The pension fund manager at Gold Corp reported concerns in market data trends which suggest that in 6 months equity prices may decline in Gold Corps portfolio holding. Gold Corps portfolio pays dividends at the rate of 0.8%. Gold Corp portfolio holding is very similar to the E-Mini S&P 500 futures contract with unit of $50 x S&P 500 Index. The Spot S&P 500 Index is at 4120 today. The continuously compounded risk-free interest rate is 3%. a) Assuming there are no transaction costs or taxes, compute the theoretical no arbitrage Futures Index for the underlying S&P 500 in the market today (Show detailed workings for the theoretical Futures Index) If the S&P 500 Futures Index is actually 4190 in the market; how could an arbitrageur benefit from the price differential? [5 marks] c) What would be the arbitrageurs profit amount per contract? [5 marks] d) What will be the new futures Index, if after three (3) months the S&P500 Index in the spot market i. Drops by 1% ii. Increases by 1.5%