formula sheet

Homework 2
Solution Key
Problem 1. Suppose that you sell short 500 shares of Intel, currently selling for $40 per share, and you give your broker $15,000 to establish your margin account. Assume Intel pays no dividends. a) If you earn no interest on the funds in your margin account, what will be your rate of return after one year if Intel stock is selling at (i) $44; (ii) $40; (iii) $36?
The gain or loss on the short position is  500  P . Invested funds are $15,000.
Therefore, your rate of return will be  500  P  / 15000 . The returns in each of the three scenarios are:
(i)
(ii)
(iii)

 500  4 / 15000  13.3%
 500  0 / 15000  0%
 500  (4) / 15000  13.3%

b) If the maintenance margin is 25%, how high can Intel’s price rise before you get a margin call? Total assets in the margin account are $20,000 from the sale of the stock plus $15,000, which was the initial margin. Your liabilities are 500P. A margin call will be issued when
35000  500 P
 .25
500 P
P  56
Problem 2: 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?
You will not receive a margin call. You borrowed $20,000 and with another $20,000 of your own equity you bought 1000 shares of Disney at $40 a share. At $35 a share the market value of the account is $35,000, your equity is $15,000, and the percentage margin is 43%, which is above the required maintenance margin.
b) How low can the price of Disney shares fall before you receive a margin call?
A margin call will be issued when
1000 P  20,000
 .35 , or when P  $30.77
1000 P

Problem 3: Suppose stock X trades on the New York Stock Exchange. Information from the limit order book (LOB) for stock X is contained below.
Limit buy orders
Price
Shares
$80.50