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Home > Financial Risk Management Checklists > Understanding Hedge Ratios

Financial Risk Management Checklists

# Understanding Hedge Ratios

## Checklist Description

This checklist describes what a hedge ratio is and how it is used.

## Definition

Hedging is the art of reducing or eliminating financial risk by entering into a transaction that will protect against loss through a compensatory price movement.

A hedge ratio, therefore, is a mechanism for calculating the number of options or other derivatives, or amount of currency, needed to hedge against the risk of loss in a portfolio of shares or other derivatives. It is also known as a delta.

A delta is commonly used to compare the value of a position protected by a hedge with the size of the actual position. For instance, you need to calculate the number of options necessary to offset a change in value resulting from a price change in 100 shares of common stock at a given point in time. If you need two options to offset the change, the delta is 2. To give a practical example, if you have a call option on shares for a particular company, a delta of 0.50 means that for every \$1.00 increase in the share price, the option price rises by \$0.50.

The hedge ratio can also identify and help to minimize any risks in futures contracts. Thus, it may be used to compare the value of a futures contract with the value of the underlying instrument (for example a cash commodity or shares) that is being hedged. Indeed, a hedge ratio can be used to hedge any kind of financial instrument.

The formula for a hedge ratio is as follows:

H = –1

where

Hedge ratio = Total delta equivalent ÷ Total stock value

No matter what instrument is being hedged against, the formula for the hedge ratio remains the same: H = –1.

Delta values change constantly, according to how the specific financial instrument is performing on the markets. The rate of change of a delta’s underlying asset price is called the gamma. In order to maintain a hedge ratio of H = –1, it must be adjusted regularly. This process is known as dynamic hedging. When a position has a hedge ratio of H = –1, it is known as delta neutral.

The value of a delta is usually equal to a one-point change up or down in the underlying security over a short time period. If an option has a high delta, it is usually more profitable to purchase the derivative, as the greater percentage movement relative to the price of the underlying security offers better leverage. For derivatives with a low delta, the reverse is true and it is better to sell.

### Articles:

• Black, F. “Universal hedging: Optimising currency risk and reward in international equity portfolios.” Financial Analysts Journal 45:4 (1989): 16–22.
• Gardner, G. W., and T. Wuilloud. “Currency risk in international portfolios: How satisfying is optimal hedging?” Journal of Portfolio Management 21:3 (1995): 59–67.
• Harris, Richard, and Jian Shen. “Robust estimation of the optimal hedge ratio.” Journal of Futures Markets 23:8 (2003): 799–816.
• Qian, Edward, and Stephen Gorman. “International benchmarks: In support of a 50% hedge ratio.” Journal of Investing 9:2 (Summer 2000).
• Shafer, Carl E. “Hedge ratios and basis behavior: An intuitive insight?” Journal of Futures Markets 13:8 (1993): 837–847.