a) The current price of a non-dividend-paying stock is $30 and the stock is expected to pay a dividend of $0

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a) The current price of a non-dividend-paying stock is $30 and the stock is expected to pay a dividend of $0.5 in one months' time and then 0.5 again in four months' time. The risk-free rate of return is 6.00% p.a. (Continuously compounded). If the price on a six-month forward contract is F0,0.5=28, is there an arbitrage opportunity? If arbitrage is possible, design a strategy to take advantage of it. What is the arbitrage profit earned from this strategy?

b) An Australia fund manager is expecting a rising stock market over the next 6 months and wants to gain an increased exposure to this trend. Their portfolio currently valued at $50.000.000 has a beta of 0.8. How many S&P200 futures contracts (with nominal value of F0,t x $25 each where F0,t = 4,000) does the fund have to transact in to increase the beta of the portfolio to 1.4? should the fund take a long or short position in these contracts? Why would the fund manager fail to get the target beta by simply investing additional money into the S&P200 stocks?