Problem 2 (50) Anna is an active stock trader, and she believes that big tech firms will continue to grow in next year. So, she contacts her broker and purchases 1000 shares of FACEBOOK (FB) at the price: $200 per share. The initial margin requirement of her account is 50%, and she borrows as much as the requirement allows. The maintenance margin is set to be 30%. Her broker charges her a 2.4% per annum margin loan interest rate (meaning if she borrows $100 for 12 months, overall she has to pay back $102.4). Assume her broker records margin loan interests every month, meaning if her position is not closed by the end of every month, margin loan interests charge is incurred. A) (5) Please write down how much margin loan Anna borrows to finance her stock purchase at the beginning? B) (5) Anna only cares about month-to-month price variation. Assume her broker assumes simple returns when calculating a monthly margin loan rate. What is the monthly margin loan rate? C) (10') Assume after one month, FB's price rises to $230. If at this moment she decides to close her position, what's the return on investment she will gain? D) (10') Assume after one month, FB's price drops to $180. Please calculate the margin of her account E) (20") Assume after one month, COVID-19 unexpectedly hit, FB's price plummeted to $130. Please calculate the margin of Anna's account. Will margin call be triggered? If so, at least how many shares does Anna have to sell to bring the margin back above 30%. Hint: After selling the shares, Anna will use the proceeds from the sales to pay back margin loans In this problem, assume prices do not move within one month and FB does not pay dividends during Anna's investment period. Problem 3 (10") Recall the example of repo contract we talked in Lecture 1. Let's now assume the hedge fund borrows SIOM cash and uses 2-year T-notes as collaterals. The repo rate is 0.1% per month Assume the hedge fund then uses the borrowed cash, SIOM, to invest in stock market and purchases $10M worth S&P 500 ETE. After one month, S&P 500 realizes a total return of +10% At the meantime, the T-note enjoys an interest rate of 0.25% per month, so that the cash lender has to return both SIOM Treasures and the interests back to the hedge fund when the contract expires. At the end of one month, the hedge fund closes all the positions. Please calculate the return on investment of this hedge fund over this month. Assume the hedge fund does not face margin requirement