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

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?