You have $500,000 to invest in the stock market. The S&P 500 index level is 4700. Shares in the SPY ETF index tracker always trade at about 1/10 of the index level. (a) Calculate the nearest whole number of ETF shares you can buy with your capital, then chart your investment value as a function of the index level within the range 0-6000. (b) Instead of buying ETFs, you deposit $500,000 in cash on a futures trading account. Based on the information below, calculate the nearest whole number of futures contracts you should buy to obtain an index exposure equivalent to (a), then chart your account value (cash + futures p/l) as a function of the futures price within the range 0-6000. Micro E-Mini S&P 500 futures: Expiry = 5 years, Price = 4800, Multiplier = 5