Guardian Wealth Management, a financial planning company in Geneva, Switzerland, buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Anne Grace has asked for your assistance in the analysis of the Elias Fund. A portion of this portfolio consists of 12 shares of stock A and 8 shares of stock B. The price of A has a mean of 100 and a variance of 25, while the price of B has a mean of 130 and a variance of 16. The correlation between prices is 0.4.

a. What are the mean and variance of the portfolio value?

b. Anne has been asked to reduce the variance (risk) of the portfolio. She offers to trade the 12 shares of stock A and receives two offers, from which she can select one: 12 shares of stock 1 with a mean price of 100, a variance of 36, and a correlation with the price of stock B equal to -0.4; or 12 shares of stock 2 with a mean price of 100, a variance of 25, uncorrelated with the price of stock B. Which offer should Anne select?