2. The contract size of one fut ures contract on the SkP 500 is S250 times the S&P 500 fatures price - an increase by 1 index point means a transfer of $250 from the short to the long position. Suppose today the S&P 50 index has reached 1 160 index points, the S&P 500 pays a dividend yield of 4.5% per year, the term structure of interest rates is Bat and the short rate is constant over time and equals 2% (..). (a) In absence of arbitrage opportunities, what is today's futures price of the SkcP 500 fut ures with maturity in 50 days? (b) The initial margin (per contract) is S22.000 and the maintenance margin is S 17,500. Supple 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 investor with 5 short positions in the S&P 500 futures, show how his margin account changes every day. Assume that the investor earns interest of 2% (cc.) on his margin account. Day 0 S&P 500 Index 1460 1455 1458 147014901482 1479