# Hedge Ratio: Definition – Explanation – Formula – Example

## What Is the Hedge Ratio? The hedge ratio is the hedged position value divided by the total position value.  A ratio of 1 or 100% means that the position is fully hedged and a ratio of 0 means it is not hedged at all.

The ratio is the comparative value of an investor’s open position to their overall position. In other words, it compares the value of the investor’s position that is protected through hedging to the total size of the position or portfolio.

Investors are subject to varying amounts of risk.  To compensate, they can actively choose to reduce certain risks through hedging.  A hedge is a crucial component of the risk management process. Hedging a portfolio helps to mitigate risk and manage one’s exposure. But how much is sufficient?  Under-hedging leaves the position exposed. Yet, over-hedging can result in unnecessary expenses that eat into potential yields and profits.   Once you have hedged your portfolio, you might want to know what portion or percentage of your portfolio is risk protected. This is where the hedge ratio formula can shed some light.

## What is the Hedge Ratio Formula?

The hedge ratio compares the value of an open position’s hedging to the overall position. A value of 1, or 100%, means that the open position has been fully hedged. On the other hand, a value of 0, or 0%, means that the open position hasn’t been hedged in any way.

### Hedge Ratio = Hedging Value / Total Position Value

The hedge ratio is expressed as a decimal or a fraction.  It identifies the amount of risk exposure assumed by remaining active in a trade or an investment. This metric can help an investor understand their exposure when establishing a trading position. A ratio of 0 means the position is not hedged.  Conversely, a ratio of 1 or 100% indicates the position is fully hedged.

## How the Hedge Ratio Works

Imagine you hold \$20,000 worth of mutual funds in an overseas market.  However, this position exposes you to currency risk. To protect your position from currency losses, you could enter into a hedge. You can arrange this through a variety of options that take an offsetting position to the foreign equity investment.  If you are hedging \$12,000 worth of the equity with a currency position, your hedge ratio is 0.6 (\$12,000 / \$20,000). In other words,  60% of your foreign equity investment is hedged from currency risk.

### Types of Hedging

There are primarily two types of hedging:

• Static hedging – The number of hedging contracts doesn’t change over time despite any movement or change in the hedging instrument’s price.  A static hedge is when the hedging position or the number of hedging contracts isn’t adjusted regardless of the movement in the price of the hedging instrument.
• Dynamic hedging – The investor changes the number of buy/sell hedging contracts so as to bring the hedge ratio towards the target ratio.  Dynamic hedging is when an increasing number of hedging contracts are bought and/or sold over the holding period.  This is to influence the hedge ratio and bring it towards the target value.

## Optimal Hedge Ratio

The optimal hedge ratio is also known as the minimum variance hedge ratio.  It is important when cross-hedging to minimize the variance of the position’s value. This metric can help to determine the optimal number of futures contracts to purchase to protect a position. It is calculated by determining the correlation coefficient between the changes in the spot and futures prices and the ratio.  This coefficient is then multiplied by the ratio of the spot price deviation to the futures price deviation.

After calculating the ratio, one can then calculate the optimal number of contracts needed to hedge a position.  This can be computed by dividing the product of the optimal hedge ratio and the units of the position being hedged by the size of one futures contract.

## What is the Optimal Hedge Ratio Formula?

The optimal hedge ratio is an investment risk management ratio for hedging an investment.  It can reveal the percentage of a hedging instrument that an investor should hedge. The ratio is also known as the minimum variance hedge ratio. It is most often used when cross-hedging.

Optimal Hedge Ratio = Correlation Coefficient x (Spot Price Deviation / Futures Price Deviation)

• Correlation coefficient of the changes in the spot and futures prices
• Standard deviation of changes in the spot price
• Standard deviation of changes in the futures price

After calculating the 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

An overland freight delivery company believes the price of fuel may increase after trading at a stable range for the past 24 months.  The shipping company expects to purchase 10 million gallons of diesel fuel over the next 12 months.  Management has decided to hedge the purchase price of its projected fuel consumption.

### Step 1

• Correlation coefficient – 0.97 is the correlation between crude oil futures and the spot price of diesel fuel.
• Crude oil futures – 5% (Standard deviation)
• Spot diesel fuel price – 3% (Standard deviation

Therefore, the optimal hedge ratio is 0.582, or [0.97 * (3% / 5%)].

### Step 2

Crude oil futures contracts typically have a contract size of 1,000 barrels or 42,000 gallons. The optimal number of contracts is calculated to be 139-140 contracts, or [(0.582 x 10 million gallons) / 42,000 gallons].

As a result, the freight shipping company would purchase approximately 139 crude oil futures contracts.

## Advantages and Disadvantages of Hedge Ratio

The advantages of the ratio:

• Optimize performance – Regular hedgers use this ratio to estimate and optimize asset performance.
• Easy to calculate – It is simple to calculate. The calculation involves the use of just two inputs – total exposure and hedge position.
• Reliable estimate – This ratio helps investors to get an idea of their exposure at the time of taking a position.

The disadvantages of the ratio:

• Potential mismatch – There may be cases of currency mismatch. This happens when there are no futures of the currency in which the investor has exposure.
• Not perfect – In practice, it is very difficult to get a perfect hedge.

## Final Words

The hedge ratio is quite useful from a risk management standpoint. It gives investors a good idea of their risk position, and also how much they need to hedge. However, investors should not exclusively depend on it. There are other measures as well to help gauge the risk level. Also, hedging is not free.  Hedging requires futures contracts to be purchased.  This additional cost will eat into potential gains and profits.  Think of hedging like insurance.  Nobody likes to pay the premiums.  However, it is great to have it when things go wrong.

## Up next: What Does It Mean – To Stem the Tide? Stem the tide is an expression meaning to stop or at least gain control of a situation.  It usually refers to something bad that is happening on a large scale.  Therefore,

In the context of an investment or a trade, to stem the tide means to find a way to stop, slow, or reverse a prevailing trend. The expression is often used when referring to one’s own trading position.

If the value of a trade or investment is losing money, closing the position would, in effect stem the tide or stop the money loss.  To stop the bleeding is another phrase in the same context describing a similar circumstance.