ger
438
COMMON ARBITRAGE SITUATIONSBT, MCI, and WCOM Market Spreads
Figure 9-5 BT/MCI(Source: Compiled by author from Bloomberg data.)
announcement onward, the average executed spread in the position isclose to the average historical spread between November 1 and July 10.This historical spread is 7.3 percent, which means that a sudden jumpto 16.2 percent will generate a loss of 8.8 percent (= 16.2 percent ± 7.3percent) on the entire position. In other words, on a position of $10million, for example, this move generated a loss of $880,000. Comparedto an expected pro®tability between 4 and 7 percent, a loss of 8.8percent represents around twice the expected pro®t.11Naturally, this loss was only a paper loss until the position wasactually unwound. In the absence of any change in the terms, arbitrageurs would have been able to make every single dollar back uponcompletion of the deal. Therefore, by widening the spread, the marketindicated very clearly that it believed the merger itself could not proceed as planned. This sentiment grew in amplitude during the following weeks as BT shareholders voiced their concerns very clearly, loud
11
Note that the loss estimate is probably conservative. In practice, many arbitrageurscould have preferred entering the arbitrage only after it had gained substance, forexample, one or two months after the announcement. In that case, the value realizedon the arbitrage would have been below 7.3 percent and the loss higher than 8.8percent.
CHAPTER 9 RISK ARBITRAGE
439
enough to prompt the two companies to enter additional negotiationsabout a possible revision of the terms.The market again gave a very clear indication about the conclusionof these negotiations. During the ®rst week of August, the spread cameback remarkably close to 0, which suggested strong expectations thatthe terms would remain unchanged. In essence, the Financial Timesonly conveyed a very pervasive judgment on August 18 when it ranan article stating exactly that. Strangely enough, however, a relativelyconservative joint announcement on August 20 drove both BT andMCI higher, tightening the spread to a negative value. This is somewhat surprising because it indicates that MCI was over its par value inthe deal, and this is unusual for such transactions. Clearly, many arbitrageurs were on the sideline at this time and refrained from entering aposition before an announcement the next day. Their absence, combined to the uncertainty about possible new terms and speculativebuying, led to this situation.The surprise came on August 21 when BT cut the deal by 16 percent for MCI. This was clearly enough to convince the market of thestrength of the deal because the spread remained very close to 0 whencorrected for the new terms until the surprise bid of WCOM onOctober 1. Meanwhile arbitrageurs were now confronted with a situation in which their initial paper loss was being converted to an actualloss. To understand why this is so, consider that we carried a positionbefore August 21 at an executed spread of 7.3 percent. In other words,we bought MCI and sold BT to lock a discount of 7.3 percent in thevalue of MCI. When MCI lost 16 percent in the new deal, we lost intotal 8.7 percent (= 16 percent - 7.3 percent). Because the new deal wasmost likely ®nal, the market adjusted the spread accordingly, and the8.7 percent lost on paper was immediately transformed into a pureloss. Arbitrageurs had to adjust the hedge ratio between BT andMCI, effectively taking their loss.The end of the story is less unusual. WCOM stepped in with a veryaggressive bid for MCI, and was joined shortly after by GTE. To secureits bid, WCOM decided to sweeten the deal by almost 20 percent, and®nally won the battle and the FCC's approval, merging with MCI onSeptember 15, 1998. Once the situation was cleared and WCOMappeared as the winner, the spread adopted a familiar shape, converging quietly and steadily toward 0.SPLS/ODPThe failed merger between Staples and Of®ce Depot is also rewardingfrom a risk management standpoint. More straightforward than BT/
440
COMMON ARBITRAGE SITUATIONS
TABLE 9-4DateSep. 4, 1996
Sep. 6, 1996Nov. 1, 1996Dec. 20, 1996
Jan. 13, 1997
Feb. 12, 1997
Feb. 13, 1997
Feb. 17, 1997
Feb. 26, 1997Feb. 28, 1997Mar. 4, 1997Mar. 6, 1997Mar. 10, 1997Mar. 12, 1997Apr. 4, 1997
Event
ODP
Staples announces it will buy rival Of®ce Depot for 28.9%$3.4 billion in stocks. Holders of Of®ce Depotshares will receive 1.14 shares of SPLS for eachof the ODP shares.Both parties agree to pay $75 million in breakup1.9%fees to the other.The FTC requests additional information in its3.2%examination of the merger.The Wall Street Journal reports that the merger1.4%could be delayed or amended because of antitrustquestions raised by the FTC.The companies announce that they have2%scheduled simultaneous shareholders' meetingson Feb. 27, 1997 to vote on the merger. The FTChas not informed the companies of any decisionregarding the merger.The FTC says it is considering a challenge to the3.1%merger unless the companies can convinceantitrust enforcers that the combination would nothurt consumers.The FTC is talking to companies to see if they are1.9%interested in buying superstores that might have tobe sold as a condition for the merger. Of®ce Max,number 3 in of®ce supplies, is seen as the mostlikely buyer.Staples and Of®ce Depot said they have agreed2.4%with the FTC to extend the antitrust review periodfrom Feb. 25 to Mar. 5.The companies announce that they postponed2%their shareholder meetings until Mar. 7.FTC review period extended from Mar. 5 to Mar.6%13.``This merger will be completed in one fashion or3.1%another,'' says Staples CEO Thomas Stemberg.The companies postpone their shareholders'1.7%meetings to Mar 14.FTC opposes merger by 4-to-1 vote.24.3%Staples reaches a tentative agreement with Of®ce 19.4%Max to sell 63 stores for about $109 million.The FTC rejects again the merger proposal,31.6%saying that the agreement with Of®ce Max doesnot resolve antitrust issues. Stemberg says it is``highly likely'' that he will ®ght the FTC's decisionin court.
SPLS3.9%
0.7%4%1.4%
3.1%
2.9%
4.7%
4.3%
4%2%4.1%0%5.4%5.4%2.9%
CHAPTER 9 RISK ARBITRAGE
441
TABLE 9-4 (continued)DateApr. 7, 1997
Apr. 9, 1997Apr. 14, 1997
Apr. 25, 1997May 27, 1997May 30, 1997Jun. 18, 1997Jun. 30, 1997
Jul. 2, 1997
Event
ODP
SPLS
Staples and Of®ce Depot announce they are goingto ``vigorously contest'' the FTC's decision in anexpedited court hearing.FTC ®les antitrust suit to block the merger.U.S. District Judge Thomas Hogan says he willstart evidentiary hearing on May 19, heararguments from lawyers on June 5, and issue aruling within two weeks.Companies postpone their shareholder meetingagain to May 28.Companies extend merger agreement until June30.Merger opposed by eight states, says antitrustof®cial in a court brief.Shareholders of both companies approve merger.Judge grants order blocking the merger until anantitrust lawsuit can be heard by an FTCadministrative law judge. Stemberg admits duringhearings that merger was motivated partly by thedesire to stop price wars and eliminatecompetition. ``Merger unlikely now,'' says Of®ceDepot CEO David Fuente.Staples and Of®ce Depot formally scrap proposedmerger. The Wall Street Journal reports estimatesof total losses to arbitrageurs around $150 million.
12.5%
3.4%
2.6%2.7%
0.6%0.9%
0.9%
0.3%
2.2%
0.6%
0%
1.8%
0.7%19.6%
1.9%4.6%
3.2%
3.7%
(Source: Compiled by author from Bloomberg and miscellaneous news sources.)
MCI, it also appeared originally as a very sensible transaction onpaper. Staples, the biggest retailer of of®ce supplies, would buy thesecond largest, Of®ce Depot. The combined entity would bene®t fromeconomies of scale, notably in procurement, inventory management,and distribution costs. As with BT/MCI, the market reacted enthusiastically to the announcement before troubles appeared. Table 9-4 is achronological presentation of the events. Even more than BT/MCI, thismerger was a bumpy ride for risk arbitrageurs. To evaluate howbumpy it is again necessary to examine the spread rather than theabsolute prices of each party. Figure 9-6 shows the deviation frompar in percentage terms for ODP.12
12
Again the convention is that if the spread is positive, ODP is trading at a discount.
442
COMMON ARBITRAGE SITUATIONSMarket Spread ODP versus SPLS
Figure 9-6 SPLS/ODP(Source: Compiled by author from Bloomberg data.)
The chart can be read very easily, and each individual event has avery distinct trace. On September 4, the announcement prompted riskarbitrageurs to aggressively enter the arbitrage. However, instead ofnarrowing progressively afterward, the spread appears to widensteadily until January 1997, re¯ecting the ongoing antitrust discussionwith the FTC.The period of March 10 through 12, 1997, is particularly interestingbecause the spread widened from 20 to 35 percent and came back to 5percent, all in a matter of days. This type of behavior is even moredramatic than what happened with BT/MCI and illustrates unambiguously an extreme case of ``convergence anxiety.'' Along the same lines,the second rejection by the FTC in April sent the spread 35 percenthigher instantly.Paradoxically, the loss associated to the failed merger is dif®cult toestimate because a risk arbitrageur had many opportunities to bene®tand many more to lose depending on the accuracy of his or her expectations. From September to December 1996, for example, the spreadwidened steadily, and nothing major happened. Day after day, arbitrageurs, and in fact the market at large, were growing more and moreskeptical about the likelihood of the merger's being completed. At thispoint it was very possible for an arbitrageur to take a position bettingon the fact that the merger would be blocked. This is in practice
CHAPTER 9 RISK ARBITRAGE
443
extremely simple to do: Instead of buying Of®ce Depot and sellingStaples, an arbitrageur would buy Staples and sell Of®ce Depot.This type of position, sometimes referred to as reverse arbitrage, haspotentially a lot of appeal because it is typically a high risk±highreward strategy. Indeed, SPLS/ODP is a brilliant illustration of thispoint. If toward the end of 1996 an arbitrageur had taken a reverseposition, he or she would have executed a spread probably between 10and 15 percent. If the merger had been approved, this is exactly whathe or she would have lost because the spread would have convergedback to zero. On the other hand a rejection is likely to widen the spreadvery suddenly and very signi®cantly, and this is exactly what happened. Playing against the merger therefore had a maximum loss of10 to 15 percent but an expected pro®t probably around twice thatamount, 25 to 35 percent.Alternatively, instead of taking a position one way or the other, anarbitrageur could have played the different waves, trying to anticipatethe most likely outcome at every juncture. This is naturally a very riskyset of bets, and in that situation, judgment, experience, and a solidunderstanding of the underlying transaction are critical.ConclusionThese two examples illustrate extremely well all the dangers associatedwith the convergence hypothesis in a risk arbitrage situation. In bothcases the spread jumped all over the place as a result of negativesurprises. With respect to our original task, which was to frame theconvergence risk and quantify it, they provide a sense of what a ``worstcase'' may look like and how we should look at it.In essence, we have now an idea of an appropriate way to performa risk analysis on a risk arbitrage position. If we de®ne S  PB r  PA ,as the mark-to-market value of the spread on a given time, the convergence risk can be expressed as:RC 
V S  
V S
This expression is a result of the standard formalism we introduced inthe chapter dedicated to risk analysis, except that it is applied to thespread and not to the prices of each stock. In addition, to be representative,  should be chosen so that the entire spread widens by at least10 percent in nominal terms.Consider as an example the case of SPLS/ODP. On October 31,1996, SPLS closed at $185/ 8 and ODP at $195/ 8. With a ratio of 1.14 SPLSfor each ODP, ODP was discounted by 7.6 percent. Its theoretical price
444
COMMON ARBITRAGE SITUATIONS
in the merger is $21.23 (= $185/ 8  1.14), and its actual price is $195/ 8. Thediscount is therefore ($21.23 $19.625)/$21.23 = 7.6 percent.On this day S was equal to $1.61 (= 1.14  $185/ 8 $195/ 8). To get arealistic evaluation of the divergence risk, we must choose  so that thespread widens, for example, from 7.6 to 17.6 percent, or more. The 10percent increase is meant to represent a fair estimation of the possibleimpact of a negative surprise. We obtain therefore a value of $3.74 (=17.6 percent  $21.23) for S + , which implies that   $2:13.To compute RC , let's assume that we hold a standard position, long1 share of ODP and short 1.14 share of SPLS. The value of this positionis V = 1  ODP 1:14  SPLS = -$1.61 = S.13 If the spread widens to$3.74, V decreases to $3.74 and we lost in total $2.13. Therefore:RC 
$3:74$1:61$2:13
1
This result comes as no surprise and con®rms what we knew beforeÐthat is, if we are long ODP, we are exposed to an increase in the spreadwith the conventions we adopted. Nevertheless, it is an importantpoint to keep in mind that every cent of variation in the spread asquoted by the market gets re¯ected entirely in the mark-to-marketP&L of the position.TimingLet's reconsider the expression of CF1 as the rigorous P&L we expectfrom a position. If we denote n the number of days to completion whenwe originally enter the arbitrage, CF1 can be written as: n n  rE  bA  PA r  dA  dTCF1  r  PA PT   1 r360360The next day, we have one day less remaining, so CF1 naturallybecomes:n 1  rEn 1 bA  PA r  dA  dTrCF1  r  PA PT   1 360360Clearly CF1 exhibits a dependence on time, precisely on the timeremaining to conversion. Consider now that on the day we take theposition, a sudden delay appears likely, such that the new number ofdays to completion is n0 > n. CF1 becomes:13
Note that this formulation of V is a simpli®cation because, in practice, we would haveto compute a rigorous stock valuation, including dividends and borrowing costs. Thisapproximation is innocuous here and allows a much simpler algebra.
CHAPTER 9 RISK ARBITRAGE
CF01  r  PA
n0  rEPT   1 360
r
n0 bA  PA360
4450
r  dA  d0T
In all likelihood CF10 6 CF1 , which means that a pro®t or a loss iscreated by the change from n to n0 . This P&L is equal to14: 0 0n nn n0Vn!n0  CF1 CF1  r  PA PT   rE r  bA  PA360360which can be written as:Vn!n0  CF01
 0n nCF1  C 360
C  r  PA
PT   rE
with:r  bA  PA
The purpose of this exercise is to realize that under most conditionsC < 0, which means that timing is also a parameter to take into consideration when evaluating a convergence risk. The term (r  PA PT ) isin general between 2 and 5 percent of r  PA as we indicated beforebecause this is the market spread, close to the overall level of pro®tability of a typical position. Therefore, the left part of C 's expression isbetween 0.12 and 0.30 percent of r  PA if we take rE  6 percent. This islower than the right term because A is a scarce resource in an arbitragesituation and borrowing it would probably cost more than 0.30 percent.Naturally in a period of high interest rates or if the spread r  PAPT is wide, C may very well turn positive because the bene®t of the®nancing on CF1 overcomes the added cost associated with carryingthe short position in A. However, if the market spread is really wide,we face again a high level of uncertainty, and the possible bene®tassociated with a change in timing is fairly insigni®cant with the consequences of a nonconvergence if we expected it. In other words,whenever C is really meaningful, chances are it is negative, and wedon't want to see any delay in the transaction. Consider, as an illustration, SPLS/ODP. In many instances, the spread was so wide that Cwould have most likely been positive, but when that happened, thetiming was clearly secondary to the antitrust issues and the possibilitythat the FTC would block the deal entirely.14
0For simpli®cation purposes we neglect the differences between d0A , dA , dT , and dT .
446
COMMON ARBITRAGE SITUATIONS
Execution
The examples of BT/MCI and SPLS/ODP were used to demonstratethe danger of nonconvergence, but they can also be illustrative ofinteresting effects in standard merger situations. In particular, a consistent observation in both cases is the fact that the spread is reallynever equal to zero and always such that the target company is pricedat a discount. This is a very frequent situation in practice, even forstraightforward mergers completed on time and without any antitrustworry. The merger of Citicorp and Travelers, for example, will con®rmthe point.A pervasive positive spread could also be the result of a distortionbecause we observe only closing prices. It would be very possible tohave a spread trading close to zero during the day and closing at avalue signi®cantly different from zero. Although there is clearly someof this effect in practice, it does not explain why the spread closessystematically positive. The only viable explanation is that the entiremarket is pricing the spread as systematically positive to account forthe noncompletion risk of the merger. Consequently, anybody is in aposition to easily execute a positive spread of a few percent at the close,and probably before as well.In that context it is fair to say that risk arbitrageurs are not underthe same pressure to execute their trades as quickly as possible. Incontrast to an index arbitrage situation in which opportunities appearand disappear within minutes, a risk arbitrage spread usually existsfor months. If a risk arbitrageur has, for example, $10 million toallocate to a particular merger, he or she has the option to tradethe spread at any time until the transaction is effective. The typicalschedule is to take a reasonable position just after the announcement,trying to bene®t from an early adjustment in the market. Afterwardthere is no need to hurry unless the risk-reward pro®le of the deal isparticularly interesting. Therefore, traders progressively build uptheir position. In a third phase, typically after shareholders or regulators have approved the merger, there is little to do at interestingprices because the risk is sharply reduced and the spread tends tonarrow or disappear.Naturally this presentation is relatively simplistic. A risk arbitrageis not a money machine in the sense that there is little or no executionskill required. A skilled trader will always make more money than apoor one. However, the nature of the competition between traders isslightly altered. In a situation of absolute convergence, the fastest electronic processing coupled to the fastest order execution system wins
CHAPTER 9 RISK ARBITRAGE
447
the game. In a situation of risk arbitrage, the smartest and most knowledgeable trader has an edge because execution, albeit important, isnevertheless secondary.
Dividends
The dividend risk embedded in a risk arbitrage is by nature differentfrom that associated with index arbitrage. In essence, in an index arbitrage situation each individual stock is diluted within the portfolio.Although there is a clear exposure on each individual component,dividends tend to increase more often than they decrease, whichgives some sense of predictability.In a situation of risk arbitrage, there are really two stocks involved,so the bene®t of diversi®cation disappears entirely. If one of the entitiesdecides for some reason to alter its dividend payment after the mergeris announced, the arbitrageur will carry an exposure to that change andmay have to take a loss. In practice, this situation is not likely tohappen because corporations tend to change their dividends only episodically and rarely in the middle of a merger. Nevertheless, the riskexists and should not be ignored. Indeed, BT/MCI offers an example ofsuch a situation. After BT revised the terms of its offer, MCI shareholders had to wait one more year before receiving a dividend from themerged company.
Short Squeezes
Much more important, in contrast, is the risk of short squeeze. Theability of an arbitrageur to build and maintain a position dependsentirely on his or her ability to ®nd and sell shares of the acquirer.For this reason in many institutions the activity of risk arbitrage isclosely related to the desk in charge of lending and borrowing stocks,and in some instances this is one single trading desk.A particularly nasty characteristic of a short squeeze is that bynature it happens at the worst moment. We developed this pointalready, but let's reconsider it for a second. If a trader carries an outright short position in a particular stock, the worst moment for him orher to buy back is when the stock has appreciated sharply.Unfortunately, that is precisely a situation in which a natural holderof the stock would want to sell and in order to do so would have torecall the shares lent out.For a risk arbitrage position, the risk is very similar. By nature, amerger has usually a very positive impact on the prices of each company. In the case of SPLS or BT, the reaction was minor, but as we will
448
COMMON ARBITRAGE SITUATIONS
see with Travelers, it can be signi®cant. Furthermore, over the course ofthe transaction the appreciation is likely to continue if the prospects ofthe companies are good. Therefore, by virtue of its impact on price, amerger already creates a natural tendency for stock lenders to considertaking their pro®t. In addition, many investors are naturally looking atthe opportunity to arbitrage the deal, which instantaneously transforms the acquirer's stock into a scarce resource, making it more dif®cult to borrow. As a result, it is certain that if shares are available in themarket, they are not cheap, and most probably the original holder willdemand the possibility to recall.15From there a short squeeze becomes a very tangible risk. Howexactly a squeeze develops is dif®cult to explain. In general, it getscreated by a punctual unbalance in the number of shares available toborrowers and grows very quickly to become a tight squeeze beforethe situation comes back to normal usually shortly after. Consider, forexample, that a strong institutional buyer tries to establish a signi®cant long position in a particular security. If this buyer is legallyallowed to lend its portfolio, and if its lending desk is even moderately active, its appearance in the market is absolutely transparent.On the other hand, consider now that this buyer is not allowed tolend these shares. This is the case of certain regulated ®nancial institutions, in the United States as well as elsewhere. The buying couldpotentially have a strong impact on the stock price, driving it sharplyhigher. At the same time all the stocks bought by this participant arevirtually withdrawn from the loan market. The combination of higherprices and lower supply of shares may create a wave of recall bylenders, which in turn would force short sellers to buy back theirpositions, driving the price even higher and magnifying the entireloop. The situation comes back to normal when short sellers haveclosed most of their positions and excess buying pressure disappears.There may naturally be other alternative scenarios. Consider, forexample, a stock for which individual investors hold massive shortpositions. This situation is not frequent but certainly not entirelyhypothetical. Individual investors are usually considered less tolerantto risk and losses; therefore, a sharp move up in the stock price couldtrigger a wave of panic buying driving the price even higher. At acertain point even professionals will get concerned and will want to15
Note that in contrast to an outright short, however, a risk arbitrage position is different because the absolute level of price is irrelevant to the arbitrageur. Even if bothstocks appreciate sharply, the position will not lose as long as the spread remainsclose to where it was when the position was initiated.
CHAPTER 9 RISK ARBITRAGE
449
cut their losses, creating the perfect environment for a squeeze todevelop.16How risk arbitrageurs react to a short squeeze is entirely dependent on the ability of their stock loan traders to ®nd and keep a reasonable number of shares through the squeeze because there is really noway to hedge this risk. In turn, this ability is highly dependent on thenetwork of relationships patiently woven between stock loan tradersand institutional lenders. Typically these lenders are institutions withlarge equity portfolios and a very low turnoverÐfor example, pensionfunds and insurance companies. Therefore, traders most likely to survive a squeeze are those already close to those institutions. In thatrespect, it is quite certain that large investment banks, notably in theUnited States, enjoy a clear advantage because of decades of relationship building in the natural conduct of their business.
ILLUSTRATIONCCI/TRV
The merger of Citicorp with Travelers in 1998 is a very straightforwardexample of a standard situation. On April 6, 1998, Travelers (TRV)announced a merger agreement with Citicorp (CCI), and the newssent the two companies' stocks sharply higher. TRV rose by 18.5 percent from $6111/ 16 to $731/ 16, and CCI rose by 26.3 percent from $1427/ 8to $1801/ 2. The economic project was to create a giant diversi®ed ®nancial institution, capable of serving the needs of corporate and individual customers covering the entire spectrum. For TRV, traditionally inthe insurance market, the merger with CCI came after the acquisition ofSalomon Brothers in mid-1997. Salomon brought a culture of proprietary trading and a wealth of expertise in understanding risk and ®nancial markets. The more traditional banking aspect was missing,however, to provide TRV with enough products to offer a one-stopsolution to its customers, and this is exactly what CCI brought to thenegotiation table.
16
Naturally the probability of a short squeeze is also highly dependent on the maturityof the market at large. In the United States and in other developed markets stockloans are common and well understood, therefore, liquidity is high and squeezesinfrequent.
450
COMMON ARBITRAGE SITUATIONS
Clearly, the market read the proposed association as extremelybene®cial, and the fact that both companies rose indicates that manyinvestors believed the combined entity had signi®cant opportunities togrow. The merger was never questioned by antitrust authorities, andthe entire transaction was wrapped up in six months, an impressiveachievement considering the size of the contenders.The deal was an exchange of 2.5 shares of TRV for each share ofCCI. Figure 9-7 presents a broad view of the spread before and after theannouncement.17 Not surprisingly, the spread remains very stable andvery low immediately after announcement, as we will see in a magni®ed view shortly. More interesting here is the shape of the chart duringthe 12 months preceding the announcement. The upward slope indicates that CCI lost around 40 percent of its value compared to TRVfrom March to December 1997, after which the relative prices of thecompanies stabilized.This particular situation offers some insight into the backstagemechanics of the merger. To TRV, probably already focused on the
Market Spread CCI versus TRV
Figure 9-7 CCI/TRV(Source: Compiled by author from Datastream data.)17
In agreement with the convention we have adopted so far, the chart plots the discount of CCI compared to its price in the offer. Therefore, the line is above the x axiswhen CCI is trading below its price in the offer.
CHAPTER 9 RISK ARBITRAGE
451
next acquisition after Salomon, the depreciation of CCI made it anincreasingly interesting target candidate because it was cheaper to®nance through a stock swap. At the end of 1997 and well into 1998,it appeared that the spread stabilized, indicating that the market didnot have any strong view any more about the prospects of TRV compared to those of CCI. The offer came only a few months after, and thisis probably not a pure coincidence. If TRV was aggressively looking toconsolidate its position in the banking industry, CCI was considerablycheaper because its own stock had appreciated tremendously. On theday of the announcement, the terms were such that TRV paid a premium close to 10 percent for CCI, as is apparent in the chart. This wasstill much cheaper than a year before, and