The shares of a company AVV are currently traded at 50. One risk- free asset is also available on the market. The borrowing rate and lending rate are the same and equal to 5% per year. It is expected that the price of the AVV shares in the next year will be as follows:

60 with probability 0.05 56 with probability 0.1 54 with probability 0.25 49 with probability 0.1 47 with probability 0.05 Calculate:

58 with probability 0.05 55 with probability 0.15

51 with probability 0.15 48 with probability 0.1

(i) The expected return on the AVV shares.

(ii) The standard deviation of this return.

(iii) An individual invests 20% of his/her money in a risk-free asset by lending money, and the remaining 80% in the shares of AVV. By using the mean-variance model, calculate the expected return and the standard deviation of such portfolio.