I managed to get this far with A and B. Looking for help with C, D and E. Thank you.

Assignment 1: Futures Pricing You manage the following S&P 500 portfolio: Market Value: 20 Million, Beta: 1.0, Dividends: 0%, Risk Free Rate: 5%. Futures available on the S&P 500 Index are: Current Index Level: 1,000, Beta: 1.0, Dividends: 0%, Maturity: 1 Year, Multiplier 250 Assume that the performance of the portfolio follows the capital asset pricing model (CAPM) a) You want to fully hedge the portfolio for the coming year. Recommend the hedge and show the performance of the hedge if the Index finishes the year at 800 or 1,350. b) Show the difference in the performance of the hedge between using the Spot Price and the Forward Price in computing the number of contracts used in hedging. For the 800 or 1,350 index scenarios reconcile the performance difference between both hedging outcomes. c) Assume that instead of a 1 year Futures contact the only contract you can sell is a 3 year contract. However you can buy a Futures contract for any maturity. You also want to target a portfolio Beta of 0.25 for the upcoming year. Show the performance of the hedged/adjusted portfolio if the Index finishes the year at 500 or 2,000. d) Assume that instead of a 1 year Futures contact the only contract you can sell or buy are 3 month contracts. You want to target a Beta of -2 for your portfolio for the upcoming year and will therefore need to replace with a new 3 month contract as the existing one expires. Show the performance of the hedged/adjusted portfolio if the Index finishes the first quarter at 800, the second quarter at 900, the third quarter at 950 and finished the year at 850. e) Outlined two unique benefits of Futures over Forwards, and two unique benefits of Forward over Futures. A. Market value of portfolio = 20 million Current Beta 1 Hedge the portfolio so the target beta = 0 Number of futures contract that needs to be purchased / sold is given as = Value of portfolio * ( Target Beta - Current Beta ) / (Price of Index* Multiplier in each contract) = 20,000,000 * (0 - 1)/(1,000 * 250 ) = -20,000,000 / 2,500,000 = -80 Contracts so you have to sell 80 contracts for a complete hedge Price of index goes down 800 S & P portfolio = Value of portfolio * Index price in future / Current index price = = 20,000,000 * 800 / 1,000 = 16,000,000 Pay of S & P portfolio = 16,000,000 20,000,000 = - 4,000,000 (loss) Pay off in future contracts = ( Sales price Purchase price ) * Number of contracts * Multiplier in each contract =(1,000 800 ) * 80 * 250 = 4,000,000 = 220 * 80 * 250 = 4,000,000 (gain) Total pay off = loss on S & P Portfolio Gain in Futures =- 4,000,000 + 4,000,000 = 0 The payoff becomes zero which means the portfolio is completely hedged. Price of index goes down to 1,350 S&P portfolio = Value of portfolio * Index price in future / Current index price - = 20,000,000 * 1,350 / 1,000 = 27,000,000 Pay off on S & P portfolio = 27,000,000 20,000,000 = 7,000,000 (Gain ) Pay off in future contracts = ( Sales price Purchase price ) * Number of contracts * Multiplier in each contract = ( 1,000 1,350 ) * 80 * 250 = 7,000,000 = 350 * 80 * 250 = 7,000,000 ( loss) Total pay off = Payoff on S & P Portfolio Payoff in Futures = 7,000,000 7,000,000 = 0 The payoff becomes zero which means the portfolio is completely hedged B. If the current index level is spot index price future on index will be = Spot price * (1 + risk free rate ) = 1,000 * 1.05 = 1,050 Market value of portfolio = 20 million Current Beta = 1 Hedge the portfolio target beta = 0 Number of futures contracts Value of portfolio * ( Target Beta - Current Beta )/(Price of futures on index * Multiplier in each contract) = 20,000,000 * (0-1)/(1,050 * 250 ) = - 20,000,000 / (1,050 * 250 ) = -76.1905 Contracts so you have to sell 80 contracts for a complete hedge Price of index goes down to 800 Value of S & P portfolio = Value of portfolio * Index price in future / Current index price = = 20,000,000 * 800 / 1,000 = 16,000,000 Pay off on S & P portfolio = ( Sales price purchase price ) * Number of contracts * Multiplier in each contract = (1,050 800 ) * 76 * 250 = 250 * 76 * 250 = 4,750,000 ( gain ) Total pay off = = loss on S & P Portfolio Gain in Futures = -4,000,000 + 4,750,000 = 750,000 Prices of index goes down to 1,350 Value of S & P portfolio = 20,000,000 * 1,350 / 1,000 = 27,000,000 =27,000,000 20,000,000 = 7,000,000 ( gain ) Pay off in future contracts = ( Sales price Purchase price ) * Number of contracts * Multiplier in each contact = (1,050 1,350 ) * 76 * 250 300 * 76 * 250 = 5,700,000 Total pay off = Payoff on S & P portfolio Payoff in Futures = 7,00,000 5,700,00 = 1,300,000 c) Assume that instead of a 1 year Futures contact the only contract you can sell is a 3 year contract. However you can buy a Futures contract for any maturity. You also want to target a portfolio Beta of 0.25 for the upcoming year. Show the performance of the hedged/adjusted portfolio if the Index finishes the year at 500 or 2,000. d) Assume that instead of a 1 year Futures contact the only contract you can sell or buy are 3 month contracts. You want to target a Beta of -2 for your portfolio for the upcoming year and will therefore need to replace with a new 3 month contract as the existing one expires. Show the performance of the hedged/adjusted portfolio if the Index finishes the first quarter at 800, the second quarter at 900, the third quarter at 950 and finished the year at 850. e) Outlined two unique benefits of Futures over Forwards, and two unique benefits of Forward over Futures. Assignment 1: Futures Pricing You manage the following S&P 500 portfolio: Market Value: 20 Million, Beta: 1.0, Dividends: 0%, Risk Free Rate: 5%. Futures available on the S&P 500 Index are: Current Index Level: 1,000, Beta: 1.0, Dividends: 0%, Maturity: 1 Year, Multiplier 250 Assume that the performance of the portfolio follows the capital asset pricing model (CAPM) a) You want to fully hedge the portfolio for the coming year. Recommend the hedge and show the performance of the hedge if the Index finishes the year at 800 or 1,350. b) Show the difference in the performance of the hedge between using the Spot Price and the Forward Price in computing the number of contracts used in hedging. For the 800 or 1,350 index scenarios reconcile the performance difference between both hedging outcomes. c) Assume that instead of a 1 year Futures contact the only contract you can sell is a 3 year contract. However you can buy a Futures contract for any maturity. You also want to target a portfolio Beta of 0.25 for the upcoming year. Show the performance of the hedged/adjusted portfolio if the Index finishes the year at 500 or 2,000. d) Assume that instead of a 1 year Futures contact the only contract you can sell or buy are 3 month contracts. You want to target a Beta of -2 for your portfolio for the upcoming year and will therefore need to replace with a new 3 month contract as the existing one expires. Show the performance of the hedged/adjusted portfolio if the Index finishes the first quarter at 800, the second quarter at 900, the third quarter at 950 and finished the year at 850. e) Outlined two unique benefits of Futures over Forwards, and two unique benefits of Forward over Futures. A. Market value of portfolio = 20 million Current Beta 1 Hedge the portfolio so the target beta = 0 Number of futures contract that needs to be purchased / sold is given as = Value of portfolio * ( Target Beta - Current Beta ) / (Price of Index* Multiplier in each contract) = 20,000,000 * (0 - 1)/(1,000 * 250 ) = -20,000,000 / 2,500,000 = -80 Contracts so you have to sell 80 contracts for a complete hedge Price of index goes down 800 S & P portfolio = Value of portfolio * Index price in future / Current index price = = 20,000,000 * 800 / 1,000 = 16,000,000 Pay of S & P portfolio = 16,000,000 20,000,000 = - 4,000,000 (loss) Pay off in future contracts = ( Sales price Purchase price ) * Number of contracts * Multiplier in each contract =(1,000 800 ) * 80 * 250 = 4,000,000 = 220 * 80 * 250 = 4,000,000 (gain) Total pay off = loss on S & P Portfolio Gain in Futures =- 4,000,000 + 4,000,000 = 0 The payoff becomes zero which means the portfolio is completely hedged. Price of index goes down to 1,350 S&P portfolio = Value of portfolio * Index price in future / Current index price - = 20,000,000 * 1,350 / 1,000 = 27,000,000 Pay off on S & P portfolio = 27,000,000 20,000,000 = 7,000,000 (Gain ) Pay off in future contracts = ( Sales price Purchase price ) * Number of contracts * Multiplier in each contract = ( 1,000 1,350 ) * 80 * 250 = 7,000,000 = 350 * 80 * 250 = 7,000,000 ( loss) Total pay off = Payoff on S & P Portfolio Payoff in Futures = 7,000,000 7,000,000 = 0 The payoff becomes zero which means the portfolio is completely hedged B. If the current index level is spot index price future on index will be = Spot price * (1 + risk free rate ) = 1,000 * 1.05 = 1,050 Market value of portfolio = 20 million Current Beta = 1 Hedge the portfolio target beta = 0 Number of futures contracts Value of portfolio * ( Target Beta - Current Beta )/(Price of futures on index * Multiplier in each contract) = 20,000,000 * (0-1)/(1,050 * 250 ) = - 20,000,000 / (1,050 * 250 ) = -76.1905 Contracts so you have to sell 80 contracts for a complete hedge Price of index goes down to 800 Value of S & P portfolio = Value of portfolio * Index price in future / Current index price = = 20,000,000 * 800 / 1,000 = 16,000,000 Pay off on S & P portfolio = ( Sales price purchase price ) * Number of contracts * Multiplier in each contract = (1,050 800 ) * 76 * 250 = 250 * 76 * 250 = 4,750,000 ( gain ) Total pay off = = loss on S & P Portfolio Gain in Futures = -4,000,000 + 4,750,000 = 750,000 Prices of index goes down to 1,350 Value of S & P portfolio = 20,000,000 * 1,350 / 1,000 = 27,000,000 =27,000,000 20,000,000 = 7,000,000 ( gain ) Pay off in future contracts = ( Sales price Purchase price ) * Number of contracts * Multiplier in each contact = (1,050 1,350 ) * 76 * 250 300 * 76 * 250 = 5,700,000 Total pay off = Payoff on S & P portfolio Payoff in Futures = 7,00,000 5,700,00 = 1,300,000 c) Assume that instead of a 1 year Futures contact the only contract you can sell is a 3 year contract. However you can buy a Futures contract for any maturity. You also want to target a portfolio Beta of 0.25 for the upcoming year. Show the performance of the hedged/adjusted portfolio if the Index finishes the year at 500 or 2,000. d) Assume that instead of a 1 year Futures contact the only contract you can sell or buy are 3 month contracts. You want to target a Beta of -2 for your portfolio for the upcoming year and will therefore need to replace with a new 3 month contract as the existing one expires. Show the performance of the hedged/adjusted portfolio if the Index finishes the first quarter at 800, the second quarter at 900, the third quarter at 950 and finished the year at 850. e) Outlined two unique benefits of Futures over Forwards, and two unique benefits of Forward over Futures