Homework Margin Purchases. Dr. Patrick Toche

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1 Homework Margin Purchases Dr. Patrick Toche

2 A dagger indicates a possibly more challenging question. Maintenance Margin 1. You are bullish on Telecom stock. The current market 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 invest $10,000 in the stock. (a) What will be your rate of return if the price of Telecom stock goes up by 10% over the (Ignore any expected dividend payments) (b) How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately. 2. You ve borrowed $20,000 on margin to buy shares in Disney, which is now selling at $40 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the stock price falls to $35 per share. (a) Will you receive a margin call? (b) How low can the price of Disney shares fall before you receive a margin call? 3. Suppose that Intel currently sells at $40 per share. You buy 500 shares, using $15,000 of your own money and borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 8%. (a) What is the percentage change in the net worth on your brokerage account if the stock price changes overnight to: (i) $44; (ii) $40; (iii) $36? (b) Suppose the maintenance margin is 25%. How low can the price fall before you get a margin call? (c) Suppose you finance the initial purchase with as little as $10,000 of your own money instead. How low can the price fall before you get a margin call? (d) Suppose again you invest $15,000 of your own money. What is the rate of return on your margined position after one year if the stock price changes to: (i) $44; (ii) $40; (iii) $36? 2

3 (e) Continue to assume that one year has passed. How low can the price fall before you get a margin call? 4. You deposit $100,000 of your own capital in a brokered account and borrow an additional $100, 000 from your broker. You invest everything in a single stock. The current market price of the stock is $100 per share. Your broker charges an interest rate of r % per year. Your broker s maintenance margin is 30%. You expect the stock to pay a semi-annual dividend payment of $5 per share. (a) What would be your annual rate of return if the stock price rose by 10% over the (b) What would be your annual rate of return if the stock price fell by 10% over the (c) You are bullish on the stock. You believe the probability of a 10% rise is 60% and the probability of a 10% fall is 40%. What is your expected rate of return? Is it positive? (d) The day after you purchase the stock, the price falls to $70. Will you receive a margin call? 5. An investor buys $11,000 worth of stock at $100 per share, contributing $7,000 and borrowing the remaining $4,000 from a broker. (b) The price falls to $60. Calculate the margin percentage after the fall. (c) The broker s maintenance margin is 30%. Do you get a margin call? 6. An investor buys $15,000 worth of stock at $50 per share, contributing $9,000 and borrowing the remaining $6,000 from a broker. (b) The price falls to $40. Calculate the margin percentage after the fall. (c) The price falls to $30. The broker s maintenance margin is 35%. Do you get a 3

4 margin call? 7. The current market price of Telecom stock is $50 per share. You have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of r% per year. Altogether you invest a total of $10,000 in the stock. Telecom stock pays no dividend. Your broker s maintenance margin is 40%. (i) What would be your annual rate of return if the stock price rose by 10% over the (ii) What would be your annual rate of return if the stock price fell by 10% over the (iii) You are bullish on Telecom stock. You believe the probability of a 10% rise is 50% and the probability of a 10% fall is 25%. What is your expected rate of return? Is it positive? (iv) The day after you purchase the stock, the price falls by $10. Will you receive a margin call? 8. The current market price of Telecom stock is $50 per share. You have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of r% per year. Altogether you invest a total of $10,000 in the stock. Telecom stock pays no dividend. Your broker s maintenance margin is 40%. (i) What would be your annual rate of return if the stock price rose by 10% over the (ii) What would be your annual rate of return if the stock price fell by 10% over the (iii) You are bullish on Telecom stock. You believe the probability of a 10% rise is 50% and the probability of a 10% fall is 25%. What is your expected rate of return? Is it positive? (iv) The day after you purchase the stock, the price falls to $10. Will you receive a 4

5 margin call? 9. An investor buys $150,000 of stock at $50 per share, contributing $90,000 and borrowing $60,000 from a broker. The broker s annual interest rate is 10% and maintenance margin 40%. (b) The investor is bullish on the stock and believes there is an 80% probability that the stock price will rise overnight by 10% and a 20% probability that it will fall by 10%. What is the expected rate of return overnight? (c) The stock price falls overnight to $40. Calculate the account s margin percentage after the fall. (d) One year later, the stock price is still $40. However, the stock has paid quarterly dividends of $2 per share. What is the annual rate of return? 10. An investor buys 3, 000 shares of stock at $50 per share, contributing 60% of the total and borrowing the rest from a broker. The investor holds the stock long for one year. The stock has paid quarterly dividends of $2 per share. The broker s annual interest rate is 10% and maintenance margin 40%. The stock price has risen to $60. (a) Calculate the account s margin percentage at the year end. (b) Calculate the annual rate of return at the year end. 11. An investor buys 3, 000 shares of stock at $50 per share, contributing 60% of the total and borrowing the rest from a broker. The investor holds the stock long for one year. The stock has paid quarterly dividends of $2 per share. The broker s annual interest rate is 10% and maintenance margin 40%. The stock price is back to $50 at the year end. (a) Calculate the account s margin percentage at the year end. (b) Calculate the annual rate of return at the year end. 5

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