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Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2309 The Statistics of Investment Risk First Semester, 2009-2010 Problem Sheet 1 1. An investor buys 2000 shares at $30 each. The initial margin requirement is 50% and the maintenance margin is 30%. Show that if the stock price falls to $25, the investor will not receive a margin call. At what price will a margin call be received? 2. You are bearish on Telecom and decide to sell short 100 shares at the current market price of $40 per share. (a) How much in cash must you put into your brokerage account if the broker’s initial margin requirement is 50% of the value of the short position? (b) How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position? 3. You are bullish on AT&T stock. The current stock price is $50 per share, and you have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of 8% per year and hence invest $10,000 in the stock. (a) What will be your profit if the price of AT&T stock goes up by 10% one year later? Calculate the simple rate of return by dividing the profit by the initial amount of investment ($5,000). (b) How far does the price of AT&T stock have to fall for you to get a margin call if the maintenance margin is 30%? 4. D´ ee Trader opens a margin account and purchases 300 shares of Internet Dreams at $40 per share. She borrows $4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. (a) What is the margin in D´ ee’s account when she first purchases the stock? (b) If the share price falls to $30 per share by the end of the year, what is the remaining margin in her account? If the maintenance margin requirement is 30%, will she receive a margin call?...
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- Spring '11