Question

4. QT has a network of 150 gasoline outlets throughout the central United States. At any ne time, the company has 1.125 million gallons of gasoline inventory. Derek Larkin has suggested that QT hedge the risk of its gasoline inventories.

a) Derek estimates the following relationship between spot (St) and futures (Ft) prices using the nearby 42000-gallon unleaded regular gasoline contract: Δ St = α + β Δ Ft + єt. If estimate of α = 0.5231 and β = 0.9217 and R2=0.88, what should QT do to hedge its inventory price risk?

b) Derek also estimated the same relationship using the nearby 42000-gallon No. 2 heating oil futures contract with the following results: α = 0.7261 and β = 0.6378 and R2=0.55. Compare the results from the two regressions and cheese the contract that would be the most appropriate.

Answer 1

Here the appropriate hedging technique would be risk minimization.In risk-minimization hedging, one trade futures contracts in the amount that will minimize the variation of the value of a portfolio composed of the cash position and the futures position. To determine the risk-minimizing hedge ratio, one regresses the price changes of the spot price against the hedging instrument’s price changes over the same time period. The slope coefficient from the regression is the risk-minimizing hedge ratio. The regression result indicates the units of the hedging commodity to trade for each unit of the spot commodity

a) QT has 1.125 million gallons of gasoline in inventory. Derek’s results suggest a hedge ratio of 0.9217 gallons of futures for each gallon of inventory. Computing the number of contracts:
No. of contracts 0.9217 (1,125,000 / 42,000) 24.7
Derek’s recommendation would be to sell 25 contracts to hedge QT’s price risk.

b) Comparing the results of the two regressions, the most important consideration is the R2. The R2 tells the percentage of spot price change variation explained by changes in the futures price. A perfect hedging instrument would explain 100 percent of the price change variation. Failing that, Derek should recommend the hedging instrument with the highest R2
. In this case, the unleaded gasoline contract
with its R2 of 88 percent dominates the No. 2 heating oil contract with its R2 of 55 percent

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