Question

You open a margin account at Chas Pigeon, a discount broker. You subsequently short 100
shares of Exciting.com at $300 per share, believing it to be overpriced. This transaction is done
on margin, which has an annual interest rate of 6 percent. Exactly one year later, Exciting has
declined to $60 a share, at which point you cover your short position. You pay brokerage costs of
$25 on each transaction you make. The margin requirement is 50 percent.
(a) Calculate your dollar gross and net gain or loss on this position, taking into account both
the margin interest and the transaction cost to sell. Round your answers to nearest whole
number
(b) Calculate the percentage return on your investment (the amount of money you put up
initially, including the brokerage costs to buy). Round your answers to nearest whole
number

Answer 1

Here Short Selling was Done. Means Sold the stock first at a higher price and later Purchased at Lowe price.

Transaction Cost = Brokerage Cost of Each Transaction * 02 = 25 * 2 = 50 ( Including Selling and Buying)

Market to Market Profit = (Selling Price - Purchase Price) * No of Share =

Selling Price = 300

Purchase Price = 60

No of Share = 100

Market to Market Profit = ( 300 - 60) * 100 = 24,000

Margin Requirement = 50 Percent

Margin Provided by Broker = 100% - Margin Requirement = 100% - 50% = 50%

Dollar Value of Margin Provided by Broker = Margin Provided by Broker * No of Share * Selling Price ( Initial Action of Stock was Short Selling)

= 50% * 100 * 300 = 15,000

Now Interest on Margin = Dollar Value of Margin * Interest Rate * Year = 15,000 * 6% * 01 = 900

So Net Gain = Market to Market Profit - ( Interest on Margin + Transaction Cost) = 24,000 - ( 900 + 50) = 23,050

Ans: dollar gross and net gain =  23,050 (Ans a)

Initial Margin Requirement =Initial Margin * No of Share * Selling Price ( Initial Action of Stock was Short Selling)

= 50% * 100 * 300 = 15,000

Transaction Cost at the time of entering Into Position = Brokerage for Single transaction = 25

Total Amount Invested = Initial Margin Requirement + Transaction Cost at the time of entering Into Position = 15,000 + 25 =15,025

percentage return on investment = Net Gain / Amount Invested

= 23050/ 15025 = 1.5341 = 153.41% `~ 153%

Ans: percentage return on investment = 153% (Ans b)