Suppose there are only two periods, period 0 and period 1, and three possible states of the world in period 1: a good weather state, a fair weather state, and a bad weather state. Apples are the only product produced in this world, and they cannot be stored from one period to the next. The following abbreviations will be used: PA = apple in the present period (i.e., present apple), GA = good weather apple in the next period, FA = fair weather apple in the next period, BA = bad weather apple in the next period. Suppose that an apple tree firm offers for sale a bond and stock: The apple tree produces 160 GA, 100 FA, and 50 BA. The bond pays 40 GA, 40 FA and 40 BA. The stock pays 120 GA, 60 FA and 10 BA. O In addition, securities C, D, and E are available Security C pays 140 GA, 80 FA, and 30 BA. Security D pays 60 GA, 30 FA, and 5 BA. Security E pays 80 GA, 20 FA, and 0 BA. The arbitrage-free price of the bond is 32 PA, and the arbitrage-free price of the stock is 44 PA. Securities C, D, and E are also priced fairly at 60 PA, 22 PA, and 20 PA, respectively. There are no arbitrage opportunities in this market. e) Verify that the principle of value additivity holds? It holds because the atomic securities are all smaller than 1. It holds because the sum of the prices of the bond and the stock is equal to the value of the tree. It holds because there are independent securities in the market It holds because the tree is risk-free and there is no default Submit f) Calculate the discount factor Submit g) Calculate the risk-free interest rate Submit h) Suppose a new security F is added to the market. Its pays 70 GA, 40 FA and 15 BA. Its price is 30 PA. Are there any arbitrage opportunities? Yes No Submit Suppose there are only two periods, period 0 and period 1, and three possible states of the world in period 1: a good weather state, a fair weather state, and a bad weather state. Apples are the only product produced in this world, and they cannot be stored from one period to the next. The following abbreviations will be used: PA = apple in the present period (i.e., present apple), GA = good weather apple in the next period, FA = fair weather apple in the next period, BA = bad weather apple in the next period. Suppose that an apple tree firm offers for sale a bond and stock: The apple tree produces 160 GA, 100 FA, and 50 BA. The bond pays 40 GA, 40 FA and 40 BA. The stock pays 120 GA, 60 FA and 10 BA. O In addition, securities C, D, and E are available Security C pays 140 GA, 80 FA, and 30 BA. Security D pays 60 GA, 30 FA, and 5 BA. Security E pays 80 GA, 20 FA, and 0 BA. The arbitrage-free price of the bond is 32 PA, and the arbitrage-free price of the stock is 44 PA. Securities C, D, and E are also priced fairly at 60 PA, 22 PA, and 20 PA, respectively. There are no arbitrage opportunities in this market. e) Verify that the principle of value additivity holds? It holds because the atomic securities are all smaller than 1. It holds because the sum of the prices of the bond and the stock is equal to the value of the tree. It holds because there are independent securities in the market It holds because the tree is risk-free and there is no default Submit f) Calculate the discount factor Submit g) Calculate the risk-free interest rate Submit h) Suppose a new security F is added to the market. Its pays 70 GA, 40 FA and 15 BA. Its price is 30 PA. Are there any arbitrage opportunities? Yes No Submit