1. The contract size of one futures contract on the S&P 500 is $250 times the S&P 500 futures price - an increase by 1 index point means a transfer of $250 from the short to the long position. Suppose today the S&P 500 index has reached 1460 index points, the S&P 500 pays a dividend yield of 4.5% per year, the term structure of interest rates is flat and the short rate is constant over time and equals 2% (c.c.). (a) In absence of arbitrage opportunities, what is today's futures price of the S&P 500 futures with maturity in 50 days? (b) The initial margin (per contract) is $22'000 and the maintenance margin is $17'500. Suppose over the next 6 days the S&P 500 index changes as follows: (Careful: the table reports index points of the index not the futures!) For an Day 0 1 S&P 500 Index 1460 1455 2 1458 3 1470 4 1490 5 6 1482 1479 investor with 5 short positions in the S&P 500 futures show how his margin ac- count changes every day. Assume that the investor earns interest of 2% (c.c.) on his margin account