Question

Use the following information:

Today is June 8^th

The company knows that it will need 20,000 barrels of jet oil oil at some time in October or November.

Heating oil futures contracts are currently traded for delivery every month on the exchange

Each contract size is 1,000 barrels.

• the standard deviation of monthly changes in the price of a jet oil is 0.55,
• the standard deviation of monthly changes in the futures prices of a heating oil is 0.71,
• and the coefficient correlation between the two changes is 0.85
• Futures price on June 8 is $85.00 per barrel.

Later, the company finds that it is ready to purchase the jet oil on October 10

Spot price (of jet fuel) and futures price (on heating oil) on Oct. 10 are $89.00 per barrel and $87.80 per barrel.

1. What is the optimal hedge ratio and what is the optimal number of contracts?
2. Should the company take LONG or SHORT?
3. Which delivery month?
4. With asset mismatch and timing mismatch, what is the total effective price paid? And what is the effective price the company paid per barrel?

5. If no cross hedging was necessary (i.e. no asset mismatch, hence the optimal hedge ratio would be 1), assuming that there was a JET OIL FUTURES, what would have been the number of contracts to enter? And what would have been the effective price per barrel and the total effective price paid on Oct. 10?

6. If it was a perfect hedge (no timing mismatch or asset mismatch at all), what would have been the effective price per barrel and the total effective price?

Answer 1

On June 8^th

The company knows that it will need 20,000 barrels of jet oil oil at some time in October or November and

heating oil futures contracts are currently traded for delivery every month on the exchange

Each contract size is 1,000 barrels

Futures price on June 8 is $85.00 per barrel.

Since the company wants 20000 barrels of jet oil as a potential buyer the company is afraid of prices going up so the company should go long on heating oil futures.

optimal hedge ratio:

Formula= coefficient of correlation*standard deviation of change in oil price/standard deviation of changein oil futures price

=0.85*0.55/0.71=0.658 times

Total number of contracts to be undertaken are 20000/1000 =20 barrels

optimal number of contracts are to get the perfect hedge is 0.658*20 =13.16 contracts since the futures are standardised we can get 13 contarcts and the balnce we can hedge by forward contracts.

IF asset and timing mismatch exists:

Futures price on june 8th is $85.00 per barrel on oct 10 the futures price $87.80 per barrel the effective price paid by the company if company long on heating oil futures @ $85(assume ie.., 20000*$(87.80-85)=$56000 gain on offsetting heating oil futures

and spot price of the jet oil is $89 per barrel =$89*20000=$1780000

EFFECTIVE PRICE=$1780000-$56000=$1724000

IF asset and timing mismatch doesnot exists:

Futures of jet oil on june 8 availble at $85 then pay @ 20000*$85=$1700000

IF perfect hedge ie..,they will take 13.16 contracts

Effective price paid= 13160*$85=$1118600