Question

An airline expects to purchase 2 million gallons of jet fuel in 1 month and decides to use heating oil futures for hedging. The standard deviation of the change in the jet fuel price per gallon. The standard deviation of the change in the futures price of heating oil per gallon. Their correlation coefficient. Each heating oil contract traded by the CME Group is on 42,000 gallons of heating oil. How many contracts should the company buy or sell? Round to the nearest whole number.

Answer 1

Optimal number of contracts to be hedged = h*(Qo/Qf)

Where Qf = size of one future contract (in units - oil)

Qo - Size of position being hedged ( in units - Jet fuel price)

and h signify the proportion of the exposure that should optimally be hedged and is given by

h =  ρ *(σS /σF)

σS = the standard deviation of ΔS, the change in the spot price (Jet fuel price) during the hedging period,

σF = the standard deviation of ΔF, the change in the futures price (Oil price) during the hedging period

ρ = the coefficient of correlation between ΔS and ΔF.

As the above values are not given in the question we can simmply put the values and can calculate the h*

Optimal number of contracts to be hedged = h*(Qo/Qf)

= h*(2,000,000)/42,000