Lisa Borga

## What Is the Hedge Ratio?

The hedge ratio is a metric that is used for risk management in a portfolio.

It is the comparative value of an investor’s open position to their overall position.

This ratio is also useful for comparing the value of futures contracts being bought or sold to that of any cash commodity that is being hedged.

A futures contract is basically an investment vehicle in which the investor locks in the price of a commodity, asset, or security that will be purchased or sold at a future date.

## Understanding the Hedge Ratio

The formula for the hedge ratio is:

The hedge value is the total dollars being invested by the investor.

The total position value is the amount the investor is investing in the asset.

The hedge ratio is presented in the form of a fraction or decimal.

The ratio is used to measure the risk an investor is taking by taking part in an investment or by trading.

If an investor uses this ratio, they can get a better understanding of the risk they are taking when making an investment.

If the hedge ratio is zero, the position is not hedged. In contrast, a hedge ratio of 1 to 100 means the position of the investor is fully hedged.

If a hedge ratio is approaching 1, it means that an investor’s exposure with regard to an underlying asset is decreasing.

If the hedge ratio gets close to zero, it will no longer be hedged.

The minimum-variance hedge ratio is of vital importance when an investor is cross-hedging, which is a way to manage risk by purchasing two similar investments that also have similar price movements so as to offset the financial risk of the one investment with the financial gain of the other.

The minimum variance hedge ratio is also crucial in deciding the ideal number of futures contracts that should be purchased in order to hedge a position.

## Ideal Hedge Ratio

The ideal hedge ratio lets an investor know what the hedge ratio of their portfolio should be.

This makes a useful comparison to the hedge ratio, which lets an investor know the percentage of their portfolio that is risk protected.

The optimal hedge ratio formula is:

ρ * (σs / σf)

ρ = correlation coefficient of the change in the future and spot price

σs = standard deviation of the change in the spot price

σf = standard deviation of the change in the future price

Here is an example using this formula.

Suppose a tofu manufacturer expects the price of soybeans to increase in the future.

They typically purchase approximately 16,000,000 bushels per year.

Because the company expects a significant price increase, the company intends to hedge the soybean’s purchase price.

Therefore, the company would like to know the l deal hedge it should attempt.

For this example, we will assume a correlation of .90 between the futures price and the spot price of soybeans.

The standard deviation for the spot price for soybeans is 4%, and the standard deviation of soybean futures is 7%.

This will give an optimal hedge quantity of 9,136,000 bushels as shown below.

[.90 x (.04 / .07)] = .571 = ideal hedge ratio

.571 x 16,000,000 = 9,136,000

### Advantages of the Hedge Ratio

There are a number of advantages to using the hedge ratio. Here are a few of them.

• The hedge ratio can easily be computed and used since it simply compares the value of the investor’s open position to their overall position.
• The hedge ratio can be used as a way to optimize the performance of your asset.
• An investor can use a hedge ratio to help understand how much of their portfolio is risk protected.

### Disadvantages of the Hedge Ratio

• The hedge ratio can lead to currency mismatch in certain situations.
• It is very difficult to achieve a perfect hedge.

## Hedge Ratio Example

Suppose a wet-mill plant is worried about the rising price of corn.

The mill is planning to purchase 25 million bushels of corn during the year.

Therefore, the plant wants to hedge the purchase price.

The correlation between the spot price of corn and the futures price is .90.

We will also assume that the standard deviation for the spot price of corn is 4%, and the standard deviation for corn futures is 7%.

This means there is a minimum variance hedge ratio of:

.514 (.90 x (.04 / .07)

The contract size for corn futures is 5,000 bushels.

Therefore, the ideal number of contracts for the wet-mill to buy would be:

2,570 [.514 x (25,000,000 / 5,000)]

Thus, the wet-mill should purchase 2,570 corn futures contracts.

## Key Takeaways

• The hedge ratio is a ratio that compares the value of a hedged position to the value of the overall position.
• The minimum variance hedge ratio can help investors to decide the best number of options contracts they should have to hedge their position.
• The minimum variance hedge ratio is crucial when cross-hedging as it allows people to minimize the variance in the value of the position.

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1. Florida International University "COMPARING HEDGE RATIO METHODOLOGIES FOR FIXED-INCOME INVESTMENTS" White paper. August 29, 2022