Question

A trader owns 55,000 gallons of jet fuel asset and decides to hedge the value of her position with futures contracts on Nat Gas. Each futures contract is on 5,000 MMBtu. The spot price of the jet fuel is $28/gallon and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.43. The futures price of the Nat Gas is $27 per MMBtu and the standard deviation of the change in this over the life of the hedge is $0.40. The coefficient of correlation between the spot price change and futures price change is 0.95.

(a) What is the minimum variance hedge ratio?
(b) Should the hedger take a long or short futures position?
(c) What is the optimal number of futures contracts when adjustments for daily settlement are not considered?

Answer 1

(a) The minimum variance hedge ratio is 1.021875.

(b) The hedger should take a long futures position.

(c) The optimal number of futures contracts is 11.

Step-by-step explanation:

(a) The minimum variance hedge ratio can be calculated using the formula:

VH = p * (SDs / SDf)

Where VH is the hedge ratio, p is the coefficient of correlation between the spot price change and futures price change, SDs is the standard deviation of the change in spot price, and SDf is the standard deviation of the change in futures price. Plugging in the given values, we get:

VH = 0.95 * (0.43 / 0.40) = 1.021875

(b) The hedger should take a long futures position because the minimum variance hedge ratio is greater than 1. This means that the hedger should buy more futures contracts than the amount of jet fuel to be hedged in order to have an effective hedge.

(c) The optimal number of futures contracts can be calculated using the formula:

Number of futures contracts = (VH * Quantity of jet fuel) / Quantity per futures contract

Plugging in the given values, we get:

Number of futures contracts = (1.021875 * 55000) / 5000 = 11.24

Since the number of futures contracts cannot be fractional, the trader should round down and take 11 futures contracts when adjustments for daily settlement are not considered.