Chapter 19 - Selected Quantitative Problems & Solutions
7.
You want to buy 100 shares of a stock currently trading at $50 per share. Your
brokerage firm allows margin sales with a 50% opening margin and a maintenance
margin of 25%. What does this mean?
If you close your position with the shares at $53.50, what is your return?
Solution: The value of the shares you want to purchase is 100  $50  $5,000. With a
50% opening margin, you can give your broker $2,500, and your broker will
lend you the rest.
A 25% maintenance margin means your equity position cannot fall below
25%. The question is how low the price can fall before you must deposit
additional funds. To find this, solve for the price X as follows:
100 X  2500
 0.25, or X $33.33.
100 X
If the price falls below $33.33, a margin call will occur.
If you close your position at a price of $53.50, the value of 100  $53.50 
$5,350, or a gain of $350. Since this only required $2,500 from you, the
percentage gain is 350/2500  14%.
8.
The limit order book for a security is:
Unfilled Limit Orders
Buy
Orders
Sell
Orders
25.12
25.20
25.23
100
500
200
25.36
25.38
25.41
300
200
200
The specialist receives the following, in order:
a. Market order to sell 300 shares
b. Limit order to buy 100 shares at 25.38
c. Limit order to buy 500 shares at 25.30
How, if at all, are these orders filled? What does the limit order book look like after
these orders?
Solution: a. is fulfilled with 200 shares @ 25.23 and 100 shares @ 25.20
b. is fulfilled with 100 shares @ 25.36
c. is not filled, and goes into the book
After these, the book looks like:
Unfilled Limit Orders
Buy
Orders
Sell
Orders
25.12
25.20
25.30
100
400
500
25.36
25.38
25.41
200
200
200
Chapter 20 - Selected Quantitative Problems & Solutions
5. Calculate the duration of a commercial loan. The face value of the loan is $2,000,000. It
requires simple interest yearly, with an APR of 8%. The loan is due in four years. The
current market rate for such loans is 8%.
Solution: The annual interest is 0.08  $2,000,000  $160,000
0
2,000,000
3.577097
1
160,000
148,148
0.074074
2
3
160,000
137,174
0.137174
160,000
127,013
0.19052
4
2,160,000
1,587,664
3.175329
This loan has a duration of 3.57 years.
6. A bank’s balance sheet contains interest-sensitive assets of $280 million and interestsensitive liabilities of $465 million. Calculate the income gap.
Solution: GAP  $280  $465  $185 million
Another way to state this is the bank has a liability-sensitive gap of $185
million.