(Calculating portfolio variances)
Marge owns three stocks, Apple (AAPL),Google (GOOG) and Facebook (FB). She expects the price per share of eachstock one month from now to be 120, 60, and 60 dollars, respectively. Ananalysis of the returns to holding these three stocks shows that the monthlystandard deviation of the price per share for each stock is 10, 8, and 8 dollars, respectively. This same analysis also concludes the covariance between theprice per share of Apple stock and the price per share of Google stock is -36(dollars squared), between Apple and Facebook is +24, and between Googleand Facebook is +19. Answer the following questions assuming that Margeowns 200 shares of Apple, 100 shares of Google, and 50 shares of Facebook.
(a) Compute the expected value of Marge's portfolio one month from now.
(b) Compute the standard deviation of the value of her portfolio one monthfrom now.
(c) It turns out that Marge's sister, Maggie, owns 200 shares of Apple, 50shares of Google, and 100 shares of Facebook. Assuming that Margeand Maggie share the same expectations about the performance of eachstock, compute the expected value and standard deviation of Maggie'sportfolio one month from now.
(d) Who do you think owns a better portfolio? Explain.