Question

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.

Answer 1

We have June spot Price = 1480.60

June Future Price = 1472.50

August Spot = 1489.70

August Future Price = 1487.80

Optimal Hedge Ratio (R) = correlation between spot and future * (Standard dev of Spot / Std dev of future)

We calculate the standard dev as = (X - X(Mean))² / (n)

Std dev spot = 6.43 , Std dev Fut = 10.81 and Corr = 1 (being the same asset both spot and future approx. have a correlation of 1)

R = 1 * (4.55 / 7.65) = 0.59

Optimal Hedge ratio = 0.59

No of contracts = R X (Hedge Amount / Contract Size)

= 0.59 X (1000 /100)

= 0.59 X 10 = 5.9 = 6 Contracts Approx