Question

Mr. Sam opened an account to short-sell 50,000 shares of MSFT at $60 per share. Assume that the margin account pays no interest, and that the initial margin requirement was 60%. 1. What is the initial margin invested by Mr. Sam? 2. If after one year, the price of MSFT has risen from $60 to $66, and the stock has paid a dividend of $1 per share. a) What is the remaining margin in the account in dollars and as a percentage? What is the rate of return on the investment? b) If the maintenance margin requirement is 30%. At what price Mr. Sam will receive a margin call?

Answer 1

1. Value of Short Sell contract = 50000 shares* $60/share = $3,000,000

Initial margin required = 60% of $3 million = $1.8 million or $1,800,000

2.  Mr. Sam lost $6 on the price and $1 on the dividend per share on the short sell,

So, total loss = $7/share * 50000 shares = $350,000

a) Remaining margin = $1800000 - $350000 = $1,450,000

Margin % = 1450000/(66*50000) = 43.94%

Rate of Return on Investment = -$350000/1800000 = - 19.44%

b) Let share price be $X when maintenance margin = 30%

Loss on portfolio = (X-60)*50000 + 50000 (dividend)

and remaining margin = 1800000 - (X-60)*50000 - 50000

So, (1750000 - (X-60)*50000)/(50000*X) = 30%

=> (95-X)/X = 0.3

=> X = 95/1.3 = 73.07

So, when the share price reaches $73.07 , there will be a margin call