You short an equity portfolio worth $50 million with a market beta of 0.7. The market index is currently at 1000.
a. Find the delta of your portfolio.
b. Suppose you buy 150 futures contracts to buy the market index one year from now. The contract multiplier is 250. What is the delta of the futures?
c. What is the dollar change in the value of your equity portfolio if the market index increases by 50 points (5%)?
d. What is the dollar change in the payoff of your futures position if the market index increases by 50 points (5%)?
e. Based on your answers in parts c and d, do you conclude that you have a favorable deal, or are you facing any risk?
f. If you want to hedge away your risk completely, what changes in your futures position should you make?