Use the following information for questions 1 - 4. Soybean futures trade in contracts of 5,000 bushels and are prices are quoted in cents per bushel. Gold futures trade in contracts of 100 ounces and prices are quoted in dollars per ounce. S&P 500 E-mini futures trade in contracts with multiples of $50 times the quoted price which is in dollars. An investor has a well-diversified stock portfolio with a beta of 1.20. The current portfolio value is $3,240,000. The investor is looking to hedge the systematic risk in her portfolio as she is increasingly concerned about a significant stock market decline in the next year or so and does not wish to rebalance her portfolio. She intends to use the E-mini S&P 500 futures (ES) contract. She would like to explore several options using the Dec 22 ES contract. S&P 500 Index spot price ES Sept 21 ES Dec 21 ES Mar 22 ES Dec 22 4,374.30 4,368.00 4,357.00 4,350.00 4,320.00 a. She is considering a target beta of 0.60. How many ES contracts would she need? b. She is also considering a target beta of 0.40. How many ES contracts would she need? c. Finally, she would like to examine a target beta of 0.20. How many ES contracts would she need? d. Consider that the stock market may rise by up to 12% or decline by as much as 25%. What would be the value of her stock portfolio at these two extremes? e. For each of the three target betas considered in the index hedge, compute the value of the profit/loss she would make on her futures position if the market increased by 12% and if the market declined by 25%. f. If she were to index hedge with a target beta of 0.60, what would be her total portfolio value if the stock market increased 12%? If it declined 25%? g. If she were to index hedge with a target beta of 0.40, what would be her total portfolio value if the stock market increased 12%? If it declined 25%? h. If she were to index hedge with a target beta of 0.20, what would be her total portfolio value if the stock market increased 12%? If it declined 25%