Question

Molly shorts 100 shares of a non-dividend-paying stock at the initial stock price of $60 per share. She invests the proceeds at the continuously compounded risk-free interest rate of 0.05 in a savings account. She does not make any subsequent withdrawals from or deposits to this account until the short sale is closed. When Molly closes the sort sale, six months later, the stock price is $55. Does she have enough money in the savings account to be able to close the short sale without using additional funds?

Answer 1

Molly has short(Sold) 100 shares of a non-dividend-paying stock at $60 per share.

The proceeds received from the short sale = Share price * No of shares sold

The proceeds received from the short sale = $60 * 100

The proceeds received from the short sale = $6000

Amount received from depositing the proceeds at 5%(Continuously compounded)

Amount in savings account after 6 months = The proceeds received from the short sale * e^{interest rate * time period}

Amount in savings account after 6 months = $6000 * e^{5% * (6/12)}

Amount in savings account after 6 months = $6151.89

Amount required to close out the short sale = Share price after 6 months  * No of Shares purchased

Amount required to close out the short sale = $55 * 100

Amount required to close out the short sale = $5500

Molly has enough funds to close out her position without the need for additional funds since Amount in savings account after 6 months is greater than Amount required to close out the short sale i.e. ($6151.89 > $5500)