Suppose that the current price of eBay is $40 per share. Suppose further that the share price of eBay one month from now depends on the state of the economy as follows:
State of Economy Probability Price
Boom .2 $52
Normal .5 $44
Recession .3 $30
Also note that eBay will not pay any dividends over the next month.
1. You buy 500 shares, using $10,000 of your own money and borrowing the remainder of the purchase price from your broker. The interest rate on the margin loan is 2% per month, and the maintenance margin is 30%. What is the expected return of your investment?
2. What is the probability that you will receive a margin call from your broker one month from now? Explain with quantitative justification.
3. Suppose you sold short 500 shares of eBay at $40, using the maximum leverage allowed, and the price went up to $52 after one month. If you close out your short position, what would be the rate of return on your investment? (Ignoring transaction costs).