Home > Articles > Business & Management > Finance & Investing

This chapter is from the book

Hedging and Risk Reduction: The Tool of Arbitrage

Hedging Defined

A hedge is used to implement an arbitrage strategy. Thus, before we examine arbitrage more carefully, we must understand how a hedge works. We have all heard someone say that he or she did something just to "hedge a bet." In a strict gambling sense, this implies that an additional bet has been placed to reduce the risk of another outstanding bet. The everyday connotation is that an action is taken to gain some protection against a potentially adverse outcome. For example, you may leave early for an appointment to "hedge your bet" that you’ll find a parking place quickly. Another example is a college student’s decision to pursue a double major because he doesn’t know what jobs will be available when he graduates.

In investment analysis, a hedging transaction is intended to reduce or eliminate the risk of a primary or preexisting security or portfolio position. An investor consequently establishes a secondary position to counterbalance some or all of the risk of the primary investment position. For example, an equity mutual fund manager would not get completely out of equities if the market is expected to fall. (Just think of the signal that would send to investors.) The risk of the manager's long equity investments could be partially offset by taking short positions in selected equities, buying or selling derivatives, or some combination thereof.11 This secondary position hedges the equity portfolio by gaining value when the value of the equity fund falls. The workings of such hedges are discussed next.

Often, an investor establishes a long asset position that is subsequently considered too risky. The investor consequently decides to partially or completely offset that risk exposure by taking another investment position that offsets declines in the original investment's value. A short position can be taken in the same asset that counterbalances the investor's risk exposure. The hedging transaction may be viewed as a substitute for the investor's preferred action in the absence of constraints that interfere with taking that action.12 The constraint could be something explicit, like a portfolio policy requirement (such as in a trust) that an investor maintain a given percentage of funds invested in a stock. Alternatively, it could be a self-imposed risk-tolerance constraint where the investor wants to keep a stock with a profit but feels compelled to offset all or part of the position's risk using a hedging transaction. For instance, this could be motivated by tax treatment issues.

As noted, it is important to understand how hedging works before exploring its use in implementing arbitrage strategies. Thus, we’ll now explain how an investor constructs a hedge that holds a stock, locks in an established profit, and neutralizes risk.

Hedging Example: Protecting Profit on an Established Long Position

Investment Scenario and Expected Results of the Hedge

Consider a stock originally bought for $85 that has risen to $100. For our purposes, we'll ignore commissions associated with buying and selling securities. What should the investor do if he is happy with the $15 profit on the investment but fears that the market may fall soon? The most obvious solution is to sell the stock and take the $15 profit now. However, what if the investor is unable or unwilling to sell the stock now but still wants to lock in the profit? Perhaps the investor wants to delay realizing a taxable gain until next year or wants to stretch an existing short-term gain into a long-term gain.13 The investor could sell short the stock at its current price of $100, which would protect against any loss of the $15 profit. Any drop in the value of the stock would then be offset by an equal appreciation in the value of the outstanding short position. The investor has a $15 profit that could be realized by selling the stock now. However, the investor substitutes a hedging short sale transaction for the direct sale of the long position. This substitute transaction protects the profit while maintaining the original long stock position.14

The Effect of Price Changes on Hedge Profitability

What would happen if the price of the stock falls from $100 to $90? Remember that the short position locks in the proceeds from selling at $100. If the price falls to $90, the stock can be purchased at that price and returned to the lending broker, thereby generating a profit of $10. However, the profit on the long position is reduced by $10 due to the price decline. Thus, there would be no net deviation from the established profit of $15.

The hedge brings both good and bad news. The good news is that the $15 profit is locked in without risk. Yet the bad news is that the investor cannot profit further from any increase in the stock price beyond $100. This is because a price increase would raise the value of the long position but would also bring offsetting losses on the short position.

What if the price moves from $100 to $110? The profit on the long position increases from $15 to $25 a share, but the short position loses $10 a share. From a cost/benefit perspective, the "benefit" of locking in the established $15 profit comes at the "cost" of eliminating the ability to gain even greater profits. In other words, the benefit of the hedge is the floor that it places on potential losses, and its (opportunity) cost is the ceiling placed on the position’s maximum profit. This makes sense in light of the risk/return trade-off. The hedge reduces or eliminates risk and therefore reduces or eliminates subsequent expected returns. Table 1.1 summarizes the potential outcomes associated with the hedge. In this scenario, an investor buys 100 shares of stock at $85 a share, and it is now selling for $100. The investor wants to lock in the $15 profit without selling the stock. For the hedging transaction, the investor sells short 100 shares at $100 a share.

Table 1.1 The Good and Bad News of Hedging






Good news of hedge: supported by price floor

Drops to $90

Loss of $10 per share

Gain of $10 per share

Profit of $15 per share is maintained

Bad news of hedge: limited by price ceiling

Rises to $110

Gain of $10 per share

Loss of $10 per share

Profit of $15 per share is maintained

Figure 1.1 portrays the results graphically.

Figure 1.1

Figure 1.1 Hedging to Protect Profits

The profit/loss potential of the long position originally established by buying at $85 intersects with the vertical axis at –$85 and intersects with the horizontal break-even axis at +$85. This indicates that the maximum loss is $85, which occurs if the stock price falls to zero. Furthermore, the break-even price of $85 is obtained if the price remains at its original purchase price. The positive, upward-sloping profit/loss line indicates that profits increase dollar-for-dollar as the stock’s price rises above the original purchase price of $85. Similarly, profits fall dollar-for-dollar as the stock’s price falls below the original purchase price. The maximum gain is, at least in theory, infinite.

The profit/loss potential of the short position established by selling borrowed shares at $100 intersects with the vertical axis at +$100 and intersects with the horizontal break-even axis at $100. This indicates that the maximum gain is +$100, which occurs if the stock price falls to zero. The break-even price of $100 occurs if the price remains at its original level. The negative, downward-sloping profit/loss line indicates that profits increase dollar-for-dollar as the stock’s price falls below the original short sales price of $100, and profits decline dollar-for-dollar as the stock’s price rises above the price at which the shares were sold short. The maximum loss is theoretically, but soberingly, infinite.

The most dramatic result portrayed in Figure 1.1 is the horizontal hedged profit line, which shows that profits are fixed at $15 per share regardless of where the stock’s price ends up. The horizontal line results from offsetting the upward-sloping long position profit/loss line against the downward-sloping short position profit/loss line. The opposite slopes of the two lines imply that when one position is losing money, the other is making money. Thus, the horizontal hedging profit line reflects the risk-neutralizing effect of combining the short (hedging) transaction with the investor’s original long position in the stock. Gains and losses on the two individual positions cancel each other out, thereby resulting in a fixed profit of $15 per share. This $15 profit is the difference between the original purchase price of the stock at $85 and the price at which it was sold short at $100.

The Rate of Return on Hedged Positions and Its Relationship to Arbitrage

In the preceding example, the investor locks in an ex post (after-the-fact) 17.65% return ($15/$85) through a hedge. The investor has effectively removed the position from the market and has an expected zero rate of return from that time on. Importantly, the position is riskless after the given 17.65% return is generated, and no deviation above or below that return is possible after the hedge is in place. However, insufficient data are given in the example to judge whether the ex post return of 17.65% is appropriate to the risk of the investment.

An investor cannot engage in arbitrage that profitably exploits mispriced investments without adding risk unless he can hedge. This is because the hedge is the means whereby the arbitrage strategy is rendered riskless. Hedging is an essential mechanism that allows arbitrage to structure asset prices.

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.


Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.


If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information

Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.


This site is not directed to children under the age of 13.


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure

Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact

Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice

We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020