[Note: There is an error in some versions of the text on page 59 in Example 3.4. The spot price on November 10 is $95 (not $92). The December futures price on November 10 is $92 as stated. That is why the basis is $3.];1. A mining company knows that it will have 2,000 ounces of gold to sell in six months. The costs of production are $900 per ounce. The six-month futures price of gold is $1,215 per ounce. One contract is for 100 ounces.;a. To reduce risk, does this company need a short hedge or a long hedge? For how many contracts?;b. Suppose the price of gold in six months turns out to be $1,100 per ounce. Find the profit/loss on production, the profit/loss on the futures contracts, and the total profit/loss.;c. Suppose the price of gold in six months turns out to be $1,400 per ounce. Find the profit/loss on production, the profit/loss on the futures contracts, and the total profit/loss.;d. Does hedging always produce a better result than not hedging? Explain, using your answers to parts (b) and (c) as examples.;2. It is now June. A company knows that it will need 5,000 barrels of medium sour crude oil in September. It uses the October CME Group futures contract to hedge the price it will pay. Each contract is on 1,000 barrels of light sweet crude.;a. Should the company take a long position or short position in the futures contract?;b. What are the two sources of basis risk in this scenario? Be specific.;c. Suppose that the correlation coefficient between medium sour and light sweet is 0.9, the standard deviation of the spot price of medium sour is 0.4, and the standard deviation of the futures price of light sweet is 0.2. Find the minimum variance hedge ratio.;d. Find the optimal number of contracts without tailing the hedge.;e. How many contracts would have been needed without accounting for the difference between medium sour and light crude? Intuitively explain the difference between this answer and the answer to part (d). Restating the formula is not an explanation.;3. A company has a $30 million portfolio with a beta of 1.4. It would like to use futures contracts on the S&P 500 to hedge its risk. The index futures price is currently 1210, and each contract is for delivery of $250 times the index. Answer these questions. Show work. Be sure to state whether the position is long or short.;a. What is the hedge that minimizes risk?;b. What should the company do if it wants to reduce the beta of the portfolio to 0.7?;c. What if it wanted to increase the beta to 1.8?;4. You own 1,000 shares of Apple stock, each worth $460. The beta of Apple is 1.2. You are confident that Apple will perform better than the market, but you are worried that the overall market will be bad. A mini S&P500 futures contract is available with a price of 1380, with one contract for delivery of $50 times the index.;a. How many contracts should be shorted? Show work.;b. Suppose that Apple stock falls 10% to 414, while the market (as measured by the S&P 500 index) falls 15% to 1173. Find the profit/loss on the 1,000 shares of Apple stock, the profit/loss on the futures contracts, and the overall profit/loss. Show work. Did the position work as intended? Explain.
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