# Question

Financial Managers, Inc., buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Andrea Colson has asked for your assistance in the analysis of the Johnson Fund. A portion of this portfolio consists of 10 shares of stock A and 8 shares of stock B. The price of A has a mean of 10 and a variance of 16, while the price of B has a mean of 12 and a variance of 9. The correlation between prices is 0.3.

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

b. Andrea has been asked to reduce the variance (risk) of the portfolio. She offers to trade the 10 shares of stock A and receives two offers, from which she can select one: 10 shares of stock 1 with a mean price of 10, a variance of 25, and a correlation with the price of stock B equal to -0.2; or 10 shares of stock 2 with a mean price of 10, a variance of 9, and a correlation with the price of stock B equal to +0.5. Which offer should she select?

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

b. Andrea has been asked to reduce the variance (risk) of the portfolio. She offers to trade the 10 shares of stock A and receives two offers, from which she can select one: 10 shares of stock 1 with a mean price of 10, a variance of 25, and a correlation with the price of stock B equal to -0.2; or 10 shares of stock 2 with a mean price of 10, a variance of 9, and a correlation with the price of stock B equal to +0.5. Which offer should she select?

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