Question

A US airline company will purchase 400,000 gallons of jet fuel after one month and the company wants to

do cross hedging using heating oil futures. The standard deviation of monthly changes in the spot price of

jet fuel is (in cents per gallon) 300; the standard deviation of monthly changes in the futures price for the

heating oil futures contract is (in cents per gallon) 407. The coefficient of correlation between the jet fuel

price changes and the futures price changes is 0.75. Each heating oil futures contract is for delivery of 2,000

gallons of heating oil. The current spot price of jet fuel is $1.55 per gallon and the futures price of heating oil is

$1.97 per gallon. What is the optimal number of contracts with tailing adjustment?

Answer 1

Answer:

Let us first understand what is tailing adjustment.Tailing Adjustment refers to the adjustment to be made to the optimal number of contracts required for hedging so as to account for the daily settlement in general and the possible cash inflows/outflows generated during the life of the hedge in particular

Optimal Number of Contracts with tailing adjustment= ($ value of position that is being hedged/$value of Futures Contract)* Minimum Variance Hedge Ratio

Now let us first calculate the Minimum Variance hedge ratio:

Minimum Variance Hedge Ratio= Correlation Coefficient*[Standard Deviation of the Asset to be hedged]/[Standard Deviation of the asset with which it will be hedged]

As given in the question: Correlation Coefficient= 0.75, Standard Deviation of the Asset to be hedged(Jet Fuel)= 300, Standard Deviation of the asset with which it can be hedged(heating oil)= 407.Putting these values into the above formula we get:

Minimum Variance Hedge Ratio= 0.75*[300/407] ie. 0.553.....................(I)

Now let us calculate the dollar value of position that is being hedged

Dollar Value of Position that is being hedged= Total Quantity of Jet Fuel Required*Spot Price of Jet Fuel

As given in the question: Total Quantity of Jet Fuel required= 400,000 gallons, Spot Price of Jet Fuel= $1.55 per gallon .Putting these values into the Dollar Value Position Formula we get:

Dollar Value Position that is being hedged= 400,000*1.55 ie. $ 620,000..................(II)

Now let us calculate the dollar value position of futures contract:

Dollar Value of Futures Contract(Heating Oil) = Contract Size* Futures Contract Price

As given in the question : Contract Size= 2000 gallons Futures Contract Price= $ 1.97 per gallon . Putting these values in the above formula we get:

Dollar Value of Futures Contract(Heating Oil) = 2000*1.97 ie. $ 3940...................(III)

Substituting (I),(II) and (III) in the formula for Optimal Contracts we get:

Optimal Number of Contracts with tailing adjustment= 0.553*[620,000/3940] ie. 87 contracts.