a) How does a commodity exchange ensure that trade volatility does not go beyond an acceptable level?

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b) What is basis risk and why does it arise?

c) On September 1, an investor holds 10,000 shares of a certain stock. The market price is $62.50 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September S&P 500 futures contract. The futures price on the index is currently 1,000 and one contract is for delivery of $250 times the index. The beta of the stock is 0.8. Using the information above, answer the following questions:

i) With a hedging motive, which position should the investor take in S&P500 futures and in how many contracts?

ii) If the market goes down and the index settles at 750 next month, what will be the gain/loss on the investor's stock portfolio? Will her futures position help her recover the loss? Explain through relevant computations.

d) The spot price for a dividend paying stock is selling for $50 today. The stock will pay a $0.50 dividend in 2 months from now. The 2-month risk-free rate is 2% p.a. compounded continuously and the 6-month risk-free rate is 4% p.a. compounded continuously. A 6-month forward contract on the stock is available at a forward price of $52. Can an arbitrageur gain from this situation? If so, compute the arbitrage profit. What should be the true forward price?