# solution

Suppose that your firm recycles waste materials with high aluminium content and sells scrap aluminium. You have just received a large shipment of waste with aluminium content and you expect to generate 5000 tonnes of scrap aluminium from this batch after processing it, which will take 2 months. Currently no scrap aluminium futures contracts trade anywhere but there are futures contracts on aluminium metal, which is mined and is distinct from scrap aluminium.
i) First, define briefly what cross-hedging is in general. How would your firm above use futures contracts on aluminium in order to hedge itself against movements in scrap aluminium prices? Specifically, would the hedge involve buying or selling aluminium futures contracts?
Cross-hedging is to hedge risk by buying two distinct assets where the price movements of the assets are positively correlated. To reduce the risk of having one of the securities you take opposite positions in each investment since you think that the price of the assets will move in opposite directions.
ii) Given the following set of parameters for the variability and correlation of weekly changes in scrap aluminium spot prices (?S) and 2-month futures prices (?F) for aluminium, determine the optimal number of aluminium futures contracts that your firm needs to buy or short in the futures market to hedge this 5000-tonne job given above. Each futures contract on the CME is on 25 tonnes. Standard deviation of weekly prices changes for spot scrap aluminium, s(?S)= \$28 Standard deviation of weekly prices changes for 2-month aluminium futures, s(?F)= \$31 The correlation coefficient between ?S and ?F, ?(?S, ?F) = 0.90.
b) Now suppose at the time of your firmâ€™s committing to the cross-hedge above, aluminium futures markets are subject to relatively high convenience yields. The spot price of aluminium is \$2250 per tonne but the 2-month futures price is \$2200 per tonne, hence the market is in backwardation. In a couple of weeks immediately after the hedge transaction, the convenience yields disappear, and even though the spot prices of either aluminium or scrap aluminium do not move, the futures market moves to its regular state of contango. Briefly explain how this change from backwardation to contango, when the spot prices are not moving, would affect your hedged position.

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