Overview
Loan pricing is the process of determing an interest rate to charge a loan in order to satisify the shareholders of the bank. In order to demonstrate the principle, we do the calculations for the following simple bank which has one loan for $100 and is funded by $5 equity and $95 of other sources of funding.
| Assets | Loans |
| Loan 100 | Interbank Funding $90 @ 3% |
| Debt $5 @ 5% | |
| Equity $5 |
Given the funding above, the bank is paying
{% $ 2.95 = 90 \times 0.03 + 5 \times 0.05 %}
in interest charges. This means that the loan rate has to be at least {% 2.95 \% %}.
Cost of Equity
The cost of equity is the return that the equity markets expect from the bank in order to justify the current equity price. That is, if the bank returns a higher rate, then the stock price is expected to rise, and if the bank fails the hurdle the cost of equity, the stock price is expected to decline.
(Note, expectation is here meant to mean a statistical expectation)
In the example given above, we assume that the cost of equity is {% 10 %}. Then, the loan needs to generate
{% $ 3.45 = 90 \times 0.03 + 5 \times 0.05 + 5 \times 0.1 %}
That is, in this simple example, the bank needs to charge a rate of {% 3.45 \% %} in order to cover its funding costs and
hurdle the cost of equity.
Credit Risk
The example given above gives the basic framework for calculating a loan price that is consistent with the banks current stock price. The example omits any discussion of credit risk.
- Current Expected Credit Losses is the expected amount of loss that occurs due to the credit risk of the loan. Typically, this amount is considered to be an exepense in the same way that the interest paid on funding is an expense. (see Current Expected Credit Losses )
- Economic Capital - is an calculation of the amount of equity that needs to be held in order to protect against the unexpected portion of loan loss from credit risk. (That is the amount of loss over and above the expectation, i.e. the current exptected credit loss) (see economic capital)
Summary
As a final term, the operational expense incurred to originate or service the loan is included, yielding a final formula
{% r_{equity} = \frac{(Income - IntExp - CECL - OpExp - Lqt - Option)(1 - r_{tax})}{capital} %}
- {% r_{tax} %} - corporate tax rate
- {% r_{equity} %} - the rate of equity return produced by the current loan
- {% Income %} - the income being generated by the loan
- {% IntExp %} - expense paid to service the loan funding
- {% CECL %} - Current Expected Credit Losses
- {% OpExp %} - allocated operational expense that the bank incurs to orgininate and service the loan. Operational expense per loan is usually calculated using a cost allocation methodology.
- {% Lqt %} - liquidity charge. A charge against the loan for taking liquidity risk.
- {% Option %} - a charge for any optionality in the loan, such as prepayment optionality
- {% Capital %} - either an economic capital figure, or the allocated equity
The formula can be turned around in order to calculate the amount of income the loan should generate in order to hurdle the return on equity. (the loan rate will then be the income divided by the principal)
{% Loan \; Income = \frac{r_{equity} \times capital}{1- r_{tax}} + IntExp + CECL + OpExp + CECL + Option + Lqt %}
Topics
- Interest Expense and Funding - details a treatment of the loan funding and the interest expense charged to the loan.
- Bank Performance Attribution
- Sample Implementation