Jumbo Airline, a hypothetical company, will purchase 2.5 million gallons of jet fuel in one month and hedges using heating oil futures. Suppose that size of one heating oil futures is unknown. From historical data sigma=0.0325, sigma= 0.0295, and sigma= 0.908. In addition, the spot price is 1.95 and the futures price is 1.98 (both dollars per gallon).

(1) What will be the size of heating oil futures if 4.51 heating oil futures are required for optimal hedge with tailing? please explain.

(2) What will be the size of heating oil futures if 4.51 heating oil futures are required for optimal hedge withour tailing? please explain