1. Create the same information with columns representing time and rows representing spot and futures market. Explain the numbers now.

2. Now verify that the profit obtained in both cases equal the amount of mispricing without the transaction cost.

TABLE 9.3 STOCK INDEX ARBITRAGE Scenario: On November 8, the S&P 500 index is at 1,305, the continuously compounded dividend yield is 3 percent, and the con tinuously compounded risk-free rate is 5.2 percent. The December futures contrad, which aspires in 40 days, is priced at 1,316.30. Its theoretical price f = 1,3056-3) = 1,308.15, where T = 40/365 0.10%. Thus, the futures contract is overpriced and the carry arbitrage transaction will be executed using $20 million. Transaction costs are as percent of the dollars invested DATE SPOT MARKET FUTURES MARKET November The S&P 500 is at 1.305. The stocks have a divided The S&P 500 futures, expiring on December 18, in at yield of 3 percent. The risk-free rate is S2 percent 1.316.30 The appropriate number of futures is Buy $20 million of stock in the same proportions $20 million/ (1 305)(250)) - 61.30 make up the SAP 500 Sell 61 contracts December 18 The S&P 500 is at 1,300.M. The stocks will be worth Putwe expires at the S&P 500 price of 1,300.36 (1.300.36/1305)($20 million) - $19.93.19 million The $20 million invated in the stocks dffectively counts ($20 million (20.100 - $20.008242 milion Transactions costs are $20 milion (0005) $100.000 (includes futures costs). Sell stocks Gowe out futures u praten Analysis Profit on stock $19.925,689 received from sake of stocka) - $20,04 212 invested in stocka) $119,393 Profit on futures 61(250)(1,316.30 (sale price of futures) --61(250)(1.300./6) purchase price of futures) $243.085 Overall profil $243085 (from futures) -$119,393 (from stock) - $100.000 (transaction costs) $23.682 The appropriate number of futures contracts to match $30 milion of stock is $20 million divided by the index price, not the futures price, times the multiplier. Even though the $20 millons allocated across 500 different stods, it is equivalent to buying $20 milion 1,305 = 15,326"shares of the S&P 500. The appropriate number of futures is one for each equivalent "Share" of the S&P 500. Each future, of course, has a $250 multiplier TABLE 9.3 STOCK INDEX ARBITRAGE Scenario: On November 8, the S&P 500 index is at 1,305, the continuously compounded dividend yield is 3 percent, and the con tinuously compounded risk-free rate is 5.2 percent. The December futures contrad, which aspires in 40 days, is priced at 1,316.30. Its theoretical price f = 1,3056-3) = 1,308.15, where T = 40/365 0.10%. Thus, the futures contract is overpriced and the carry arbitrage transaction will be executed using $20 million. Transaction costs are as percent of the dollars invested DATE SPOT MARKET FUTURES MARKET November The S&P 500 is at 1.305. The stocks have a divided The S&P 500 futures, expiring on December 18, in at yield of 3 percent. The risk-free rate is S2 percent 1.316.30 The appropriate number of futures is Buy $20 million of stock in the same proportions $20 million/ (1 305)(250)) - 61.30 make up the SAP 500 Sell 61 contracts December 18 The S&P 500 is at 1,300.M. The stocks will be worth Putwe expires at the S&P 500 price of 1,300.36 (1.300.36/1305)($20 million) - $19.93.19 million The $20 million invated in the stocks dffectively counts ($20 million (20.100 - $20.008242 milion Transactions costs are $20 milion (0005) $100.000 (includes futures costs). Sell stocks Gowe out futures u praten Analysis Profit on stock $19.925,689 received from sake of stocka) - $20,04 212 invested in stocka) $119,393 Profit on futures 61(250)(1,316.30 (sale price of futures) --61(250)(1.300./6) purchase price of futures) $243.085 Overall profil $243085 (from futures) -$119,393 (from stock) - $100.000 (transaction costs) $23.682 The appropriate number of futures contracts to match $30 milion of stock is $20 million divided by the index price, not the futures price, times the multiplier. Even though the $20 millons allocated across 500 different stods, it is equivalent to buying $20 milion 1,305 = 15,326"shares of the S&P 500. The appropriate number of futures is one for each equivalent "Share" of the S&P 500. Each future, of course, has a $250 multiplier