# Hedge Ratio

## 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.

## BREAKING DOWN 'Hedge Ratio'

For example, imagine you are holding \$10,000 in foreign equity, which exposes you to currency risk. If you hedge \$5,000 worth of the equity with a currency position, your hedge ratio is 0.5 (50 / 100). This means that 50% of your equity position is sheltered from exchange rate risk. The hedge ratio is important for investors in futures contracts, as it identifies and minimizes basis 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 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 level. The airline company expects to purchase 15 million gallons of jet fuel over the next year and wishes to hedge its purchase. However, there are not enough futures contracts available to hedge the company's entire purchase. 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.

Over the past three years, the standard deviation of the percentage changes in crude oil futures is 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.