Minimum Variance Hedge Ratio Overview Practice Questions PDF

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Professor Joel Rentzler
Overview of the concept of the minimum variance hedge ratio and one example question as to how it is used in the futures market...

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Minimum Variance Hedge Ratio Overview & Practice Questions Minimum Variance Hedge Ratio The Minimum Variance Hedge Ratio (MVHR) is the ratio of futures contracts to cash that provides the smallest variance of price changes of a hedged position The MVHR allows investors to know the amount of futures contracts they need to purchase that provides them with an efficient hedging strategy while taking lower risks The MVHR is denoted by the symbol

h∗ h∗ = ρ(ΔS, ΔF )

σ(ΔS ) σ(ΔF )

Where

ρ(ΔS, ΔF ) is the coefficient correlation between the change in the spot market prices and futures market prices

σ(ΔS ) is the standard deviation in the change in the spot market prices σ(ΔF ) is the standard deviation of the change in the futures market prices

Applying MVHR to Short & Long Hedges Now when we look at the profit of a hedge position for both long and short hedgers changes to

ΠS H ∣LH = ΔS − h ∗ ΔF

Practice Question: American Airlines

Scenario: American Airlines believes that it will need to buy 840,000 galloons of jet fuel in 3 months. The standard deviation of the change in price per galloon of jet fuel over a 3-month period is calculated as 0.032. The company chooses to hedge by taking a position in futures contracts on heating oil. The standard deviation of the change in the futures price over a 3-month period is 0.040. The coefficient of correlation between the 3-month change in the price of jet fuel and the 3-month change in the futures price is 0.8. One heating oil futures contract is 42,000 gallons 1. What type of hedger should American Airlines be - short or long? 2. What is the minimum variance hedge ratio? 3. How many futures contracts should they use to obtain the minimum variance hedge ratio? 4. What could happen to jeopardize this hedge? a. What is this risk called Given Information

ρ(ΔS, ΔF ) = 0.8 σ(ΔS ) = 0.032 σ(ΔF )= 0.040 Futures Contract Multiplier = 42,000 Spot position size = 840,000 Solve 1. American Airlines should be a Long Hedger as the company is looking to purchase spot three months in the future which means its hedging against price increases. AA can make up for potential losses in the spot market by making a profit in the futures market with a long position. 2. Minimum Variance Hedge Ratio Equation

h∗ = ρ(ΔS, ΔF )

σ(ΔS ) σ(ΔF )

h∗ = 0.8

0.032 0.040

h∗ = 0.64 3. The amount of futures contract they need to obtain is 13 contracts

840, 000 42, 000 840, 000 42, 000

∗ 0.64

∗ 0.64 = 12.8 ≈ 13

4. The hedge can be jeopardize in the event that the prices of the futures market do not offset the losses incurred in the spot market. Since AA is hedging their spot position (jet fuel) with a futures contract (heating oils) they are subjected to cross hedging....