You hold a portfolio of $10m consisting of 5 "small-cap" stocks, which have a portfolio beta of 1.2. The risk-free rate is r=2%pa. (simple rate) The value of the S&P500 index is currently 1000 (2nd January) and the index futures price (on the S&P500), with 1-year maturity is F0 = S0 (1+rT) = 1020. For the purposes of this question, you can ignore dividends, and you can assume that interest rates remain unchanged.

 

(a)  Explain how you can use stock index futures contracts to hedge over the next2 months.

(b)  What gain or loss will you make on the hedge if the S&P500 index rises by 10%over the next 2 months? 

(c)  Suppose that on 2nd January you believe that the stock market will rise substantially over the next 2 months. Explain how you could achieve an "effective/desired beta" of 3. 

(d)  Assume that you construct the position as in your answer to part (c) of this question. Explain what happens if the S&P500 falls by 5% over the next 2 months.