If the minimum-variance hedge ratio is -1, then which of the following statements is true? (a)...

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.
		(b) The standard deviations of spot and futures price changes are the same.
		(c) The minimum-variance hedge for a long spot exposure is a short futures exposure of the same size.
		(d) All of the above.

Solutions

Expert Solution

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

jeff jeffy answered 1 year ago

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