1. [18 points] An investor wants to purchase a stock that is predicted to perform differently conditional on the state of the economy over the next period, as indicated in the table below: Probability 0.3 0.5 0.1 State of Economy Boom Normal Recession Return 12% 8% -2% (1) Please calculate the expected return, standard deviation, and 10% Value-at-Risk (VaR) of the stock. (6 points) (2) Suppose the stock is currently worth $100 (i.e., at T = 0). It turns out the actual changes of the price follow the path below: T 1 Price per share $120 $125 $110 Dividend per share $0 $0 $2 2 3 Period 1 Period 2 Period 3 1 2 T=0 1 3 (1) What is the holding period return for period 1? (2 points) (ii) What is the capital gain yield and dividend yield respectively for period 3? (4 points) (iii) Suppose the investor initially invests $100 at T=0. He buys another two shares at the beginning Period 2 (i.e., T=1), sells one share at the beginning of Period 3 (i.e., T=2). He sells the remaining shares at the end of period 3 (i.e., T=3). What is the appropriate method to calculate the average performance of this investor, and why? Please write down the equation to solve the appropriate average return on the investment. (Note: you only need to put down the equation, no calculation is need.) (6 points)