I. Mathematical Problems
1. According to the analysts, the return on Company A's stock in the coming year could be -10%, 1%, 7%, or 15%. The corresponding probabilities are 25%, 15%, 20%and 40%, respectively.
In comparison, the return on Company B's stock in the coming year could be - 5%, - 1%, 4%, or 12%. The corresponding probabilities are 10%, 30%, 20%, and 40%, respectively.
Suppose we have invested 35% of our capital in A's stock and 65% in B's stock. Historical data suggest that the correlation coefficient between the two stocks is 0.65.
What is the standard deviation of each stock
What is the expected return on our portfolio?
What's the standard deviation of the return on our portfolio?
2. Company BW will pay dividends of $1.05, $1.18, and $1.56 over next three years (dividend will be paid at the end of each year). You are expecting the stock price to be $57.57 right after the company pays the 3rd dividend. In the following three years, the annual expected return on the market is 6.88%, annual T-bill rate is 0.58%.
Data suggest that company BW's beta is 1.78 and you are expecting the beta to remain the same in the following three years. What is the maximum price you are willing to pay for this stock today?
II. Theory Questions
- Why diversification of investments can reduce total risk? In other words, how does diversification work?
- Explain the Arbitrage Pricing Theory?
- Explain the Capital Asset Pricing Model. Please include your understanding on systematic/non-systematic risks, diversification, market security line, and beta.