SECTION I: PROBLEM SOLVING QUESTIONS
1. (10 points) Suppose a banks assets and liabilities have been classified into assets and liabilities that are rate sensitive and those that are not. The data (in millions of dollars) are as follows:
Assets
Liabilities
Rate Sensitive
Short-term securities
35
Rate Sensitive
Variable CDs
20
Variable mortgage
50
Short-term debt
25
Fixed Rate
Long-term securities
5
Fixed Rate
Long-term debt
50
Physical capital
10
Capital (equities)
5
Total
100
Total
100
a) (3 points) Calculate the effect of a decline of interest rates by 3% on bank income. Clearly indicate the direction (sign) of the change and the unit of measurement. SHOW your calculations!
b) (3 points) Calculate the effect of a decline of interest rates by 3% on interest margin. Clearly indicate the direction (sign) of the change and the unit of measurement. SHOW your calculations!
c) (4 points) Supposed the bank management is trying to change the sizes of their assets and liabilities such that the rate change (re decline of interest rates by 3%) produces an interest income of $1.35 million. Fill in the balance sheet to achieve such profit.
Assets
Liabilities
Rate Sensitive
Short-term securities
Rate Sensitive
Variable CDs
Variable mortgage
Short-term debt
Fixed Rate
Long-term securities
Fixed Rate
Long-term debt
Physical capital
Capital (equities)
Total
Total
2. (15 points) XYZ Bank has total asset value of $200 million, and total liability value of $200 million where $20 million is the equity capital. The average duration of the assets is calculated to be 2.5, and the average duration of liabilities is 1.1.
a. (2 points) What is the duration gap for XYZ bank? (Round to two decimal places) Show your calculations!
b. (3 points) What is the change in the market value of net worth as a percentage of assets (?NW/A) if interest rates fall from 6% to 5%? (Round to one decimal place) Show your calculations!
c. (4 points) (Round to one decimal place) Show your calculations!
a. What is the percentage change in the market value of assets (%?A)?
b. What is the dollar change in the market value of assets?
d. (4 points) (Round to one decimal place) Show your calculations!
a. What is the percentage change in the market value of liabilities (%?A)?
b. What is the dollar change in the market value of liabilities?
e. (2) What is the dollar change in the net worth? (Round to one decimal place) Show your calculations!
2. (10 points) One of the ways the Bank of Canada exercises control over the monetary base is through its purchases and sales of government securities in the open market, called open market operations.
a) (3 points) How will a Bank of Canada purchase of $100 of government bonds from banks affect the monetary base? Fill in the following T-accounts in arriving at your answer. Clearly mention what asset and/or liability item will be affected, the direction of the change ((+) or (-)) and the dollar amount of the change.
Banking System
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