James W. has a portfolio that includes 20 shares of Disney and 30 shares of Amazon. The price of Disney stock is normally distributed with a mean of 25 and a variance of 80. The price of Amazon is also normally distributed with a mean of 40 and a variance of 119. James finds out that these stocks are negatively correlated, with δ = -0.4.
(a) Find the mean and standard deviation of James W.'s portfolio.
(b) Would you advice James to sell Amazon and buy Disney?
(c) What is the probability that the value of the portfolio is greater than $2,000?
(d) What is the mean and standard deviation of James' portfolio if stocks are not correlated?