Question

Today you short sell 500 shares of Stock Z, which is trading at $30 per share.  Stock Z does not pay any dividend, and the interest rate is 0%.

(a) The initial margin is 40%.  What is the amount of equity in your account?

(b) A day later you receive a margin call, when the price is $40.  What is the maintenance margin?  (You will not receive a margin call if the price is $39.99.)

(c) When you receive the margin call at $40, you decide to close your account: you cover your short position by buying back 500 shares.  What is your return on equity (ROE) in this short sale?

Answer 1

a) Initial Margin =40% of $30 =$12 per share (note that this is in addition to the money one gets by selling)

Total Margin money deposited =$12 * 500 =$6000

As the Short sale is done today, the initial margin is the same as margin balance =$6000

So Equity today = Total margin balance  

=$6000

b) When the price moves to $40

Total Loss = $10 per share * 500 shares = $5000

Equity = Margin Balance =$ 6000 -$5000 = $1000

Today the value of 500 shares =$40*500 =$20000

So, Maintenance margin = $1000/$20000= 5%

c)When 500 shares are bought back at $40 per share

Total Loss = 500*( 30 - 40) = $5000 on deposit/investment of $6000

Equity = Final Margin balance =$6000 -$5000 =$1000

So, ROE = (Final Equity - Initial Equity) / Initial Equity = ($1000-$6000)/$6000 = -83.33%