Managing Risk with Derivative Securities

Transcription

1 23 Managing Risk with Derivative Securities O U T L I N E Chapter NAVIGATOR 1. How can risk be hedged with forward contracts? 2. How can risk be hedged with futures contracts? 3. What is the difference between a microhedge and a macrohedge? 4. How can risk be hedged with option contracts? 5. How can risk be hedged with swap contracts? 6. How do the different hedging methods compare? DERIVATIVE SECURITIES USED TO MANAGE RISK: CHAPTER OVERVIEW Chapters 20 through 22 described ways financial institutions (FIs) measure and manage various risks on the balance sheet. Rather than managing risk by making on-balance-sheet changes, FIs are increasingly turning to off-balance-sheet instruments such as forwards, futures, options, and swaps to hedge these risks. As the use of these derivatives has increased, so have the fees and revenues FIs have generated. For example, revenue from derivatives transactions at commercial banks averaged $11.27 billion per year from 1999 to We discussed the basic characteristics of derivative securities and derivative securities markets in Chapter 10. This chapter considers the role that derivative securities contracts play in managing an FI s interest rate risk, foreign exchange, and credit risk exposures. Although large banks and other FIs are responsible for a significant amount of derivatives trading activity, FIs of all sizes have used these instruments to hedge their asset-liability risk exposures. FORWARD AND FUTURES CONTRACTS To present the essential nature and characteristics of forward and futures contracts, we first review the comparison of these derivative contracts with spot contracts (see also Chapter 10). Derivative Securities Used to Manage Risk: Chapter Overview Forward and Futures Contracts Hedging with Forward Contracts Hedging with Futures Contracts Options Basic Features of Options Actual Interest Rate Options Hedging with Options Caps, Floors, and Collars Risks Associated with Futures, Fowards, and Options Swaps Hedging with Interest Rate Swaps Currency Swaps Credit Risk Concerns with Swaps Comparison of Hedging Methods Writing versus Buying Options Futures versus Options Hedging Swaps versus Forwards, Futures, and Options Derivative Trading Policies of Regulator Appendix 23A: Hedging with Futures Contracts (at Appendix 23B: Hedging with Options (at Appendix 23C: Hedging with Caps, Floors, and Collars [at 629

2 630 Part 5 Risk Management in Financial Institutions spot contract An agreement to transact involving the immediate exchange of assets and funds. forward contract An agreement to transact involving the future exchange of a set amount of assets at a set price. Spot Contract. A spot contract is an agreement between a buyer and a seller at time 0, when the seller of the asset agrees to deliver it immediately for cash and the buyer agrees to pay in cash for that asset. 1 Thus, the unique feature of a spot contract is the immediate and simultaneous exchange of cash for securities, or what is often called delivery versus payment. A spot bond quote of $97 for a 20-year maturity bond means that the buyer must pay the seller $97 per $100 of face value for immediate delivery of the 20-year bond. 2 Forward Contract. A forward contract is a contractual agreement between a buyer and a seller, at time 0, to exchange a prespecified asset for cash at some later date. For example, in a three-month forward contract to deliver 20-year bonds, the buyer and seller agree on a price and amount today (time 0), but the delivery (or exchange) of the 20-year bond for cash does not occur until three months hence. If the forward price agreed to at time 0 was $97 per $100 of face value, in three months time the seller delivers $100 of 20-year bonds and receives $97 from the buyer. This is the price the buyer must pay and the seller must accept no matter what happens to the spot price of 20-year bonds during the three months between the time the contract was entered into and the time the bonds are delivered for payment. As of December 2004, commercial banks held $7.97 trillion in forward contracts off their balance sheets. Forward contracts often involve underlying assets that are nonstandardized (e.g., sixmonth pure discount bonds). As a result, the buyer and seller involved in a forward contract must locate and deal directly with each other to set the terms of the contract rather than transacting the sale in a centralized market. Accordingly, once a party has agreed to a forward position, canceling the deal prior to expiration is generally difficult (although an offsetting forward contract can normally be arranged). futures contract An agreement to transact involving the future exchange of a set amount of assets for a price that is settled daily. marked to market Describes the prices on outstanding futures contracts that are adjusted each day to reflect current futures market conditions. naive hedge A hedge of a cash asset on a direct dollar-for-dollar basis with a forward or futures contract. 1 Futures Contract. A futures contract is usually arranged by an organized exchange. It is an agreement between a buyer and a seller at time 0 to exchange a standardized, prespecified asset for cash at some later date. As such, a futures contract is very similar to a forward contract. The difference relates to the price, which in a forward contract is fixed over the life of the contract ($97 per $100 of face value with payment in three months), but a futures contract is marked to market daily. This means that the contract s price and the future contract holder s account are adjusted each day as the futures price for the contract changes. Therefore, actual daily cash settlements occur between the buyer and seller in response to this marking-to-market process, i.e., gains and losses must be realized daily. This can be compared to a forward contract for which cash payment from buyer to seller occurs only at the end of the contract period. 3 In December 2004, commercial banks held $3.41 trillion in futures contracts off their balance sheets. Hedging with Forward Contracts To understand the usefulness of forward contracts in hedging an FI s interest rate risk, consider a simple example of a naive hedge (a hedge of a cash asset on a direct dollar-for-dollar basis with a forward or futures contract). Suppose that an FI portfolio manager holds a 20-year, $1 million face value government bond on the balance sheet. At time 0, the market values these bonds at $97 per $100 of face value, or $970,000 in total. Assume that the manager receives a forecast that interest rates are expected to rise by 2 percent from their current level of 8 percent to 10 percent over the 1. Technically, physical settlement and delivery may take place one or two days after the contractual spot agreement in bond markets. In equity markets, delivery and cash settlement normally occur three business days after the spot contract agreement, so-called T Throughout this chapter, as we refer to the prices of various securities, we do not include the transaction fees charged by brokers and dealers for conducting trades for investors and hedgers. 3. Another difference between forwards and futures is that forward contracts are bilateral contracts subject to counterparty default risk, but the default risk on futures is significantly reduced by the futures exchange guaranteeing to indemnify counterparties against credit or default risk.

3 Chapter 23 Managing Risk with Derivative Securities 631 next three months. Knowing that if the predicted change in interest rates is correct, rising interest rates mean that bond prices will fall, the manager stands to make a capital loss on the bond portfolio. Having read Chapters 3 and 22, the manager is an expert on duration and has calculated the 20-year maturity bond s duration to be exactly nine years. Thus, the manager can predict a capital loss, or change in bond values ( P), from the duration equation of Chapter 3: 4 P D R P 1 R where P Capital loss on bond? P Initial value of bond position $970,000 D Duration of the bond 9 years R Change in forecast yield.02 1 R 1 plus the current yield on 20-year bond 1.08 P.02 9 a $970, b P 9 $970,000 a b $161,667 As a result, the FI portfolio manager expects to incur a capital loss on the bond of $161,667 as a percentage loss ( P/P) 16.67% or a drop in price from $97 per $100 face value to $ per $100 face value. To offset this loss in fact, to reduce the risk of capital loss to zero the manager may hedge this position by taking an off-balance-sheet hedge, such as selling $1 million face value of 20-year bonds for forward delivery in three months time. 5 Suppose that at time 0, the portfolio manager can find a buyer willing to pay $97 for every $100 of 20-year bonds delivered in three months time. Now consider what happens to the FI portfolio manager if the gloomy forecast of a 2 percent rise in interest rates is accurate. The portfolio manager s bond position has fallen in value by percent, equal to a capital loss of $161,667. After the rise in interest rates, however, the manager can buy $1 million face value of 20-year bonds in the spot market at $ per $100 of face value, a total cost of $808,333, and deliver these bonds to the forward contract buyer. Remember that the forward contract buyer agreed to pay $97 per $100 of face value for the $1 million of face value bonds delivered, or $970,000. As a result, the portfolio manager makes a profit on the forward transaction of: $970,000 $808,333 $161,667 (price paid by (cost of purchasing bonds forward buyer to in the spot market at forward seller) t month 3 for delivery to the forward buyer) As you can see, the on-balance-sheet loss of $161,667 is exactly offset by the offbalance-sheet gain of $161,667 from selling the forward contract. In fact, for any change in interest rates, a loss (gain) on the balance sheet is offset by a partial or complete gain (loss) on the forward contract. Indeed, the success of a hedge does not hinge on the manager s ability to accurately forecast interest rates. Rather, the reason for the hedge is the lack of ability to perfectly predict interest rate changes. The hedge allows the FI manager to protect 4. For simplicity, we ignore issues relating to convexity here (see Chapter 22). 5. Since a forward contract involves the delivery of bonds at a future time period, it does not appear on the balance sheet, which records only current and past transactions. Thus, forwards are one example of off-balance-sheet items (see Chapter 12).

4 632 Part 5 Risk Management in Financial Institutions immunize To fully hedge or protect an FI against adverse movements in interest rates (or asset prices). microhedging Using a futures (forward) contract to hedge a specific asset or liability. basis risk A residual risk that occurs because the movement in a spot (cash) asset s price is not perfectly correlated with the movement in the price of the asset delivered under a futures or forward contract. macrohedging Hedging the entire duration gap of an FI against interest rate changes even if they are not perfectly predicted. Thus, the FI s net interest rate exposure is zero, or, in the parlance of finance, it has immunized its assets against interest rate risk. Hedging with Futures Contracts Even though some hedging of interest rate risk does take place using forward contracts such as forward rate agreements commonly used by insurance companies and banks prior to mortgage loan originations most FIs hedge interest rate risk either at the micro level (called microhedging) or at the macro level (called macrohedging) using futures contracts. Before looking at futures contracts, we explain the difference between microhedging and macrohedging. Microhedging. An FI is microhedging when it employs a futures or a forward contract to hedge a particular asset or liability risk. For example, we earlier considered a simple example of microhedging asset-side portfolio risk in which an FI manager wanted to insulate the value of the institution s bond portfolio fully against a rise in interest rates. An example of microhedging on the liability side of the balance sheet occurs when an FI, attempting to lock in a cost of funds to protect itself against a possible rise in short-term interest rates, takes a short (sell) position in futures contracts on CDs or T-bills. In microhedging, the FI manager often tries to pick a futures or forward contract whose underlying deliverable asset closely matches the asset (or liability) position being hedged. The earlier example of exactly matching the asset in the portfolio with the deliverable security underlying the forward contract (20-year bonds) was unrealistic. Because such exact matching often cannot be achieved, the usual situation produces a residual unhedgeable risk termed basis risk. This risk occurs mainly because the prices of the assets or liabilities that an FI wishes to hedge are imperfectly correlated over time with the prices on the futures or forward contract used to hedge risk. Macrohedging. Macrohedging occurs when an FI manager wishes to use futures or other derivative securities to hedge the entire balance sheet duration gap. This contrasts with microhedging in which an FI manager identifies specific assets and liabilities and seeks individual futures and other derivative contracts to hedge those individual risks. Note that macrohedging and microhedging can lead to quite different hedging strategies and results. In particular, a macrohedge takes a whole portfolio view and allows for individual asset and liability interest sensitivities or durations to net out each other. This can result in a very different aggregate futures position than when an FI manager disregards this netting or portfolio effect and hedges only individual asset and liability positions on a one-to-one basis. 6 The Choice between Microhedging and Macrohedging. Several factors affect an FI s choice between microhedging and macrohedging interest rate risk. These include riskreturn considerations, accounting rules, and for depository institutions, federal regulation. Risk-Return Considerations. Ideally, an FI would like to reduce its interest rate or other risk exposures to their lowest possible level by buying or selling sufficient futures to offset the interest rate risk exposure of its whole balance sheet or cash positions in each asset and liability. For example, this reduction might be achieved by macrohedging the duration gap. However, since reducing risk also reduces expected return, not all FI managers seek to do this. Rather than taking a fully hedged position, many FIs choose to bear some interest rate risk as well as credit and FX risks because of their comparative advantage as FIs (see Chapter 1). 6. P. H. Munter, D. K. Clancy, and C. T. Moores found that macrohedges provided better hedge performance than microhedges in a number of different interest rate environments. See Accounting for Financial Futures: A Question of Risk Reduction, in Advances in Accounting (1986), pp See also R. Stoebe, Macrohedging Bank Investment Portfolios, Bankers Magazine, November December 1994, pp

5 Chapter 23 Managing Risk with Derivative Securities 633 For example, an FI manager may generate expectations regarding future interest rates before deciding on a futures position. As a result, the manager may selectively hedge only a portion of its balance sheet position, or microhedge. Alternatively, the FI manager may decide to remain unhedged or even to overhedge by selling more futures than the cash or on-balance-sheet position requires, although regulators may view this as speculative. Thus, the fully hedged position becomes one of several choices depending, in part, on managerial interest rate expectations, managerial objectives, and the nature of the return-risk tradeoff from hedging Accounting Rules and Hedging Strategies. The Financial Accounting Standards Board (FASB) the main regulator of accounting standards has made a number of rulings regarding the accounting and tax treatment of futures transactions. 7 In hedge accounting, a futures position is a hedge transaction if it can be linked to a particular asset or liability. An example is using a T-bond futures contract to hedge an FI s holdings of long-term bonds as investments. In 1997, the FASB required that all gains and losses on derivatives used to hedge assets and liabilities on the balance sheet be recognized immediately as earnings, together with the offsetting gain or loss on the hedged item. Thus, the 1997 ruling effectively requires derivatives to be marked to market. Additionally, U.S. companies that hold or issue derivatives must report their trading objectives and strategies in public document disclosures such as annual reports. 8 Because of the volatility in earnings that futures introduce as they are marked to market, an FI manager may choose to selectively hedge only a portion of the FI s balance sheet positions (microhedge) rather than take large positions on futures contracts needed to hedge the entire balance sheet (macrohedge). Policies of Bank Regulators. The main bank regulators the Federal Reserve, the FDIC, and the Comptroller of the Currency have issued uniform guidelines for banks taking positions in futures and forwards. These guidelines require a bank to (1) establish internal guidelines regarding its hedging activity, (2) establish trading limits, and (3) disclose large contract positions that materially affect a bank s risk to shareholders and outside investors. Overall, regulatory policy is to encourage the use of futures for hedging and to discourage their use for speculation, although on a practical basis, it is often difficult to distinguish between the two. Finally, as Chapter 13 discusses, futures contracts are not subject to the risk-based capital requirements imposed by regulators on depository institutions; by contrast, over-the-counter forward contracts are potentially subject to capital requirements because of the presence of counterparty risk (see below). Other things being equal, the risk-based capital requirements favor the use of futures over forwards. To the dismay of some legislators in Congress and regulators, the use of derivative securities in some nondepository FIs especially hedge funds remains virtually unregulated. 9 Microhedging with Futures. The number of futures contracts that an FI should buy or sell in a microhedge depends on the interest rate risk exposure created by a particular asset or liability on the balance sheet. The key is to take a position in the futures market to offset a loss on the balance sheet due to a move in interest rates with a gain in the futures market. Table 23 1 shows part of an interest rate futures quote from The Wall Street Journal for January 10, 2005 (see also Table 10 5). In this list, a June 2005 Eurodollar futures contract can be bought (long) or sold (short) on January 10, 2005, for percent of the face value of the Eurodollar CD contract, or the yield on the Eurodollar CD contract deliverable in 7. FASB Statement No. 80, Accounting for Futures Contracts (1984) is probably the most important. 8. See Called to Account, Risk Magazine, August 1996, pp See Long-Term Capital Management: Regulators Need to Focus Greater Attention on Systematic Risk, GAO/GGD-00-3 (October 1999).

6 634 Part 5 Risk Management in Financial Institutions TABLE 23 1 Futures Contracts on Interest Rates, January 10, 2005 Source: The Wall Street Journal, January 11, 2005, p. C11. Reprinted by permission of The Wall Street Journal Dow Jones & Company, Inc. All Rights Reserved Worldwide. DO YOU UNDERSTAND? 1. The difference between a futures contract and a forward contract? 2. What the major differences between a spot contract and a forward contract are? 3. How a naive hedge works? 4. What is meant by the phrase an FI has immunized its portfolio against a particular risk? 5. When a futures position is a hedge transaction according to FASB rules? June 2005 will be 3.28 percent (100% 96.72%). The minimum contract size on one of these futures is $1,000,000, so a position in one contract can be taken at a price of $967,200. The subsequent profit or loss from a position in June 2005 Eurodollar futures taken on January 10, 2005, is graphically described in Figure A short position in the futures will produce a profit when interest rates rise (meaning that the value of the underlying Eurodollar contract decreases). Therefore, a short position in the futures market is the appropriate hedge when the FI stands to lose on the balance sheet if interest rates are expected to rise (e.g., the FI holds Eurodollar CDs in its asset portfolio). 10 In fact, if the FI is perfectly hedged, any loss in value from a change in the yield on an asset on the balance sheet over the period of the hedge is exactly offset by a gain on the short position in the Eurodollar futures contract (see Figure 23 2). A long position in the futures market produces a profit when interest rates fall (meaning that the value of the underlying Eurodollar CD contract increases). 11 Therefore, a long position is the appropriate hedge when the FI stands to lose on the balance sheet if interest rates are expected to fall. 12 Table 23 2 summarizes the long and short position. Appendix 23A to this chapter located at the book s Web site ( presents mathematical details and numerical examples of hedging with futures contracts. 10. We assume that the balance sheet has no liability of equal size and maturity (or duration) as the CD. If the FI has such a liability, any loss in value from the CD could be offset with an equivalent decrease in value from the liability. In this case, there is no interest rate risk exposure and thus there is no need to hedge. 11. Notice that if rates move in an opposite direction from that expected, losses are incurred on the futures position that is, if rates rise and futures prices drop, the long hedger loses. Similarly, if rates fall and futures prices rise, the short hedger loses. 12. This might be the case when the FI is financing itself with long-term, fixed-rate certificates of deposit.

7 Chapter 23 Managing Risk with Derivative Securities 635 FIGURE 23 1 Profit or Loss on a Futures Position in Eurodollar Futures, Taken on January 10, 2005 Gain Short Position Futures Prices Fall (rates rise) Futures Prices Rise (rates fall) Gain Long Position Futures Prices Fall (rates rise) Futures Prices Rise (rates fall) Futures 0 0 Price 96.72% 96.72% Futures Price Loss Loss FIGURE 23 2 FI Value Change On and Off the Balance Sheet from a Perfect Short Hedge Value Change Gain Change in Capital Value Due to Change in Asset Value 97% Asset Price at End of Hedge Value Change Loss Asset Price at Beginning of Hedge Change in Capital Value Due to Hedge Position TABLE 23 2 Summary of Gains and Losses on Microhedges Using Futures Contracts Change in Type of Hedge Interest Rates Cash Market Futures Market Long hedge (buy) Decrease Loss Gain Short hedge (sell) Increase Loss Gain OPTIONS This section discusses the role of options in hedging interest rate risk. FIs have a wide variety of option products to use in hedging, including exchange-traded options, over-thecounter (OTC) options, options embedded in securities, and caps, collars, and floors (see Chapter 10). Not only have the types of option products increased in recent years but the use of options has increased as well. In December 2004, commercial banks held $3.13 trillion in

8 636 Part 5 Risk Management in Financial Institutions FIGURE 23 3 Function for the Buyer of a Call Option on a Bond Gain Function 0 EP EP CP Bond Price CP Loss exchange trade options and $14.62 trillion in OTC options as part of their off-balance-sheet exposures. We begin by reviewing the four basic option strategies: buying a call, writing (selling) a call, buying a put, and writing (selling) a put. 13 Basic Features of Options In describing the features of the four basic option strategies that FIs might employ to hedge interest rate risk, we summarize their return payoffs in terms of interest rate movements (see Chapter 10 for the details). Specifically, we consider bond options whose payoff values are inversely linked to interest rate movements in a manner similar to bond prices and interest rates in general (see Chapter 3). Buying a Call Option on a Bond. The first strategy of buying (or taking a long position in) a call option on a bond is shown in Figure Notice two important things about bond call options in Figure 23 3: 1. As interest rates fall, bond prices rise, and the call option buyer has a large profit potential; the more rates fall (the higher bond prices rise), the larger the profit on the exercise of the option. 2. As interest rates rise, bond prices fall and the potential for a negative payoff (loss) for the buyer of the call option increases. If rates rise so that bond prices fall below the exercise price, EP, the call buyer is not obligated to exercise the option. Thus, the buyer s losses are truncated by the amount of the up-front premium payment (call premium, CP) made to purchase the call option. Thus, buying a call option is a strategy to take when interest rates are expected to fall. Notice that unlike interest rate futures, whose prices and payoffs move symmetrically with changes in the level of interest rates, the payoffs on bond call options move asymmetrically with changes in interest rates. 14 As we discuss below, this often results in options being the preferred hedging instruments over futures contracts. 13. The two basic option contracts are puts and calls. However, an FI could potentially be a buyer or seller (writer) of each. 14. This does not necessarily mean that options are less risky than spot or futures positions. Options can, in fact, be riskier than other investments since they exist for only a limited period of time and are leveraged investments (i.e., their value is only a fraction of the underlying security). To compare an option position to a spot position one must consider an equal dollar investment in the two positions over a common period of time.

9 Chapter 23 Managing Risk with Derivative Securities 637 FIGURE 23 4 Function for the Writer of a Call Option on a Bond Gain CP 0 EP EP CP Bond Price Loss Function Writing a Call Option on a Bond. The second strategy is writing (or taking a short position in) a call option on a bond shown in Figure Notice two important things about this payoff function: 1. When interest rates rise and bond prices fall, the potential for the writer of the call to receive a positive payoff or profit increases. The call buyer is less likely to exercise the option, which would force the option writer to sell the underlying bond at the exercise price, EP. However, this profit has a maximum equal to the call premium (CP) charged up front to the buyer of the option. 2. When interest rates fall and bond prices rise, the probability that the writer will take a loss increases. The call buyer will exercise the option, forcing the option writer to sell the underlying bonds. Since bond prices are theoretically unbounded in the upward direction, although they must return to par at maturity, these losses could be very large. Thus, writing a call option is a strategy to take when interest rates are expected to rise. Caution is warranted, however, because profits are limited but losses are unlimited. As discussed below, this results in the writing of a call option being unacceptable as a strategy to use when hedging interest rate risk. Buying a Put Option on a Bond. The third strategy is buying (or taking a long position in) a put option on a bond, shown in Figure Note the following: 1. When interest rates rise and bond prices fall, the probability that the buyer of the put will make a profit from exercising the option increases. Thus, if bond prices fall, the buyer of the put option can purchase bonds in the bond market at that price and put them (sell them) back to the writer of the put at the higher exercise price. As a result, the put option buyer has unlimited profit potential; the higher the rates rise, the more the bond prices fall, and the larger the profit on the exercise of the option. 2. When interest rates fall and bond prices rise, the probability that the buyer of a put will lose increases. If rates fall so that bond prices rise above the exercise price, EP, the put buyer does not have to exercise the option. Thus, the maximum loss is limited to the size of the up-front put premium (PP). Thus, buying a put option is a strategy to take when interest rates are expected to rise.

10 638 Part 5 Risk Management in Financial Institutions FIGURE 23 5 Function for the Buyer of a Put Option on a Bond Gain 0 EP PP EP Bond Price PP Function Loss Writing a Put Option on a Bond. The fourth strategy is writing (or taking a short position in) a put option on a bond, shown in Figure Note the following: 1. When interest rates fall and bond prices rise, the writer has an enhanced probability of making a profit. The put buyer is less likely to exercise the option, which would force the option writer to buy the underlying bond. However, the writer s maximum profit is constrained to equal the put premium (PP). 2. When interest rates rise and bond prices fall, the writer of the put is exposed to potentially large losses. The put buyer will exercise the option, forcing the option writer to buy the underlying bond at the exercise price, EP. Since bond prices are theoretically unbounded in the downward direction, these losses can be unlimited. Thus, writing a put option is a strategy to take when interest rates are expected to fall. However, profits are limited and losses are potentially unlimited (i.e., the investor could potentially lose his or her entire investment in the option). As with the writing of a call option (and discussed below), this results in the writing of a put option being unacceptable as a strategy to use when hedging interest rate risk. FIGURE 23 6 Function for the Writer of a Put Option on a Bond Gain PP Function 0 EP PP EP Bond Price Loss

11 Chapter 23 Managing Risk with Derivative Securities Actual Interest Rate Options FIs have a wide variety of OTC and exchange-traded options available. Table 23 3, from Table 10 8 and The Wall Street Journal s business section, reports exchange-traded interest rate futures options traded on the Chicago Board of Trade (CBT) and the Chicago Mercantile Exchange (CME) on January 10, We discussed these contracts and the operations of the markets in detail in Chapter Hedging with Options Figures 23 7 and 23 8 describe graphically the way that buying a put option on a bond can potentially hedge the interest rate risk exposure of an FI that holds bonds as part of its asset investment portfolio. Figure 23 7 shows the gross payoff of a bond and the payoff from buying a put option on it. In this case, any losses on the bond (as rates rise and bond values decrease) are offset with profits from the put option that was bought (points to the left of point X in Figure 23 7). If rates fall, the bond value increases, yet the accompanying losses on the purchased put option positions are limited to the option premiums paid (points to the right of point X). Figure 23 8 shows the net overall payoff from the bond investment combined with the put option hedge. Note in Figure 23 8 that buying a put option truncates the downside losses on the bond following interest rate rises to some maximum amount and scales down the upside profits by the cost of bond price risk insurance the put premium leaving some positive upside profit potential. Notice too that the combination of being long in the bond and buying a put option on a bond mimics the payoff TABLE 23 3 Futures Options on Interest Rates, January 10, 2005 Source: The Wall Street Journal, January 11, 2005, p. C11. Reprinted by permission of The Wall Street Journal Dow Jones & Company, Inc. All Rights Reserved Worldwide.

12 640 Part 5 Risk Management in Financial Institutions FIGURE 23 7 Buying a Put Option to Hedge the Interest Rate Risk on a Bond Gain Function of a Bond in an FI s Portfolio 0 X Bond Price PP Function from Buying a Put on a Bond Loss function of buying a call option (compare Figures 23 3 and 23 8). Conversely, an FI can buy a call option on a bond to hedge interest rate risk exposure from a bond that is part of the FI s liability portfolio. Option contracts can also be used to hedge the aggregate duration gap exposure (macrohedge), foreign exchange risk, and credit risk of an FI as well. Appendix 23B to this chapter located at the book s Web site ( presents mathematical details and numerical examples of hedging with options. Caps, Floors, and Collars As discussed in Chapter 10, caps, floors, and collars are derivative securities that have many uses, especially in helping an FI hedge interest rate risk exposure as well as risks FIGURE 23 8 Net of Buying a Bond Put and Investing in a Bond Net Gain Net Function 0 X Bond Price Loss

13 Chapter 23 Managing Risk with Derivative Securities 641 unique to its individual customers. Buying a cap means buying a call option or a succession of call options on interest rates. Specifically, if interest rates rise above the cap rate, the seller of the cap usually a bank compensates the buyer for example, another FI in return for an up-front premium. As a result, buying an interest rate cap is like buying insurance against an (excessive) increase in interest rates. Buying a floor is similar to buying a put option on interest rates. If interest rates fall below the floor rate, the seller of the floor compensates the buyer in return for an up-front premium. As with caps, floor agreements can have one or many exercise dates. A collar occurs when an FI takes a simultaneous position in a cap and a floor, such as buying a cap and selling a floor. The idea here is that the FI wants to hedge itself against rising rates but wants to finance the cost of the cap. One way to do this is to sell a floor and use the premiums on the floor to pay the premium on the purchased cap. Thus, these three over-the-counter instruments are special cases of options; FI managers use them like options to hedge the interest rate risk of an FI s portfolios. In general, FIs purchase interest rate caps if they are exposed to losses when interest rates rise. Usually, this happens if they are funding assets with floating-rate liabilities such as notes indexed to the LIBOR (or some other cost of funds) and they have fixed-rate assets or they are net long in bonds, or in a macrohedging context their duration gap is greater than zero, or D A kd L 0. By contrast, FIs purchase floors when they have fixed costs of debt and have variable rates (returns) on assets or they are net short in bonds, or D A kd L 0. Finally, FIs purchase collars when they are concerned about excessive volatility of interest rates or more commonly to finance cap or floor positions. Appendix 23C to this chapter located at the book s Web site ( presents details and examples of hedging with calls, floors, and collars. DO YOU UNDERSTAND? 1. How interest rate increases affect the payoff from buying a call option on a bond? How they affect the payoff from writing a call option on a bond? 2. How interest rate increases affect the payoff from buying a put option on a bond? How they affect the payoff from writing a put option on a bond? 3. What the outcome is if an FI hedges by buying put options on futures and interest rates rise (i.e., bond prices fall)? 4. The difference between a cap, a floor, and a collar used to hedge interest rate risk? 5. The risks involved with hedging with forwards, futures, and options? RISKS ASSOCIATED WITH FUTURES, FORWARDS, AND OPTIONS Financial institutions can be either users of derivative contracts for hedging and other purposes or dealers that act as counterparties in trades with customers for a fee. At the end of 2004, approximately 680 banks were users of derivatives, with three big dealer banks (J.P. Morgan Chase, Bank of America, and Citigroup) accounting for some 90 percent of the $87,880 billion derivatives held by the user banks. However, these securities entail risk for the user banks. For example, Allied Irish Banks suffered a $750 million loss on its derivative positions due to trades by a rogue employee in the early 2000s. This section discusses the various types of risk involved with futures, forwards, and options trading. Contingent credit risk is likely to be present when FIs expand their positions in forward, futures, and option contracts. This risk relates to the fact that the counterparty to one of these contracts may default on payment obligations, leaving the FI unhedged and having to replace the contract at today s interest rates, prices, or exchange rates. Further, such defaults are most likely to occur when the counterparty is losing heavily on the contract and the FI is in the money on the contract. This type of default risk is much more serious for forward contracts than for futures contracts. This is so because forward contracts are nonstandard contracts entered into bilaterally by negotiating parties such as two FIs and all cash flows are required to be paid at one time (on contract maturity). Thus, they are essentially over-the-counter arrangements with no external guarantees should one or the other party default on the contract. For example, the contract seller might default on a forward foreign exchange contract that promises to deliver 10 million in three months time at the exchange rate $1.70 to 1 if the cost to purchase 1 for delivery is $1.90 when the forward contract matures. By contrast, futures contracts are standardized contracts guaranteed by organized exchanges such as the New York Futures Exchange (NYFE). Futures contracts, like forward contracts, make commitments to deliver

14 642 Part 5 Risk Management in Financial Institutions foreign exchange (or some other asset) at some future date. If a counterparty were to default on a futures contract, however, the exchange assumes the defaulting party s position and payment obligations. Thus, unless a systematic financial market collapse threatens the exchange itself, futures are essentially default risk free. 15 In addition, default risk is reduced by the daily marking to market of future contracts. This prevents the accumulation of losses and gains that occur with forward contracts. Option contracts can also be traded by an FI over the counter (OTC) or bought/sold on organized exchanges. If the options are standardized options traded on exchanges, such as bond options, they are virtually default risk free. If they are specialized options purchased OTC such as interest rate caps, some element of default risk exists. 5 SWAPS The market for swaps has grown enormously in recent years the value of swap contracts outstanding by U.S. commercial banks was $56.41 trillion in December The five generic types of swaps, in order of their notional principal, are interest rate swaps, currency swaps, credit risk swaps, commodity swaps, and equity swaps (see Chapter 10). 16 The instrument underlying the swap may change, but the basic principle of a swap agreement is the same in that it involves the transacting parties restructuring asset or liability cash flows in a preferred direction. In this section, we consider the role of the two major generic types of swaps interest rate and currency in hedging FI risk. We then examine the credit risk characteristics of these instruments. Hedging with Interest Rate Swaps To explain the role of a swap transaction in hedging FI interest rate risk, we use a simple example. Consider two FIs: the first is a money center bank that has raised $100 million of its funds by issuing four-year, medium-term notes with 10 percent annual fixed coupons rather than relying on short-term deposits to raise funds (see Table 23 4). On the asset side of its portfolio, the bank makes commercial and industrial (C&I) loans whose rates are indexed to annual changes in the London Interbank Offered Rate (LIBOR). Banks often index most large commercial and industrial loans to either LIBOR or the federal funds rate in the money market. As a result of having floating-rate loans and fixed-rate liabilities in its asset-liability structure, the money center bank has a negative duration gap; the duration of its assets is shorter than that of its liabilities. D A kd L 0 One way for the bank to hedge this exposure is to shorten the duration or interest rate sensitivity of its liabilities by transforming them into short-term floating-rate liabilities that better match the rate sensitivity of its asset portfolio. The bank can make changes either on or off the balance sheet. On the balance sheet, the bank could attract an additional $100 million in short-term deposits that are indexed to the LIBOR rate (at, say, LIBOR plus 2.5 percent) in a manner similar to its loans. The proceeds of these deposits would be used to pay off the medium-term notes. This reduces the duration gap between the bank s assets and liabilities. Alternatively, the bank could go off the balance sheet and sell an interest rate swap that is, enter into a swap agreement to make the floating-rate payment side of a swap agreement. The second party of the swap is a thrift institution (savings bank) that has invested $100 million in fixed-rate residential mortgages of long duration. To finance this residential mortgage portfolio, the savings bank had to rely on short-term certificates of deposit 15. More specifically, the default risk of a futures contract is less than that of a forward contract for at least four reasons: (1) daily marking to market of futures, (2) margin requirements on futures that act as a security bond, (3) price limits that spread extreme price fluctuations over time, and (4) default guarantees by the futures exchange itself. 16. There are also swaptions, which are options to enter into a swap agreement at some preagreed contract terms (e.g., a fixed rate of 10 percent) at some time in the future in return for the payment of an up-front premium.

15 Chapter 23 Managing Risk with Derivative Securities 643 TABLE 23 4 Money Center Bank Balance Sheet Assets Liabilities C&I loans (rate indexed Medium-term notes (coupons to LIBOR) $100 million fixed at 10% annually) $100 million TABLE 23 5 Assets Savings Bank Balance Sheet Liabilities Fixed-rate mortgages $100 million Short-term CDs (one year) $100 million plain vanilla A standard agreement without any special features. with an average duration of one year (see Table 23 5). On maturity, these CDs must be rolled over at the current market rate. Consequently, the savings bank s asset-liability balance sheet structure is the reverse of the money center bank s: D A kd L 0 The savings bank could hedge its interest rate risk exposure by transforming the short-term floating-rate nature of its liabilities into fixed-rate liabilities that better match the long-term maturity (duration) structure of its assets. On the balance sheet, the thrift could issue longterm notes with a maturity equal or close to that on the mortgages (at, say, 12 percent). The proceeds of the sale of the notes can be used to pay off the CDs and reduce the repricing gap. Alternatively, the thrift can buy a swap that is, take the fixed-payment side of a swap agreement. The opposing balance sheet and interest rate risk exposures of the money center bank and the savings bank provide the necessary conditions for an interest rate swap agreement between the two parties. This swap agreement can be arranged directly between the parties. However, it is likely that an FI another bank or an investment bank would act as either a broker or an agent, receiving a fee for bringing the two parties together or to intermediate fully by accepting the credit risk exposure and guaranteeing the cash flows underlying the swap contract. By acting as a principal as well as an agent, the FI can add a credit risk premium to the fee. However, the credit risk exposure of a swap to an FI is somewhat less than that on a loan (this is discussed later in this chapter). Conceptually, when a third-party FI fully intermediates the swap, that FI is really entering into two separate swap agreements, one with the money center bank and one with the savings bank. For simplicity, we consider an example below of a plain vanilla fixed-floating rate swap (a standard swap agreement without any special features) in which a third-party intermediary acts as a simple broker or agent by bringing together two DIs with opposing interest rate risk exposures to enter into a swap agreement or contract. EXAMPLE 23 1 Expected Cash Flows on an Interest Rate Swap In this example, the notional (or face) value of the swap is $100 million equal to the assumed size of the money center bank s medium-term note issue and the four-year maturity is equal to the maturity of its note liabilities. The annual coupon cost of these note liabilities is 10 percent. The money center bank s problem is that the variable return on its assets may be insufficient to cover the cost of meeting these fixed coupon payments if market interest rates fall. By comparison, the fixed returns on the savings bank s mortgage asset portfolio may be insufficient to cover the interest cost of its CDs should market rates

16 644 Part 5 Risk Management in Financial Institutions TABLE 23 6 Financing Cost Resulting from Interest Rate Swap (in millions of dollars) Money Center Bank Savings Bank Cash outflows from balance sheet financing 10% $100 (CD Rate) $100 Cash inflows from swap 10% $100 (LIBOR 2%) $100 Cash outflows from swap (LIBOR 2%) $100 10% $100 Net cash flows (LIBOR 2%) $100 (8% CD Rate LIBOR) $100 Rate available on Variable-rate debt LIBOR 2 1 2% Fixed-rate debt 12% FIGURE 23 9 Fixed Floating Rate Swap Money Center Bank Short-Term Assets (C&I indexed loans) Cash Flows from Swap 10 Percent Fixed Savings Bank Long-Term Assets (fixed-rate mortgages) Long-Term Liabilities (4-year, 10 percent notes) LIBOR+2 Percent Short-Term Liabilities (1-year CDs) rise. As a result, the swap agreement might dictate that the savings bank send fixed payments of 10 percent per annum of the notional $100 million value of the swap to the money center bank to allow the money center bank to cover fully the coupon interest payments on its note issue. In return, the money center bank sends annual payments indexed to the oneyear LIBOR to help the savings bank cover the cost of refinancing its one-year renewable CDs. Suppose that the money center bank agrees to send the savings bank annual payments at the end of each year equal to one-year LIBOR plus 2 percent. 17 We depict this fixed floating rate swap transaction in Figure 23 9; the expected net financing costs for the FIs are listed in Table As a result of the swap, the money center bank has transformed its four-year, fixed-rate liability notes into a variable-rate liability matching the variability of returns on its C&I loans. Further, through the interest rate swap, the money center bank effectively pays LIBOR plus 2 percent for its financing. Had it gone to the debt market, the money center bank would pay LIBOR plus 2.5 percent (a savings of.5 percent with the swap). The savings bank also has transformed its variable-rate CDs into fixed-rate payments similar to those received on its fixed-rate mortgages it has successfully microhedged. Note in Example 23 1 that in the absence of default/credit risk, only the money center bank is really fully hedged. This happens because the annual 10 percent payments it receives from the savings bank at the end of each year allows it to meet the promised 10 percent coupon rate payments to its note holders regardless of the return it receives on its 17. These rates implicitly assume that this is the cheapest way each party can hedge its interest rate exposure. For example, LIBOR plus 2 percent is the lowest-cost way that the money center bank can transform its fixed-rate liabilities into floating-rate liabilities.

17 Chapter 23 Managing Risk with Derivative Securities 645 variable-rate assets. By contrast, the savings bank receives variable-rate payments based on LIBOR plus 2 percent. It is quite possible that the CD rate that the savings bank must pay on its deposit liabilities does not exactly track the LIBOR-indexed payments sent by the money center bank that is, the savings bank is subject to basis risk exposure on the swap contract. This basis risk can come from two sources. First, CD rates do not exactly match the movements of LIBOR rates over time since the former are determined in the domestic money market and the latter in the Eurodollar market. Second, the credit/default risk premium on the savings bank s CDs may increase over time; thus, the plus 2 percent add-on to LIBOR may be insufficient to hedge the savings bank s cost of funds. The savings bank might be better hedged by requiring the money center bank to send it floating payments based on U.S. domestic CD rates rather than on LIBOR. To do this, the money center bank would probably require additional compensation since it would then bear basis risk. Its asset returns would be sensitive to LIBOR movements while its swap payments were indexed to U.S. CD rates. currency swap A swap used to hedge against foreign exchange rate risk from mismatched currencies on assets and liabilities. Currency Swaps Swaps are long-term contracts that can also be used to hedge an FI s exposure to currency risk. The following section considers a plain vanilla example of how currency swaps can immunize FIs against foreign exchange rate risk when they mismatch the currencies of their assets and liabilities. Fixed-Fixed Currency Swaps. Consider a U.S. FI with all of its fixed-rate assets denominated in dollars. It is financing part of its asset portfolio with a 50 million issue of four-year, medium-term British pound notes that have a fixed annual coupon of 10 percent. By comparison, an FI in the United Kingdom has all its assets denominated in pounds; it is partly funding those assets with a $100 million issue of four-year, medium-term dollar notes with a fixed annual coupon of 10 percent. These two FIs are exposed to opposing currency risks. The U.S. FI is exposed to the risk that the dollar will depreciate against the pound over the next four years, which would make it more costly to cover the annual coupon interest payments and the principal repayment on its pound-denominated notes. On the other hand, the U.K. FI is exposed to the risk that the dollar will appreciate against the pound, making it more difficult to cover the dollar coupon and principal payments on its four-year, $100 million note issue from the pound cash flows on its assets. The FIs can hedge the exposures either on or off the balance sheet. Assume that the dollar/pound exchange rate is fixed at $2/ 1. On the balance sheet, the U.S. FI can issue $100 million in four-year, medium-term dollar notes (at, say, 10.5 percent). The proceeds of the sale can be used to pay off the 50 million of four-year, medium-term pound notes. Similarly, the U.K. FI can issue 50 million in four-year, medium-term pound notes (at, say, 10.5 percent), using the proceeds to pay off the $100 million of four-year, mediumterm dollar notes. Both FIs have taken actions on the balance sheet so that they are no longer exposed to movements in the exchange rate between the two currencies. EXAMPLE 23 2 Expected Cash Flows on a Fixed Fixed Currency Swap Off the balance sheet, the U.K. and U.S. FIs can enter into a currency swap by which the U.K. FI sends annual payments in pounds to cover the coupon and principal repayments of the U.S. FI s pound note issue, and the U.S. FI sends annual dollar payments to the U.K. FI to cover the interest and principal payments on its dollar note issue. 18 We summarize this 18. In a currency swap, it is usual to include both principal and interest payments as part of the swap agreement. (For interest rate swaps, it is usual to include only interest rate payments.) The reason for this is that both principal and interest are exposed to foreign exchange risk.