Margin and Short Sale

# Suppose you short sell 100 shares of IBM, now selling at $120 per share.
a) What is your maximum possible loss?
b) What happens to the maximum loss if you simultaneously place a stop-buy order at $128?

a. In principle, potential losses are unbounded, growing directly with increases
in the price of IBM.
b. If the stop-buy order can be filled at $128, the maximum possible loss per
share is $8. If the price of IBM shares goes above $128, then the stop-buy order
would be executed, limiting the losses from the short sale.

# Dee opens a brokerage account and buys 300 shares of IBM at $40 per share. She borrows
$4000 from her broker to help pay for the purchase; The interest rate on the loan is 8%.
a) What is the margin in Dee's account when she first buys the stock?
b) If the stock falls to $30, what is the remaining margin in her account? If the maintenance
margin requirement is 30%, will she receive a margin call?
c)What is the rate of return on her investment?

a. The stock is purchased for: 300 x $40 = $12,000
The amount borrowed is $4,000. Therefore, the investor put up equity, or margin, of $8,000.

b. If the share price falls to $30, then the value of the stock falls to $9,000. By the end of the
year, the amount of the loan owed to the broker grows to:
$4,000 x 1.08 = $4,320
Therefore, the remaining margin in the investor's account is:
$9,000 - $4,320 = $4,680
The percentage margin is now: $4,680/$9,000 = 0.52 = 52%
Therefore, the investor will not receive a margin call.

c. The rate of return on the investment over the year is:
(Ending equity in the account - Initial equity)/Initial equity
= ($4,680  $8,000)/$8,000 = -0.415 = -41.5%



# OET opened a brokerage account to short 1000 shares of IBM. The initial margin
requirement is 50%. A year later, IBM rises from $40-$50 and the stock paid a $2 dividend.
a) What is the remaining margin in the account?
b) If the maintenance margin requirement is 30%, will OET receive a margin call?
c) What is the rate of return on the investment?

a. The initial margin was: 0.50 x 1,000 x $40 = $20,000
As a result of the increase in the stock price Old Economy Traders loses:
$10 x 1,000 = $10,000
Therefore, margin decreases by $10,000. Moreover, Old Economy Traders must pay the
dividend of $2 per share to the lender of the shares, so that the margin in the account
decreases by an additional $2,000. Therefore, the remaining margin is:
$20,000 - $10,000 - $2,000 = $8,000

b. The percentage margin is: $8,000/$50,000 = 0.16 = 16%
So there will be a margin call.

c. The equity in the account decreased from $20,000 to $8,000 in one year, for a rate of
return of: (-$12,000/$20,000) = -0.60 = -60%

# You are bullish on Telecom stock. The current market price is $50 and you have $5000 of
your own to invest. You borrow an additional $5000 from your broker at an interest rate of
8% per year and invest $10,000 in the stock.
a) What will be your rate of return if the price of Telecom stock goes up by 10% during the
next year? Ignore dividends.
b)How far does the price of Telecom stock have to fall for you to get a margin call if the
maintenance margin is 30%? Assume the price fall happens immediately.

a. You buy 200 shares of Telecom for $10,000. These shares increase in value by 10%, or
$1,000. You pay interest of: 0.08 x $5,000 = $400
The rate of return will be:
($1000-$400)/$5000 = 0.12 = 12%

b. The value of the 200 shares is 200P. Equity is (200P - $5,000). You will receive a margin
call when:
(200P - $5000)/200P = 0.30 --> when P = $35.71 or lower

# You are bearish on Telecom and decide to short 100 shares at the current market price of
$50 per share.
a)How much in cash or securities must you put into your brokerage account if the broker's
initial margin requirement is 50% of the value of the short position?
b)How high can the price of the stock go before you get a margin call if the maintenance
margin is 30% of the value of the short position?

a. Initial margin is 50% of $5,000 or $2,500.

b. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for margin).
Liabilities are 100P. Therefore, equity is ($7,500 - 100P). A margin call will be issued when:
($7500 - 100P)/100P = 0.30 --> when P = $57.69 or higher

# You've borrowed $20,000 on margin to buy shares in Disney, which is now selling at $40
per share. Your account starts at the initial margin requirement of 50%. The maintenance
margin is 35%. Two days later, the stock price falls to $35 per share.
a) Will you receive a margin call?
b) How low can the price of Disney shares fall before you receive a margin call?

a. You will not receive a margin call. You borrowed $20,000 and with another $20,000 of
your own equity you bought 1,000 shares of Disney at $40 per share. At $35 per share, the
market value of the stock is $35,000, your equity is $15,000, and the percentage margin is:
$15,000/$35,000 = 42.9%
Your percentage margin exceeds the required maintenance margin.

b. You will receive a margin call when:
(1000P - $20,000)/1000P = 0.35 --> when P = $30.77 or lower





# On Jan 1, you sold short one round lot (100 shares) of Zenith stock at $14 per share. On
March 1, a dividend of $2 per share was paid. On April 1, you covered the short sale by
buying the stock at a price of $9 per share. You paid 50 cents per share in commissions for
each transaction. What is the value of your account on April 1?

The proceeds from the short sale (net of commission) were: ($14 x 100) - $50 = $1,350
A dividend payment of $200 was withdrawn from the account. Covering the short sale at $9
per share cost you (including commission): $900 + $50 = $950
Therefore, the value of your account is equal to the net profit on the transaction:
$1350 - $200 - $950 = $200
Note that your profit ($200) equals (100 shares x profit per share of $2). Your net proceeds
per share was:
$14 selling price of stock
-$9 repurchase price of stock
-$2 dividend per share
-$1 2 trades x $0.50 commission ea.
$2


# FBN Inc has just sold 100,000 shares in an IPO. The underwriter's explicit fees were
$70,000. The offering price for the shares was $50, but immediately upon issue, the share
price jumped to $53.
a) What is your best guess as to the total cost to FBN of the equity issue?
b) Is the entire cost of the underwriting a source of profit to the underwriters?

a. In addition to the explicit fees of $70,000, FBN appears to have paid an implicit price in
underpricing of the IPO. The underpricing is $3 per share, or a total of $300,000, implying
total costs of $370,000.
b. No. The underwriters do not capture the part of the costs corresponding to the
underpricing. The underpricing may be a rational marketing strategy. Without it, the
underwriters would need to spend more resources in order to place the issue with the public.
The underwriters would then need to charge higher explicit fees to the issuing firm. The
issuing firm may be just as well off paying the implicit issuance cost represented by the
underpricing.

# If you place a stop-loss order to sell 100 shares of stock at $55 when the current price is
$62, how much will you receive for each share if the price drops to $50?
a) $50
b) $55
c) $54.87
d) cannot tell from information given

The broker will sell, at current market price, after the first transaction at $55 or less.