Exercise Sheet 2

Exercise 2.1A margin account is used to buy 200 shares on margin at $35 per share.

$2000 is borrowed from the broker to complete the purchase. Determine theactual margin:a. When the purchase is made;b. If the price of the stock rises to $45 per share;c. If the price of the stock falls to $30 per share.Solution 2.1a. The value of the purchase is 200� 35 = $7000: The initial margin is

7000� 20007000

� 100 = 71:429%

b. The margin if the stock price rises is

45� 200� 200045� 200 � 100 = 77:778

c. The margin if the stock price falls is

30� 200� 200030� 200 � 100 = 66:667

Exercise 2.2An investor buys 2000 shares at $30 each. The initial margin requirement

is 50% and the maintenance margin is 30%. Show that if the stock price fallsto $25, the investor will not receive a margin call. At what price will a margincall be received?Solution 2.2If the initial margin is 50% then half of the investment is �nanced by a loan

from the broker.The investment costs

2000� 30 = $60000so the loan is $30000. The margin at a price of $25 is

25� 2000� 3000025� 2000 � 100 = 40%

The margin exceeds the maintenance margin so a margin call will not be re-ceived. The highest stock price at which a margin call will be received is

p� 2000� 30000p� 2000 � 100 = 30

A margin call is received at the price

p = $21:429:

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Exercise 2.3600 shares are purchased on the margin at the beginning of the year for $40

per share. The initial margin requirement was 55%. Interest of 10% was paidon the margin loan and no margin call was ever faced. A dividend of $2 pershare is received. Calculate the annual return if:a. The stock are sold for $45 per share at the end of the year;b. If the stock are sold for $25 per share at the end of the year.c. Calculate the return for (a) and (b) if the purchase had been made using

cash instead of on the margin.Solution 2.3The total value of the investment is

600� 40 = $24000:

The initial margin requirement of 55% means that the value of loan from thebroker must satisfy

24000� L24000

� 100 = 55

HenceL = $10800

and the investor uses24000� 10800 = $13200

of their own funds. (Note that $10800 = 0:45� $24000:)a. The return on the investment when the stock are sold at $45 can now be

found as

(45� 600� 10800) + 2� 600� 0:1� 10800� 1320013200

� 100 = 23:636%

b. The return on the investment when the stock are sold at $25 is

(25� 600� 10800) + 2� 600� 0:1� 10800� 1320013200

� 100 = �67:273%

c. Using cash to �nance the investment the returns in the two cases are

45� 600 + 2� 600� 2400024000

� 100 = 17:5%

25� 600 + 2� 600� 2400024000

� 100 = �32:5%

Exercise 2.4Using a margin account, 300 shares are short sold for $30 per share. The

initial margin requirement is 45%.a. If the price of the stock rises to $45 per share, what is the actual margin

in the account?

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b. If the price of the stock falls to $15 per share, what is the actual marginin the account?Is it true that the potential loss on a short sale is in�nite? What is the

maximum return?Solution 2.4The proceeds from the short sale are

300� 30 = $9000:

With an initial margin requirement of 45% the investor has to deposit

9000� 0:45 = $4050

with the broker.a. The actual margin is given by

Actual Margin =Proceeds + Margin Payment - Value

Value� 100

=9000 + 4050� 45� 300

45� 300 � 100

= �3:333

b. The actual margin is given by

Actual Margin =9000 + 4050� 15� 300

15� 300 � 100

= 190

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