## What is the 'Hedge Ratio'

The hedge ratio compares the value of a position protected through the use of a hedge with the size of the entire position itself. A hedge ratio may also be a comparison of the value of futures contracts purchased or sold to the value of the cash commodity being hedged. Futures contracts are essentially investment vehicles that let the investor lock in a price for a physical asset at some point in the future.

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## BREAKING DOWN 'Hedge Ratio'

For example, imagine you are holding \$10,000 in foreign equity, which exposes you to currency risk. You could enter into a hedge to protect against losses in this position, which can be constructed through a variety of positions to take an offsetting position to the foreign equity investment. If you hedge \$5,000 worth of the equity with a currency position, your hedge ratio is 0.5 (\$5,000 / \$10,000). This means that 50% of your foreign equity investment is sheltered from currency risk.

## Minimum Variance Hedge Ratio

The minimum variance hedge ratio is important when cross hedging, which aims to minimize the variance of the position's value. The minimum variance hedge ratio, or optimal hedge ratio, is an important factor in determining the optimal number of futures contracts to purchase to hedge a position. It is calculated as the product of the correlation coefficient between the changes in the spot and futures prices and the ratio of the standard deviation of the changes in the spot price to the standard deviation of the futures price. After calculating the optimal hedge ratio, the optimal number of contracts needed to hedge a position is calculated by dividing the product of the optimal hedge ratio and the units of the position being hedged by the size of one futures contract.

## Optimal Hedge Ratio Example

For example, assume that an airline company fears that the price of jet fuel will rise after the crude oil market has been trading at depressed levels. The airline company expects to purchase 15 million gallons of jet fuel over the next year, and wishes to hedge its purchase price. Assume that the correlation between crude oil futures and the spot price of jet fuel is 0.95, which is a high degree of correlation. Further assume the standard deviation of crude oil futures and spot jet fuel price is 6% and 3%, respectively. Therefore, the minimum variance hedge ratio is 0.475, or (0.95 * (3%/6%)). The NYMEX Western Texas Intermediate (WTI) crude oil futures contract has a contract size of 1,000 barrels, or 42,000 gallons. The optimal number of contracts is calculated to be 170 contracts, or (0.475 * 15 million)/42,000. Therefore, the airline company would purchase 170 NYMEX WTI crude oil futures contracts.

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