It is March 15, 2020 and an investment company holds a portfolio of stocks worth 100 mil. USD with a beta factor of 1.6. The company would like to hedge against negative stock market movements during the period of next 2 months by using June 2020 E-Mini S&P 500 futures contracts (with each contract being on the delivery of $ 50 times the index). The current S&P 500 index value is 2711, the risk-free interest rate is 2% p.a. for all maturities, and the dividend yield of the stock index is 3% p.a.

(a) Calculate the equilibrium price of the June 2020 E-Mini S&P 500 futures contract

(b) Assuming that the futures price equals to the equilibrium futures price, calculate what position should the company take in order to hedge itself against the stock index movements over the next 2 months?

(c) Estimate the profit/loss on the hedged portfolio in the case that the S&P500 index moves 10% up or 10% down over the next 2 months, assuming that the futures price after 2 months is equal to the equilibrium futures price in 2 months and the interest rate and dividend yield stay the same

(d) What position should the company take if it decides instead that it wants to increase its beta to 2.4?