Suppose you own a portfolio of two stocks Stock A and Stock B. The number of shares you own of Stocks A and B are and respectively. The market value of your portfolio W=X+Y where X and Y are prices of Stocks A and B respectively. You are interested not only in the return and value of your portfolio, but also in the risk that comes with stock price volatility. Portfolio diversification is one way of managing risk, but what portfolio combinations work better than others? Let us suppose that the uncertainty associated with Stocks A and B is described by the following joint probability distribution of stock prices:

1.Find the marginal distributions of X and Y, and the means and variances of each.

2.Then obtain the covariance and correlation between X and Y.

3.Suppose you have 5 shares of Stock A (=5)and 10 shares of stock B (=10). Find the mean and standard deviation of the value of your portfolio.

Suppose that the joint probability distribution was different. Specifically, assume that it is now as follows.

4.It can be shown that this distribution implies that the mean and variance of each stock is unchanged (you do not need to show this). The covariance between the two stocks can be shown to be -59.2. Explain why you would prefer this portfolio? What is the reason for this difference, and what does this mean intuitively?

Price of Stock B (Y) $40 $50 $60 $70 Price of Stock A (X) $45 $50 $55 $60 0.24 0.003333 0.003333 0.003333 0.003333 0.24 0.003333 0.003333 0.003333 0.003333 0.24 0.003333 0.003333 0.003333 0.003333 0.24 Price of Stock B (Y) Price of Stock A (X) $45 $50 $55 $60 $40 0.003333 0.003333 0.003333 0.24 $50 0.003333 0.003333 0.24 0.003333 $60 0.003333 0.24 0.003333 0.003333 $70 0.24 0.003333 0.003333 0.003333 Price of Stock B (Y) $40 $50 $60 $70 Price of Stock A (X) $45 $50 $55 $60 0.24 0.003333 0.003333 0.003333 0.003333 0.24 0.003333 0.003333 0.003333 0.003333 0.24 0.003333 0.003333 0.003333 0.003333 0.24 Price of Stock B (Y) Price of Stock A (X) $45 $50 $55 $60 $40 0.003333 0.003333 0.003333 0.24 $50 0.003333 0.003333 0.24 0.003333 $60 0.003333 0.24 0.003333 0.003333 $70 0.24 0.003333 0.003333 0.003333