b) An Australian fund manager is concerned about a falling stock market over the next 4 months and wants to reduce exposure to this possible trend. Their portfolio, currently valued at $10,000,000 has a beta of 1.4. How many S&P200 futures contracts (with nominal value of F_0,T x $25 each where F_0,T = 4,100) does the fund have to transact in to decrease the beta of the portfolio to 0.5? Should the fund take a long or short position in these contracts? Explain the reason that this transaction is able to lower the overall beta below that of the portfolio (beta = 1.4) or the futures contract (beta = 1).

(5 marks)