In: Finance
If the minimum-variance hedge ratio is -1, then which of the following statements is true?
(a) Changes in spot and futures prices are perfectly negatively correlated. |
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(b) The standard deviations of spot and futures price changes are the same. |
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(c) The minimum-variance hedge for a long spot exposure is a short futures exposure of the same size. |
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(d) All of the above. |
Let explore every option one by one
A) Changes in spot and futures prices are perfectly negatively correlated.
Formula for minimum variance hedge ratio = correlation between spot and future prices * standard deviation of spot / standard deviation of futures = -1
As standard deviation cannot be negative, correlation between spot and futures comes to be negative. The ratio can come out to be -1 only if standard deviation of both spot and futures is equal and correlation between the prices is -1.
So, statement A is true.
B) The standard deviations of spot and futures price changes are the same.
As explained in A part, statement B is true.
C) The minimum-variance hedge for a long spot exposure is a short futures exposure of the same size.
Correlation between prices of spot and futures is perfectly negatively correlated. It means 1% increase in spot price would lead to 1% decrease in futures. It means that, if we long (buy) spot , it is equivalent to shorting ( sell) future, for same quantity, The results would be same as perfect negative correlation exists.
Hence statement C is also true.
Correct answer - Statement D