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

The hedge ratio is 0.9, and the company has an exposure of 100 million gallons. The company should take a position of approximately 90 million gallons in gasoline futures, which corresponds to about 2143 contracts.

Step-by-step explanation:

The hedge ratio can be calculated using the formula Hedge Ratio = Correlation Coefficient * (Standard Deviation of the Asset's Price Changes / Standard Deviation of the Futures Price Changes). Given that the correlation between the new fuel's price changes and gasoline futures price changes is 0.6 and the standard deviation of the new fuel's price changes is 50% greater than that of gasoline futures, the hedge ratio is 0.6 * (1 + 0.5) = 0.9.

The company's exposure measured in gallons is the amount it stands to lose for a 1 cent increase in the price per gallon of the new fuel. As it loses $1 million for each 1 cent increase, and each gallon increments by 1 cent, the exposure is $1 million / ($0.01/gallon) = 100 million gallons.

Given this exposure, the company should take a position in gasoline futures that is the product of the exposure and the hedge ratio: 100 million gallons * 0.9 = 90 million gallons. To find out the number of gasoline futures contracts to be traded, we divide the gallons hedged by the size of one contract: 90 million gallons / 42,000 gallons per contract ≈ 2143 contracts. Therefore, the company should trade approximately 2143 gasoline futures contracts to hedge its exposure.

Answer 2

0.9; 100 million; 90 million; 2,143

Step-by-step 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