BUS 322: Financial Markets and Institutions
Homework 3 (due 4/15/2010)
Solution
Part 1 – Individual Part
Chapter 8 – Quantitative Problems: 3, 4
Chapter 17 – Quantitative Problems: 2, 5, 7, 8
Chapter 24 – Quantitative Problems: 1, 3, 9, 11
Chapter 25 – Quantitative Problems: 2, 7, 8, 12
________________________________________
Chapter 8 – Quantitative Problems: 3, 4
3.
The Federal Reserve wants to increase the supply of reserves, so it purchases $1 million
dollars worth of bonds from the public. Show the effect of this open market operation using
T-accounts.
Answer:
Banking System
Assets
Liabilities
$1 million
Reserves
Checkable Deposits
$1 million
Federal Reserve System
Assets
$1 million
Securities
4.
Liabilities
$1 million
Reserves
Use T-Accounts to show the effect of the Federal Reserve being paid back a $500,000
discount loan from a bank.
Answer:
Banking System
Assets
Liabilities
$500,000
Reserves
Discount Loans
$500,000
Federal Reserve System
Assets
Discount Loans
$500,000
Liabilities
Reserves
$500,000
Chapter 17 – Quantitative Problems: 2, 5, 7, 8
2. X-Bank reported an ROE of 15% and an ROA of 1%. How well capitalized in this bank?
Solution: ROE  ROA  EM
0.15  0.01  EM
EM  15  assets/equity
So equity/assets  6.66%.
5. For the upcoming week, Nobel National Bank plans to issue $25 million in mortgages and
purchase $100 million 31-day T-bills. New deposits of $35 million are expected, and other
sources will generated $15 million in cash. What is Nobel’s estimate of funds needed?
Solution: $25 M  $100 M  $35 M  $15 M  $75 M
7.
NewBank started its first day of operations with $6 million in capital. $100 million in
checkable deposits is received. The bank issues a $25 million commercial loan and another
$25 million in mortgages, with the following terms:
 mortgages; 100 standard 30-year, fixed-rate with a nominal annual rate of 5.25% each
for $250,000.
 commercial loan: 3-year loan, simple interest paid monthly at 0.75%/month.
If required reserves are 8%, what does the bank balance sheets look like? Ignore any
loan loss reserves.
Solution:
Assets
Liabilities
Required Reserves
Excess Reserves
Loans
8.
$ 8 million
$48 million
$50 million
Checkable Deposits
Bank Capital
$100 million
$ 6 million
NewBank decides to invest $45 million in 30-day T-bills. The T-bills are currently trading at
$4,986.70 (including commissions) for a $5,000 face value instrument. How many do they
purchase? What does the balance sheet look like?
Solution: The bank can purchase $45 M/$4,986.70, which is about 9,024 T-bills. The actual
cost is $44,999,980.80.
After the transaction, the balance sheet is:
Assets
Required Reserves
Excess Reserves
T-bills
Loans
Liabilities
$ 8 million
$ 3 million
$45 million
$50 million
Checkable Deposits
Bank Capital
$100 million
$ 6 million
Chapter 24 – Quantitative Problems: 1, 3, 9, 11
1.
A bank issues a $100,000 variable-rate, 30-year mortgage with a nominal annual rate of
4.5%. If the required rate drops to 4.0% after the first six months, what is the impact on the
interest income for the first 12 months? (Don’t worry about this question)
3.
Calculate the duration of a $100,000 fixed-rate, 30-year mortgage with a nominal annual
rate of 7.0%. What is the expected percentage change in value if the required rate drops to
6.5% immediately after the mortgage is issued?
Solution: The duration calculation should be completed using a spreadsheet. Although the
technique is the same, there are 360 months to handle. Doing this, the duration
can be calculated as 10.15 years.
P
i
  Duration 
 10.15  (0.005/1.07)  4.74%
P
1 i
9.
The following financial statement is for the current year. From the past, you know that 10%
of fixed-rate mortgages prepay each year. You also estimate that 10% of checkable deposits
and 20% of savings accounts are rate sensitive.
Second National Bank
Assets
Reserves
Securities
 1 Year
1 to 2 Years
 2 years
Residential Mortgages
Variables-rate
Fixed-rate
Commercial Loans
 1 Year
1 to 2 Years
 2 years
Buildings, etc.
Total
Liabilities
$ 1,500,000
$ 6,000,000
$ 8,000,000
$ 12,000,000
$ 7,000,000
$ 13,000,000
$
$
$
$
1,500,000
18,500,000
30,000,000
2,500,000
$100,000,000
Checkable Deposits
Money Market Deposits
Savings Accounts
CDs
Variables-rate
 1 Year
1 to 2 Years
 2 years
Fed funds
Borrowings
 1 Year
1 to 2 Years
 2 years
Bank Capital
$ 15,000,000
$ 5,500,000
$ 8,000,000
Total
$100,000,000
$
$
$
$
$
15,000,000
22,000,000
5,000,000
2,500,000
5,000,000
$
$
$
$
12,000,000
3,000,000
2,000,000
5,000,000
What is the current Income GAP for Second National Bank? What will happen to the bank’s
current net interest income if rates fall by 75 basis points?
Solution: RSA  6 M  7 M  (0.10  13 M)  1.5 M  $15.8 million
RSL  (0.10  15 M)  5.5 M  (0.20  8 M)  15 M  22 M  5 M  12 M
$62.6 million
GAP  $15.8 million  $62.6 million
GAP  $46.8 million
I 46.8 million  (0.0075)
$351,000
11. A bank added a bond to its retained portfolio. The bond has a duration of 12.3 years and cost
$1,109. Just after buying the bond, the bank discovered that market interest rates are
expected to rise from 8% to 8.75%. What is the expected change in the bond’s value?
Solution:
P
i
 Duration 
P
1 i
0.0075
P  12.3 
 $1,109  $94.73
1  0.08
Chapter 25 – Quantitative Problems: 2, 7, 8, 12
(Don’t worry about this for exam 3.)
2.
You would enter into a contract that specifies that you will sell the $25 million of 8s of 2015
at a price of 110 one year from now.
7. The put option is out of the money because you would not want to take the option to sell the
futures at 95 when the price at expiration is 120. Since the premium is $4,000 and you did
not exercise the contract, your loss on the contract is $4,000.
8. You have a profit of 1 point ($1000) when you exercise the contract, but you have paid a
premium of $1500 for the call option, so your net profit is $500, a loss of $500.
12. You would hedge the risk by buying 80 euro futures contracts that mature 3 months from
now.