Terlingua Transportation Co. (TTC) is a regional shipper. It is most cost efficient for the companys diesel fuel trucks to refuel at retail outlets along the shipping routes. However, retail prices tend to be volatile. Hence, managers at TTC have decided to hedge future retail purchases of fuel by means of New York Harbor ULSD (ultra low sulphur diesel) futures contracts. Each contract has 42,000 gallons as the underlying asset.

You are a financial analyst for TTC. Today is April. Your immediate task is to hedge the price risk of diesel future purchases in three months (i.e., in July). You expect that TTC trucks will need to buy a total of 700,000 gallons of diesel fuel in July. You plan to apply dynamic hedging.

Based on calculations for a 3-month hedge, you determine that your company needs to take a long position in 20 of the August futures contracts today.

Time passes. Today now is May. Forecast for quantity of the July purchase of diesel fuel is unchanged. You plan to continue hedging with August contracts.

You have the following statistical data. All spot prices are retail prices for diesel fuel. All futures prices are for the New York Harbor ULSD futures. Standard deviations are in cents per gallon.

• standard deviation of 1-month changes in spot prices: 19
• standard deviation of 2-month changes in spot prices: 24
• standard deviation of 3-month changes in spot prices: 27

• standard deviation of 1-month changes in futures prices: 20
• standard deviation of 2-month changes in futures prices: 26
• standard deviation of 3-month changes in spot prices: 36

• 1-month correlation between spot and futures prices: 1.13
• 2-month correlation between spot and futures prices: 1.07
• 3-month correlation between spot and futures prices: 0.86

In your calculations for optimal number of futures contracts, you optimize using the formulas for cross hedging. Calculate the change in optimal number of futures contracts that your company should be long.

Report the change as an integer value. If you decrease the number of contracts, report a negative number. (When you calculate the new value for N*, round to the nearest integer.)