, we would have to consider bT Ðthat is,the cost of borrowing T, not A. The reasoning would be modi®ed accordingly.4Note that we could also include the revenue generated by lending T out. In practice, weknow for a fact that we will have to pay a borrowing fee for A, but we cannot be surethat T can be lent out. Therefore, we leave this out for simplicity without any loss ofgenerality. The total pro®t we obtain can be considered conservative.2
CHAPTER 9 RISK ARBITRAGE. Sell r shares of A at PA .5
. Lend an amount equal to r  PA
425
PT until exiry at rE .
These operations generate a cash ¯ow CF0 equal to:CF0 
PT  r  PA
r  PA
PT   0
There is no cash ¯ow at establishment of the position, so we do nothave any overnight cost of carry. Alternatively, we would decide not toenter the money market transaction in which case the residual r  PAPT would be carried at the overnight rate until expiry.On t1 :. Deliver r shares of A to the original lender.
. Receive r shares of A from the exchange of T.. Receive (r  PA
PT   1  rE ).. Pay borrowing fee r  bA  PA .
. Pay accumulated dividends on A to original lender:r  dA  r  1  rA   dA .. Receive accumulated dividends on T : dT  1  rT   dT .
The cash ¯ow CF1 is:CF1  r  PA
PT   1  rE 
r  bA  PA
r  dA  dT
This cash ¯ow represents in fact the P&L associated with the entirearbitrage. The original indicator r  PA PT has been modi®ed toaccount for three distinct adjustments:. The ®nancing of the pro®t until maturity
. The costs associated to enter the arbitrage by borrowing A. The
opportunity costÐor pro®tÐassociated with the dividenddifferential between A and T
Out of these adjustments, it is important to make a distinction betweenwhat is a clear loss and what is a clear pro®t. The ®nancing of r  PAPT is undeniably a pro®t if we execute the arbitrage appropriatelyÐthat is, if r  PA PT > 0. The longer the carry of the position, the betterfor us because (1  rE ) increases with time.6 In contrast, r  bA  PA is5
We implicitly assume that there is no payment ¯ow required to enter the borrowing,only the delivery of a collateral equal to the nominal of the stocks borrowed, which isthe case in practice. In other words, we get the full proceeds from the sale, and the feeis paid in full upon closing of the position.6This ®nancing term did not appear anywhere in an index arbitrage because the entirepro®t was realized on expiry, whereas here it effectively appears in treasury at theinitiation of the arbitrage.
426
COMMON ARBITRAGE SITUATIONS
undeniably a cost and is also dependent on the time remaining untilthe expiry. Finally, the dividend differential (dT r  dA ) can be positiveor negative, and its dependence with time is limited to the frequency ofdividend distributions. For example, in the United States dividends arepaid quarterly, so the differential varies only quarter by quarter.The purpose of this short discussion is to understand how theoverall pro®t is dependent on time, precisely on ``time to expiry,''which is fundamentally different from an index arbitrage situation.We will come back to this particular issue, but it is already clear thatthe timing of the convergence should be considered as a new risk, inaddition to its likelihood.As a numerical illustration of a hypothetical arbitrage, consider thefollowing set of parameters: PA  $50, PT  $98, r  2, rE  6 percent,t1 t0  6 months, bA  0:30 percent, dA  $0:75, and dT  $0.99. Thetotal pro®t is then given by:66 %P&L  CF1  2  $50 $98  1 12 6 $50 2  $0:75  $0:99  $1:42  0:30 % 12When compared to an initial nominal close to $100, the arbitrage yieldsan annual return of 2.8 percent ( $1:4=$100  12=6). If, however, theentire position had to be kept for an entire year with the same nominalpro®t at initiation, the yield would be only 1.4 percent.
EXPLICIT CONVERGENCEAs an illustration of a class of arbitrage where convergence is notcertain although it is highly likely, risk arbitrage should fall withinthe framework we introduced originally to consider arbitrage situations in general. Speci®cally, Table 9-1 shows the case of risk arbitrage,somewhere in between absolute and hypothetical. Considering that weare outside the safe harbor of an absolute convergence, we need toexamine this particular risk and the implication it has in terms ofvaluation and risk analysis. We will naturally have to consider alsoexecution, hedge, and risk of carry because these are important parameters albeit somewhat less critical than in the case of index arbitrage.Meanwhile, as we did in the previous section, let's start by a general
CHAPTER 9 RISK ARBITRAGE
427
TABLE 9-1Convergence
Absolute
Hypothetical
Risk ArbitrageBoth should beperformed.Public, but personaljudgment is key.Can be high,situation speci®c.Medium.Fixed quantity(merger ratio).Can be high (stockborrowing cost).Uncertain butestimated.Relatively short.Situation speci®c.Medium.Not really applicable.
Valuation
Theoretical
Mark to market
Convergence type
Public
Highly proprietary
Convergence risk
Low to nonexistent Critical
Execution riskHedge
CriticalFixed quantity
Risk of carry
Important
Time horizon
Known or bounded Unknown
Window of opportunity Very shortPro®tability10  1RobustnessStrongImplicationsPricing
LowFixed quantity ordeltaLow
Longer1  10WeakNone (Inef®cientmarket?)
discussion about typical opportunities and pro®tability for risk arbitrage strategies.
OPPORTUNITIES AND PROFITABILITYOpportunity
It is an understatement to say that mergers and acquisitions havebecome a major component of the modern corporate landscape. Inparticular, in telecommunications, be it Internet or entertainmentrelated, scale seems to be the credo of the day, and the amount andnumber of transactions is simply staggering. Figure 9-3, for example,shows the evolution of these two statistics over the past 30 years fortransactions executed between U.S. companies.Clearly, consolidation is happening at a faster rate today, and it isdif®cult to say exactly when and how it will stop. Furthermore, if thiseffect is clearly visible in the United States, it is more and more common on other continents like Europe or Asia. With the implementationof the single currency, Europe has ®nally progressed on its way to adeeper economic integration, even if political integration is still more autopia than a reality. Takeovers, traditionally very infrequent, have
428
COMMON ARBITRAGE SITUATIONS
Figure 9-3 Mergers and Acquisitions(Source: Mergerstat, www.mergerstat.com. Reprinted with permission. 1999 data upto October 1999.)
become relatively common, including across borders and in some caseson hostile terms. We will consider below one of these takeovers, theacquisition of CreÂdit Commercial de France (CCF) by Hong-Kong andShanghai Bank (HSBC).In Asia, industrial consolidation is also very active; however, it isnot fueled by a modernization of the environment and a strengtheningeconomic growth. Rather, the Asian crisis has led many developingcountries to ask for help from international ®nancial institutions suchas the International Monetary Fund (IMF), and the money came underconditions of more transparency and more openness to foreign capital.As a result, Korea, for example, but also Thailand, Malaysia, and to alesser extent Indonesia, have experienced a renewed interest frominternational investment bankers shopping around for valuable assetsat postcrisis prices. Although Japan does not fall under this particularcategory of developing economy, the same scenario is unfolding thereas well. The acquisition of Nissan by Renault is an example. France ifanything had always been caricatured as a fortress of unionism andadministrative inef®ciency, and the automobile industry was certainlya very strong pocket of these. The Japanese economic crisis, however,was so strong and so pervasive following the market crash at the endof the 1980s that even legendary corporations such as Nissan were
CHAPTER 9 RISK ARBITRAGE
429
forced to look for ®nancial support. Europe opened itself after decadesof painful economic evolution, whereas Asia was forced into openingup because its economic model by and large proved unsustainable overthe long run. Regardless, the market for corporate control is now moretransparent and active than ever before, and investment banks in theUnited States and elsewhere probably have a few more fat years tocome.Indeed, Figure 9-4 provides a numerical illustration of capital concentration in different markets, and the trend is unambiguous. InFrankfurt, for example, the 5 percent largest listed companiesaccounted for 10 percent more of the total listed capitalization in1998 than in 1997. Except for Nasdaq, where this particular statisticmay be explained partly by an active listing of very small companies,everywhere else the primary explanation is a concentration of assets onthe balance sheets of fewer and fewer entities.For the risk arbitrageur, this discussion has several interestingimplications. On one side, it is very clear that risk arbitrage opportunities have increased by several orders of magnitude, at least in number. Even if all transactions turn out to be unequally pro®table, at leastthere are many more to choose from. From a relatively quiet and specialized activity, risk arbitrage has risen to the status of an industrialstrategy with both more people and more capital committed.
Figure 9-4 The 5 Percent Largest Listed Companies(Source: Compiled by author from FIBV data.)
430
COMMON ARBITRAGE SITUATIONS
The second consequence is also relatively positive from an arbitrageur's perspective: The market is expanding and has become trulyglobal over the past few years. A diversi®ed risk arbitrageur shouldnow be able to consider deals in Europe and Asia in addition to theUnited States, because the ®nancial markets are probably less maturethere and consequently opportunities should be more pro®table, allelse being equal.Finally, the third consequence points toward more risk as a balanceto more opportunities. This particular evolution can be perceived in twoareas. On one hand, an accelerated increase in corporate concentrationhas to draw sooner or later the attention of regulators. Indeed, in theUnited States as well as Europe, even if bigger deals are occurring morefrequently, both the Federal Trade Commission (FTC) and the EuropeanCommissioner in charge of monitoring competition within the Unionhave voiced concern over many proposed transactions, effectively preventing some of them from proceeding because they would have toosigni®cantly affected the competitive landscape within their industry.From a pure risk perspective, regulators are one more source of uncertainty, and in fact more and more so. On the other hand, the occurrenceof more deals has changed the nature of the game because the average``quality'' of each deal has probably decreased, making it more uncertain and risky. The term acquisition strategy is, for example, often used asa viable option to ``buy growth.'' Beyond the fact that this view isdebatable, integration is a legitimate concern because it is unclear thatan acquisition can be digested soon enough and well enough to deliverits promises before the next one is consummated. Even if arbitrageursare not exposed in any way to the risk that a merger fails over the longrun, this delicate question has signi®cantly increased the risk that shareholders fail to recognize the virtues of a particular transaction pushedby their CEO. This situation is more frequent than ever, and arbitrageurs have to be careful in making their own assessment of the likelihood that the deal will proceed as planned.This last remark raises in fact an interesting ambiguity that weuncovered several times before. The expectations of an arbitrageurare related to the occurrence of a deal, regardless of whether it destroysshareholders' value or decreases social welfare by creating, for example, a de facto monopoly in a given industry. In other words, arbitrageurs do not care in any way about the industrial project, althoughthey probably have to have some sort of understanding of its underlying economics. Here their interest differs radically from that of theinvestors of each ®rm, and from that of the investing community,assuming this community is more or less pursuing higher share-
CHAPTER 9 RISK ARBITRAGE
431
holders' value. By arbitraging the merger, they provide a service andmake the market more ef®cient, even if their immediate target may bein direct con¯ict with the interests of much larger groups of investors.7
Pro®tability
Measuring pro®tability with risk arbitrage is an exercise more dif®cultthan with index arbitrage. One important difference is the risky natureof the arbitrage. If we want to talk about pro®tability, we need todiscount the results by the riskiness of each particular position, toobtain risk-adjusted returns, assuming we have all the data to makethis transformation. In addition, there are less academic studies to offera starting point for such a measurement. The world of corporate control is extremely well documented, and many researchers have tried tounderstand all the aspects of corporate events, from the original humanor economic motivations to the postintegration life of the company.Still, risk arbitrage as a systematic trading strategy seems to be lessdocumented especially when compared to the wealth of informationavailable for index arbitrage. One possible reason for this difference isthat index arbitrage acquired its notoriety essentially in the aftermathof October 1987 as a possible culprit, and again in 1989 under similarcircumstances, whereas risk arbitrage was never really under the spotlight of public scrutiny.It is also dif®cult to take the approach we have taken for indexarbitrage, which is based on empirical observations. Following oneindex and its futures is easy, but it is much more dif®cult to followhundreds or thousands of corporate transactions and extract aggregateinformation from them. Therefore, we will have to take a somewhatless direct path, and accordingly we will have a less robust estimate.
7
For example, in the takeover battle between SocieÂteÂ GeÂneÂrale (SG), Banque Nationalede Paris (BNP), and Paribas in France in 1999, risk arbitrageurs holding positions ofParibas because SG had announced its intention to buy it had later the option to tenderthese shares to BNP when BNP bid for both SG and Paribas. Although their absoluteweight was relatively low, the uncertainty as to whether they would favor one tenderto the other was considered a sizable part of the uncertainty surrounding the entirebattle.A number of recent studies show that mergers in general are less successful thanmany CEOs would like to believe. A recent study by KPMG found that more than halfdestroyed shareholders' value while another third made no discernible difference. See,for example, ``How Mergers Go Wrong,'' The Economist, July 22 2000, for an introduction to a series of six articles on the subject.
432
COMMON ARBITRAGE SITUATIONS
The idea here is to use data from hedge funds that are involved inrisk arbitrage. Performance data from hedge funds in the United Statesare relatively straightforward to obtain and provide at least a goodindication of the aggregate pro®tability of this family of funds.Naturally, many hedge funds have ¯exible charters; therefore, theymay report risk arbitrage as the primary focus and trade other strategiesepisodically. Alternatively, many funds enter risk arbitrage situationswhen they have a chance to do soÐthat is, when they hold the appropriate position after trading their ``natural'' strategy. In any case, we willconsider the data as good as they get and extract some results from them.Table 9-2 shows, for example, the yearly performance of riskarbitrage hedge funds from 1990 to 1999. For example, theannual compounded yield of the entire family of risk arbitragefunds was 8.75 percent from 1990 to 1992 or 13.23 percent overthe period 1990 to 1996. The purpose of this table is to get asense of how stable the results are depending on the period overwhich a risk arbitrage strategy is applied. When considered overa single year, the strategy generated between 5.18 and 23.48percent, exhibiting an important variability. Over a six-year period, however, it generated between 13.23 and 14.75 percent, amuch narrower interval.Therefore, it is fair to conclude that on average over a reasonableperiod of timeÐthat is, three to ®ve yearsÐthe yield of a diversi®edportfolio of risk arbitrage hedge funds would have been between 12and 15 percent. This is not, however, the expected pro®tability from atypical risk arbitrage desk because hedge funds are generally lever-
TABLE 9-2Year
1Y
2Y
3Y
4Y
5Y
6Y
1990199119921993199419951996199719981999
12.45%5.18%19.66%7.15%23.48%12.53%17.37%9.18%12.84%
8.75%12.19%13.23%15.03%17.88%14.92%13.20%10.99%
12.27%10.48%16.55%14.19%17.71%12.98%13.08%
10.97%13.60%15.53%14.98%15.52%12.94%
13.37%13.38%15.90%13.79%14.98%
13.23%14.04%14.75%13.63%
(Source: Compiled by author from HedgeFund.Net data.)
CHAPTER 9 RISK ARBITRAGE
433
aged. Suppose we invest $1 in a fund. If the fund is leveraged 10 to 1,the total nominal of the position is $10. Therefore, a return of $0.10,which would amount to 10 percent on our original investment, represents only 1 percent on the nominal of the trading position. A yield of12 to 15 percent must be divided by the leverage ratio if we want toprovide a measure of pro®tability consistent with the one we used forindex arbitrageÐthat is, a nominal return. This adjustment introducesa new dif®culty because we need to estimate the average leverage ofhedge funds dedicated to risk arbitrage, and this is a dif®cult exercise.Assuming a leverage between 2 and 3, which is probably as good asany other ®gure, the typical pro®tability of a risk arbitrage strategy canbe estimated roughly between 4 and 7 percent. This is a wider rangecompared to the results we obtained for index arbitrage, but again themethodology is such that we could not hope for much. In fact, themagnitude is really what we are looking for, and this entire discussionshows that risk arbitrage pro®tability amounts probably to less than 10percentÐthat is, signi®cantly more than index arbitrage that wouldtypically be below 1 percent.8Finally, a few words about the organization of a risk arbitrageposition. Whereas index arbitrage is usually run on a very small number of indices, a risk arbitrageur will take more positions, each beingrelatively small. The total nominal can be sizable, several hundredmillion dollars, but still below the few billion dollars that would normally be dedicated to index arbitrage. The obvious reason for such afragmented portfolio is the bene®t of diversi®cation with respect to theconvergence risk.
RISKSConvergence
Risk arbitrage is dramatically different from index arbitrage becausethe convergence at expiry is uncertain. The fact that the convergence8
These ®gures are gross returns in the sense that they are not adjusted for the level ofrisk inherent in the strategy. In reality, the decision to allocate resources to one particular type of strategy depends on the risk aversion and cost of capital of a particular®nancial institution. For example, although there are literally hundreds of hedge fundsdedicated to risk arbitrage, there are almost none dedicated to index arbitrage. Thereason is probably that risk arbitrage is more pro®table under capital constraints, evenon a risk-adjusted basis. Large diversi®ed ®nancial institutions are in general lessconstrained than other institutions in their access to capital and therefore enjoy acompetitive advantage that allows them to engage aggressively in index arbitrage.
434
COMMON ARBITRAGE SITUATIONS
fails to materialize can be explained by numerous factors. If the proposed transaction is hostile, for example, the takeover target will naturally try to escape the threat with the consequence that the outcomeremains highly uncertain for a very long time, typically until the outcome of a tender offer or a proxy ®ght is known and made public. Evenin the case of a friendly transaction, many dif®culties and/or delaysmay appear along the way. Regulators such as the Federal TradeCommission (FTC) in the United States have to give their go-ahead,which can take some time. Shareholders of one of the parties, who mayor may not be entirely satis®ed with the proposed terms, might want toforce their management team to reconsider or renegotiate the deal.Even unexpected delays in the preparatory work to get the dealdone might force some adjustments compared to the planned schedule.There are really two elements in the convergence, its occurrenceand its timing. As far as occurrence is concerned, the case of BritishTelecom (BT) and MCI Communications (MCI) provides a particularlyrich illustration of what may go wrong, and that of Staples (SPLS) andOf®ce Depot (ODP), an example of the intervention power of the FTCto block a transaction. Both will help us understand what the nature ofthe risk is and how to quantify it. With respect to timing, we will take amore formal approach and introduce the notion of theta, a parameterwe used several times before to capture a dependence on time.BT/MCIThe merger of BT and MCI will probably remain in the history of riskarbitrage as the perfect example of a supposedly great deal turnedsour. On paper the proposed transaction made perfect sense onevery dimension: The industry, telecommunications, was just ripe fora consolidation worldwide and particularly in the United States afterthe Telecommunications Act of 1996 virtually ended the monopoly ofthe Baby Bells on local services. BT was a British carrier, already holding 20 percent of MCI, which indicated that both companies hadalready had the opportunity to get acquainted with each other whiletheir merger offered new opportunities to build a cross-border giantcarrier. Finally, the terms were judged very favorable to MCI shareholders, with an offer 43 percent above the last closing price of MCIbefore the announcement. There were concerns over regulatory issuesfrom the Federal Communications Commission, but this was the ®rstdeal of this nature, and there was no real indication that the industrywas in any way too concentrated already.First words of the merger were leaked to the public on November1, 1996, before the close of the U.S. market. MCI shot up 23 percent
CHAPTER 9 RISK ARBITRAGE
435
before being suspended by the Nasdaq. This original merger wasexpected to become effective within a year but eventually never tookplace as Worldcom (WCOM) madeÐand wonÐa competing bid forMCI one year later. To set the stage and gain a more detailed understanding, Table 9-3 contains a short chronology of the facts. It is veryclear from the individual performances that the market reacts extremely quickly and sometimes with excess to all announcements regardingthe likelihood of a given transaction. However, absolute prices in asituation of risk arbitrage do not tell the entire story because what isreally important is the spread between the two stocks and its deviationfrom par.Indeed, we indicated on several occasions that the ultimate indicator of the certainty of the convergence was the marketÐin particular,the market spreadÐand this is essentially why a mark-to-marketvaluation is absolutely necessary in addition to a theoretical one,which indicates the expected pro®t if all goes well. As an illustrationof this point, consider Figure 9-5, which constitutes a visualization ofthe chain of events from November 1996 to September 1998. The chartshows the spread between MCI and its implied price in the merger,expressed in percentage terms.9 The continuous line above the x axistherefore indicates that MCI is trading at a discount compared to itsparity with BT. Similarly, the dotted line above the x axis indicates thatMCI is trading at a discount compared to its parity with WCOM.During the period from November 1, 1996, to July 11, 1997, atheoretical valuation of a risk arbitrage position between BT andMCI would have been unable to measure the market appreciation ofthe likelihood of the deal. It is apparent from the chart that the marketwas indeed more and more comfortable with the merger, and over aperiod of eight months the spread narrowed steadily, indicating favorable expectations.On July 11, suddenly MCI announced it was expecting a $800million loss in its local phone business, more than twice the amountit originally predicted. Its stock tumbled 21.1 percent following theannouncement, while BT remained relatively unchanged in comparison, losing only 6.4 percent. As a result, the spread widened from 4.9 to16.2 percent.10 In other words, MCI lost 11.3 percent (= 16.2 percent ±4.9 percent) relative to its implied price in the merger agreement. Risk9
In other words, the quantity plotted is the difference between the market price and thetheoretical price of MCI.10Note that the spread does not widen by 14.7 percent (= 21.1 percent 6.4 percent)because the ratio between BT and MCI is not 1 for 1 and incorporates a cash portion.
436
COMMON ARBITRAGE SITUATIONS
TABLE 9-3DateNov. 1, 1996
Jul. 11, 1997
Aug. 18, 1997
Aug. 20, 1997
Aug. 21, 1997
Aug. 26, 1997
Oct. 1, 1997
Event
BT
MCI
WCOM
MCI announces it has enteredmerger negotiation with BT, whichowns 20 percent of its capital. MCIstock price gains 23 percent beforebeing temporarily suspended. BTagrees to pay $6 in cash and 0.54share of its ADR for each share ofMCI.aMCI announces it could lose morethan $800 million in its localbusiness and even more in 1998because of delays in penetrating thelocal market recently deregulatedaway from the Baby Bells. MCIannounces that it has noti®ed BTthat the present outlook is worsethan expected.The Financial Times announces thatterms for the merger between BTand MCI will probably remainunchanged despite complaints fromBT shareholders.BT and MCI announce that they arehaving discussions on the prospectsof both companies. There can be noassurance as to the outcome of thediscussions, says MCI.BT announces it is revising theterms of the proposed merger,cutting the deal by 16 percent. BTwill pay $7.75 in cash and 0.375share of its ADR. In addition, MCIholders will have to wait one moreyear before getting dividends fromthe merged entity.One more MCI shareholder ®les suitagainst the merger. This occurrencefollows at least six other similaractions.WCOM unveils a $33.88 billion bidfor MCI, at $41.50 a share. WCOMagrees to pay 1.2206 share of itsstock for each share of MCI.
3.7%
20.4%
N/S
6.4%
21.1%
N/S
0.2%
3.3%
N/S
1.9%
6.0%
N/S
7.1%
16.7%
N/S
2.2%
3.5%
N/S
8.1%
20.2%
2.8%
CHAPTER 9 RISK ARBITRAGE
437
TABLE 9-3 (continued)DateOct. 3, 1997
Oct. 15, 1997Oct. 16, 1997
Nov. 10, 1997
Nov. 11, 1997
Sep. 15, 1998
a
Event
BT
WCOM ®les a suit against both BT 1.67%and MCI to remove MCI's ``poisonpill'' and to remove the $450 milliontermination fee that would bepayable to BT if MCI broke the termsof its agreement with BT.GTE offers to buy MCI for $40 a3.72%share, valuing MCI at $32.5 billion.MCI announces that MCI and BT1.5%have mutually waived a provision intheir strategic merger agreementthat would have restricteddiscussions with GTE and WCOM.WCOM announces that it has3.3%sweetened the deal for MCI to $51 ashare, or 1.2439 shares of WCOM.MCI agrees to use its poison pill to0.6%block any offer competing withWCOM, and BT also agrees to blockcompeting bids through June 30,1998, when its right to do so expires.WCOM agrees to pay BT $465million to end BT's competingpurchase agreement with MCI. MCIagrees to a $750 million breakup feeand reimbursement of $465 million ifit terminates the agreement. WCOMwill pay MCI $1.6 billion if theagreement does not get regulatoryand shareholder approvals by theend of 1998 and an additional $750million for canceling the accord.N/SMCI merges with WCOM with a ratioof 1.2439 shares of WCOM for eachshare of MCI. MCI is delisted fromNasdaq.
MCI
WCOM
1.2%
0.5%
3.6%
4.4%
1.9%
3.4%
6.4%
12.5%
2.4%
0.0%
N/S
N/S
British Telecom is listed as an American Depository Receipt (ADR) in the United States. EachADR is equivalent to 10 ordinary shares.
(Source: Compiled by author from Bloomberg and miscellaneous news sources.)
arbitrageurs were naturally exposed unfavorably to this shock, andthey lost a signi®cant amount of money on this position. It is easy toestimate what this loss must have been. Assuming an arbitrageurentered the position progressively and steadily from the mer