Hedging

Hedging is a risk-management strategy in which an investor, business, or other market participant takes a position intended to offset or reduce the potential adverse effect of an existing exposure.

Hedging is commonly used to manage risks arising from changes in asset prices, interest rates, exchange rates, commodity prices, credit conditions, and other financial variables. A hedge generally reduces exposure to a particular risk rather than eliminating all investment or business risk.

Concept

A simplified hedging relationship can be represented as:

$\text{Hedged Position}=\text{Original Exposure}+\text{Offsetting Position}$

The objective is to reduce the sensitivity of the combined position to an adverse movement in the underlying risk factor.

A simplified change in value can be expressed as:

$\Delta V_p=\Delta V_o+\Delta V_h$

where:

• $\Delta V_p$ = change in value of the combined position;
• $\Delta V_o$ = change in value of the original exposure;
• $\Delta V_h$ = change in value of the hedging position.

An effective hedge generally seeks to make the offsetting change in value reduce the adverse effect on the original exposure.

Purpose of hedging

The principal purpose of hedging is to manage unwanted risk.

Market participants may hedge to:

• reduce potential losses;
• stabilize cash flows;
• protect asset values;
• reduce earnings volatility;
• manage commodity-price exposure;
• manage foreign-exchange exposure;
• manage interest-rate exposure;
• manage equity-market exposure;
• manage credit exposure;
• improve certainty over future revenues or costs.

Hedging does not necessarily maximize expected returns. Its primary objective is generally risk reduction or risk transformation.

Types of hedging

Hedging strategies can be classified according to the type of exposure being managed and the instrument used.

Common forms include:

• currency hedging;
• interest-rate hedging;
• commodity hedging;
• equity hedging;
• credit hedging;
• portfolio hedging;
• inflation hedging.

Hedges can also be classified as direct, indirect, static, or dynamic depending on how the offsetting position is established and managed.

Derivative hedging

Derivatives are commonly used for hedging because their values are linked to an underlying asset, rate, index, or other variable.

Common derivative instruments used for hedging include:

• futures contracts;
• forward contracts;
• options;
• swaps.

For example, a company expecting to purchase a commodity in the future may use a futures contract to reduce uncertainty about the future purchase price.

Futures hedging

A futures hedge uses a standardized futures contract to offset exposure to changes in the price of an underlying asset.

A simplified position is:

$\text{Hedged Exposure}=\text{Underlying Exposure}+\text{Futures Position}$

A producer exposed to falling commodity prices may sell futures contracts. If the commodity price falls, losses on the physical commodity may be partially offset by gains on the short futures position.

Forward hedging

A forward contract allows two parties to agree on a price for a transaction that will occur in the future.

For example, a company expecting to receive foreign currency may enter into a forward contract to sell that currency at an agreed exchange rate.

This can reduce uncertainty about the domestic-currency value of the future receipt.

Options hedging

Options can provide protection while retaining some potential benefit from favorable price movements.

An investor holding an asset may purchase a put option to protect against a decline in its value.

A simplified protective-put position is:

$\text{Protective Put}=\text{Long Underlying}+\text{Long Put}$

The put can provide a minimum effective value at expiration, subject to the strike price and premium paid.

The cost of this protection is generally reflected in the option premium.

Swap hedging

Swaps can be used to exchange one type of financial exposure for another.

For example, a borrower with a floating-rate liability may enter into an interest-rate swap under which it pays a fixed rate and receives a floating rate.

A simplified relationship is:

$\text{Net Interest Exposure}=\text{Floating-Rate Liability}+\text{Swap}$

The swap can reduce exposure to increases in the underlying floating interest rate.

Currency hedging

Currency hedging is used to manage the effect of exchange-rate movements.

Suppose an investor holds a foreign asset denominated in currency $F$ and measures returns in currency $D$.

A simplified domestic-currency value is:

$V_D=V_F\times S_{F/D}$

where:

• $V_D$ = value in the domestic currency;
• $V_F$ = value in the foreign currency;
• $S_{F/D}$ = applicable exchange rate.

Changes in the exchange rate can therefore affect the domestic-currency value even when the foreign asset itself does not change in price.

A currency hedge seeks to reduce this exchange-rate exposure.

Interest-rate hedging

Interest-rate hedging is used to manage the effect of changes in interest rates on borrowing costs, investments, or other financial positions.

For a floating-rate liability, interest expense can be represented in simplified form as:

$\text{Interest Expense}=P\times r$

where:

• $P$ = principal;
• $r$ = applicable interest rate.

An increase in $r$ therefore increases interest expense.

A borrower may use an interest-rate swap, futures contract, or option to reduce this exposure.

Commodity hedging

Businesses exposed to commodity prices may use hedging to reduce uncertainty about future revenues or costs.

For example:

• an oil producer may hedge against falling oil prices;
• an airline may hedge fuel costs;
• a food manufacturer may hedge agricultural commodity prices;
• a mining company may hedge the price of its output.

The objective is generally to reduce the effect of adverse commodity-price movements on operating cash flow or profitability.

Equity hedging

Equity investors can hedge exposure to individual securities, sectors, or broad equity markets.

Common instruments include:

• equity-index futures;
• index options;
• put options;
• inverse instruments;
• offsetting equity positions.

For example, an investor with a diversified equity portfolio may purchase index puts to reduce downside exposure during a period of elevated market risk.

Portfolio hedging

A portfolio hedge seeks to reduce the sensitivity of an investment portfolio to a particular risk factor.

A simplified portfolio return can be represented as:

$R_p=\sum _{i=1}^n{w}_i{R}_i$

where:

• $R_p$ = portfolio return;
• $w_i$ = weight of asset $i$;
• $R_i$ = return of asset $i$.

A hedge adds an offsetting position whose return is expected to have an inverse or otherwise favorable relationship with the portfolio's unwanted exposure.

Hedge ratio

The hedge ratio represents the size of the hedging position relative to the exposure being hedged.

A simple hedge ratio is:

$h=\frac{\text{Value of Hedging Position}}{\text{Value of Exposure}}$

For example, if an investor has a $1 million exposure and establishes a $600,000 hedging position:

$h=\frac{600,000}{1,000,000}=0.6$

The hedge ratio is therefore 0.6.

The appropriate ratio depends on the relationship between the underlying exposure and the hedging instrument.

Minimum-variance hedge ratio

When the objective is to minimize portfolio variance, a simplified minimum-variance hedge ratio can be expressed as:

$h^{\ast }={\rho }_{XY}\frac{{\sigma }_X}{{\sigma }_Y}$

where:

• $h^{\ast }$ = minimum-variance hedge ratio;
• ${\rho }_{XY}$ = correlation between the exposure and hedging instrument;
• ${\sigma }_X$ = standard deviation of the exposure;
• ${\sigma }_Y$ = standard deviation of the hedging instrument.

This formulation illustrates that hedge size depends not only on the nominal value of the exposure but also on volatility and correlation.

Basis risk

Basis risk arises when the hedging instrument does not move exactly in line with the exposure being hedged.

The basis can be represented as:

$B=S-F$

where:

• $B$ = basis;
• $S$ = spot price;
• $F$ = relevant futures price.

Changes in the basis can cause the hedge to be imperfect.

Basis risk is particularly relevant when the hedging instrument and the underlying exposure are related but not identical.

Perfect and imperfect hedges

A perfect hedge would completely offset the relevant risk exposure.

In practice, most hedges are imperfect.

A simplified measure of the effectiveness of a hedge can be expressed as:

$\text{Hedge Effectiveness}=1-\frac{\mathrm{Var}(R_H)}{\mathrm{Var}(R_U)}$

where:

• $R_H$ = return of the hedged position;
• $R_U$ = return of the unhedged position.

The precise definition of hedge effectiveness can vary according to the purpose and methodology of the analysis.

Static and dynamic hedging

A static hedge is established and generally maintained without frequent adjustment.

A dynamic hedge involves periodically adjusting the hedging position as market conditions, prices, volatility, or portfolio exposures change.

Delta hedging is an example of a dynamic hedging approach.

A simplified delta-hedging relationship is:

${\Delta }_{\text{Portfolio}}\approx 0$

after the appropriate offsetting position has been established.

Because delta changes as the underlying asset price changes, the hedge may need to be adjusted.

Natural hedging

A natural hedge occurs when an entity's ordinary business activities naturally offset a financial exposure without requiring a separate derivative transaction.

For example, a company that earns revenue in a foreign currency and also incurs costs in the same currency may naturally offset part of its currency exposure.

A simplified net exposure is:

$\text{Net Currency Exposure}=\text{Foreign-Currency Receipts}-\text{Foreign-Currency Payments}$

A smaller net exposure reduces the amount that may need to be hedged externally.

Hedging and speculation

Hedging and speculation have different primary objectives.

A hedger generally takes an offsetting position to reduce an existing exposure.

A speculator generally takes a position to benefit from an expected market movement.

The distinction can be represented as:

$\text{Hedging}\to \text{Risk Reduction or Risk Transformation}$

$\text{Speculation}\to \text{Risk Taking for Potential Return}$

A single transaction can, however, have both hedging and speculative characteristics depending on the underlying exposure and the size and structure of the position.

Hedging and diversification

Diversification and hedging are related but distinct risk-management techniques.

Diversification reduces exposure to individual assets or risks by spreading investments across different assets.

Hedging directly establishes an offsetting position against a particular exposure.

A diversified portfolio can therefore still contain substantial systematic risk that may require hedging.

Costs of hedging

Hedging can involve direct and indirect costs, including:

• option premiums;
• bid-ask spreads;
• brokerage and transaction costs;
• exchange and clearing fees;
• financing costs;
• margin requirements;
• collateral requirements;
• opportunity costs.

A hedge may also reduce gains when the underlying exposure moves favorably.

For example, an investor holding an asset and buying a put option incurs the option premium even if the asset subsequently rises and the put expires unused.

Risks of hedging

Hedging does not eliminate all financial risk.

Potential risks include:

• Basis risk;
• Correlation risk;
• Liquidity risk;
• Counterparty risk;
• Market risk;
• Model risk;
• Leverage risk;
• Execution risk;
• Roll risk;
• Opportunity cost.

The hedging instrument may also introduce risks that were not present in the original position.

Over-hedging and under-hedging

Under-hedging occurs when the hedging position is insufficient to offset the desired exposure.

Over-hedging occurs when the hedging position is larger than the exposure being managed.

A simplified net exposure is:

$\text{Net Exposure}=\text{Original Exposure}-\text{Hedge Exposure}$

If the hedge is too small, material residual exposure remains. If the hedge is too large, the investor may effectively take a new directional position.

Hedging and accounting

Businesses that use derivatives to hedge financial or operational exposures may be subject to specific hedge accounting rules.

Hedge accounting can affect how gains and losses on hedging instruments and the related hedged items are recognized in financial statements.

The accounting treatment depends on the applicable accounting framework and the type of hedge.

Importance

Hedging is an important component of financial risk management. It allows investors, companies, financial institutions, and other market participants to modify their exposure to adverse changes in prices, rates, currencies, commodities, and other risk factors.

An effective hedge can reduce volatility and improve certainty over future cash flows, but hedging generally involves costs and can introduce basis, liquidity, counterparty, model, and other risks. Hedging therefore represents risk management rather than complete elimination of financial risk.

See also

• Hedge (finance)
• Risk management
• Financial risk
• Derivative (finance)
• Option (finance)
• Futures contract
• Forward contract
• Swap (finance)
• Hedge ratio
• Basis risk
• Delta hedging
• Natural hedge
• Hedge accounting
• Portfolio management
• Diversification (finance)
• Speculation
• Market risk
• Liquidity risk
• Counterparty risk