3. Suppose that you are given two stocks S and S2, the current stock prices are $112.70 for S1 and $1550.00 for S1. Their prices have with the following dynamics: from time t = 0 to t= 1 (one year), Si goes up by 15% with probability or goes up by 5% with probability 2. If Si goes up by 15%, then the stock S2 goes up by 15% with probability z or does not change with probability }. If S goes up by 5%, then S2 goes up by 20% with probability 1. The dynamics of the returns can also be summarized as follows 1 2 1 Pr(K1 = 15%) = 2 1 Pr(K1 = 5%) = 2 Pr(K2 = 15%|K1 = 15%) = - COIN = = Pr(K2 = 0|K1 = 15%) Pr(K2 = 20%|K1 = 5%) = 1 Winter loading por een = (a) (8 pts) Find the data of the market: M1, M2, 01, 02 and 01,2. (b) (7 pts) Suppose that you buy 80 shares of S1 and 3 shares of S2. What is the mean and variance of your portfolio return? (c) (10 pts) Suppose that you decide to spend $17,000 in the two stocks. How many shares of each stock should you buy (or short-sell) such that your portfolio return has the minimum possible risk? ? 23 3. Suppose that you are given two stocks S and S2, the current stock prices are $112.70 for S1 and $1550.00 for S1. Their prices have with the following dynamics: from time t = 0 to t= 1 (one year), Si goes up by 15% with probability or goes up by 5% with probability 2. If Si goes up by 15%, then the stock S2 goes up by 15% with probability z or does not change with probability }. If S goes up by 5%, then S2 goes up by 20% with probability 1. The dynamics of the returns can also be summarized as follows 1 2 1 Pr(K1 = 15%) = 2 1 Pr(K1 = 5%) = 2 Pr(K2 = 15%|K1 = 15%) = - COIN = = Pr(K2 = 0|K1 = 15%) Pr(K2 = 20%|K1 = 5%) = 1 Winter loading por een = (a) (8 pts) Find the data of the market: M1, M2, 01, 02 and 01,2. (b) (7 pts) Suppose that you buy 80 shares of S1 and 3 shares of S2. What is the mean and variance of your portfolio return? (c) (10 pts) Suppose that you decide to spend $17,000 in the two stocks. How many shares of each stock should you buy (or short-sell) such that your portfolio return has the minimum possible risk? ? 23