Management - University of Texas at...

Recent Innovations in Interest Rate Risk

Management and the Reintermediation of

Commercial Banking

Keith C. Brown and Donald J. Smith

Keith C. Brown is an Assistant Professor of Finance at the University of Texas, Austin, and Donald J. Smith is an Assistant Professor of Finance and Economics at Boston University, Boston, MA.

* A dominant theme of commercial banking in the 1980s has been the search for off-balance sheet, fee- based income to improve return on equity. As money center and large regional banks recover from the bur- dens of the international debt and energy loan crises, new product lines are being sought which meet those criteria. One promising line is Interest Rate Risk Man-

The authors were Senior Consultants to the Corporate Professional Development Department at Manufacturers Hanover Trust Com- pany while on leave and thank the many bank officers who aided them in their understanding of the products discussed in this paper, particularly Kevin Mangan, Barbara Luttich, Tom Gregory, and Ty Tes- sitore. The authors alone are responsible for any errors or omissions.

agement (IRRM). Commercial banks have become market makers in IRRM products such as forward rate agreements and interest rate swaps, caps, collars, and floors. These products are often versions of, and com- panions to, instruments that are used to manage a firm's foreign exchange risk exposure.

The movement toward market making in IRRM products represents a new form of bank intermediation, a form distinct from the classic function of transforming household savings into corporate borrowings. In this new role commercial banks intermediate between long and short positions in forward and options contracts taken by other banks, thrifts, and corporations. The market maker assumes the role of the clear- ing-house, hedging residual exposure resulting from an imbalance between the opposing sides in the transac-

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FINANCIAL MANAGEMENT/WINTER 1988

tions. In fact, banks now offer products that directly compete with exchange-traded interest rate futures and options contracts.

I. The Sources of Corporate Demand and Bank Supply of IRRM Products

Deposit disintermediation used to be the bane of the commercial banking system. Whenever market rates rose above the Regulation Q ceilings, funds would flow out of banks and into market instruments. This flow would be direct (such as with the purchase of Treasury Bills) or indirect (such as with investments in money market mutual funds). Ironically, the Federal Re- serve's resolution of that problem in the late 1970s- namely, by the authorization of new deposit accounts with rates tied to Treasury yields and eventually, de- regulated instruments such as money market deposit accounts-coincides with the emergence of another problem, that of asset-base disintermediation. Led by their success in the commercial paper market, many major corporations found financial savings by funding directly in the capital markets and bypassing the banking system altogether. Indeed, banks often facilitated this process by writing standby letters of credit to support the commercial paper that was being issued. Fur- ther, in the 1980s commercial banks bid to underwrite and lead-manage the capital market issues via note is- suance and revolving underwriting facilities.

The loss of major corporate customer debt from the asset base induced banks to seek new lines of business. Unfortunately, the growth opportunities in the international and energy sector credits of the 1970s became the non-performing loans of the mid-1980s, culminat- ing in the unprecedented provision for loan loss reserves in the second quarter of 1987. The search for off-balance sheet, fee-based income is a natural out- come given the inadequate results from the more traditional areas of business. The development of IRRM products is only one of the avenues being taken. Others include the origination, servicing, and packaging of mortgages for resale on the secondary market, financial guarantee programs like letters of credit, and advising on mergers, acquisitions, and corporate restructurings.

Corporate demand for IRRM products stems from the historic volatility in interest rates in the late 1970s and early 1980s following the Federal Reserve's decision to key on bank reserves rather than the federal funds rate in pursuit of money supply targets. Cor- porate treasurers were convinced to actively assess and

manage interest rate exposure by the realization that an unanticipated movement in market rates can quick- ly erase an otherwise strong operating performance. However, the highly structured nature of the available exchange-traded futures and options contracts limits corporate applicability. For example, margin accounts and daily mark-to-market valuation and settlement, essential features of an exchange-traded contract, require a substantial investment in the corporate treasury function to adequately monitor the positions. Additional- ly, contract standardization in terms of delivery dates, qualifiable securities, reference index rates, and denomination (also essential features for exchange-traded futures and options) inherently create degrees of basis risk for hedging programs. These technical com- plications, as well as an undeserved reticence over the

reputation of the futures and options industry, opened the ground for banks to enter the IRRM market.

The essential difference between over-the-counter and exchange-traded IRRM products is the formal distinction between forward and futures contracts. A forward contract is a negotiated agreement between two

parties, setting all prices and terms but deferring delivery and payment until a specified future date. While

gaining flexibility over dates, denomination, maturity, and reference rates, the parties must bear each other's credit risk until delivery and payment. Also, the parties bear liquidity risk since cancellation of the agreement would require a negotiated, or at least prespecified, settlement. On the other hand, futures are standardized forward contracts traded on an exchange. Liquidity risk is resolved to the extent that the contracts are actively traded. The exchange itself resolves the credit risk

problem via margin accounts and daily mark-to-market valuation and settlement. In sum, the tradeoffs are more (less) flexibility and less (more) basis risk with forwards (futures) versus more (less) credit and li-

quidity risk. Commercial bank IRRM products are flexible, ne-

gotiated, over-the-counter forward and option contracts. The banks make a two-way market, offering both bid and ask prices. This provides liquidity at current rates, albeit with less marketability than if an exchange were available. Typically there are no margin accounts nor are there any periodic mark-to-market settle- ments, although some transactions could require col- lateral or other credit enhancement. In general, the bank, as the intermediary, bears the credit risk of the counterparty. Commercial banks are willing and able to take on that function because of their immense human capital investment in credit analysis and ac-

46

BROWN AND SMITH/REINTERMEDIATION OF COMMERCIAL BANKING

cumulated firm-specific data. From a bank account officer's perspective, there is little difference between evaluating the credit quality of a term loan and an interest rate swap. While other financial service firms are active in the swap market, notably investment banks and life insurance companies, the ability to assess and manage credit risk provides a competitive edge to commercial banks (particularly in the mid-sized corporate market).

A second type of risk which arises from intermediat- ing IRRM products is the exposure from an imbalance between acquired long and short positions. A futures or options exchange avoids this risk by always main- taining a "matched book," in that every transaction involves both a buyer and seller of the contract. In other words, the exchange itself does not take one-sided positions; instead it acts as a conduit, or clearinghouse. Conversely, as a two-way market maker, a bank typically will hedge its net exposure in the cash or futures markets. The technological and theoretical capability to accurately manage that residual risk is a fairly recent development. For example, computer-based hedging and option valuation programs are necessary prereq- uisites. As a result, comercial banks now offer IRRM products that directly compete with the organized futures and options exchanges for corporate businesses, yet need the exchanges themselves to hedge their residual risk.

The development of IRRM products represents a reintermediation of commercial banking, a trend counter to the deposit-base and asset-base disintermedia- tions of past years. The intermediary's traditional role is to transform the nature of its sources and uses of funds. This transformation takes place on several di- mensions: denomination, maturity, interest payment, and rate reset periodicity, among others. The bank tailors the contracts to meet the needs of its depositors as well as its borrowers. The same process is at work with IRRM products. The bank designs contracts to stand between those firms which seek to hedge against rising rates and those which seek to hedge against fall- ing rates. Even when the contracts on each side are perfectly matched there is credit risk, which is borne by the intermediary. When the contracts are not perfectly matched and differ along the lines of traditional intermediation, there is also interest rate (or "gap") risk. Bank regulators, aware of these risks, are now impos- ing greater reporting and capital reserve requirements (see Whittaker [13]). The Federal Reserve Bank has recently approved new capital adequacy guidelines for off-balance sheet items such as swaps. Banks will be re-

quired to hold reserves against their risk exposure from IRRM product intermediation.

II. Basic IRRM Products: Forwards Inasmuch as commercial banks first ventured into

the over-the-counter IRRM markets with the creation of forward-oriented products, it is appropriate to begin the discussion in this area. Specifically, two different vehicles will be examined: forward rate agreements and interest rate swaps.

A. Forward Rate Agreements Forward (or Future) Rate Agreements, or FRAs,

are a prototypical example of the reintermediation of commercial banking via IRRM products. In essence, FRAs are over-the-counter, cash settlement futures contracts stripped of their margin account and mark- to-market daily settlement features. In fact, FRAs are priced and hedged with exchange-traded futures contracts, most notably the Eurodollar contract traded at the IMM (International Monetary Market at the Chic- ago Mercantile Exchange).

Forward rate agreements are usually transacted on the three-month London Interbank Offer Rate, or LI- BOR. The 3 x 6 contract (read "3 against 6") refers to three-month LIBOR, three months forward. For example, as a two-way market maker, the commercial bank might be willing to sell the 3 x 6 FRA at its offer rate of 7.10% and to buy at its bid rate of 7.00%. In market parlance, to buy the FRA contract means to agree to pay the given fixed rate; to sell the contract means to receive the fixed rate. Notice that this ter- minology reverses that used in the futures market. If one goes long in a futures contract, one gains if the rate at delivery is lower than the pre-specified rate (implied by the initial futures price). If one buys an FRA, however, one gains if the rate at settlement is higher than the fixed rate. This reversal is only nominal since futures focus on prices and FRAs on rates, and prices and rates are inversely related.

Typically, no cash is exchanged upon entering into the FRA. The cash settlement payment (CSP) is determined by the future spot market reference rate (R), realized three months hence in the case of a 3 x 6 FRA, vis-a-vis the pre-specified fixed limit rate (L). If the net settlement is made on the "maturity" date (month 6), the CSP is calculated based on the specified notional principal (NP) as follows:

CSP = (R - L) (NP) (#days/360). (1)

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The term (#days/360) is the fraction of the year cov- ered by the reference rate while the notional principal is equivalent to the delivery amount on a futures contract.1 If net settlement is made in advance on the "delivery" date (month 3), the present value of the CSP in Equation (1) is paid, using the realized reference rate as the discount factor. FRAs transacted between banks usually settle in advance so as to not prolong credit exposure. Corporate FRAs usually settle in ar- rears in order to coincide with the timing of the cash flows being hedged, for example, payments on a revolving credit facility.

Suppose that the commercial bank simultaneously buys a 3 x 6 FRA from Firm A at 7.00% and sells a 3 x 6 to Firm B at 7.10% for the same notional principal. Regardless of the future three-month LIBOR level, the bank expects a 10 basis point (b.p.) spread. For instance, if future LIBOR turns out to be 7.25 %, the bank would receive the CSP from Firm A based on a rate differential of 25 b.p. and pay to Firm B the CSP based on 15 b.p. This 10 b.p. bid-ask spread is compensation for bearing the credit risk of each counterparty in lieu of holding margin accounts and requiring periodic mark- to-market valuation and settlement.

A market maker will rarely have completely offset- ting FRA positions of the type illustrated by the above example. Since flexibility is one of the motivations for the product, the notional principals might come in odd amounts (although typically in million dollar multi- ples). Also, nontraditional FRAs such as a 2 x 5 or 8 x 11 can be transacted. Open positions are usually hedged with exchange-traded futures contracts. There- fore, the FRA bid-ask spread must cover the assumed credit risk and the hedging costs created by the futures positions, i.e., the uncertain timing of cash flows due to daily settlement and any opportunity loss from posting margin. In practice, the bid-ask quotes on FRAs are based on the futures contracts required to hedge the agreement-the bid rate is a markdown from, and the ask rate a markup over, the futures rate.

Pricing and hedging FRAs is relatively straightfor- ward when the FRA time period exactly matches the delivery dates on the futures exchanges in March, June, September, and December, the so-called IMM dates. A 3 x 6 FRA sold in January, however, requires a hedge

1U.S. dollar LIBOR is quoted on a 360-day basis; the term would be (#days/365) for a pound sterling FRA, since sterling LIBOR is quoted on a 365-day basis.

Exhibit 1. Eurodollar (IMM) and Treasury Bond (CBT) Futures Average Daily Open Interest and Trading Volume In July 1988

Delivery Month Open Interest %

September 1988 December March 1989 June September December March 1990 June

September December March 1991 June

Avg. Tot. Open In Avg. Trading Voli

September 1988 December March 1989 June September December March 1990

Avg. Tot. Open In Avg. Trading Voli

Eurodollar Contract 164,893.8 88,917.2 57,943.1 27,193.4 19,746.8 16,639.9 16,864.3 14,461.9 11,361.3 10,490.8 4,810.0 2,994.2

iterest 436,316.7 ume 80,223.3

Treasury Bond Contract 296,393.0

59,267.3 44,223.9 27,112.3 6,883.7 2,196.0

311.4 iterest 436,387.6 ume 256,647.3

37.79% 20.38 13.28 6.23 4.53 3.81 3.87 3.31 2.60 2.40 1.10 0.70

100.00%

67.92 13.58 10.14 6.21 1.58 0.50 0.07

100.00%

composed of fractional positions in both the March and June futures contracts. Also, a 3 x 9 FRA, based on six-month LIBOR, involves a cross hedge since the Eurodollar futures contracts settle on three-month LI- BOR. From the market maker's perspective these additional hedging risks and costs must be built into the bid-ask spread on the FRA. The risk to the bank, and subsequently to the Federal Reserve System and the Federal Deposit Insurance Corporation, is that the competitively determined spread might not adequately cover the hedging and credit risks involved in the transactions.

The FRA market to date is primarily interbank and is centered in New York and London, with an es- timated notional principal volume of $100 billion by the end of 1986. The impact of the FRA market can be seen by the extraordinary growth of the Eurodollar futures contract traded at the IMM. The open interest (number of outstanding contracts) in Eurodollar futures now parallels that of the Treasury Bond contract traded on the Chicago Board of Trade. To see this con-

48


sider Exhibit 1, which shows the daily average open interest and trading volume in each contract for the twen- ty trading days in July 1988. The Eurodollar contract was extended in July of 1987 from eight to twelve delivery months to support the extension of the FRA market into a third year. Also, note that the open interest in the Treasury Bond contract drops off rapidly after the first available delivery month. The much slower drop-off in the Eurodollar contract is indirect evidence of the hedging activity behind the FRA market. Moreover, notice the large difference in the trading volume of each contract. Treasury Bond futures appear to be a short-term trading instrument with attention on the next delivery date. Eurodollar futures appear to be more of a buy-and-hold hedging contract, again indicating the major role of the FRA market.

B. Interest Rate Swaps Interest rate swaps are the best known of the IRRM

products and have received increasing attention in the literature; see, for instance, Felgran [2], Smith, Smith- son, and Wakeman [5], Bicksler and Chen [1], and Turnbull [10]. A swap is in essence an exchange of coupon payments based on some agreed notional principal. In effect, an interest rate swap is a series of forward rate agreements; conversely, an FRA is a one-date swap. This analogy is pictured in Exhibit 2, using a cash flow format and an arbitrarily chosen path of future interest rates. The solid boxes represent fixed rate cash flows and the open boxes floating rate flows. In the upper panel a corporation is assumed to buy a series of FRAs from the commercial bank. The corporation will receive a net settlement payment whenever the floating rate, say LIBOR, exceeds the fixed rate. Notice that each individual FRA has a different fixed rate, increasing over time to reflect an upwardly sloping yield curve. Each FRA at origination has a zero expected value as does the series overall.

The lower panel to Exhibit 2 pictures an interest rate swap, whereby the corporation pays the fixed rate and the bank counterparty the floating rate. Net settlement each period would be based on a CSP formula similar to Equation (1). The two parties to the swap do not, in fact, exchange coupon payments; they settle for the net difference based on a notional principal amount. No- tice that a single fixed rate applies to each period. Over- all, the swap has a zero expected value but, unlike the series of FRAs, some of the individual settlement payments have a negative, and others a positive, expected value. In this interpretation an interest rate swap is a

series of "off-market" or "non-par value" forward rate contracts.

Another interpretation of an interest rate swap is as a combination of long and short positions in capital markets instruments. Assume that in the lower panel of Exhibit 2 there is an additional exchange of the notional principal amount at origination and again at maturity. Of course, such an exchange is redundant and not actually made on interest rate swaps. However, if it were to be made, a swap in which the corporation pays the fixed rate and the bank the floating rate has the same net cash flows as if the corporation issued a par value fixed rate note to, and bought a par value floating rate note at LIBOR from, the bank counterparty.

This capital market interpretation indicates that a corporation could construct a "homemade" swap with appropriate balance sheet transactions. Again, a pay- fixed swap is essentially equivalent to a long position in a floating rate note and a short position in a fixed rate security. Why then enter into a swap agreement? First, a swap entails lower transaction costs, avoiding the underwriting commissions on a capital market debt issue. Second, it does not alter the firm's debt-to-equity ratio. Third, a swap minimizes default risk exposure. Suppose that the corporation had bought a floating rate note and issued a fixed rate note. If the issuer of the floating rate obligation defaults, the corporation is at risk for the stream of coupon and principal payments, yet it still has its own debt outstanding. If one party to a swap defaults, the other is not obligated to continue its payments. Thus, a swap is an "executory" contract in that the performance of one party is condi- tional on the performance of the other.

A commercial bank views the credit risk on its portfolio of interest rate swaps from a replacement cost perspective. If any given counterparty were to default, the swap could be replaced at the current fixed rate for the remaining maturity. The loss (or gain) is the present value of the annuity represented by the difference between the original and replacement fixed rates, multiplied by the notional principal. This amount is merely the mark-to-market value of the swap. Note that a bank would never actually gain upon the bankruptcy of a counterparty. If the swap has economic value, meaning that the counterparty is paying a "below-market" or receiving an "above-market" fixed rate, the trustees to the bankruptcy proceedings would continue to honor the "in-the-money" transaction.

At inception, the credit risk of a swap is zero, assuming that the fixed rate is the current market rate and there is no initial cash payment.2 As time passes and

49


Exhibit 2. Comparison Between a Series of FRAs and an Interest Rate Swap

Upper Panel: Series of Pay-Fixed FRAs

Variable Cash Inflows

Fixed Cash Outflows

Lower Panel: Pay-Fixed Interest Rate Swap

Variable Cash Inflows

Fixed Cash Outflows

the fixed rate on the replacement swap changes, credit risk shifts to one side of the transaction while remaining at zero on the other. It is important to note that

2At times, banks enter into "off-market" or "non-par value" swaps at a fixed rate above or below the current market rate. For example, a corporate counterparty might want to exactly match the fixed rate on the swap to the coupon rate on a certain debt issue. Then, an upfront cash payment is made or received for the present value of the annuity, based on the difference between the contractual fixed rate and current market fixed rate, multiplied by the notional principal amount. With off-market swaps there is initial credit risk exposure.

credit risk exposure can develop even if the floating rate exactly follows its expected path or, in the extreme, were nonstochastic. This is because a swap uses the same fixed rate for all settlement periods. Refer again to the lower panel of Exhibit 2 and suppose that the future floating rates which determine the variable cash inflows are known with certainty. The fixed rate on the

swap would have been set such that the present values of the inflows and outflows were equal. However, as time passes the credit risk increases, so that by the fourth period the fixed-payer expects to receive net cash settlement payments for the remainder of the term. Note also that there would be no credit risk ex-

4Mmm&rlNmmp6 ksrea~8cabae

50


posure on the series of FRAs, since each is priced and traded separately and each fixed rate reflects the expected future rate. Therefore, the credit risk on a swap owes to the stochastic nature of interest rates and the structural design of applying a single fixed rate to all settlement periods.

The interest rate swap market can be segmented into a short-term sector with maturities out to three years and a long-term sector with maturities between three and ten years. Short-term swaps are, in fact, treated as a package of FRAs at a single fixed rate and are priced and hedged using Eurodollar futures contracts. The fixed rate on long-term swaps is quoted as a spread over the yield on the most recently issued ("on-the-run") Treasury note. The floating rate side to the swap is usually three-month or six-month LIBOR, although some swaps are tied to a commercial paper or Treasury Bill index. Commercial banks can act as brokers (receiving an arrangement fee) but now more commonly act as true intermediaries, in that they are the counterparty to each transaction. The net exposure from an imbalance between being the fixed-payer and fixed- receiver in a portfolio of swap positions is usually hedged in the Treasury cash and futures markets. As with FRAs, the bid-ask spread must be sufficient to cover the credit and hedging risks assumed by the intermediation process and, now, the capital adequacy reserve requirements.

There are a variety of applications for interest rate swaps in corporate financial management. One is the well-chronicled credit risk arbitrage story described by Bicksler and Chen [1]. This usage, which parallels that of comparative advantage in international trade theory, maintains that a swap transaction can arbitrage differential credit risk premia in the fixed versus floating rate markets. By each issuing debt in the capital market where it has a relative advantage, both counter- parties can lower the cost of their desired debt structure upon exchanging coupon payments. However, it is probably as difficult to accurately measure an arbitrage gain as it is to obtain. For example, the various cove- nants in the documentation and included call and put options in each funding structure need to be separately priced, and the potential credit risk on the swap-related transaction needs to be assessed. Moreover, as argued by Smith, Smithson, and Wakeman [5], arbitrage opportunities of this sort should not persist in an efficient capital market. The extraordinary growth of the international swap market, to almost $900 billion in notional principal by the end of 1987, indicates that there are other motivations as well.

The interpretation of a swap as a series of forward rate agreements suggests a market completion argu- ment. Swaps allow for flexible management of interest rate risk exposure out to ten years, extending the hori- zon available with exchange-traded futures contracts. The key point is that corporations, thrifts, and commercial banks can alter the interest rate sensitivity of their assets and liabilities with swaps at low transactions costs (see Loeys [3] for further discussion). In principle, formal balance sheet restructuring accom- plishes the same end but is often constrained by call deferment provisions on existing debt, registration and rating costs and procedures, and concern over disrupt- ing the established investor base. In addition, swap transactions allow the restructuring to be temporary and kept off the balance sheet. Then, if the interest rate sensitivity of assets and liabilities changes, the risk management transactions can be reversed without further disruption of the balance sheet.

Another driving force behind the development of the swap market is that commercial banks have actively fostered and promoted this IRRM product line for the motives discussed in the previous section. While supply does not create its own demand in the financial services industry, banks have nevertheless aggressively marketed their swap capabilities. This is often in the guise of product innovations: forward swaps (having a deferred start date), variable notional principal swaps (to match amortization schedules or seasonal cash flows), asset swaps (packaging a swap with a market- able security), and swap options (rights to enter into or exit from swap transactions). Also, banks have been active in standardizing documentation and tax and ac- counting treatment of swaps.

Underlying many of these innovations is a major structural development in swap market making. At first, swaps were matched transactions-meaning that the market maker would act as the intermediary between two explicit end-users. That often would neces- sitate a search for an appropriate counterparty and effectively rule out some innovative transactions. Now market makers use a portfolio approach to managing swap positions. Banks can enter into forward or variable notional principal swaps without having to find a counterparty. The swap transactions merely represent so many cash flows, the present value of which is hedged using futures and/or options contracts. This development was technological as well as theoretical, requiring computer-based cash flow and valuation programs; see Wakeman [12] for further discussion of the portfolio approach.

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III. Basic IRRM Products: Options The fundamental difference between exchange-

traded futures and options contracts is that while both instruments provide the right to conduct a future transaction at prespecified terms only the latter also allows the holder to avoid completing a deal on what prove to be unfavorable terms. Of course, in order to acquire such a one-sided obligation, the option holder must

pay a front end premium to the option writer. Conse- quently, for the corporation attempting to hedge its interest rate exposure with these instruments a natural tradeoff arises between the initial expense and future flexibility, which in turn, expands the variety of choices available to the firm to meet its view on future interest rate movements. It is not surprising that the market for bank-traded IRRM products has also expanded beyond the forward-based vehicles just described in order to satisfy the growing corporate demands for over-the-counter interest rate options. As with FRAs and with swaps, the primary function of the bank in the options market is to act as an intermediary between the rigid standardization of exchange-traded contracts and the specific requirements of the corporate user. The two basic IRRM option products are caps and floors. Each instrument is considered below.

A. Interest Rate Caps An interest rate cap is an agreement in which the

cap buyer makes an initial payment in exchange for future compensation from the cap seller if the prevailing interest rate level exceeds a pre-specified strike (or limit) rate (Lc) on each of a series of settlement dates. The reference rate (R) usually used to create a cap agreement is three or six-month LIBOR. Furthermore, since the entire arrangement is based on rate movements, the cap also specifies an initial notional principal (NPc) to determine the exact amount of any future settlement payments. For example, a cap agreement with the initial premium of Pc would require the following exchange from seller to buyer on each settlement date:

= (R - Lc) (NPc) (#days/360) if R > Lc CSP= R Lc

0 if R < Lc, (2)

where #days represents the number of days between each settlement period and the subscript c refers to the cap agreement.

By comparing Equations (1) and (2), the inherent distinction between the cap and an interest rate swap

should be clear. For the holder of the forward contract

(i.e., the swap or FRA), the cash settlement can be either a positive or negative amount indicating that either a receipt or payment of funds is possible. Con-

versely, the holder of the cap will only receive cash set- tlements and is under no obligation to the seller if R < Lc beyond the initial payment of Pc. In this con- text, the cap can be viewed as a series-or portfolio- of European interest rate options each maturing on a different settlement date throughout the life of the

agreement. The importance of this interpretation from the bank's perspective is that virtually any cap can be

priced with conventional techniques by summing the

present values of the individual components.3 The most common user of an interest rate cap is a

corporation that is trying to limit its exposure on a variable rate liability, such as a revolving credit agreement or floating rate note. While paying the fixed rate on a

swap agreement would also serve the same purpose, the advantage of the cap is that it limits the upside cost of funding without removing the benefit that would ac- crue to the firm if R < Lc on a particular settlement date. Therefore, as stated earlier, the decision that the

company seeking to hedge must make is between the

certainty of the present cap premium (Pc) and the

potential for reduced funding costs in the future (Lc -

R). The complexity of this choice is compounded by the fact that while there will only be one current par value fixed rate in the swap market for a desired maturity, a wide variety of caps can be created by altering the strike rate, Lc.

Finally, it is also interesting to consider the credit risk involved with a cap agreement. Notice that in the above situation the bank that sold the cap will have no credit exposure to the cap purchaser. The cap writer will receive the premium from the cap holder at the in-

ception of the deal and nothing more. In fact, it is the

company purchasing the cap that will bear the credit risk of the bank since it is depending on the bank for future settlement payments if market rates rise above the cap rate. Once again, the importance of this from the intermediary's perspective is that if the bank de- cided to hedge its cap sale with the purchase of an of-

Throughout this discussion we are resisting the temptation to describe the interest rate cap as a series of either call or put options. In

fact, both labels apply depending on whether the underlying security is viewed as a bond price (put) or the interest rate itself (call) and the

comparative statics of their pricing relationships obtain from either definition. See Smith [6] for a more developed discussion on this

point.

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fsetting agreement from another bank or corporate counterparty, credit risk would only be a concern in the second transaction. Further, if the bank hedged the rate exposure created by the cap sale with the purchase of a series of exchange-traded options, it could limit its credit exposure to the exchange itself. Of course, the cost of reducing credit risk in this manner would be a likely increase in basis risk caused by a mismatch in the terms of the various contracts.

B. Interest Rate Floors Just as a cap sets an upper limit on rate movements,

an interest rate floor sets a lower limit beneath a floating rate index. Formally, the floor seller receives an initial premium in exchange for the guarantee that the buyer will be compensated if the reference rate falls below a pre-specified floor rate (Lf) on any settlement date. In a manner comparable to Equation (2), this cash settlement is based on a particular level of notional principal (NPf) and can be expressed:

(Lf - R) (NPf) (#days/360) if R < Lf CSP = (3)

0 ifR >Lf.

As with the cap, the floor agreement (denoted by the subscriptf) is best thought of as a series of cash settlement European options, whereby the holder receives a payment whenever the reference rate falls below the strike level on any expiration date.

Since interest rate caps are typically used to hedge the exposure associated with a floating rate liability, it is natural to think of interest rate floors as providing a hedge to the holder of a floating rate asset. Specifical- ly, in exchange for an upfront price (Pf) the floor holder will be assured that the return on the floating rate asset will never fall below Lf. Of course, since the cost of the floor varies directly with the limit rate, the floor holder is trading off the certainty of a front end premium against the possibility that the asset's future return level will fall beneath Lf. From this point of view, an interest rate floor can be thought of as an insurance policy for the floating rate asset that becomes more ex- pensive as the guaranteed level of return increases. For this reason, floors are usually purchased so as to be out of the money (i.e., R > Lf)4

4Similarly, a cap can be viewed as an insurance policy against rising funding costs and is usually purchased when out-of-the money (i.e., R < Lc).

As a final point, it should again be noted that there is no credit risk to the bank in selling a floor due to the unilateral obligation built into the instrument. There- fore, in evaluating the credit exposure of its whole interest rate option book, the market maker need only be concerned with those transactions requiring the purchase of an option from another counterparty. Further, as with the bank's FRA and swap book, the net exposure in the option portfolio is hedged to the extent possible with exchange-traded options. Once again, it is in this way that commercial banks intermediate between corporate users of IRRM products.

IV.Recent Innovations: Product Combinations

It has been stressed in previous sections that the new intermediation products offer corporate customers a variety of basic tradeoffs in the management of interest rate exposure. Specifically, it was argued that it is necessary for the firm to consider the cost of a particular hedging technique in relation to its anticipated performance. For example, although a typical interest rate swap requires no front end expense, it also moves the company out along the yield curve to a fixed funding cost that remains impervious to interest rate declines. Conversely, the interest rate cap, which provides the desired rate ceiling without any restrictions, often requires a substantial initial payment. While hedging instruments such as these generate a considerable array of choices, it is perhaps not surprising that corporations have sought to extend the set of available alternatives by demanding various combinations of the underlying products. In general, the point of all such hedge portfolios is to acquire the necessary protection against rate exposure, while transforming the initial fee into a more acceptable method of payment. Further, as will be demonstrated shortly, it is possible to create any of these combinations by taking the appropriate positions in the option-based products alone.

A.Combining Caps and Floors: Collars The natural concern of a corporation with a variable

rate liability is to limit the extent of its exposure to rising costs. This concern can be managed by purchasing an interest rate cap. In addition, it is possible for the company to sell a floor in order to obtain some or all of the funds necessary to buy the cap. Using earlier notation, the net cost of this approach to hedging can be written:

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(NPc)(Pc) - (NPf)(Pf) = C, (4)

where C is expressed in dollar terms. Since the cap agreement provides the desired protection, the notional principal on the cap is typically set equal to the level of the funding liability. Also, for any particular ceiling rate, market conditions will dictate the price of the cap, and so the net cost of the hedge will depend upon the characteristics of the floor that is sold. More exactly, the firm will have to decide on two variables when selecting the floor agreement: (i) the floor rate, which will then determine Pf, and (ii) the notional principal. Depending on which variable it first sets, the firm can create an interest rate collar or an interest rate participation agreement.

Interest rate collars are based on the concept that the company selects the notional principal on the floor to be equal to that of the cap (i.e., NPc = NPf). Having done so, any desired level of net expense can then be achieved by selecting a floor rate sufficient to yield the necessary price. One important special case of this procedure is to create a collar that has no initial net expense. That is, a zero-cost hedge portfolio can be generated by selecting a floor rate such that Pf = Pc. This, in turn, will have the effect of setting C = 0. Assuming that the funding cost on the underlying liability is reset periodically to the prevailing reference rate, the net cost of funds (COF) for the "collared" liability, expressed as an annual percentage rate, can be written:

C Lc COF= R

Lf

ifR > Lc

ifLf < R < Lc ifR <Lf ,

COF = R + max [0, Lf- R] - max [0, R- Lc]. (5')

Once again, Lf, Lc, and R represent the floor and cap limit rates, and the reference rate, respectively.

In establishing an interest rate collar, the relationship between LfandLc is important for several reasons. First, at the inception of the arrangement, it is typical that Lf < R < Lc. In terms of the way the cap and the floor are defined, this implies that both options are out of the money when the collar is created. Second, since the company determines Lc and NPc in conjunction with its hedging needs, it cannot also select both Lf and C. In particular, for any given level of net initial expen- diture, there will only be one floor rate corresponding to the desired cap rate. On the other hand, for any specific level of C, there are numerous combinations of Lf and Lc that will yield the requisite dollar offset. In

general, however, the more severely the company at- tempts to restrict its risk exposure (i.e., the lower the level of Lc), the higher the floor rate will need to be to generate a particular level of C. Consequently, from an examination of Equation (5), a third point can be made that the collar allows the firm to create a tradeoff between the initial cost of the hedge and the extent to which it is able to take advantage of market interest rates below Lc. That is, the sale of the floor effectively converts the front-end expense of the cap into poten- tially higher future funding costs by restricting COF to a minimum of Lf. Notice, then, that the periodic cost of funds will be limited on the upside to the desired cap level of Lc but fluctuate directly with R until the floor rate of Lf is reached.

Finally, while none of the new IRRM products represent funding vehicles per se, it should be clear from Equation (4) that it is possible to select a (Lf, Lc) combination such that C is negative. Put differently, if Lf is set sufficiently high so that Pf > Pc, the firm will receive more from the sale of the floor than is paid for the ac- quisition of the cap. However, what typically mitigates this initial receipt of funds is that the floor will general- ly have to be in-the-money in order to more than offset the price of any non-trivial cap. In all likelihood, this situation would obligate the firm to make immediate payments on the short position in the floor at each reset date until such time when R > Lf. Thus, although the collar can be used to raise funds in the same way that the sale of any option can, it is seldom employed as any- thing other than a means of reducing the initial cost of the hedge.

B. Combining Caps and Floors: Participation Agreements

A second general method of combining caps and floors in the management of interest rate risk is the participation agreement.5 Recall from Equation (4) that the company, having selected NPc and Lc according to its funding obligation, must also determine the total dollar proceeds needed from the sale of a floor in order to meet its front-end hedging cost objective. The participation agreement, unlike the collar which established a floor rate (i.e., Lf) after first setting NPf = NPc,

5In the work to follow, the term participation agreement will be used to describe a particular variation of the cap-floor hedging combination. It should be noted, however, that participation agreements can be found under several trade names. In particular, Salomon Brothers markets them under the PART acronym while at Manufacturers Hanover they are called PIRAs.

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approaches the problem by equating the limit rates on the cap and the floor (i.e., Lf = Lc). Assuming that R < Lf = Lc at the time the arrangement is made, this action guarantees that Pf > Pc inasmuch as the floor and the cap will be in and out of the money, respectively. The effect of this is that it will not be necessary to sell the floor in the same notional principal amount to achieve the desired cost reduction. From Equation (4), the required level of NPf can be expressed:

(NPc)(Pc) - C

NPf = Pf

Exhibit 3. Comparing the Funding Expense of the Collar and Participation Agreements

COF

L C

Lf

Participation Agreement

Collar

(6)

It follows from (6) that whenever (NPc)(Pc) > C > 0 it will be the case that NPc > NPf. That is, as long as the participation agreement is used strictly as a means of reducing the initial expense of the cap protection (rather than as a funding source), the floor can be sold with a lower notional principal than that on the cap.

While Equation (6) represents the general case, it is more instructive to consider the mechanics of the participation agreement for the special case when C = 0. With such a zero-cost assumption, (6) reduces the NPf = NPc(Pc/Pf). Notice that in this calculation it is the ratio of the cap and floor prices that determines the

appropriate notional principal percentage, with the amount of the cap being nothing more than a scaling factor. Further, by setting C = 0 it is quite easy to consider how the firm using the participation agreement actually "participates" in a lower funding cost whenever R <Lc.

Overall, the net funding cost of using a participation agreement to hedge a floating rate liability which resets at R is expressed:

{ Lc if R > Lc COF = (7)

R + (Pc/Pf)(Lc- R) ifR < Lf,

COF = R + (Pc/Pf) max [0, Lf- R] - max [0, R- Lc], (7')

since the arrangement requires that Lc = Lf. Notice in (7) that any time the market rate exceeds this common limit rate, the cost of the liability will be capped at the desired ceiling rate. Conversely, whenever R falls below the limit rate the company will not fully benefit from the reduced funding cost because of the short position in the floor. However, since the floor was not sold for the same notional principal as the cap, the net expense to the firm will not be constant. Instead, as long as R

R

declines away from Lc, COF will also continue to de- cline, but to a lesser extent. With this in mind, the ex- pression in (7) can be rewritten as follows:

COF = Lc - (1- Pc/Pf) max [0, Lc - R]. (8)

Equation (8) indicates that the effective cost of funds will be equal to the cap rate less the difference between the reference rate and the cap rate (provided R < Lc) adjusted by (1 - Pc/Pf). The factor (1 - Pc/Pf) is called the participation rate and represents the proportion of the difference between R and Lc that the firm will get to "keep" after compensating the purchaser of the floor. This participation rate will decrease as Lc decreases since the cap will then become less out-of-the-money, thereby increasing Pc. Consequently, a larger notional principal amount on the floor will needed to be sold in order to reduce the net initial cost to zero.

Exhibit 3 presents a graphical comparison of the cost-benefit tradeoff between the collar and participation agreement. For both cap-floor combinations, the net funding expense is given under the assumption that a cap rate of Lc is selected to hedge a liability in the amount of NPc. The collar, which specifies NPf = NPc, requires a floor rate of Lf < Lc in order to generate a net position such that C = 0. From the graph, it is clear that the firm enjoys 100% participation anytime R is less than Lc but greater than Lf. However, as R declines below Lf, the participation rate on the collar falls to zero as the floor rate becomes a binding expense con- straint. As an alternative to this all-or-nothing format, the participation agreement starts by setting Lf = Lc and then finds NPf < NPc so that the initial dollar out- lay for the hedge is exactly offset. This reduction in the up-front fee manifests itself by allowing the firm to par-

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ticipate in only (1 - Pc/Pf) of the differential that exists whenever R < Lc. Thus, while both the collar and

participation agreements establish the desired funding limit, they each offer a different means of financing the

hedge through the possibility of future payments to the bank that purchased the floor.

Before concluding this discussion of cap-floor combinations, it is worth noting that the participation agreement can also be viewed as a combination of a cap and an interest rate swap. To see this, recall that the

participation agreement consists of buying NPc of a cap and selling NPf of a floor. Since both the cap and floor are based on the same limit rate (i.e., Lc = Lf)--which is assumed to be above the current level of R-then

NPf* < NPc. The notional principal of the cap can therefore be expressed as NP = [NPf* + (NPc - NPf )]. By segmenting the notional principal in this manner, the total amount of the cap purchased can be thought of as consisting of two portions: an amount equal to the notional principal of the floor (NPf ), and an "un- restricted" amount comprised of NPc - NPf. Therefore, the entire agreement consists of: (i) the simultaneous purchase of a cap and sale of a floor having an identical limit rate (Lc) and notional principal; and (ii) the additional purchase of (NPc - NPf ) of a cap with the same ceiling rate. With this convention it is possible to see that any time the purchase of a cap is combined with the sale of a floor at identical amounts and strike rates, the resultant combination will be equivalent to an interest rate swap with a fixed rate of Lc. To illustrate this

point, it is sufficient to recognize that the cost of funds for this portion of the participation agreement will be:

COF = R + max [0, Lf- R] - max [, R - Lc], (9)

where the first term corresponds to the underlying liability and the second and third terms represent the contribution of the floor and cap, respectively. From (9) it should be apparent that, since Lc = Lf no matter what the level of the market rate, the funding cost will be equal to the limit rate. Specifically, when R > Lc, the firm will exercise the cap to acquire the lower rate, whereas if R < Lf the floor will be in-the-money and exercised against the company. Of course, this is the same result the firm could have accomplished had it

6This result, which can be dubbed the "swap-floor-cap" parity theorem, is a simple extension of the well-known put-call theorem of Stoll [9]. For a more complete option-oriented interpretation of interest rate swaps, see Ritchken [4].

Exhibit 4. The Participation Agreement as a Cap and a Swap

COF

L

(NPf/ NP) Swap

/ 4/ ( NP ) Participation Agreement

-- [( NPc - NPf) / NP] Cap

R

agreed to buy an interest rate swap by paying a fixed rate of Lc.6 Further, since the present market rate is assumed to be less than the ceiling rate, a swap created in this manner will obligate the company to make future payments that will be higher than those currently available in the regular swap market. Consequently the firm demands sufficient front-end compensation in lieu of the lower periodic increments it forgoes. As such, this arrangement, commonly called an "off-market" swap, serves as a funding source adequate enough to cover the cost of the cap purchased for the remaining (NPc - NPf ) in notional principal. Thus, NPc of a

participation agreement can be created by combining NPf of a swap with (NPc - NPf ) of a cap. Of course, the immediate consequence of this result for the cor-

porate customer is that it places one more "no ar-

bitrage" restriction on the ability of the market maker to price the separate products. This type of financial

engineering is illustrated in Exhibit 4.7

V. Assessing the Significance of Bank Innovation

In his presidential address to the American Finance Association, Van Horne [11] cautioned against the blind acceptance of what he termed "financial excesses," that is, products or strategies that are innovative in form without providing any substantive economic value. According to Van Horne [11], a new product must either meaningfully expand the set of available in-

7As mentioned in the introduction, the term "financial engineering" has become synonymous with the emergence of IRRM products and strategies in the commercial banking sector. For a more

thorough analysis of this topic, see Smith [7] and Smithson [8].

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vestment alternatives (i.e., complete the market) or improve the operational efficiency of those markets that already exist in order to be truly innovative. Although Van Home's primary concern was in the area of mar- ketable securities, it is nevertheless relevant to consider whether the myriad of bank-generated IRRM instruments can be similarly classified. Put differently, since each of the products just described can be simu- lated to some extent by positions in either the exchange-traded or over-the-counter futures and options markets, is it possible that some of them are unneces- sary additions? To focus on the two extreme answers to this question (that is, those instruments which genu- inely add value in the marketplace and those which can be called excessive), we will consider the basic IRRM products and combinations of these products separately.

To begin with, from the preceding discussion on intermediation, it should be clear that FRAs, swaps, caps, and floors all provide hedging mechanisms that are quite adaptable to the needs of the corporate client. However, since each instrument also has an exchange- traded analogue, it is difficult to attribute their popu- larity among investors to a market completion criterion. For example, we have shown that a pay-fixed swap can be viewed as: (i) a strip of "off-market" pay- fixed FRAs, (ii) a short position in a fixed coupon bond and a long position in a floating rate note, and (iii) the

purchase of a cap and sale of a floor at the same strike rate. Therefore, do swaps (as well as the other basic products) offer enough operating improvements to merit the innovation label? The answer is an unquali- fied yes. For the several reasons cited earlier (i.e., lower transaction costs, less basis risk, no permanent capital structure ramifications) swap agreements are clearly the most cost-efficient way for the corporate customer to exchange a series of variables for fixed cash flow commitments. Consequently, although its hedging properties can be approximated in a variety of ways, there is no comparable synthetic combination that dominates the swap. In fact, since FRAs, caps, and floors were also borne out of the desire to reduce basis risk, all of the basic IRRM products can be classified as legitimate innovations under the Van Home's second condition.

On the other hand, not all of the option portfolios described in the previous section deserve a similar endorsement. Recall that zero-cost collars and participation agreements represent two general approaches to obtaining protection against rising interest rates with no initial expense. From a comparison of

Equations (5) and (8), it is clear that both strategies provide the same cap rate; the difference between the two is the timing and amount of future compensation to the floor holder. However, it is also true that interest rates must fall substantially before the participation agreement dominates the collar on a cost basis. To see this, the breakeven market reference rate (Rb) for the two strategies' funding cost levels can be shown from Equations (5) and (8) to be Rb = Lc - (Lc - Lfc)(l -

Pc/Pfp)-~, where Lc is the common cap rate, Lfc is the floor strike rate on the collar and Pfp is the price of the floor in the participation agreement.8 With this result it is easily established that any time the reference rate exceeds (falls below) Rb, the funding cost associated with the participation agreement will be greater (less) than that of the collar. Further, it is also easily calculated that Rb < Lfc, which becomes an important con- sideration given that both the cap and floor which comprise the collar were chosen to be out-of-the- money (i.e., Lfc < R < Lc). The conceptual problem confronted by the participation agreement, then, is that the corporate treasurer desiring the upside protection from the cap must expect that market rates will stay substantially below the cap rate before its use makes sense relative to the collar. Although there undoubted- ly are different sets of probabilistic circumstances in which the participation agreement would be the preferred alternative, the preceding analysis suggests that under typical circumstances it would not. Thus, for practical purposes, the participation agreement ap- pears to be a product of excess in the IRRM market.

In summary, it is important to realize that not all of the hedging strategies developed by commercial banks can be characterized as "value adding." Said differently, just because an IRRM product can be developed does not mean that it will be accepted by the marketplace. This would seem to be the case with the participation agreement, which, while certainly a creative combination of other more basic products, is often dominated by the collar agreement. Just as importantly, however, none of the products analyzed in this paper (including the participation agreement) rely on pricing inefficien- cies to justify their existence. In fact, with the ability of both banks and their corporate clients to engineer syn- thetically equivalent structures, it is unlikely that any

8Formally, Rb can be established by finding the reference that sets the floor rate on the collar (Lfc) equal to the funding cost of the

participation agreement (i.e., Equation (8)). This solution can also be inferred from a visual inspection of Exhibit 3.

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IRRM vehicle will require an inefficient market to secure its success.

VI. Concluding Comments There can be little doubt that the nature of commer-

cial banking has been irrevocably altered by the events of the last several years. From the asset-base disintermediation of the 1970s to the increased interest rate volatility which characterizes the present day, a conflu- ence of economic phenomena has led major money center banks to assume a more active role in the management of interest rate risk. Several of the leading over-the-counter IRRM products and strategies which, to date, have received little attention in the literature, have been examined. These instruments can be viewed as being equivalent to either an option or a forward contract. This interpretation was essential to the realization that commercial banks are once again serving as intermediaries, this time between the futures and option exchanges and the corporation with the ul- timate hedging requirement.

Before concluding, it must be stressed that because of the dynamic nature of the banking industry itself, no list of IRRM products or strategies can ever be fully descriptive. Perhaps then the crucial message in the preceding discussion is that there is no completely cost- less way for a firm to effectively manage its interest rate exposure. Instead, a corporation must decide among a series of tradeoffs between the present cost and the future flexibility of its preferred hedging mechanism. That banks have succeeded in enhancing the array of choices presently available is beyond question. The challenge for the coming years, of course, is whether

the financial services community can continue to create the kinds of vehicles that will add to the market value of its clientele.

References 1. J. Bicksler and A. Chen, "An Economic Analysis of Interest Rate

Swaps," Journal of Finance (July 1986), pp. 645-656. 2. S. Felgran, "Interest Rate Swaps: Use, Risk and Prices," New

England Economic Review (November/December 1987), pp. 22- 32.

3. J. Loeys, "Interest Rate Swaps: A New Tool for Managing Risk," Federal Reserve Bank of Philadelphi- Business Review (May/June 1985), pp. 17-25.

4. P. Ritchken, Options: Theory, Strategy, and Applications, Glen-

view, IL, Scott Foresman, 1987. 5. C. Smith, C. Smithson, and L. Wakeman, "The Evolving Market

for Swaps," Midland Corporate Finance Journal (Winter 1986), pp. 20-32.

6. D. Smith, "Putting the Cap on Options," Euromoney Corporate Finance (January 1987), pp. 20-22.

7. , "The Arithmetic of Financial Engineering," Journal of

Applied Corporate Finance, forthcoming. 8. C. Smithson, "A LEGO Approach to Financial Engineering,"

Midland Corporate Finance Journal (Winter 1987), pp.16-28. 9. H. Stoll, "The Relationship Between Put and Call Option

Prices," Journal of Finance (December 1969), pp. 801-824. 10. S. Turnbull, "Swaps: A Zero Sum Game?" Financial Management

(Spring 1987), pp.15-21. 11. J. Van Horne, "Of Financial Innovations and Excesses," Journal

of Finance (July 1985), pp. 621-631. 12. L. Wakeman, "The Portfolio Approach to Swap Management,"

unpublished manuscript, May 1986. 13. J. G. Whittaker, "Interest Rate Swaps: Risk and Regulation,"

Federal Reserve Bank of Kansas City Economic Review (March 1987), pp. 3-13.

CALL FOR PAPERS THE AMERICAN RISKAND INSURANCE ASSOCIA TION

1989 ANNUAL MEETING August 20-23, 1989

Denver, CO

You are encouraged to submit a proposal for a presentation at the 1989 ARIA meeting. Proposals should include: title, purpose, research methodology, and a timetable for completion of the paper. All proposals will be judged using a blind review process. Deadline for submission is January 16, 1989. Send proposals to ARIA Vice President and 1989 Program Chairperson:

Sandra G. Gustavson 206 Brooks Hall, ILSRE

University of Georgia Athens, GA 30602

(404) 542-4290

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