In: Statistics and Probability
Marge owns three stocks: Apple, Google and Facebook. She expects the price per share of each stock one month from now to be 120, 60, and 60 dollars, respectively. An analysis of the returns to holding these three stocks shows that the monthly standard deviation of the price per share for each stock is 10, 8, and 8 dollars, respectively. This same analysis also concludes the covariance between the price per share of Apple stock and the price per share of Google stock is -36 (dollars squared), between Apple and Facebook it is +24, and between Google and Facebook it is +19. Assume Marge owns 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 month from now.
(c) Marge’s sister, Maggie, owns 200 shares of Apple, 50 shares
of Google, and 100 shares of Facebook. Who has the better
portfolio? Explain and show any related work.