(A) 7 point The annually compounded interest rate per annum is 10%. A stock market is comprised of 3 stocks, which are X, Y, Z. The stock market index M is a market value weighted one On day 1, the share prices of X, Y, and Z are $7, $8, and $9, respectively. The numbers of shares outstanding for X, Y, and Z are 7, 8, and 9, respectively, too. The level of M is 100 on day 1. On day 2, the share prices of X, Y, and Z change to $7, $7, and $7, respectively. F is the index futures of M and has 1 year maturity from day 2, and its level on day 2 is still 100. F is priced at $1,000 times the level of the index (1 point of F is $1,000) You can trade only one unit of the futures contract and do not have money on day 2. A-1, In order to make an arbitrage profit in one year, on day 2, how many shares of stocks X, Y, and Z should you buy (or sell short)? Show your work. A-2, If the prices of the three stocks are all $10 in one year, how much arbitrage profit will you make in one year? Show your work. You should sum up the profit/loss in your stock position and that in your futures position in one year to answer this question. (B) 10 point The current share price of Samsung is S, where S>0. In one year, the price will be either Su (node A) or S/u (B), where u>1. Similarly, in two years, from node A, the price will evolve to Su2 (C) or S (D), and from node B, the price will evolve to S (D) or S/(u2) (E). Use annual compounding, and the one year risk free rate = r, where 11+r

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