Unit 6 The financial sector: Debt, money, and financial markets
6.4 Introducing a bank
As a first step towards understanding the role of the financial sector, we introduce a bank into the example of Marco and Julia, and examine what happens if, instead of agreeing a bilateral debt contract, they save and borrow at a bank.
A model with Julia, Marco, and a bank
There are now three actors in the model: Julia, Marco, and the bank owner. As before, there are two periods; initially Marco has 100 units of grain (the only good) and Julia has no wealth. There is no government or central bank, and no currency.
The bank accepts deposits and makes loans in the form of grain. In addition:
- equity
- Shares (stocks) in a business are known collectively as equity. The total value of the equity held by the shareholders is equal to the net worth of the business, and an individual shareholder’s equity in the business is the total value of the shares they own. The term equity is also used more generally for a share of ownership of any asset, and for the net worth of any household, business, or project. There is a second entirely different use of the term, meaning fairness, as in ‘an equitable division of the pie’. See also: net worth.
- The bank has ten units of grain stored in its strongroom. In this example, this grain is equal to the owner’s initial equity in the bank.
In Section 6.3, we noted that the term ‘equities’ is often used as an alternative to ‘shares’, reflecting the fact that the shareholders in a company collectively own everything the company owns. Here, there is assumed to be a single shareholder.
How can Marco and Julia use services provided by the bank to achieve their objectives?
- Marco can save 50 units of grain by depositing it at the bank in period 1. In other words, he can lend 50 units to the bank at the rate of interest it offers on deposits, and withdraw it for consumption in period 2.
- Julia can borrow 50 units of grain from the bank in period 1, at the rate of interest at which the bank lends. She can consume, invest, and produce grain just as before, and repay the bank in period 2.
This is our first example of financial intermediation. The bank owner acts as an intermediary between Julia and Marco, simultaneously borrowing grain from Marco and lending to Julia. The bank will make a profit if the interest rate Julia pays on her loan is greater than the interest rate on Marco’s deposit, and the owner will receive any profits obtained.
The bank’s balance sheet
We can use balance sheets to summarize the bank’s interactions with its customers (Julia and Marco). Initially the bank has one asset—grain reserves of ten units—and no liabilities. Its net worth is ten, which means the single owner of this bank owns ten units of grain.
Figure 6.7 shows the bank’s balance sheet after Marco has deposited 50 units, and the bank has lent 50 to Julia. Marco’s deposit now appears on the right-hand side of the bank’s balance sheet, as a liability: it is a debt owed by the bank, which must be repaid in future. The loan to Julia is on the left: this is an asset for the bank, since she has promised to repay it later.
| Bank’s balance sheet | ||
|---|---|---|
| Assets | Liabilities | |
| Marco’s deposit | 50 | |
| Loan to Julia | 50 | |
| Grain (in strongroom) | 10 | |
| Total | 60 | 50 |
| Net worth (‘equity’) | 10 | |
Figure 6.7 The balance sheet of the bank as an intermediary between Julia and Marco.
The only other asset of this bank is its grain reserves. What we would find in the bank would be a strongroom containing grain, and detailed records of loans (its other assets) and deposits (its liabilities) expressed in units of grain.
Note one key feature of this balance sheet. The bank started out with equity of ten units of grain. After the deposit and the loan, the net worth of the bank (hence the ‘equity’, owned by the owner of the bank) is unchanged, because the bank’s liabilities and its assets have risen precisely in line.
This very simple example also shows an important feature of banks: their net worth is typically small relative to their assets. Unlike other businesses, they have liabilities that are almost as big as their assets.
Grain is still the only good. So it is not only consumed and invested; it continues to play two other roles in the model:
- Grain is again the unit of account. The value of the bank’s liabilities (what it owes to Marco), and its assets (its loan to Julia) are measured in grain.
- At this stage, we are still assuming that borrowing and lending take place using grain. To make a deposit, Marco walks into the bank with sacks of grain. The bank in turn, when it lends to Julia, does so by handing over grain to Julia, again in exchange for her promise to repay (in the form of a loan contract).
The bank in our model is still some way away from an actual bank. But we shall address both these features as we build on the model later in the unit.
Question 6.6 Choose the correct answer(s)
Suppose that Marco and Julia are the only customers of a bank. The bank starts with ten units of grain. Marco deposits 53 units of grain and Julia borrows 48 units. Based on this information, read the following statements and draw up the bank’s new balance sheet. Using the balance sheet, choose the correct option(s).
- Marco will hand over 53 units of grain to the bank, but the bank will lend out 48 units of grain to Julia. So its holdings of grain will increase by five units to 15 units and its assets increase by 53 (48 units of grain which is the loan to Julia and five additional units of grain for its strongroom).
- The bank’s assets are now 63: its initial grain holdings (ten units), plus the loan of 48 to Julia, plus five additional units of grain (the remainder of Marco’s deposit, not lent out).
- The bank now owes Marco 53 units of grain.
- The bank’s net worth remains unchanged; its assets and liabilities have both increased by 48.
Back to Julia and Marco’s balance sheets
When Marco and Julia use the bank to save and borrow 50 units of grain, their balance sheets look similar to those for the bilateral loan contract. Work through Figure 6.8 to analyse the balance sheets of all three actors together.
Since we are introducing many new terms in this unit, we again simplify by focusing on a narrow slice of the economy. You may ask what the bank’s owner consumes in the first period, for example. You can assume that they are engaged in lending and borrowing with other households in the economy and receive a return from providing that service, which enables them to consume in both periods. The bank only gets a profit from its transactions with Julia and Marco in the second period.
The outcome in the second period
What happens in the second period is also similar to the outcome of the bilateral loan contract. At the beginning of period 2, Julia harvests the grain she has produced from her investment in period 1, repays the bank (with interest), and consumes the remaining grain. The bank pays interest to Marco, and Marco withdraws the original deposit (plus interest), and consumes the grain. But in addition, depending on the interest rates on the loan and deposit, the bank will hope to make a profit.
Suppose the bank offers 6% interest on deposits, and lends at 10%. As in Figure 6.4 under the bilateral contract, we assume that Julia invests 30 units of the grain she borrows, and produces 90 units in the second period, and that she then fulfils her promise to pay 55 units back to the bank (her original loan plus interest) and Marco can withdraw 53 units from the bank (his deposit plus interest). Figure 6.9 shows what happens to the grain in this case. The bank’s profit is two units of grain—the difference between the amounts of interest received and paid out.
| If Marco deposits 50 units at a 6% interest rate, and Julia borrows 50 units at a 10% interest rate | |||||
|---|---|---|---|---|---|
| Grain | Marco consumes | Julia consumes | Julia invests | Bank’s profit | |
| Marco’s grain in period 1 | 100 | 50 | 20 | 30 | 0 |
| Julia’s output in period 2 | 90 | 53 | 35 | 2 | |
Figure 6.9 Saving and lending at the bank: what happens to Marco’s 100 units of grain.
The bank’s profit and net worth in the second period
Commercial banks are capitalist firms—that is to say, companies in the private sector (although in many countries they may be owned directly or indirectly by the government). So they aim to make profit. The bank receives a return on its lending (the majority of its assets); and pays its customers a return on their deposits (the bank’s liabilities).
Remember that the rate of interest on a loan is defined:
\[\text{rate of interest} = \frac{\text{extra amount borrower promises to pay back}}{\text{loan}}\]Continuing to assume, as we have done so far in our model of Marco and Julia, that the borrower will repay the loan as promised, the lender’s revenue on a loan is the interest rate multiplied by the loan. For the bank:
\[\begin{align*} \text{revenues from lending} &= \text{interest rate on loans} \times \text{total lending} \\ \text{payments to depositors} &= \text{interest rate on deposits} \times \text{total deposits} \end{align*}\]and (ignoring other assets and costs) we can express its overall profit as:
\[\begin{align*} \text{profit} &= \text{revenues} \ – \ \text{costs} \\ &= \text{revenues from lending } – \text{ payments to depositors} \end{align*}\]Since a bank’s liabilities are almost as high as its assets (net worth is small relative to total assets), total deposits are approximately equal to total lending, and hence, in general:
\[\text{profit} \approx (\text{interest rate on loans} − \text{interest rate on deposits}) \times \text{total lending}\]In our example, this expression holds exactly since the bank’s loans are equal to their deposits, and the bank’s only other asset, grain, pays no interest, so the bank’s profit in Figure 6.9 is \((10\% \text{ } – \text{ } 6\%) × 50 = 2\). This expression for profit is useful because it illustrates that banks will increase profit:
- the more they lend, and
- the bigger the gap between the interest rates on assets and liabilities.
What about net worth?
At the point where the bank makes the loan and takes the deposit, this has no effect at all on net worth in the first period. So why should the bank bother?
The answer is that in the next period, if the bank makes a profit, then its net worth will increase. Therefore, using the numbers in Figure 6.9, the bank starts out with equity = net worth = 10 units of grain. In the second period, once Julia has repaid her loan, if, as in Figure 6.9, we assume that the bank simply repays Marco’s deposit, it would have an extra two units of grain, so its net worth, which is equal to the equity of the bank’s owner, will increase to 12 units.
Of course, actual banks do not simply close up their operations after a single period, as happens in our stylised two-period model. They will usually make new loans or accept new deposits, or roll over existing loans and deposits, on which they would hope to make a profit in the next period. This is why, in calculating revenues and costs, we ignored the repayment of the loan and the deposit, which in any case in this example are exactly equal, and hence exactly offset each other.
But remember, these outcomes for profits and net worth arose under that assumption that loans are always repaid. What happens if they aren’t?
Default, risk, and the bank’s expected returns
If Marco and Julia could choose between a bilateral debt contract and using the bank to borrow and save, which would they prefer?
Under the assumptions we have made so far, we might expect them to prefer bilateral debt, because the bank would want to make a profit from them by setting a higher interest rate on loans than deposits. If the bank is offering 10% on loans and 6% on deposits, Marco and Julia could in principle do better by cutting out the ‘middleman’—that is, the bank—and agreeing on a bilateral loan at 8% interest. But an obvious problem with bilateral debt is that any individual Marco may not meet a Julia who wants to borrow exactly the amount he wants to lend.
But there are two distinct reasons why Marco, in particular, may prefer to lend to a bank. The first is that in a world of multiple Marcos and Julias, any individual Marco may not meet a Julia who wants to borrow exactly the amount he wants to lend. The second is that even if a bilateral debt contract for the exact amount were available, we need to consider the risk involved in making a loan.
To understand why they might prefer the bank, even if a bilateral debt contract was available, we need to consider the risk involved in making a loan.
- default
- A borrower who fails to repay a loan, or repays less than is required under the contract, is said to default on the loan. More generally, any failure to meet the terms of a contract can be described as a default.
- rate of return
- The rate of return on a loan, or any investment, is the net amount the lender or investor gets back (that is, the total amount minus what they lent or put in) as a proportion of what they put in.
In practice, there is always a risk that a borrower will default: that is, repay less than the loan contract specifies. For Julia, bad weather may damage her crop of grain, leaving her unable to repay in full. If the crop were completely destroyed, she would pay back nothing at all; then the lender (either Marco or the bank) would make a loss equal to the full amount of the loan.
When there is a possibility of default, the profit on the loan will depend on how much the borrower actually repays. So we define the rate of return on a loan as:
\[\text{rate of return on loans} = \frac{\text{total amount borrower actually pays back − loan}}{\text{loan}}\]This formula tells us that if the borrower repays in full, with interest, then the rate of return on a loan is equal to the interest rate on lending, but otherwise it is lower. In the most extreme case, if the borrower does not pay back anything at all, then the rate of return is equal to –1 (or –100% in percentage terms), which means that the lender loses the entire value of the initial loan.
The lender’s revenues therefore depend on the rate of return:
\[\text{revenues from lending} = \text{rate of return} \times \text{loan}\]If the borrower repays fully, the rate of return on a loan is equal to the interest rate on lending; but otherwise it is lower.
- diversify, diversification
- An individual, bank, or company that holds risky assets can reduce the overall risk to their wealth by diversifying: that is, holding a diverse range of risky assets. Although some of their assets will generate low (or negative) profits, the profits on others will be high, with the result that they make a reasonable profit on average.
The lender in a bilateral loan contract therefore faces a lot of risk: Marco’s return from lending directly to Julia could be anything from a gain equal to the full amount of interest, to a loss of the full amount of the loan. However banks are able to ‘spread the risk’ by diversifying: in other words, ‘not putting all their eggs in one basket’. If the bank in our model lends to many different borrowers like Julia at the same time (‘Julias’), it knows that some of them will be unlucky with the weather, but also that most will repay.
Suppose, for example, that the bank estimates that only 90% of Julias will repay in full, while 10% will lose the whole of their crop and will repay nothing. For reasons that will shortly become evident, we assume that the bank sets an interest rate of 20%, distinctly higher than the 10% rate we previously assumed. Then it can be fairly confident that on 90% of its loans it will get back what it lends, plus interest, but on the remainder it will get nothing. As a result the expected amount it will get back on the average loan will be
\[(0.9 \times 1.2 \times \text{loan}) + (0.1 \times 0) = 1.08 \times \text{loan}\]This formula implies an expected return of just 8%, which is well below the interest rate of 20%. While its actual rate of return on its portfolio of loans may be a little higher or lower than the expected return, the bank faces much less risk—less variability—than a lender in a bilateral contract. And, assuming that the loans are to individuals whose risks are not correlated, the more it lends, the less variable is the overall return on lending.
For other examples of how to calculate expected values when outcomes are uncertain, read Extension 4.12 in the microeconomics volume.
- default premium
- If there is a risk that borrower will default on a loan, the lender may still be prepared to lend if the interest rate is higher than it would be without this risk. The difference between the two rates is the default premium.
Given the rate of interest, the higher the probability of default is, the lower the expected return is. So, as in our numerical example, when they make loans to borrowers whose probability of default is believed to be high, lenders typically set a higher interest rate—they raise the interest rate for these borrowers by adding a default premium.
Section 9.1 of the microeconomics volume describes the case of the moneylenders in Chambar, Pakistan, who offer loans to farmers at an interest rate of around 78%.
In summary, the reduction in risk from diversification means that all three actors in the model can benefit from the bank acting as an intermediary, provided that Marco is certain to get back his deposits.
Default risk and insolvency
- capital adequacy requirements
- At both the national and international level, regulators require banks to hold a minimum amount of equity or capital relative to their assets. The objective of this regulation is to reduce risk-taking by banks. If unregulated, banks, believing they are too large or too interconnected to be allowed to fail, may take excessive risks and impose costs on society were they either to fail or to be rescued. Regulators assess the riskiness of a bank’s assets (its loans) and specify the capital that must be held relative to their risk-weighted assets.
In practice, most of us can and do assume that banks are a safe way to save. The main source of risk to our savings is that the bank’s borrowers may default. Diversified lending reduces this risk. However, since banks cannot be certain, despite diversification, about the proportion of loans that will be repaid, they are obliged by law to have sufficient equity or net worth (also referred to as ‘capital adequacy requirements’) to meet their liabilities if the return on loans is lower than expected.
In our model, we have assumed that the bank’s owner has ten units of equity (the bank’s net worth). As recorded in the balance sheet of the bank, its net worth is equal to the value of its assets (its loans plus its grain holdings) minus the value of its liabilities (what it owes Marco). So a fall in the value of its loans due to a poor harvest may mean that the only way Marco can be repaid in full is for the bank to repay him with some of its own grain, thereby reducing its equity.
Even when banks have the regulatory minimum amount of net worth (equity), it is still possible for there to be a banking crisis if large numbers of borrowers are unable to repay their loans. A bank in which liabilities exceed its total assets is insolvent, and cannot continue to operate. When this happens, typically the government steps in—an issue we shall come back to in Section 6.10, and also discuss in Unit 8.
Withdrawing deposits on demand: The liquidity risk of a bank
One of the ways that actual banks attract depositors is by guaranteeing that current account deposits are not only risk-free, but also liquid: they can be withdrawn on demand. This exposes banks to a second source of risk: liquidity risk as well as default risk. Liquidity risk reflects another difference between a bank’s assets and its liabilities. Deposits are liquid but loans, like the one to Julia in the model or a mortgage loan today, are likely to be illiquid—the bank cannot just demand that a loan be repaid in full whenever it wishes.
Hence such deposits are also referred to as ‘demand deposits’. In contrast, deposits in savings accounts, which usually pay a higher interest rate, may be tied up for a fixed period, or may be withdrawn only with an interest penalty.
- bank run
- A situation in which depositors withdraw funds from a bank because they fear that it may go bankrupt and not honour its liabilities (that is, not repay the funds owed to depositors).
Suppose now that the bank in our model allows its depositors to withdraw its deposits in full in grain, at any time, and that Marco is a typical depositor. The balance sheet in Figure 6.7 shows that the bank simply will not have enough grain to repay all its depositors immediately. Knowing this, individuals like Marco in the model may decide to withdraw their deposits, causing a self-fulfilling bank run to take place. The logic of a self-fulfilling bank run is straightforward: suppose something triggers a panic about the bank. Because the depositor at the front of the queue will certainly get some of their deposit back, there is an incentive to be the first to withdraw if there is a danger that everyone will do so. No one wants to be last in the queue. This is enough to produce a run on a bank even if its net worth is positive. A solvent bank can be illiquid because of a panic among depositors.
- mortgage (or mortgage loan)
- A loan contracted by households and businesses to purchase a property without paying the total value at one time. Over a period of many years, the borrower repays the loan, plus interest. The debt is secured by the property itself, referred to as collateral. See also: collateral.
Going beyond our model, this feature of illiquidity of loans is particularly the case if the bank has lent in the form of mortgages that have been used to buy houses, which are often repaid over several years or even decades, or if it has made a long-term loan to a firm. In such cases, we refer to a ‘maturity mismatch’ between assets, with loans that will be paid back only in the long term, and deposit liabilities that the bank must be able to repay immediately.
The run on Silicon Valley Bank in 2023 was unusual because the size of many deposits (many clients were tech entrepreneurs) was larger than the value covered by the US deposit guarantee scheme.
During the nineteenth and early twentieth centuries, bank runs were quite frequent events. To understand why bank runs have become less of a problem, we need to bring in the government, which we do in the next sections. For now, we can say that it is generally agreed among economists that the introduction of government-sponsored schemes that guarantee bank deposits up to a certain value, coupled with regulations that require banks to hold a minimum share of liquid assets (a topic we come back to in Section 6.8), has been sufficient to prevent bank runs being a major problem. While a few bank runs did take place during the global financial crisis of 2007–2009, very few, if any, depositors actually lost out.
