity (what is called ELA in the Eurozone) for banking needs then it means that the banks can allocate their loans based on demand and not based on their liquidity constraints; what the Central Bank essentially does is eliminate the liquidity constraints in the short-run by lending banks. 

The situation would unfold as following: In period 1, banks face increased demand and decide that they should lend 60 units each instead of the 45 they are allowed by their liquidity constraints. This means that the Central Bank has agreed to lend an additional 21 units of currency (additional 10 to cover for the difference from 50 to 60 and another 11 so that they can have their regulatory minimum and not fact trouble in their day-to-day operations) to each bank with the banks promising to return it at a later date. The banks' balance sheets would now look like:

Notice that the Tier 1 ratio was 28% in Example 1's first period while it is 21% now. The reason is simple: more loans can be generated in less time using the Central Banks' available liquidity. 

A question is how the Central Bank will get its money back; after all this funding is nothing but a loan to the bank. Notice now that the bank who received the funding still has received 60 units of capital as deposits back. Now, according to the rules, the bank only has to maintain 11 units (10% of total deposits, i.e. 110) for liquidity. This means that it can afford to give the liquidity back to the Central Bank, hold the regulatory minimum for liquidity and still have 28 units (60-21-11) at hand which it will be able to lend in the next period.  That is if the bank does not get any more funding from the Central Bank to boost its loans.

As with example 2, in reality things are a little different. Banks not only borrow from the Central Bank but from each other as well, since their liquidity is changed every day (as stated before loan grants and demand is unequal between banks) and they may find themselves in need of some extra cash or have some extra liquidity which they prefer to lend out in order to get some interest instead of having it idle.

From the above examples we can derive the following conclusions:

• Deposits matter with regards to liquidity. Yet, they do not matter to the amount of loans to be given. As the balance sheets have indicated loans cancel out since their creation is a simultaneous creation of an asset and a liability. Thus, the bank has no limitation to the amount of loans it can create other than the regulatory capital requirements (e.g. Tier 1)
• The amount of money given by the Central Bank will be returned to it, yet its effect will be permanent. If the Central Bank agrees to give X units of currency to the banks then the money supply will be increased by more than X permanently even if banks return it to the Central Bank. This happens because that money is created by the banks and even if the extra liquidity is returned the amount of loans in the economy would have still been increased.
• The starting value of deposits is irrelevant. It does not matter whether initial deposits were 10 units of 10 million units. The amount of loans to be granted will be exactly equal to the amount allowed by the regulatory requirements and not by the initial state of deposits (obviously, deposits have to be greater than 0 for this to work since the bank cannot print money).
• The more cash at hand and the more government bonds banks purchase the more money supply they can create since both instruments are of zero risk weight and are thus excluded from the calculation.
• Increased regulatory requirements at a given amount of equity, means that less loans can be created, thus making money supply will in general be less; an increase in the regulatory requirement (e.g. from 10% to 11%) means that ceteris paribus less new loans will be created in the future. This situation is evident in the EU at the moment.
• The only way for money supply to be increased is for banks to raise more equity. If it is raised then more money can be created in the economy.

As the reader has seen through this analysis, the way banking works is not as complicated as we usually think it is. Nevertheless, understanding how the banking system works is paramount to the economy and has been an issue which had received much less attention than it should have. As stated above, the examples can be very easily extended to include more complexity; yet understanding the larger image can most of the times provide us with more knowledge than by narrowing our focus to the specifics of banking.