Question

A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuel's price change has a standard deviation that is 50% greater than price changes in gasoline futures prices. If gasoline futures are used to hedge the exposure what should the hedge ratio be? What is the company's exposure measured in gallons of the new fuel? What position measured in gallons should the company take in gasoline futures? How many gasoline futures contracts should be traded? Each contract is on 42,000 gallons.

Answer 1

Answer:

0.9; 100 million; 90 million; 2,143

Explanation:

The new fuel's price change has a standard deviation that is 50% greater than price changes in gasoline futures prices.

So, if standard deviation of future prices is taken as '1' then for spot price it will be 50% higher, i.e 1.5

The hedge ratio:

= Correlation × (standard deviation of spot price ÷ Standard deviation of future prices)

= 0.6 × (1.5 ÷ 1)

= 0.9

The company has an exposure of 100 million gallons of the new fuel.

Gallons in future gasoline:

= Hedge ratio × 100 million gallons of the new fuel

= 0.9 × 100

= 90 million

Each contract is on 42,000 gallons, then

Number of gasoline futures contracts should be traded:

= 90,000,000 ÷ 42,000

= 2,142.9 or 2,143