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).