# Optimal Hedge Ratio Calculator

Created by Wei Bin Loo
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Sep 29, 2023

We built our optimal hedge ratio calculator to help you calculate the optimal proportion of your investment portfolio that should be hedged to minimize investment risks. In other words, this metric can inform you of the value of your portfolio that should be hedged to protect you from market risks.

This article will explain what the optimal hedge ratio is and how to calculate the metric using the optimal hedge ratio formula. Furthermore, we will help you understand the concept by showing you some optimal hedge ratio examples.

## What is the optimal hedge ratio?

The optimal hedge ratio is a very famous risk management metric. It is defined as the proportion of hedging instruments a portfolio should have to minimize its risk. You can use this metric to calculate risk. This metric is calculated using the standard deviation of the asset's spot and future price, as well as the correlation between them.

Risk in a portfolio is usually defined as its variance or standard deviation. The higher the variance, the higher the investment risk. Thus, the optimal hedge ratio is also the proportion of the hedging instrument that will minimize the portfolio's variance.

Without further ado, let's look at how the optimal hedge ratio calculator works.

## How to calculate the optimal hedge ratio? The optimal hedge ratio formula

Now, let's take the Portfolio Alpha in Company Alpha as an optimal hedge ratio example in calculating the metric:

• Portfolio: Portfolio Alpha;
• Standard deviation of the spot price: 0.05;
• Standard deviation of the future price: 0.072; and
• Correlation coefficient between the changes in the spot and futures prices: 0.83.

The optimal hedge ratio calculation requires four steps:

1. Calculate the standard deviation of the spot price

The spot price sd., which is the standard deviation of the spot price, is the dispersion of the spot price from its mean. The higher the standard deviation, the more risky the asset.

In our example, the spot price sd. is 0.05.

2. Determine the standard deviation of the future price

The future price sd., which is the standard deviation of the future price, is the variance of the future price. The future price sd. for Portfolio Alpha is 0.072.

3. Determine the correlation coefficient of the changes in the spot and futures prices

The correlation coefficient is the metric that measures the correlation between spot and futures prices. The higher the correlation coefficient, the higher the correlation between the spot and futures prices.

Company Alpha's correlation coefficient is 0.83.

4. Calculate the optimal hedge ratio

Now, it is time to calculate the optimal hedge ratio. It can be calculated using the optimal hedge ratio formula below:

optimal hedge ratio = correlation coefficient × (spot price sd. / future price sd.)

where sd. stands for standard deviation. Thus, the optimal hedge ratio of this portfolio is 0.83 × (0.05 / 0.072) = 0.58.

If all of these still seem confusing, don't worry. Just put in the inputs and let our optimal hedge ratio calculator do the job for you.

## The applications of the optimal hedge ratio calculator

After discussing what the optimal hedge ratio is and looking at a optimal hedge ratio example, let's talk about some of the applications of this metric.

The optimal hedge ratio has two main applications in portfolio management:

1. It is used to measure and allow investors to evaluate the riskiness of the portfolio.

2. The optimal hedge ratio formula can act as a guideline to help investors create an optimal portfolio.

However, it is essential to realize that the metric is not absolute and can only act as a guideline as different investors have different investment requirements.

## FAQ

### Can optimal hedge ratio be negative?

Mathematically speaking, yes, the optimal hedge ratio can be negative. As standard deviations cannot be negative under any conditions, the optimal hedge ratio can only be negative when the correlation between the spot price and the future price is negative.

### What is hedging?

Hedging is a form of risk management where the party eliminates the risks of huge losses at the expense of reducing some potential profits. Hedging is normally carried out by commodity producers such as crude oil companies.

### What is standard deviation?

Standard deviation is a statistic metric that measures the dispersion of the prices from their mean. In investing, the standard deviation is often interpreted as risk.

### What is future price?

Future price is the price of an asset that is agreed upon by two parties for buying and selling the assets in the future. On the other hand, the spot price is the current price of an asset.

### How can I calculate the optimal hedge ratio?

You can calculate the optimal hedge ratio in four steps:

1. Determine the standard deviation (sd.) of the spot price.
2. Determine the standard deviation (sd.) of the future price.
3. Determine the correlation coefficient of the changes in the spot and futures prices.
4. Apply optimal hedge ratio:

optimal hedge ratio = correlation coefficient × (spot price sd. / future price sd.)

Wei Bin Loo
SD. of changes in spot price
SD. of changes in future price
Correlation coefficient
Optimal hedge ratio
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