3) You have decided to place a market order to buy 8,000 shares of stock ABC at and ask price of $30.00 per share. Your broker offers you a financing fee of 0% annual, your initial margin is 45% and your maintenance margin is 30%.
a) What is the minimum amount of equity required to place the order?
b) Suppose that you hold the 8,000 shares over a year. If the share price one year from now can be either $33.00 or $27.00, compute the return (over equity) one year from now (both scenarios).
c) If the price is $27.00, do you have a margin call?
d) Compute the share price that triggers a margin call.
e) If the share price is $23.57, compute the additional amount of equity required to restore the margin account to the maintenance margin.
How does your answer to a), b), c), d) and e) change if the broker offers you a financing fee of 5%? Discuss.
4) The current stock price of MSFT is $37.08. You expect the price of MSFT to drop below its current level one year from now. Based on your information, you have decided to short sell 1,500 shares of MSFT at an ask price of $37.08 per share. Your broker offers you a financing fee of 0% annual, your initial margin is 45% and your maintenance margin is 30%.
a) Compute the minimum amount of equity required to open the account and execute the transaction.
b) Moving against your expectations, one year from now, the price of MSFT increases to $42.00 per share. Compute the margin at this price level. Is there a margin call?
c) If the stock price is $42.00, compute the additional amount of equity required to restore the margin account to its maintenance level of 30%.
d) Right after the stock price reaches $42.00 and the margin account is restored to its maintenance level, the share price increases to $50.00. Is there a new margin call? Compute the additional amount of equity required to restore the margin account to its maintenance level if the stock price is now $50.00.
5) You are managing a $1,000,000 portfolio. Your boss would like to know how large your potential losses could be over the next month. Specifically, she wants to know the Value at Risk (VaR). You have monthly portfolio returns for the last 50 months, and you sort them in order from lowest to highest. The five lowest returns are shown below:
-52.3% -50.8% -48.6% -44.3% -40.9%
a) Assuming past returns are a reasonable estimate of potential future returns, what is the 2% VaR in dollars?
b) What are some of the potential risks of using historical (i.e., actual) returns to calculate VaR?
6) You have $20,000 to invest and you have decided to buy Tesla (TSLA) on margin. Your broker requires an initial margin of 60% and a maintenance margin of 40%. Currently, Tesla is trading for $160 per share.
a) Approximately how many shares can you buy in total?
b) Assuming you bought as many shares as you could in part (a), how far can the price fall before your broker issues a margin call?
7) You would like to make an equity investment in Ford (F). Currently, the stock is trading at $13.49, the bid is $13.47x100 and the ask is $13.50x150.
a) If you want to buy 100 shares, what price would you expect to pay?
b) If you want to sell 200 shares, would you expect the price to be higher, lower, or equal to $13.47?
c) Should the ask price typically be above or below the bid price? Briefly explain why.
8) Suppose X and Y are two random variables with mean 0.2 and 0.5, respectively, standard deviation 0.2 and correlation of -0.3.
a) Compute the return and variance of the portfolio that invests 30% in X and 70% in Y.
b) Compute the return and variance of the portfolio that invests -130% in X and 30% in Y.
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