You use silver wire in manufacturing. You are looking to buy 100,000 oz of silver in
three months’ time and need to hedge silver price changes over these three months.
One COMEX silver futures contract is for 5,000 oz. You run a regression of daily silver
spot price changes on silver futures price changes and find that
δs = 0.03 + 0.89δF +
What should be the size (number of contracts) of your optimal futures position? Should
this be long or short?
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To determine the optimal futures position, we need to consider the hedge ratio. The hedge ratio is the coefficient of the futures price changes in the regression equation, which in this case is 0.89.
The hedge ratio represents the sensitivity of the spot price changes to the futures price changes. A hedge ratio of 0.89 means that a 1% change in the futures price is expected to lead to a 0.89% change in the spot price.
Since you are looking to buy 100,000 oz of silver, we need to calculate the number of contracts required.
Number of contracts = (Total ounces to buy) / (Ounces per contract)
Number of contracts = 100,000 oz / 5,000 oz per contract
Number of contracts = 20 contracts
Now we know that the optimal futures position should involve 20 contracts.
To determine whether the position should be long or short, we need to consider the regression equation. The coefficient of the futures price changes (0.89) is positive, indicating a positive relationship between spot and futures prices. Therefore, the optimal futures position should be long.
Hence, the optimal futures position is 20 contracts and it should be long.
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