Consider a 1m position in an equity portfolio with a beta of 5. The current value of a stock index is 4,000 points with a continuously compounded dividend yield of 3%. A futures contract written on the index has a contract multiple of 10 and 4 months to maturity. The relevant risk-free rate of interest is 5%.

a) Calculate the futures position required to hedge the portfolio using a beta hedge.

b) After 3 months the spot price of the index has fallen by 10% to 3,600 and the futures position is closed out. What will be the new quoted futures price be and what will be the gain/loss on the futures and spot positions.