Limited Arbitrage in Equity Markets*MARK MITCHELL, TODD PULVINO, and ERIK STAFFORDABSTRACTWe examine 82 situations where the market value of a company is less than itssubsidiary. These situations imply arbitrage opportunities, providing an idealsetting to study the risks and market frictions that prevent arbitrageurs fromimmediately forcing prices to fundamental values. For 30 percent of the sample,the link between the parent and its subsidiary is severed before the relative valuediscrepancy is corrected. Furthermore, returns to a specialized arbitrageur wouldbe 50 percent larger if the path to convergence was smooth rather than asobserved. Uncertainty about the distribution of returns and characteristics of therisks limits arbitrage.* Mitchell and Stafford are at Harvard University, and Pulvino is at Northwestern thank Brad Cornell, Kent Daniel, Mihir Desai, Rick Green, Ravi Jagannathan, OwenLamont, André Perold, Mitch Petersen, Julio Rotemberg, Rick Ruback, Tuomo Vuolteenaho, ananonymous referee, and seminar participants at the Federal Reserve Bank of New York, HarvardBusiness School, Ohio State University, and the 2001 Spring NBER Asset Pricing ProgramMeetings for helpful comments. We also thank Asma Qureshi for research assistance,Ameritrade Holding Corporation for short-rebate data, and especially Ken French for insightfulcomments and discussions. Harvard Business School’s Division of Research provided researchsupport.
This paper examines impediments to arbitrage in equity markets using a sample of 82 situationsbetween 1985 and 2000, where the market value of a company is less than that of its ownershipstake in a publicly-traded subsidiary. These situations suggest clear arbitrage opportunities, yet,they often persist, and therefore provide an interesting setting in which to study the risks andmarket frictions that prevent arbitrageurs from quickly forcing prices to fundamental is one of the central tenets of financial economics, enforcing the law of oneprice and keeping markets efficient. In its purest form, arbitrage requires no capital and isriskfree (see Dybvig and Ross (1992)). By simultaneously selling and purchasing identicalsecurities at favorably different prices, the arbitrageur captures an immediate payoff with no up-front capital. Unfortunately, pure arbitrage exists only in perfect capital markets. In the realworld, imperfect information and market frictions make what is referred to as “arbitrage” bothcapital intensive and information and market frictions can impede arbitrage in two different , when there is uncertainty over the economic nature of an apparent mispricing and it is atleast somewhat costly to learn about it, arbitrageurs may be reluctant to incur the potentiallylarge fixed costs of entering the business of exploiting the arbitrage opportunity (Merton (1987)).Uncertainty over the distribution of arbitrage returns, especially over the mean, will deterarbitrage activity until would-be arbitrageurs learn enough about the distribution to determinethat the expected payoff is large enough to cover the fixed costs of setting up shop. Even withactive arbitrageurs, opportunities may persist while the arbitrageurs learn how to best , once the fixed costs of implementing the arbitrage strategy are borne, imperfectinformation and market frictions often encourage specialization. Specialization limits the degreeof diversification in the arbitrageur’s portfolio and causes him to bear idiosyncratic risks forwhich he must be rewarded. For example, if there is a purely random chance that prices will notconverge to fundamental value, a highly specialized arbitrageur who cannot diversify away thisrisk will invest less than one who can. Furthermore, even if prices eventually converge to1
fundamental values, the path of convergence may be long and bumpy. While waiting for theprices of the mispriced securities to converge, they may temporarily diverge. If the arbitrageurdoes not have access to additional capital when the security prices diverge, he may be forced toprematurely unwind the position and incur a loss (DeLong, et al. (1990), Shleifer and Summers(1990), and Shleifer and Vishny (1997)). The prospect of incurring this loss will further limit theamount that a specialized arbitrageur is willing to empirically address the limits of arbitrage in equity markets, we construct a sample ofsituations where a firm’s market value is less than the value of its ownership stake in a publicly-1traded subsidiary. These situations are commonly referred to as “negative-stub-values” and canarise following equity carve outs of subsidiaries or from the partial acquisition of a publicly-traded firm. We track each parent/subsidiary pair until an event occurs that eliminates the linkbetween the two entities or until the mispricing disappears. Favorable outcomes include pricesadjusting to eliminate the relative value discrepancy and distributions of the subsidiary shares tothe parent firm’s shareholders, while unfavorable terminations tend to be associated withacquisitions of the subsidiary and performance-related delistings of the parent. We attempt tocontrol for the role that market frictions play in explaining the persistence of negative-stub-values by incorporating estimates of market frictions such as brokerage commissions, short-rebates, and capital requirements into the analysis. The empirical results provide considerable2support for the argument that there are costs that limit arbitrage in equity show that negative-stub-values are not riskfree arbitrage opportunities. The linkbetween parent and subsidiary firms disappears without convergence of the arbitrage spread 30percent of the time. This happens when there is a corporate event that permanently alters therelative mispricing in a manner that is detrimental to the arbitrageur’s profits. For example, insome negative-stub-value situations in our sample, the parent firm goes bankrupt after using itssubsidiary stake as collateral to issue debt. As a result, the link between the parent andsubsidiary firms’ market values is permanently severed without convergence of the
We also find that there is substantial variability in the time to termination, even fornegative-stub-value investments that eventually converge. The average time between the initialmispricing and a terminating event is 236 days, the median is 92 days, the minimum is one day,and the maximum is 2,796 days. As a result of this uncertainty, even if convergence iseventually achieved, the negative-stub-value investment often underperforms the riskfree rate,thereby discouraging investments by arbitrageurs who are uncertain of the time to convergenceand unable to close the arbitrage spread on their analysis indicates that annual returns to a specialized arbitrageur would be roughly50 percent higher if the path to termination was smooth rather than the observed bumpy estimate that when an investor posts sufficient collateral to insure against the bumpiness ofthe path to termination, returns are just barely larger than the riskfree rate. However, the effectof the volatile path can be substantially mitigated by combining negative-stub-value investmentswith the market portfolio or with other “special situations” such as merger arbitrage. Thisbenefit of diversification, combined with the infrequent occurrence of negative-stub-valuesituations, suggests that it is unlikely that an arbitrageur would focus solely on , we document that the general uncertainty over the distribution of returns is asignificant contributor to the persistence of negative-stub-values. We find (1) that statisticalreliability of abnormal returns is fairly low at the end of our 16-year sample period, and thereforeunreliable near the beginning of the sample, (2) very unusual events cause extreme adversevaluation changes 13 years into the sample time series, such that even a seasoned arbitrageurwould likely be caught off guard, and (3) statistically and economically large price movementsoccur on the day that uncertainty over the outcome is resolved. For example, when parentcompanies announce their intentions to distribute the subsidiaries’ shares to parent companyshareholders, or when they announce receipt of favorable IRS tax rulings regarding thedistribution of shares, the value of the arbitrageur’s position increases substantially over the threedays surrounding the announcement. Even in the lowest risk cases, where the parent has3
previously announced its intention to distribute subsidiary shares, the value of the arbitrageposition increases percent when the parent announces receipt of a favorable IRS ruling orspecifies a date for the distribution. Moreover, with no change in the availability of shares forshorting, prices quickly adjust such that estimated stub-values are no longer negative once thisuncertainty is paper is organized as follows. Section I describes the data, Section II discusses themeasurement of investment returns and performance, Section III reports results relating to thefundamental risk of negative-stub-value investments, Section IV reports results relating to thefinancing risk of negative-stub-value investments, Section V interprets the results and discussesarbitrage in imperfect capital markets, and Section VI . Data DescriptionA. Sample Selection CriteriaTo be included in the sample, the parent’s stub assets must, at some time, have an impliedmarket value less than zero. Stub assets are defined as the market value of the parent’s equityless any measurable net assetsnet of the parent’s unconsolidated liabilities.(1)V=MV−MV−[MV−MV].StubEquityStakeOther AssetsLiabilitiesWe use two different methods to determine whether the stub assets have a negative value. Thefirst method, which we refer to as Rule 1, assumes that the market value of the parent’s non-subsidiary assets is equal to the market value of its liabilities. Therefore, the stub-value isnegative whenever the market value of the parent’s equity stake in the subsidiary exceeds theparent’s total market equity value:MV(2)StakeRule #1:V<0 if> EquityOur second approach to identifying negative-stub-values is to assume that the differencebetween the market value of the parent’s non-subsidiary assets (other assets) and the market4
value of the parent’s unconsolidated liabilities equals the parent’s unconsolidated book gives us Rule 2:(3)MV+BVStakeParent EquityRule#2:V<0 if> EquityNeither Rule 1 nor Rule 2 is problem-free. First, the ratios may not account for off-balance sheet liabilities, which could be substantial. For example, potential tobacco liabilitiesare not reported on Nabisco Brands’ (sample firm) balance sheet, yet they might explain asignificant portion of Nabisco Brand’s negative-stub-value. As a practical matter, obtainingestimates of the market values of off-balance sheet liabilities is difficult, and we do not attempt3to measure them in this paper. Second, the book value of the non-subsidiary assets may notaccurately portray the market value of those assets. Nonetheless, the empirical results are robustto the choice of the rule used to identify . Sample ConstructionWe construct the sample of negative-stub-value stocks using a two-step process. First,we search the Securities Data Corporation (SDC) database from 1985 through 2000 for all initialpublic offerings (IPO) where another publicly-traded firm owned the IPO shares prior to theoffering. For each of these parent-IPO pairs, we use stock price data from CRSP (pre-2000) andDatastream (during 2000) to calculate the ratios specified by Rule 1 and Rule 2 from the time ofthe IPO through December 2000. If, at any time, the estimate of the stub-value using either Rule1 or Rule 2 is negative, we include the parent-IPO pair in the , we search the financial press and trade publications for extreme relative valuesituations during the 1985 to 2000 period. As in the first step, we use CRSP and Datastreamstock price data to ensure that the inclusion criteria are resulting sample, covering the period from 1985 through December 2000, contains70 parent/subsidiary pairs that satisfy the criterion specified by Rule 1 and 82 parent/subsidiary5
pairs that satisfy the criterion specified by Rule 2. Table I provides an annual summary of thenegative-stub-value situations included in our sample by industry sector identified using Rule A shows that the sample covers a range of sectors, with a relatively high concentration inthe technology sector during the latter part of the sample period. Panel B reports that many ofthe subsidiaries in the latter part of the sample period are firms with an “Internet” focus.[Insert Table I around here]C. Shares Outstanding, Returns, and Short-RebatesIn order to estimate the stub-value in cross-holding situations, the number of parentshares outstanding and the number of subsidiary shares held by the parent are needed. We4collect data on shares outstanding from quarterly company filings of financial reports. Becauseestimates of arbitrage profits depend crucially on the numbers of shares outstanding at each pointin time, we identify exact dates at which shares outstanding change whenever the number ofshares indicated in quarterly reports change by at least 10 percent. Exact dates are determined bysearching the financial press for relevant addition to share price and share ownership data, accurately assessing the risks andmarket frictions associated with negative-stub-value trades requires estimates of “short-rebates.”Short-rebate refers to the rate paid to investors on the proceeds obtained from short selling astock. We obtained short-rebate data from Ameritrade Holding Corporation, a large online retailbroker. This short-rebate data covers the December 1998 through October 2000 time data represent the interest rates that other institutions (typically large Wall Street investmentbanks) received from Ameritrade on the cash collateral that they posted to borrow Ameritrade’sshares. Generally, the short-rebate is 25 to 50 basis points less than the federal funds , the short-rebate is occasionally lower and can even be negative. Because we observeshort-rebates only for securities borrowed from Ameritrade, it is likely that our short-rebatesample is biased toward stocks that are in high demand for shorting. Otherwise, the borrowinginstitutions would take them directly from their own inventory and would not need to borrowthem from
II. Measuring Investment ReturnsIn order to calculate returns and characterize risks associated with negative-stub-valueinvestments, we begin by specifying an investment strategy. Implementing this strategy requiresthat the investor define the following four items: (1) the criterion by which the stub is judged tobe mispriced, (2) the buy threshold, (3) the sell threshold, and (4) the amount of financialleverage used (the short position in the subsidiary’s shares makes it impossible to invest in anegative-stub-value situation on an unlevered basis).A. Investment Criteria and ThresholdsWe consider two criteria by which to judge the mispricing of the stub assets. These twocriteria mirror the selection criteria used to build the sample, as described in Section I. The firstcriterion, Rule 1 compares the market value of the stake of the subsidiary’s equity held by theparent to the market value of the parent’s equity:MV(4)StakeRule#1:Placetradeif>BuyThresholdMVParent EquityMVStakeTerminatetradeif < EquityFor example, a buy threshold of would imply that a trade is placed when the value of theparent’s stake in the subsidiary is worth more than the entire equity value of the parent. Todetermine the sensitivity of our return calculations to the thresholds chosen, we present returnsfor buy/sell thresholds of and Emphasis is on buy thresholds of andlarger because investors are likely to require some cushion over their estimates of mispricing. Todetermine robustness we also consider a strategy specified by Rule 2:(5)MV+BVStakeParent EquityRule#2:Placetradeif>BuyThresholdMVParent EquityMV+BVStakeParent EquityTerminatetradeif < Equity7
B. Investment Capital and Financial LeverageA final parameter that must be specified before returns can be calculated is the initialinvestment capital. Although straightforward for portfolios that contain only long positions, theappropriate denominator for calculating returns for a portfolio with both long and short positionsis less obvious. In a frictionless capital market, the object of interest would simply be a shortposition in the subsidiary and a long position in the parent, which holds shares in the long position would be fully financed by the proceeds from the short position. This does notwork in real markets because the investor must post collateral for both long and short , the investor does not receive full use of the proceeds from a short , we calculate the return on the capital that is required to undertake the arbitrage example, an investor wishing to buy one share of a parent stock trading at $ and sellshort shares of a subsidiary stock with a price of $ is required to contribute capitalof at least $ (50 percent of both long and short position) to satisfy minimum initial capitalrequirements imposed by the Federal Reserve Board. To calculate returns, the total payoff fromthe long- and short-stock positions, as well as the net interest payments from any excess cashminus margin borrowing is divided by the $ equity capital base. In addition to posting therequired capital, investors may choose to allocate additional precautionary capital to lower theleverage of the position. Because choosing the denominator in the return calculation requiresone to specify financial leverage, and since financial leverage has a direct effect on both thereturn and the risk, we present results using three leverage refer to the first leverage level as “textbook” leverage. Results calculated usingtextbook leverage are based on two assumptions. The first assumption is based on Regulation Tinitial margin requirements and assumes that the initial invested capital is equal to 50 percent of5the long market value and 50 percent of the short market value. The second assumption is thatthere are no maintenance margin requirements so that arbitrageurs never face margin
The second leverage level we refer to as “Regulation T” leverage. As described above,Regulation T sets boundaries for the initial maximum amount of leverage that investors, bothindividual and institutional, can employ. In addition to Regulation T of the Federal ReserveBoard, stock exchanges (., NYSE) and self-regulatory organizations (., NASD) haveestablished maintenance margin rules to be followed after the initial transaction. For example,the NYSE and NASD require that investors maintain a minimum margin of 25 percent for long6positions and 30 percent for short positions. If security prices move such that the investor’sposition has less than the required maintenance margin, he will receive a margin call and will berequired to, at a minimum, post additional collateral or reduce his position so as to satisfy the7maintenance margin requirements. To avoid biasing returns upward by allowing arbitrageurs topost additional collateral when a margin call is received, yet avoid counting the additionalcollateral in the initial investment if a margin call is not received, we assume that the arbitrageurresponds to margin calls by partially liquidating his refer to the third leverage level as “conservative” leverage. Conservative leverage isdefined to preclude all margin calls ex-post, and therefore could not be determined by an investorex-ante. Nonetheless, this gives some insight into the effect on returns from setting asideadditional capital to avoid forced liquidations. Specifically, for each investment strategy, weiterate over various initial leverage ratios to find the highest leverage ratio that can be usedwithout triggering a margin call in any of the individual investments in our . Assessing Investment PerformanceWe summarize the performance of negative-stub-value investments assuming that theseinvestments are held individually as well as in a portfolio. Investment performance measures fornegative-stub-values held in isolation include the mean annualized return in excess of theriskfree rate, the frequency of negative returns, and the frequency of margin calls. In calculatingthese returns, we assume that the investment horizon is one year. For investments that terminateless than one year from the initial investment date, we assume that the investment proceeds are9
invested in the riskfree security for the remainder of the one-year holding period. The reason forcalculating returns in this way is that investments with modest daily returns, but very shortdurations, can have extremely high annualized returns, even though the returns are not obtainablefor more than a few days. Including extreme annualized returns in a small sample skews thedistribution dramatically, making it difficult to interpret the mean return as a measure principle, analyzing negative-stub-value investments from the perspective of someonewho holds them in isolation is reasonable if the investments are truly arbitrage , there are many reasons to believe that few arbitrageurs would employ such a , the negative-stub-value investments are not likely to be true riskfree arbitrageopportunities. Second, even if they are certain to converge, the path to convergence forindividual investments may not be smooth. Diversification will have a potentially importanteffect on smoothing the arbitrageur’s returns. Therefore, we also summarize the returns from acalendar-time portfolio investment strategy relative to the expected returns from the Fama andFrench (1993) three-factor portfolio analysis is based on monthly investment returns that satisfy Regulation Tinitial margin requirements and NYSE/NASD rules governing maintenance margin -stub-values are included in the portfolio from the close of market on the day that thebuy threshold is reached until the close of market on the “resolution” day. The resolution day isthe close of market on the day that either the sell threshold is reached or the negative-stub-valueis terminated by some other returns are obtained by compounding daily portfolio returns, which requirescalculation of daily equity values for a portfolio of negative-stub-value investments. Equity isdefined as the difference between assets and liabilities. Assets are the sum of the market valuesof long positions in the parent firms, cash proceeds from short sales of the subsidiaries, and are the sum of the market value of short positions and margin loans. Each day, theseaccounts are marked-to-market and net interest is paid. Cash balances receive the riskfree rate,10
margin loans pay 50 basis points more than the riskfree rate, and proceeds from short sales8receive three percent per ensure that the portfolio is at least partially diversified, we impose a “diversificationconstraint,” which allows no more than 20 percent of the portfolio’s equity to be initiallyinvested in any one negative-stub-value transaction. As a result, the portfolio is not always fullyinvested in negative-stub-values, but sometimes includes a large fraction of cash, which earns theriskfree rate. The portfolio is rebalanced only to (1) add and remove negative-stub-values thathave crossed the buy or sell threshold, (2) close positions that have been terminated by an event,or (3) satisfy a maintenance margin call. Portfolio returns are calculated assuming directtransaction costs of $ per share in the 1980s and $ per share . Fundamental RiskIn this paper, fundamental risk refers to the possibility that the negative-stub-value tradeis terminated before prices converge to fundamental values (see DeLong et al. (1990) andShleifer and Summers (1990)). The arbitrage trade involves holding a long position in the parentfirm and a short position in the subsidiary firm. The long position in the parent firm gives thearbitrageur an indirect holding of the subsidiary firm, which can be shorted out, leaving a netposition in only the stub assets. The key to the trade is the link between the parent and thesubsidiary firm created by the parent’s substantial ownership of the subsidiary. In our sample,fundamental risk relates to the unexpected severing of this link before the mispricing risk of a terminating event before prices converge is substantial. Panel A of Table IIsummarizes the frequency of convergence for negative-stub-value investments at the time of dealtermination. The time of deal termination is determined either by the occurrence of an event thatbreaks the link between the parent’s and subsidiary’s stock prices or by the disappearance of therelative mispricing. Results are presented for samples defined by both Rule 1 and Rule 2,assuming a buy threshold of . For example, of the 70 negative-stub-value situations identified11
using Rule 1 and a buy threshold of , 66 had terminated and four still existed as of December31, 2000. Of the 66 deals that terminated, the mispricing was not eliminated for 18 () of the deals. With respect to the 82 negative-stub-value deals identified using Rule 2,77 have terminated as of December 31, 2000. Of the 77 terminated deals, the mispricing was noteliminated for 27 ( percent) of the deals. Changing the threshold ratio from to andto for both Rules 1 and 2 does not substantially alter the frequency of deals that closedwith/without elimination of mispricing.[Insert Table II around here]Panel B of Table II describes the causes of negative-stub-value termination eventsassociated with Rule 1. Fifteen of the 48 successful terminations were caused by favorablechanges in the parent’s and subsidiary’s stock prices in the absence of an event. Twelve of the48 successful terminations were caused by the distribution of the subsidiary’s stock to theparent’s shareholders. In all cases where there is a successful distribution, the parent andsubsidiary stock prices converge and the negative-stub-value investment yields a positive , it is important to note that even though, ex-post, distributions are associated withpositive returns, there is no guarantee, ex-ante, that the distribution will occur. The followingtext published in PFSWeb’s IPO prospectus suggests that even with planned distributions, thereis a chance that the distribution will be delayed or canceled:“Daisytek [the parent of PFSWeb] recently announced that it had received anunsolicited offer to acquire all of Daisytek's outstanding shares. After consideringa variety of factors, Daisytek's board determined that the offer was inadequate andinconsistent with Daisytek's previously disclosed plans to complete the , however, the bidder decides to begin a tender offer for the outstanding sharesof Daisytek without the approval of Daisytek's board, such an offer, orstockholder litigation in connection with such an offer, could significantly divertour attention away from our operations and disrupt or delay our proposed spin-offfrom Daisytek. In addition, if the bidder is successful in acquiring control ofDaisytek prior to the proposed spin-off, it would control a majority of our shares9and the spin-off would likely not occur.”12
The remaining causes of successful termination (21 of the 48) include acquisitions and delistingof the parent’s and/or the subsidiary’s previously mentioned, the mispricing was not eliminated in 18 of the 66 () negative-stub-value situations that were terminated prior to December 31, 2000. Anacquisition of the parent and/or subsidiary is the single most common reason for adversetermination. Acquisitions account for 14 of the 18 adverse deal terminations. The negative-stub-value trade associated with Howmet International (the subsidiary) and Cordant Technologies (theparent) provides an example of the adverse effect that an acquisition can have on a negative-stub-value investment. On November 11, 1999, Cordant owned million shares of a price of $ per share, Cordant’s investment was worth $ billion. At the same time,Cordant’s million shares outstanding were trading at $, implying a marketcapitalization of $ billion. An arbitrageur that had previously placed a stub-value trade wouldhave shorted ( = / ) Howmet shares for every one share that Cordant November 12, 1999, Cordant announced an offer to buy Howmet's publicly-tradedshares for $17 per share. Howmet's shares closed that day at $, up $. Cordant's sharesincreased slightly, up $. As a result of Cordant's bid to acquire Howmet's publicly-traded10shares, the arbitrageur experienced a -25 percent one-day return. Since Cordant’s acquisition11of Howmet terminates the arbitrage opportunity, the arbitrageur would realize a remaining four adverse terminations documented in Panel B of Table II are causedby delisting of the parent company’s stock. For example, some of the parent firms significantlyincreased their debt obligations by pledging subsidiary shares as collateral. When the underlyingbusinesses failed to generate sufficient cash flows to service the debt repayments, the debt holderlaid claim to the collateralized asset, thereby terminating the arbitrage opportunity to thedetriment of the percent (Rule 1) and percent (Rule 2) of the stub-value investmentsterminating before the mispricing is eliminated, it is clear that fundamental risk exists and thatthese investments are far from riskfree arbitrage opportunities. Investments that are known to13
converge have shorter time horizons, larger mean returns, and far fewer negative returns than thefull sample of negative-stub-values. Section IV reports that the median investment horizon fordeals that eventually converge is roughly 75 percent as long as that for the full sample. Dealsthat are known to converge have mean annualized returns in excess of the riskfree rate that areroughly 50 percent to 100 percent larger than the returns for the full . Financing RiskA significant risk faced by an arbitrageur attempting to profit from negative-stub-valuesis that the path to convergence can be long and bumpy. Shleifer and Vishny (1997) argue thatarbitrageurs must deal with the possibility of interim liquidations even in the case whenconvergence is certain. In addition, the length of the interval over which convergence will occuris unknown. Increasing the length of the path reduces the arbitrageur’s return, a risk we refer toas “horizon risk.”Increasing the volatility of the path increases the likelihood that the arbitrageur will beforced to terminate the negative-stub-value trade prematurely. There are two possible causes offorced liquidation related to the volatility of the path. First, if the arbitrageur faces a margin call,he will be forced to post additional collateral or partially liquidate. We refer to this risk as“margin risk.” The second cause of forced liquidation stems from the fact that negative-stub-value trades require the arbitrageur to short the subsidiary’s stock. If the arbitrageur is unable tomaintain his short position, he will be forced to terminate the trade. We refer to the risk offorced termination because of an inability to maintain the short position as “buy-in risk.” In this12section, we describe the magnitudes of horizon risk and margin risk. The discussion of buy-inrisk is postponed until Section . Horizon RiskTable III presents the distribution of the number of days between the initial investment ina negative-stub-value trade and the termination date. Unlike previous tables where the unit of14
observation is a negative-stub-value situation, the unit of observation in Table III is aninvestment. Fluctuations in stub-values can cause the buy and sell thresholds to be crossednumerous times resulting in multiple investments per parent/subsidiary pair. Distributionsshown in Table III are presented for investment criteria specified by both Rule 1 and Rule 2. Forexample, using Rule 1 combined with a buy threshold of and a sell threshold of , theminimum number of days invested is one, the maximum is 2,796, and the median is the buy threshold, the sell threshold, or the investment criterion has a relatively smalleffect on the distribution of the length of the arbitrage trade. However, in all cases, the varianceof the number of days until deal termination is large. To get an idea of the effect of this variationon returns, consider an investment that is expected to generate a percent return over themedian of 92 trading days. This investment would generate an annualized return of 47 decrease in the number of days until termination from the median to the 25 percentile wouldincrease the annualized return to 238 percent. Similarly, an increase in the number of days untilthtermination from the median to the 75 percentile would decrease the annualized return to 14percent.[Insert Table III around here]Uncertainty over the time until convergence is large and has a significant effect onreturns. Using Rule 1 to identify mispricings, the arbitrageur would have been better offinvesting in riskfree securities rather than in the arbitrage trade in roughly 10 percent of thesituations that eventually converge in our sample, and in nearly 25 percent of the situations usingRule . Margin . Creative Computers/Ubid ExampleTo describe margin risk in negative-stub-value investments, we consider the example of13Creative Computers (parent) and Ubid (subsidiary). On December 4, 1998 Creative Computerscarved out 20 percent of its online auction subsidiary Ubid in an IPO. At the time of the IPO,15
Creative Computers also announced its intention to distribute, after a minimum of six months,the remaining shares of Ubid that it owned in a tax-free spin-off to Creative Computers’shareholders. At the end of the first day of trading, Ubid’s total equity value was $439 implied value of Creative Computers’ 80 percent Ubid stake was greater than CreativeComputers’ total market value by approximately $80 million, far in excess of the approximately$3 million of debt on Creative Computer’s balance sheet. Because it is common for the typicalIPO to be unavailable for shorting for a few days following the IPO, we assume that thearbitrageur’s initial trade was placed on December 9, 1998, four days after the IPO. At the closeof trading on December 9, 1998, the value of the stub assets had increased to negative $28million. An arbitrageur attempting to profit by buying Creative Computers’ negative $28 millionstub assets would have shorted shares of Ubid for every share of Creative Computerspurchased. In six months, if the remaining Ubid shares were distributed to Creative Computers’shareholders, the value of the stub assets would turn positive. Assuming that the arbitrageurused Regulation T leverage, the anticipated return from his investment would be approximately1445 percent at the end of six 1 shows the paths of stock prices for both Creative Computers and Ubid. ByDecember 18, 1998, the discrepancy between Creative Computers and Ubid stock prices hadincreased substantially—the value of the stub assets had decreased from negative $28 million tonegative $94 million. Using margin maintenance requirements specified by NYSE and NASD,the arbitrageur would have faced a margin call and would have been forced to partially liquidate15his position to satisfy maintenance margin requirements. The arbitrageur would have lost 26percent in seven trading days.[Insert Figure 1 around here]On December 21, 1998, the value of Creative Computers’ stub assets decreased tonegative $254 million. For a second trading day in a row, the arbitrageur would have faced amargin call and been forced to reduce his position even further, incurring an additional one-dayloss of 84 percent. Bad luck continued when, on the following trading day, the value of Creative16
Computers’ stub assets fell to negative $505 million causing a one-day loss of 91 percent. OnDecember 23, 1998, the value of Creative Computers’ stub assets reached its minimum level ofnegative $766 million. The arbitrageur received his fourth and final margin call and anadditional one-day loss of 63 1 shows that after December 23, 1998, the prices of Ubid and Creative Computersconverged. As promised by Creative Computers’ management, the remaining Ubid shares weredistributed to Creative Computers’ shareholders six months later. The portion of thearbitrageur’s capital that was not liquidated returned 150 percent between the peak mispricing onDecember 23, 1998 and the spinoff on June 7, 1999. However, because the arbitrageur lost mostof his capital prior to December 23, 1999, his overall return from the Creative Computers/Ubidinvestment was negative 99 percent. In order to avoid the costly margin calls, the arbitrageurwould have had to post $ of excess cash for every one dollar of long position. Doing sowould have generated a return of percent between December 9, 1998, and June 7, 1999. Thisis significantly lower than the percent that the arbitrageur could have obtained with thesame initial investment had he not been required to liquidate to meet margin . Full Sample Results for Individual InvestmentsThe Creative Computers/Ubid example suggests that ignoring margin requirementsresults in overestimation of returns from negative-stub-value investments. To determine whetherthis is generally the case, we estimate returns for each of the negative-stub-value investments inour sample using the three leverage levels previously described—textbook leverage (RegulationT initial margin imposed, no maintenance requirements imposed), Regulation T leverage (bothinitial and maintenance margin requirements imposed), and conservative leverage (maximumasset/equity ratio for which no margin calls are received). Returns are estimated usinginvestment strategies defined by Rule 1 using buy/sell thresholds of
Table IV presents annualized returns in excess of the riskfree rate obtained by followingthe investment strategy specified by Rule 1. Panel A presents results for buy/sell thresholds When all deals are included in the sample, the mean return obtained using textbookleverage is percent whereas the mean return using Regulation T leverage is difference between these two returns is a result of the maintenance margin rules imposed byNYSE and NASD, suggesting that the effect of margin calls described by the CreativeComputers/Ubid example is present in many of the individual investments. Of the 110investments included in Panel A, percent receive margin calls when maintenance marginrequirements are imposed. Interestingly, margin calls are not always detrimental to thearbitrageur’s profits. In cases where the arbitrage spread widens after a margin call is received,the margin call forces the arbitrageur to liquidate his position and saves him from further is this effect that causes the minimum return to occasionally be lower for textbook leveragethan for the usually more stringent Regulation T leverage.[Insert Table IV around here]One way of preventing margin calls is to initially post additional collateral. Returns forconservative leverage in Table IV are obtained by choosing the assets/equity ratio that precludesa margin call across all deals in the sample for a given investment strategy. Insuring against amargin call has the benefit of reducing downside risk—the percentage of investments losingmoney relative to the riskfree investment is only percent using conservative leveragecompared to percent using Regulation T leverage. However, the cost of insuring againstmargin calls for an individual investment is high. After insuring against margin calls by postingadditional capital, the mean annualized excess return drops to addition to returns for the full sample, Table IV also presents returns after restrictingthe sample to those negative-stub-value situations that eventually converged. Even with thesedeals, where fundamental risk is ex-post known not to have had a detrimental effect, returns arestill frequently negative. Moreover, the difference between mean returns when maintenancemargin requirements are satisfied and when they are avoided remains substantial for this sub-18
sample. In other words, the bumpiness of the path to convergence is costly to the suggests that both horizon risk and margin risk are important for individual investmentseven when fundamental risk is B and C of Table IV present results for different buy/sell thresholds, again usingRule 1 as the investment strategy. Results are similar to those presented in Panel A indicatingthat results are not strongly dependent on the levels of the thresholds. Overall, the resultsindicate that while annual excess returns from negative-stub-value investments are positive on16average, they are not . Portfolio ResultsTable V displays calendar-time portfolio regression results for the negative-stub-valueinvestments over the period January 1985 through December 2000. The portfolio returns arecalculated as described earlier, satisfying Regulation T initial margin requirements as well asNYSE/NASD maintenance margin rules. In addition, we impose a diversification constraint that17limits the initial investment in any one deal to 20 percent of total equity. Portfolio returns arecalculated assuming short-rebates of three percent per year and direct transaction costs of $ share in the 1980s and $ per share thereafter.[Insert Table V around here]The investment strategy that uses Rule 1 to identify mispricing and a buy/sell threshold produces the largest and only statistically significant average abnormal returns: per month, or percent per year ( percent x 12 months), with a t-statistic . The estimated coefficient on the market excess return is slightly negative ( with at-statistic of ) and the coefficients are close to zero for the SMB and HML risk other investment strategies produce similar overall results, although the monthlyabnormal return estimates are not statistically reliable or as economically large, ranging percent to percent for the other Rule 1 strategies (t-statistics of and ,19
respectively), and from percent to percent for the Rule 2 strategies (t-statistics and , respectively).Figure 2 shows that margin risk cannot be completely diversified away by holding aportfolio of negative-stub-values, as the effects of the Creative Computers/Ubid investment showup clearly in December 1998. At this time, the equity value drops below the maintenance margin18requirement, and some of the portfolio holdings must be liquidated. Nonetheless, an investorin a portfolio of negative-stub-values is considerably less sensitive to margin risk than oneholding them individually. For example, when the Creative Computers/Ubid arbitrage spreadwidens in December 1998, an investor holding the portfolio of negative-stub-values receives onemaintenance margin call, while the investor holding just Creative Computers/Ubid receives fourmargin calls.[Insert Figure 2 around here]Another way to see that the bumpiness of the path is costly to a specialized arbitrageurholding a portfolio of negative-stub-value investments is to completely relax the maintenancemargin requirements, going so far as to allow equity values to go negative without requiringliquidation. As with the individual investments, returns are considerably larger whenmaintenance margin requirements are not enforced. The ending equity value climbs to $ margin requirements versus $ with maintenance margin requirements. Again, we seethat margin risk will at least partially deter a specialized . Specialization of the ArbitrageurThe calendar-time portfolio results are descriptive of the risks and returns that a highlyspecialized arbitrageur would face. By investing in just a few negative-stub-values at each pointin time, and often holding sizeable cash balances, the arbitrageur is effectively able to diversifyaway fundamental risk, but still bears sizeable financial risk. The returns to such a strategy seemeconomically large, but for the most part, statistically
There are few, if any arbitrage funds that exclusively engage in such an investmentstrategy. On the other hand, there are many arbitrage funds that engage in “special situationsarbitrage,” which includes negative-stub-value investments. Although these funds oftenspecialize in one specific type of arbitrage trade, such as merger arbitrage, they only do so ifthere are sufficiently many transactions. This suggests that the specialized arbitrageur describedso far is a bit of a straw more realistic assessment of the risks faced by the likely investor can be obtained bycombining negative-stub-value returns with those from complimentary strategies. Table VIreports annual returns to our negative-stub-value investor following the investment strategydefined by Rule 1 and buy/sell thresholds as well as for the market portfolio, a mergerarbitrage index portfolio, and two hybrid funds, which combine the negative-stub-value19investments with either the market or the merger arbitrage index. The portfolio of negative-stub-value investments has the largest mean return of any of the portfolios over the sampleperiod, but also the largest standard deviation, over 60 percent larger than that for the value-weight market.[Insert Table VI around here]Returns from the negative-stub-value portfolio are negatively correlated with the market,such that a combination of the negative-stub-value portfolio with the market will achievediversification. The maximum in-sample Sharpe ratio of is reached with 36 percentinvested in the negative-stub-value portfolio and 64 percent in the market. This “fund-of-funds”approach actually understates the benefits of combining these investment strategies because thecapital invested in the market cannot be used as collateral to offset the financial risk faced by theportfolio of negative-stub-values. In other words, the path would have been much smoother sothat there would have been fewer forced liquidations to satisfy margin calls. A similar analysiswas performed using combinations of the negative-stub-values and the merger arbitrage indexportfolio. The maximum in-sample Sharpe ratio from this strategy is with 13 percent21
invested in the negative-stub-value portfolio and 87 percent in the merger arbitrage suggests that fundamental and margin risks, which are clearly important forsomeone investing in individual negative-stub-values, are less likely to create a seriousimpediment to the likely arbitrageur of these relative . Arbitrage in Imperfect Capital MarketsA. Costs of Short Selling and Buy-In RiskIn addition to the risks discussed above, the persistence of the mispricing in negative-stub-value situations may be the result of short-selling frictions (see Lamont and Thaler (2001)).The arbitrage strategy requires selling short shares in the subsidiary firm, which generally havelow public floats. In other words, the percentage of outstanding shares available to be publicly-traded is small because the parent firms, and often the firms’ managers, own the vast majority ofthe shares. As a result, the number of marginable shares that can be sold short may be indication that short selling may be costly is shown by the “short-rebate.” Short-rebate refers to the interest rate that investors are paid on the proceeds they obtain fromborrowing and selling a stock. Generally, institutional investors are paid 25 to 50 basis pointsbelow the federal funds rate on short proceeds, but this discount can vary, and occasionally theshort-rebate is negative. That is, in addition to keeping the interest on the investor’s shortproceeds, the broker sometimes charges the investor to maintain the short course, the short-rebate is a market price, representing both supply and demand. Tounderstand the market for selling short shares, we talked with several industry practitioners andobtained short-rebate data from Ameritrade Holding Corporation, a large retail on-line brokeragefirm. All indications are that this is a very active and liquid market (see D’Avolio (2001) andGeczy, Musto, and Reed (2001)). The stock-loan department at Ameritrade lends shares out ofits customers’ margin accounts to large investment houses and hedge funds. If an investmenthouse such as Goldman Sachs is unable to provide shares to loan to a client short seller out of its22
own customers’ accounts or its proprietary account, they will try to borrow the shares fromanother institution such as State Street Bank or from a broker-dealer, such as VII displays summary statistics of the Ameritrade short-rebate data set. During theDecember 1998 through October 2000 period for which short-rebate data are available, there are28 firms in our sample that qualify under Rule 1 with a buy threshold . Of these 28 firms, 24( percent) are in the Ameritrade database. Six (25 percent) of the firms in the Amertradedatabase have negative rebates. As displayed in Table VII, similar patterns exist for the otherbuy thresholds and for Rule 2. We also note that out of roughly 10,000 NYSE, AMEX, andNasdaq stocks during the December 1998 through October 2000 interval, there are a total of 48firms in the Ameritrade database that have negative short-rebates. Of these 48 firms, seven (15percent) are from our sample. Clearly, the price for selling short the subsidiary shares is highrelative to the typical firm.[Insert Table VII around here]Panel B of Table VII reports the minimum short-rebates paid for subsidiary sharesreported for each subsidiary firm in the Ameritrade database. The data show that the minimumshort-rebate transaction prices tend to be close to zero, suggesting that negative short-rebates areunlikely to be the full story behind the persistence of negative-stub-values. Excluding the twomost extreme observations, the minimum short-rebates range from negative eight percent to sixpercent per year, with the median short-rebate of one the case of the most extreme negative short-rebate in the sample, StratosLightwave. According to the data, an arbitrageur wishing to exploit the relative mispricing ofMethode/Stratos Lightwave would have been charged a 40 percent annual interest rate on shortproceeds from short selling Stratos Lightwave. Following the investment strategy described byRule 1 and buy/sell threshold of the arbitrageur would have invested in the deal on July11, 2000, and would have still been invested at the end of the year. Over this period, the equityvalue of the position increased percent before including the effects of the negative short-20rebate. However, after paying nearly six months of negative short-rebate, the arbitrageur’s23
return is reduced to negative percent. This example highlights that the real impediment is notthe short-rebate, but instead the uncertainty over how long you will be paying it. In other words,an arbitrageur should be more than willing to pay a short-rebate of negative 100 percent per yearif he can correct a 25 percent mispricing in a shares available for shorting are most scarce, brokers cannot maintain their client’sshort positions no matter what interest rate the investor is willing to pay. This situation, whicharises when owners of the stock demand that their loaned-out shares be returned, is often referredto as being “bought-in.” Of the 24 negative-stub-value trades in the Ameritrade short-rebatedatabase, identified using Rule 1 and a buy threshold of , three were partially bought-in beforethe arbitrage spread converged. Similar results are found for Rule 2 and other buy , casual empiricism suggests that the risk of being bought-in is greatest when thearbitrage spreads of several negative-stub-value investments have widened, suggesting that thisrisk may not be completely idiosyncratic. The possibility of being bought-in at an unattractiveprice provides a disincentive for arbitrageurs to take a large position and represents a substantialfriction to executing the arbitrage . Imperfect Information and the Persistence of Negative-Stub-ValuesSo why do negative-stub-values persist? To gain perspective on this question, it may beimportant to consider the details of this particular mispricing phenomenon. Merton (1987)argues that one must be careful when drawing inferences about market anomalies relative to aperfect capital market because imperfections, especially imperfect information, can induceserious distortions. We believe this to be the case for this , there is enormous uncertainty over the economic nature of the apparent mispricingand it will take time to learn about it. Uncertainty over the distribution of returns makes itdifficult to know whether the arbitrage trades will on average be worthwhile investments, andhow they should best be exploited. In other words, at the onset, it is not known whether the24
estimated abnormal returns will be reliably positive, and how sensitive they are to the exacttrading strategy setting up a fund to exploit the type of mispricing analyzed in this paper. Onewould need to collect data and carefully analyze their characteristics, much as we have the 16 years of data used in this paper sufficient to infer details of the distribution of returns?In 16 years we were able to find around 75 occurrences of negative-stub-values from which toestimate the distribution of example, in our sample we find that 30 percent of the time the arbitrage opportunityterminates without convergence. The events causing disadvantageous termination are fairlyrandom, such that this “fundamental risk” seems to be idiosyncratic. Unless an arbitrageur mustbe very highly specialized to exploit these investment opportunities, it is unlikely thatfundamental risk on its own will be much of an impediment to arbitrage activity since it can bediversified away. A potentially larger problem is that the distribution of “bad outcomes” is notknown ex-ante. Even now, the 30 percent estimate of adverse terminations is more accurate information, it is difficult to know whether negative-stub-values representa sample of opportunities caused by mispricings or simply a sample of fairly priced firms withmajor off-balance sheet , uncertainty over the distribution of returns makes it difficult to know exactlyhow to best exploit these opportunities. Figure 2 shows that an investor with over 13 years ofexperience exploiting negative-stub-values learns a lot about how to manage their portfolio whenthe arbitrage spread of Creative Computers and Ubid widens dramatically. On the fourth day ofconsecutively losing roughly 50 percent of invested capital on the Creative Computers/Ubiddeal, the specialized investor receives a margin call and must decide whether to partiallyliquidate that deal or another. With hindsight it is clear that holding onto the CreativeComputers/Ubid investment is the right decision, but at the time it would have been hard toknow what to do. The spread could continue to widen, requiring still more capital, or the dealcould simply terminate without ever converging. There had never been another arbitrage spread25
that had widened so much so quickly, and one would surely be questioning whether they hadmissed something important in their analysis. The opportunity to learn presents itself again oneyear later when 11 out of 15 arbitrage spreads widen over a three-week period. Again, there islittle in the data that could have prepared the investor for this outcome, as this was the first timethat so many negative-stub-values existed at one time. What at first may have seemed like anopportunity to diversify, turns out to drive the equity value of the portfolio way to see that there is considerable uncertainty about the outcomes of negative-stub-values is to examine stock price reactions around announcements of news concerningdistributions and the IRS tax treatments of these transactions. Specifically, we identifyannouncements of (1) the intent of parent to eventually distribute subsidiary shares toshareholders, (2) a tentative or definitive date for distribution, and (3) IRS approval of21distribution as a tax-free transaction. Table VIII reports mean and median stock price reactionsto the release of this information using three-day event windows. The dates of the informationreleases are collected from the Wall Street Journal and the Dow Jones News Retrieval of the sample firms had at least one news story discussing a “distribution” or the “IRS.”The average stock price reaction to the release of this information was percent for the parentfirm (t-statistic = ) and percent for the subsidiary (t-statistic = ). The averagethree-day return for the net long-short position held by an arbitrageur is percent (t-statistic =) and the median return is percent (p-value = ). Importantly, stock pricereactions tend to be just as large for firms that had previously indicated their intention todistribute the subsidiary shares to shareholders in their prospectus as for the firms that reveal thisintention for the first time.[Insert Table VIII around here]It is also interesting to note that the reaction is larger for the firms where the mispricingratio initially indicates a negative-stub-value. Using Rule 1, many of the negative-stub-valueshave converged prior to these announcements, but for the firms that still have a negative-stub,the average stock price reaction is percent and the median is percent. For this26
subsample, where Rule 1 indicates a mispricing prior to the announcement, the medianmispricing ratio falls from before the announcement to immediately after the22announcement. In other words, with no change in the availability of shares for shorting, nomodifications to the rules governing capital requirements, and no reduction in direct transactioncosts, virtually all of the mispricing is immediately eliminated once the uncertainty over theoutcome is , we note that our assessment of the risks associated with investing in negative-stub-value situations is based on the entire history of these trades, from 1985 through the end of2000. An arbitrageur investing at any point during the sample period would not have had thebenefit of seeing as much data. Stated differently, the arbitrageur’s estimates of the risksassociated with negative-stub-value investments almost surely would have been less precise thanthose presented in this paper. This added uncertainty provides another impediment to arbitrageand also helps to explain the persistence of seemingly obvious . ConclusionThis paper studies the impediments to arbitraging relative mispricings of corporate crossholdings, where the parent firm is worth less than its ownership stake in a publicly-tradedsubsidiary. We find that there are costs that limit arbitrage in equity markets, which tests our23faith in market forces keeping prices at fundamental biggest friction impeding arbitrage appears to be the costs associated with imperfect24information (Merton (1987) and Fama (1991)). In order for arbitrage to keep prices atfundamental values, the arbitrageur must have a reasonable understanding of the economicsituation. Becoming informed about negative-stub-value investing is difficult when there is littleevidence to examine. Furthermore, the ex-ante benefits from becoming informed are not payoffs will be large only if there are numerous opportunities or the magnitude of theopportunities is large. Over a 16-year period, we are able to identify fewer than 100 negative-stub-value situations. The total amount of capital that can be employed in this investment27
strategy is low since the effective size (controlling for the public float) of the subsidiary tends tobe very addition, imperfect information and transaction costs may encourage at least somespecialization of arbitrageurs, which limits the effectiveness of diversification. Because poorlydiversified investors will require compensation for idiosyncratic risks, fundamental risksassociated with negative-stub-values can limit arbitrage activity. Even more serious are thefinancial risks borne by highly specialized arbitrageurs. As we show, the returns to a highlyspecialized arbitrageur investing in negative-stub-values would be 50 percent to 100 percentlarger if capital requirements were relaxed. This drives a large wedge between the range ofprices that will be arbitraged away in imperfect capital markets versus those in perfect , to the extent that the initial mispricing is due to noise traders bidding up thesubsidiary share prices, we can say something about their long-term prospects with respect tothis event. Arbitrageurs’ profits are made at the expense of the investors who are long thesubsidiary’s stock. The abnormal returns to an equal-weight portfolio that is long parent firmsare zero, while the abnormal returns to an equal-weight portfolio that is long subsidiary firms arereliably negative. This suggests that the subsidiary shares somehow become overpriced beforearbitrageurs force them back down to fundamental values. Thus, the evidence is consistent withthe arguments of Friedman (1953) and Fama (1965) that investors who make mistakes willexperience losses and over time will be driven out of the market. Market forces are workinghard to keep prices at fundamental values, but the effectiveness of these efforts is
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Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocksand bonds, Journal of Financial Economics 33, , Milton, 1953, The case for flexible exchange rates, in Essays in Positive Economics(University of Chicago Press, Chicago, IL).Geczy, Christopher, David Musto, and Adam Reed, 2001, Stocks are special too: An analysis ofthe equity lending market, Wharton Working , Richard C., and Kristian Rydqvist, 1997, The valuation of non-systematic risks and thepricing of Swedish lottery bonds, Review of Financial Studies 10, , Robert, and Maureen O’Hara, 1989, Primes and scores: An essay on marketimperfections, Journal of Finance 44, , Owen, and Richard Thaler, 2001, Can the market add and subtract? Mispricing in techstock carve-outs, University of Chicago Working , Charles, Andrei Shleifer, and Richard Thaler, 1991, Investor sentiment and the closed-endfund puzzle, Journal of Finance 46, , Jun and Francis Longstaff, 2000, Losing money on arbitrages: Optimal dynamic portfoliochoice in markets with arbitrage opportunities, UCLA Working , Francis, 1992, Are negative option prices possible? The callable . Treasury-Bondpuzzle, Journal of Business 65, , Robert C., 1987, A simple model of capital market equilibrium with incompleteinformation, Journal of Finance 42, , Mark, and Todd Pulvino, 2001, Characteristics of risk and return in risk arbitrage,Journal of Finance,
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1 Throughout this paper, we refer to the company in which the parent holds an ownership stakeas a subsidiary, even though the parent may not own more than 50 percent of the company'svoting Cornell and Liu (2000), Lamont and Thaler (2000), Schill and Zhou (2000), and Tezel andSchnusenberg (2000) examine 10 negative-stub-values during 1998 through 2000. Theyconclude that high demand for a limited number of subsidiary shares coupled with short saleconstraints produce irrationally high prices. Relative mispricings in other markets have beenstudied by many authors, for example, Cornell and Shapiro (1989), Jarrow and O’Hara (1989),Rosenthal and Young (1990), Lee, Shleifer, and Thaler (1991), Longstaff (1992); Dammon,Dunn, and Spatt (1993), and Green and Rydqvist (1997).3 Another potential liability is the capital gains tax arising from the distribution of the subsidiaryshares to the existing parent firm shareholders. In general, to qualify for a tax-free distributionthe subsidiary business must have been in existence for at least five years and the parent firmmust control at least 80 percent of the subsidiary voting shares. However, the 80 percentownership rule can be circumvented. For example, the parent firm can create a new entity thatbuys the non-subsidiary assets and then the subsidiary firm can acquire the remaining parentassets in a tax-free stock merger, effectively distributing the subsidiary shares to existing parentfirm shareholders (see Andrade, Gilson, and Pulvino (2001)).4 Collecting shares outstanding data in this way ensures that errors in CRSP’s daily sharesoutstanding do not affect our return The Securities Exchange Act of 1934 granted the power to establish initial margin requirementsto the Federal Reserve Board, which on October 1, 1934 instituted Regulation T. Since 1934,Regulation T has been amended numerous times, primarily to change the initial marginrequirement. Regulation T was last amended in 1974 when the initial margin requirement wasset at 50
6 There are special margin requirements for shorting stocks that have a price less than fivedollars. For stocks priced between and including $ and $, the maintenance marginrequirement is 100 percent. For stocks priced below $, the maintenance requirement is$ per share Note that brokerage firms typically impose higher maintenance requirements for retail investorsthan the maintenance requirements stipulated by the NYSE and NASD. For example, CharlesSchwab & Co. has a minimum maintenance requirement of 35 percent for long positions. Inaddition, brokerage firms often set higher initial and maintenance margin requirements forcertain securities depending on volatility. In all cases, the higher requirement, whether imposedby the Federal Reserve Board, the exchange/self-regulatory organization, or the broker, The short-rebate estimate of three percent reflects a discount from the more typical rate of 50basis points below the federal funds rate. Section V discusses short-rebates in more PFSWeb IPO prospectus, December 2, 1999, pp. This calculation assumes that 50 percent of the long position and 50 percent of the shortposition (per Regulation T) was posted as Ultimately, Howmet's board rejected Cordant's $17 offer and on March 13, 2000 Alcoa offeredto buy Cordant Technologies for $57 per share in cash. It also announced its intention to buyHowmet's publicly-traded shares. As of March 22, 2000, assuming the arbitrageur had theforesight, fortitude, and financial resources necessary to hold his position, his investment inHowmet and Cordant on November 11, 1999 would have returned 35 percent in four Liu and Longstaff (2000) examine horizon risk and margin risk in bond arbitrage show that it is often optimal for investors to refrain from taking the maximum positionallowed by margin constraints, even when the arbitrage spread is guaranteed to converge in
13 See Pulvino and Das (1999) for a case study on Creative Computers' carve-out of Throughout this example, we assume that the arbitrageur does not earn interest on his postedcollateral or short proceeds. In the full sample analyses that follow, we assume that cashbalances earn the Treasury bill rate and short proceeds earn three Alternatively, the arbitrageur could contribute additional capital. However, allowing thearbitrageur to do this would imply that a pool of capital had been allocated, ex-ante, to meetmargin calls. Thus, the denominator in the return calculation should include this pool of reservecapital. To avoid this, we assume that the arbitrageur partially liquidates his position in responseto margin calls. This assumption has the effect of decreasing calculated returns if the subsequentarbitrage spread converges, and increasing calculated returns if subsequent arbitrage We repeated the analysis presented in Table IV using Rule 2 to identify mispricing (results notreported). This change in the investment strategy has only a small effect on the resultssuggesting that the risks and returns are not overly sensitive to the method used to quantify We originally chose the 20 percent diversification constraint as a reasonable level that anarbitrageur might choose. Subsequent analyses coincidentally showed that 20 percent is the levelof diversification that maximizes portfolio returns over the sample Positions are liquidated randomly to satisfy margin calls. Chance had this particularinvestment strategy liquidate a position other than Creative Computers/Ubid to cover the margincall. This proved fortunate for the arbitrageur as the Creative Computers/Ubid investmentexperienced a huge return on the very next day causing the equity value of the portfolio toincrease
19 Merger arbitrage index returns are obtained from the analysis described in Mitchell andPulvino (2001).20 This calculation assumes the maximum initial leverage allowed by Regulation T and ignoresnet interest on cash and debit Often these announcements are made The mean mispricing ratio falls from before the announcement to after We thank Ken French for discussions on this See also Brav and Heaton (2002).35
Share PriceFigure 1. Paths of Stock Prices for Creative Computers and Ubid$160Margin Call #4 12/23/98Margin Call #3 12/22/98$140Margin Call #212/21/98$120Ubid (x .72)Margin Call #1$10012/18/98CreativeComputers$80Invest$6012/9/98$40$20$012/1/981/1/992/1/993/1/994/1/995/1/996/1/9936
Portfolio ValueFigure 2. Daily Portfolio Values of Negative-Stub Investments Ignoring Maintenance Margin figure shows the value of one dollar invested at the beginning of the period from 1986 to 2000 in negative-stub-value investments. Negative-stub-valueportfolio values are obtained from an investment strategy based on Rule 1 (below) using a buy threshold of and a sell threshold of :MVMVStakeStakePlacetradeif> and Terminatetradeif < EquityParent EquityThe portfolio value calculation cumulates daily payoffs from the arbitrage positions and ignores maintenance capital requirements, allowing the value of investedcapital to become negative.$20$15$10Creative Computers / Ubid Spread Widens$1 Initial Investment$5$09/12/869/12/889/12/909/12/929/12/949/12/969/12/989/12/00-$511 out of 15 Spreads Widen-$1037
Table ISample SummaryThis table presents a summary of the negative-stub-value situations included in our sample. Rule 1 is used as the criterion for inclusion:MVStakeRule1:V<0if> EquityPanel A presents the frequency of situations by industry sector and year. Panel B presents negative-stub-value trades where either the parent or the subsidiary isan Internet firm. Internet firms are also included in the appropriate cells in Panel A. For situations that persist over many years, the year is determined by thedate at which the stub-value first goes negative. Numbers in each cell refer to subsidiaries/ A: Frequency of Negative-stub-Value Situations by Industry Sector and YearIndustry/Year1985198619871988198919901991199219931994199519961997199819992000Basic Materials2/11/00/11/01/01/00/1Capital Goods2/11/00/10/10/1Consumer (Cyclical)1/02/21/01/03/20/1Consumer (Non-cyc.)3/22/11/12/3EnergyFinancial1/0Healthcare1/11/0Conglomerate0/1 1/20/30/20/10/20/1Services2/11/11/01/11/11/11/10/15/62/1Technology1/10/11/01/11/04/31/12/18/73/3Transportation0/11/1Utilities0/1Panel B: Frequency of “Internet” Negative-stub-Value Situations by YearIndustry/Year1985198619871988198919901991199219931994199519961997199819992000Internet2/01/09/03/038
Table IIFrequency of Deals for Which Mispricing is EliminatedThis table presents a summary of the frequency with which mispricings associated with negative-stub-valueinvestments are eliminated at the time of deal termination. Results are presented using the following two mispricingcriteria:MVStakeRule1:V<0if> EquityMV+BVStakeParent EquityRule2:V<0if> Equitywhere V is the value of the parent’s stub assets. Panel A describes the proportion of deals for which theStubmispricing is ultimately eliminated and Panel B describes the events that cause the mispricing to be A: Frequency of Convergence for Negative-stub-Value InvestmentsMispricingTotal SampleNumber (percentage) of DealsNumber (percentage) of Deals forMeasurementSizefor Which Mispricing isWhich Mispricing is NotEliminatedEliminatedRule 16648 (%)18 (%)Rule 27750 (%)27 (%)Panel B: Description of Negative-stub-Value Termination Events (Rule 1)EventNumber ofMispricingMispricing NotOccurrencesEliminatedEliminatedParent distributes subsidiary shares to12120parent shareholdersThird party acquires subsidiary1358Parent acquires the subsidiary shares that it532does not already ownThird party acquires both parent and743subsidiaryThird party acquires parent211Subsidiary acquires parent220Parent stock is delisted844Both parent and subsidiary are delisted220Parent and subsidiary stock price changes15150eliminate mispricingMispricing not eliminated as of4--December 31, 2000Total70481839
Table IIIInvestment HorizonThis table presents a summary of the number of days invested using two different trading strategies. Panels A and Bshow the number of days invested using Rule 1, for the full sample and for converged deals, respectively. Rule 1 isdefined as:MVMVStakeStakePlacetradeif>BuyThreshold and Terminatetradeif < EquityParent EquityPanels B and D show the number of days invested using Rule 2 for the full sample and for converged deals, whereRule 2 is defined as:MV+BVStakeParent EquityPlacetradeif>BuyThresholdMVParent EquityMV+BVStakeParent EquityTerminatetradeif < EquityConverged deals are identified as those where the mispricing ratio is smaller at termination than at the initial are presented for various buy and sell thresholds. Table entries, other than buy and sell thresholds, representtrading A: Number of Days Invested Using Rule 1 for all InvestmentsPercentilethththBuySellNumber ,,, B: Number of Days Invested Using Rule 1 for Converged InvestmentsPercentilethththBuySellNumber ,,, C: Number of Days Invested Using Rule 2 for all InvestmentsPercentilethththBuySellNumber ,,, D: Number of Days Invested Using Rule 2 for Converged InvestmentsPercentilethththBuySellNumber ,,,
Table IVIndividual Investment Returns Using Rule 1This table summarizes annualized excess returns from investments in parent/subsidiary pairs using the followinginvestment strategy:MVMVStakeStakePlacetradeif>BuyThreshold and Terminatetradeif < EquityParent EquityReturns are presented for various buy and sell thresholds and also for various leverage levels. Textbook leveragereturns are calculated assuming Regulation T initial margin requirements but no maintenance margin T leverage returns are calculated using Regulation T initial and maintenance margin requirements; whenmargin calls are received, positions are partially liquidated such that maintenance margin requirements are leverage returns are calculated using an Assets/Equity ratio that precludes margin calls for allparent/subsidiary pairs in the sample. All returns are annualized holding period returns in excess of the riskfreeholding period return and assume that the riskfree rate is paid on short ThatMinimumMeanMaximumWith NegativeReceive MarginSampleReturnReturnReturnReturns (%)Calls (%)SizePanel A: Buy Threshold = ; Sell Threshold = deals Textbook %%%%---110 Regulation T %%%%%110 Conservative %%%%%110Converged deals Textbook %%%%---79 Regulation T %%%%%79 Conservative %%%%%79Panel B: Buy Threshold = ; Sell Threshold = deals Textbook %%%%---75 Regulation T %%%%%75 Conservative %%%%%75Converged deals Textbook %%%%---40 Regulation T %%%%%40 Conservative %%%%%40Panel C: Buy Threshold = ; Sell Threshold = deals Textbook %%%%---39 Regulation T %%%%%39 Conservative %%%%%39Converged deals Textbook %%%%---20 Regulation T %%%%%20 Conservative %%%%%2041
Table VCalendar-Time Portfolio Regression Results for the Negative-Stub-Value Investments(January 1985 through December 2000)This table presents results from the following regression of monthly returns from a portfolio of negative-stub-valueinvestments on common risk factors: Rp - Rf = a + b(Rm – Rf) + sSMB + hHML + e, where the dependenttttttttvariable is the monthly return on a portfolio of negative-stub-value investments, Rp in excess of the one-monthTreasury Bill yield, Rf. The independent variables are the excess return of the market, Rm - Rf; the differencebetween a portfolio of “small” stocks and “big” stocks, SMB; and the difference between a portfolio of “high”book-to-market stocks and “low” book-to-market stocks, HML. See Fama and French (1993) for details on theconstruction of the factors. Results are presented for two investment strategies. Panel A shows the abnormalinvestment returns using Rule 1 defined as:MVMVStakeStakePlacetradeif>BuyThreshold and Terminatetradeif < EquityParent EquityPanel B shows the abnormal investment returns using Rule 2, defined as:MV+BVStakeParent EquityPlacetradeif>BuyThresholdMVParent EquityMV+BVStakeParent EquityTerminatetradeif < EquityRegression coefficients are presented for various buy and sell thresholds, with t-statistics in parentheses. Thenumber of monthly portfolio returns are denoted by A: Abnormal Investment Returns Using Rule 12BuySellNo. ofabshAdj. RAnnualizedThresholdThresholdInvestments[N]%()()()()[186]%()()()()[172]%()()()()[168]Panel B: Abnormal Investment Returns Using Rule 22BuySellNo. ofabshAdj. RAnnualizedThresholdThresholdInvestments[N]%()()()()[192]%()()()()[192]%()()()()[192]42
Table VINegative-Stub-Value Portfolio Return SeriesThis table presents the annual return series for the portfolio of negative-stub-value investments. Returns arepresented for the pure negative-stub-value portfolio, the negative-stub-value portfolio combined with the marketportfolio (41% negative-stub-values, 59% market), and for the negative-stub-value portfolio combined with amerger arbitrage portfolio (15% negative-stub-values, 85% merger arbitrage). Negative-stub-value portfolio returnsare obtained from an investment strategy based on Rule 1 (below) using a buy threshold of and a sell thresholdof :MVMVStakeStakePlacetradeif> andTerminatetradeif < EquityParent EquityValue-weighted CRSP returns are presented for comparison purposes. Merger arbitrage index returns are fromMitchell and Pulvino (2001). For the combination portfolios, weights are chosen to maximize the in-sample Sharperatio. Sharpe ratios are calculated using annual returns and annualized standard deviations. All annual returns areobtained by compounding monthly returns. Annualized standard deviations (Std) are obtained by multiplying thestandard deviation of monthly returns by -stub-ValueNegative-stub-ValueValue-MergerNegative-Portfolio CombinedPortfolio CombinedweightedArbitragestub-Valuewith the Marketwith the MergerCRSPIndex ReturnPortfolioPortfolioArbitrage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Sharpe
Table VIIShort-Rebate DataThis table summarizes short-rebate data provided by Ameritrade Holding Corporation over the period December1998 through October 2000. Panel A displays the number of sample firms with negative-stub-values betweenDecember 1998 and October 2000, the number covered by the Ameritrade short-rebate database, the number (andfraction) with negative short-rebates, and the number (and fraction) with buy-ins. Panel B reports the minimumshort-rebate transaction price paid for each subsidiary firm in the short-rebate A: Summary Statistics on Short-Rebate DataRule 1Rule 2> > > > > > of firms with negative-stub-values between December 1998 and282117323123October 2000Number of firms in short-rebate241815272619databaseNumber of firms in short-rebate665777database with negative short-rebate(%)(%)(%)(%)(%)(%)Number of firms in short-rebate332444database with buy-ins(%)(%)(%)(%)(%)(%)Panel B: Minimum Short-Rebates Paid for Subsidiary SharesCompany NameTransaction DateMinimum Short-RebateStratos LightwaveJuly 6, %PalmJuly 28, %Net2PhoneOctober 1, %RetekJune 26, %Plug PowerSeptember 18, %PFSWebJanuary 20, %MIPS TechnologySeptember 28, %Williams CommunicationsSeptember 19, %XpediorDecember 30, %IturfSeptember 24, %UbidJanuary 26, % 25, %Intimate BrandsFebruary 23, %IXNetSeptember 7, %InterspeedOctober 6, %DigexAugust 16, %NetSiliconSeptember 30, %XM Satellite RadioJanuary 24, %US SearchMarch 28, %Veritas SoftwareJune 7, %Barnes & NobleAugust 23, %Kaiser AluminumDecember 22, %Nabisco BrandsJuly 19, %Keebler FoodsAugust 8, %CareInSiteDecember 16, %Superior TelecomSeptember 27, % 31, %%%44
Table VIIIStock Price Reactions to the Release of News Concerning Distributions and Tax StatusThis table presents the stock price reactions over the three days surrounding news announcements about spinoffdistributions and IRS approval of these distributions as tax-free transactions. News announcements come from DowJones News Retrieval and the Wall Street Journal. Panel A describes the announcement period effects of allannouncements by a single parent/subsidiary pair. Panel B describes the announcement period effects for firmswhere the prospectus indicates their intention to distribute the shares of the subsidiary to shareholders. Panel Cdescribes the individual announcement period effects, treating multiple announcements by the sameparent/subsidiary pair as distinct observations. Panel D describes the individual announcement period reactions tonews, given that the mispricing ratio described by Rule 1 is greater than :MVStakeRule1:V<0if> EquityThe t-statistics are calculated using the standard error of the mean. The p-values are calculated using the Wilcoxonsigned rank A: Effect of all News Announcements for a Given FirmParentSubsidiaryNet %%%%%% B: Effect of all News Announcements for Firms Where Prospectus Indicates Intention toDistribute SharesParentSubsidiaryNet %%%%%% C: All Announcements Treated SeparatelyParentSubsidiaryNet %%%%%% D: All Announcements Where the Mispricing Ratio Using Rule 1 is Greater Than %%%%%%
