On June 20, a Palladium user knows that they need 1,000 troy ounces of Palladium on August 20 so they enter a long position on a Palladium futures contract.

It has agreed to buy Palladium at the spot price on August 20.

On June 20, the spot price is $1,480.60 and the futures price is $1,472.50.

Each futures contract is for the delivery of 100 troy ounces of Palladium.

The company can hedge its exposure by buying 10 August futures contracts.

It closes out its long August futures position in August.

Spot Price on August 20 = $1,489.70

• Futures price on August 20 = $1,487.80
• Futures gain = 1,489.70-1,487.80- = $1.90
• Price paid with hedging = 1,487.80-1.90 = $1,485.90

Specify the optimal hedge ratio and the optimal number of futures contracts for your hedge. Assume the variability of the spot and futures price movements over the two-month period prior to the last trading date was consistent with that of the previous two months.