Question

1. Suppose Jon Snow decides to buy 500 shares of Winterfell, Inc., a climate change research firm. The price of the stock is $60 per share at the time he buys the stock. Jon decides to borrow $10,000 from his broker to help pay for the purchase. The interest rate on the loan is 7%.

1. What is the margin in Jon Snow’s account when he initially purchases the stock? (5 Points)
2. Winterfell announces its statistical models for climate change are flawed and this news causes the stock price to plummet to $35 per share. What is the margin in Jon Snow’s account after this news is announced? Show your calculations. (5 Points)
3. If the maintenance margin requirement is 30%, will Jon receive a margin call? Show your calculations and explain. (5 Points)

4. Assuming he sells the Winterfell shares after the announcement in part (b), what rate of return does Jon Snow receive on his investment? Show your calculations. (5 Points)

5. How does borrowing money from the broker to buy the Winterfell stock affect Jon Snow’s rate of return? In other words, is he better off or worse off in terms of his rate of return from the investment because of borrowing? Show your calculations and explain. (5 Points)

Question doesn't give a time period for the interest rate so I'm assuming it will just be one month or 1

Answer 1

a. margin in the account = value of shares purchased - loan amount

margin in the account = 500*$60 - $10,000 = $30,000 - $10,000 = $20,000

margin % = margin/value of shares purchased = $20,000/$30,000 = 0.6667 or 66.67%

the margin in Jon Snow’s account when he initially purchases the stock is $20,000 or 66.67%.

b. new or current margin = current value of shares - loan amount

new or current margin = 500*$35 - $10,000 = $17,500 - $10,000 = $7,500

margin % = margin/current value of shares = $7,500/$17,500 = 0.4286 or 42.86%

the margin in Jon Snow’s account after this news is announced is $7,500 or 42.86%.

c. new margin % calculated in part b is 42.86% which is higher than maintenance margin requirement of 30%. so, Jon will not receive a margin call.

d. assuming time period of 1 month between purchase and sell of shares.

rate of return on investment = [(sale value - loan amount - interest on loan)/initial margin] - 1

rate of return on investment = [(500*$35 - $10,000 - $10,000*7%/12)/$20,000] - 1

rate of return on investment = [($17,500 - $10,000 - $58.33)/$20,000] - 1 = ($7,441.67/$20,000) - 1 = 0.3720835 - 1 = -0.6279 or -62.79%

Jon Snow receives -62.79% rate of return on his investment.