1. At the beginning of the year, you decide to build a portfolio with a 1-year call option on S&P500 stock index and 12-month Treasury bills. Assume the risk-free rate on the T-bill is 5%. One year at the money call on S&P500 is $10. The price of the S&P500 index fund is $100. You have $10000 to invest. Your goal is to never lose money at the end of year and earn a fraction of the market index return.
   1. How much money should you invest in the Treasury bills?
   2. How much money should you invest in the call option?
   3. Assume the market index return is -20%, what is your portfolios return?
   4. Assume the market index return is 20%, what is your portfolios return?