Thoughts on Banking: An Example
My earlier post left people confused. Let me give an example to clarify my model of financial intermediation with no information asymmetries. We plant fruit trees this year. The total cost to plant them is $5 million. Next year, there is a 60 percent chance the trees will be worth $10 million and a 40 percent chance that they will be worth $1.1 million. The one-year, risk-free interest rate is, say, 10 percent. I’ll wave my hands about where that interest rate comes from.
The trees are financed with $4 million in equity, held in a mutual fund, and $1 million in debt. There cannot be more than $1 million in debt, because there are no information asymmetries, so that everybody knows that more than $1 million in debt would be a false promise.
A mutual fund handles all of the equity. People who are willing to take risk take lots of equity. Others prefer debt.
At the initial probabilities, the expected value of the trees in one year is 0.6 times $10 plus 0.4 times 1.1, or $6.44 million. Subtracting the value of the debt, the expected future value of the equity is $5.44 million. Its present value is $4.0 million, because of the combination of the discount rate of 10 percent and a risk premium of about 20 percent. I’ll wave my hands about where the risk premium comes from.
Every day brings new information about the probability of success. If the probability of a good outcome goes up, the value of the equity goes up. If the probability goes down, the value of the equity goes down. For example, if the first day the probability of success gets revised down from 0.6 to 0.3, the future value of the equity becomes $3.77 million. The present value, risk-adjusted, might be about $2.8 million.
A bank handles everyone’s accounts. Fruit is the medium of exchange and a store of value. The dollar is the unit of account. People can have either positive or negative balances at the bank. Those with positive balances earn instantaneous interest that works out to 10 percent at an annual rate. Those with negative balances pay 10 percent interest. Every instant, balances change, and new interest is calculated. The bank collects fees to cover its costs. All of this is risk-free. The bank makes no economic profit and need not fear a loss.
After the negative balances of some people have been netted against the positive balances of other people, the total positive balance in the bank will be $1 million, which is the amount of risk-free debt that can exist in this economy. After one year, nobody will have a negative balance. All loans will be paid off, either before or at that time.
The entrepreneurs who own fruit trees are the ones who owe the net $1 million. (If the bank includes their debt in its accounts, then the bank shows a net balance of zero.) The entrepreneurs are sure to be able to repay this loan. Consumers who have equity in fruit trees can borrow against that equity from other consumers who have more fruit than they wish to consume. However, they can only borrow for an instant, and they can borrow no more than the minimum possible value for their equity in the next instant.
For example, suppose that I have $100 in equity, but it could lose 15 percent of its value in an instant. In that case, I can only borrow $85 for an instant. Of course, if my equity retains its value or appreciates for a while, then I can roll over my loan, or even take out a bigger loan.
Perhaps the right way to think about this bank is to treat it as having no assets and no liabilities. It is simply a broker/accountant for the principals in the economy. If there were no bank, people would lend to one another. If there were no bank, the debt of the fruit tree entrepreneurs to lenders would be recorded in some other accounting book. Maybe calling this institution a bank is what is confusing–you tend to want to attribute to it properties of real-world banks that are not appropriate for this bank.
Truly,all the action in the economy is in the mutual fund. Each instant between now and when the fruit trees mature, new information arrives about probabilities of success. This new information changes the value of the mutual fund. That in turn changes people’s consumption paths. If the news is good, people are more willing to consume during the year and risk having less to eat when the trees mature. If the news is bad, people worry more about not having enough to eat when the trees mature, so they cut back on consumption today.
The point of all this is that in an economy with no information asymmetries, financial institutions are pretty trivial. You cannot have a financial institution that introduces new risk into the economy, unless there are people who enjoy gambling–in which case you would get a casino, not a bank or mutual fund. You can only have financial institutions that can fail or debt contracts that might not be honored if there is asymmetric information. In the earlier post, I tried to explain how default-able debt or banks that might fail can arise when there is asymmetric information.
The information asymmetry might be real–Sue knows more than Fred about something real in the economy. Or it might be due to bias or irrationality–Sue thinks she knows more than Fred, but she really doesn’t, and Fred takes advantage of her. I actually think that a lot of real-world financial institutions exploit the latter type of information problem.