Suppose you own a $1,000,000 equity portfolio with a beta of 1.4, and are concerned with how the market will turn out in the next six months and want to reduce the beta to 0.8.
You are given the following information:
S and p 500 index: 1,800
S and p 500 7 month futures price: 1830
Risk-free int. rate: 2.5% annual
Div. Yield on the index: 1.5% annual
Question 1: If one futures contract is 250 times the index, how would you create a hedge that accomplishes this goal of reducing the hedge?
Question 2: the 1-month s and p 500 futures price is expected to be 0.2% higher than the actual index in six months. If the S and P index is 1,700 at that time, what is the value of the hedged and the unhedged portfolio?
Question 3: What happens to the futures position if the S and p 500 index rises to 1,900?