A bank had the following balance sheet ($mm) in 2020:

Assets

Business Loans 50

Government Bonds 20

Cash 6

Liabilities

Demand Deposits 16

Time Deposits 45

Inter-Bank Borrowing 11

Equity 4

(Well ignore physical assets, such as real estate, equipment and furniture; as well as other liabilities, such as notes and bonds it has issued.)

Here are the interest rates for the year:

Loans 8%

Bonds 3.5%

Demand deposits 0%

Time deposits 3%

Inter-Bank 4%

I Interest Spread is the average rate earned on interest-bearing assets less the average rate paid on interest-bearing liabilities. Calculate it.

II Net Interest Margin is net interest income (interest received minus interest paid) divided by interest-bearing assets. Calculate it.

III Suppose reserve requirements are 3% for demand deposits and 1% for time deposits. What are the banks Required Reserves? How much Excess Reserves does the bank carry?

IV Suppose capital requirements are 8% for loans and 0.5% for government bonds. What is the banks Required Capital? Is the bank meeting its capital requirements?

V Assume that $10mm of the banks loan portfolio stems from a $12mm credit line to a customer. Drawdowns carry the 8% interest rate, while the unused credit line has a charge of 0.25%.

Assume the bank also earned $120,000 by revising various Trust services. It also incurred $1.3mm in operating cost (salaries, rent, etc.). What is the banks net profit for the year (ignore taxes) and ROE?

VI A banks overall Gap (as opposed to the monthly measure explained in class) calculates the difference between the (average) maturity of its assets and its liabilities. This is a measure of risk, because if, for example, a time deposit matures and the loan that was made with that deposit money does not mature yet, the bank must rollover (issue another deposit) at an interest rate that might be much higher (which compresses, and may even make negative, the interest margin.

Suppose the maturities are as follows:

Loans 1 year

Bonds 2 years

Demand deposits 0

Time deposits 6 months

Inter-Bank debt 3 months

Calculate the Gap by:

multiplying each asset by its maturity and summing them

multiplying each liability by its maturity and summing

subtracting the latter from the former

dividing by total assets