Risk Arbitrage Performance for Stock Swap Offers with Collars

Transcription

1 Risk Arbitrage Perormance or Stock Swap Oers with Collars Ben Branch Isenberg School o Management University o Massachusetts at Amherst, MA Phone: branchb@som.umass.edu Jia Wang Isenberg School o Management University o Massachusetts at Amherst, MA Phone: jiaw@som.umass.edu Keywords: Stock Swap Oers with Collars, Risk Arbitrage, Delta Hedging JEL Classiication: G10, G12, G34

2 Risk Arbitrage Perormance or Stock Swap Oers with Collars Abstract Herein we investigate the risk return characteristics o risk arbitrage or a sample o 187 stock swap oers in the orm o collars or the period. Using cross sectional analysis, we ind that arbitrage spreads, deined as the percentage dierence between the oer price and the target market price ater the merger announcement, are signiicantly positively correlated with the acquirer s stock volatility and the deal duration. We also ind that arbitrage spreads are signiicantly lower or successul deals than or ailed deals; lower or challenged deals than or unchallenged deals. Using time series analysis, we identiy a signiicant non-linear relationship in the risk return proile or risk arbitrage portolios: Both strategy I (long the target or the ixed value collar oers; long the target and short the acquirer or the ixed ratio collar oers) and strategy II (delta hedging) produce returns that are strongly positively correlated with the market return in a severely declining market and are not signiicantly correlated with the market return in a lat or rising market. Given the nonlinear payo pattern, linear asset pricing models tend to mis-estimate the magnitude o excess returns. For strategy I, our samples produced an estimated annual excess return o 6.3% when we used contingent claims analysis as our base model. This estimated excess return level is less than the 11.88% return when CAPM, or the 10.27% return when Fama-French three actor models are assumed to be the base model. For strategy II, assuming contingent claims analysis as our base model produced an annual excess return o 22.7%. Using CAPM and Fama- French models produced annual excess returns o 9.25% and 8.6% respectively or our sample o collar mergers.

3 Risk Arbitrage Perormance or Stock Swap Oers with Collars I. Introduction Risk arbitrage is oten linked with Ivan Boesky who was charged by the SEC with insider trading o target stocks in mergers in the mid-1980s. Ironically, the press coverage o the case brought the topic o risk arbitrage strategy to the public s attention. Rather than trading prior to the merger announcement, proessional risk arbitrageurs generally wait until the announcement to establish their initial positions. Following the announcement o a takeover attempt, the target stock usually trades at a discount rom the oer price. Arbitrageurs will make a bet on the takeover deal s successul completion and attempt to lock up the arbitrage spread. Positions are established that closely link to the deal s consideration-structure. In a cash deal or a ixed value stock swap deal, arbitrageurs purchase the target stock and hold the position until deal completion. In a ixed exchange ratio stock swap deal, arbitrageurs purchase the target stock, and at the same time hedge their positions by shorting δ shares o the acquirer stock, where δ represents the exchange ratio, speciied in the merger agreement. The existing literature on risk arbitrage ollows two lines: cross sectional analysis and time series analysis. Cross sectional analysis is used to explore deal-speciic actors that help explain the cross-sectional variation o the initial arbitrage spread 1 or the risk arbitrage return over the event window. 2 Jindra and Walking (1999) ind that the arbitrage spreads on cash tender oers are negatively correlated with the magnitude o 1 Arbitrage spreads are normally deined as the percent dierence between the oer price and the target post announcement price. 2 Cross sectional arbitrage returns are normally deined as the event returns rom a buy and hold strategy in each deal. For e.g. a cash deal event return is the return on a single target share rom two days ater announcement through completion or withdrawal. 1

4 price revision and positively correlated with oer duration. Branch and Yang (2003) ind that the risk arbitrage returns or the event window are correlated with the probability o deal success in a non-linear way. Deals that have a 50% chance to succeed generate the highest return. The second research line, time series analysis involves the construction o risk arbitrage index portolios by including all o the active transactions on a calendar time basis (having available data) and ocuses on perormance evaluation. More speciically, time series analysis is designed to investigate abnormal returns and the systematic risk actors or risk arbitrage portolios. Baker and Savasoglu (2002) report an annualized excess return o approximately 11.35% or a sample o both cash and stock swap oers using either the CAPM or the Fama-French three actor model as their base returns models. Mitchell and Pulvino (2001) ind signiicant nonlinearity in risk arbitrage returns: positively correlated with market returns in severely declining markets (market excess return less than -4%), but uncorrelated with market returns in lat and appreciating markets. In other words, returns to risk arbitrage are analogous to those obtained rom a short position in index put options. With the presence o such a nonlinear relationship, excess returns estimated by Jensen s alpha or the intercept rom the Fama-French model are likely to be misleading. Mitchell and Pulvino (2001) apply contingent claims analysis, which explicitly values the nonlinearity. They ind an excess return o about 16%. Ater controlling or transaction costs, they ind an excess return o about 4%. The previous literature s results have been derived rom samples, which only include ixed ratio stock swap oers. They do not include stock swap oers that contain collars, a type o oer, which has become an increasingly popular deal structure. About 2

5 20% o the stock swap oers involve collars as part o the deal structure (Oicer 2000). We classiy collar oers into Fixed Value (FV) Collar Oers and Fixed Exchange Ratio (FEX) Collar Oers. FV collar oer augments a cap and a loor on the exchange ratio such that the dollar value o the deal is ixed or a given range o the acquirer s stock price and varies i the acquirer s price moves beyond the boundaries, also known as a collar on the ratio structure. The reerence price is usually the acquirer s average closing price or a number o days prior to the date o deal consummation. Consider the merger agreement between BioShield Technologies Inc. and AHT Corp. as an example. The exchange ratio o the stock or stock merger is subject to a collar protection and will be determined based on the ollowing: 1. The number o shares o BioShield Common Stock to be issued to AHT shareholders will luctuate within the collar so that AHT shareholders receive $1.75 worth o BioShield Common Stock i the average closing trading price o BioShield Common Stock, as determined in accordance with the merger agreement, is between $6.00 and $18.00 per share. 2. The exchange ratio outside o the collar will be ixed. AHT shareholders will receive BioShield Shares or each AHT share i the BioShield stock price is $6.00 or less and BioShield shares i the BioShield stock price is $18.00 or above FEX collar oer augments a cap and a loor on the dollar value o the deal such that the exchange ratio is ixed or a given range o the acquirer s stock price, also known as collar on the value structure. Consider the deal between First Union (FU) and BancFlorida Financial (BFF) as an example. Under the terms o the agreement, BancFlorida's shareholders would receive shares o First Union common stock or each share o BancFlorida common stock i First Union's common stock price is between $ and $ per =1.75/ =1.75/18 3

6 share. I First Union's common stock price is below $41.875, BancFlorida's shareholders would receive $28 5 o First Union common stock or each share o BancFlorida common stock. I First Union's common stock price is above $44.875, BancFlorida shareholders would receive $30 6 o First Union common stock or each share o BancFlorida common stock. The calculation o First Union's common stock price will be based upon the average closing price o First Union common stock or the ten trading days prior to the eective date o the acquisition The payo o the target or the above two examples are illustrated in igures 1.1. and 1.2. It s obvious rom the diagrams that the use o collars in takeover oers is analogous to the use o derivatives in the stock market. A FV collar oer provides the target shareholder a contingent claim against the bidder, which (assuming the takeover oer is successul) has a similar risk exposure to a combination o a long position in call options and a short position in put options on the bidding irm. For example, a share o AHT is similar to shares o call options on BioShield with a strike price o $18.00 and a short position o shares o puts with a strike price o $6, as illustrated in igure 1.3. In contrast, a FEX collar oer can be replicated by a bullish spread: a long position in calls with a lower strike price and a short position in calls with a higher strike price. For example, a share o BFF is analogous to calls on FU with a strike price o $ and a short position o calls with a strike price o $44.875, as illustrated in igure 1.4. We call such combination o options Equivalent Option Strategy (EOS). This paper seeks to extend the previous literature by exploring the return perormance o collar oers. Speciically, we explore 1. The actors that help explain the 5 28=0.669* =0.669*

7 cross-sectional variation in the initial arbitrage spread on collar oers. 2. The risk arbitrage perormance o collar oers. To construct risk arbitrage portolios, we utilized two strategies. Strategy I: For a FV collar oer, the target common stock is purchased and held until deal consummation (successul or withdrawal). For a FEX stock swap oer, a share o target stock is purchased and at the same time δ shares o the acquirer s common stock are sold short in order to hedge the position, where δ is the number o shares that the acquirer will exchange or one share o the target stock given that the reerence price stays within the boundaries. Strategy II: Delta hedging: the target stock is purchased and at the same time δ shares o the acquirer s stock are sold short, where δ is delta o the equivalent option strategy and is calculated using Black-Scholes model. The δ is readjusted on a daily basis. E.g. or the AHT and Bioshield deal (FV), δ = *(Delta o the call option) * (Delta o the put option). The strike prices or the call and the put are $18, $6 respectively. Time to maturity is equal to the deal duration or both options. 7 For the BFF and FU deal, δ =0.669*(Delta o the call option 1) 0.669*(Delta o the call option 2). The strike prices or the call option 1 and the call option 2 are $ and $ respectively. Time to maturity is equal to the deal duration or both options. We utilize three asset-pricing models; CAPM, Fama-French three-actor model and contingent claims analysis, to investigate the risk return relationship on risk arbitrage o collar oers. We analyze a sample o 187 stock swap oers in the orm o collars or the period. With cross sectional analysis, we ind that arbitrage spreads are signiicantly positively correlated with both the acquirer s stock return volatility and with 7 We used the ex post deal duration in the calculation. 5

8 the deal s duration. We also ind that arbitrage spreads are signiicantly lower or successul deals than or ailed deals; lower or challenged deals than or unchallenged deals. With time series analysis, we identiy a signiicant non-linear relationship in the risk return proile or risk arbitrage portolios: The risk arbitrage portolio returns derived rom strategy I are strongly positively correlated with the market return in a severely declining market (market excess return less than -3.7% 8 ) and are not signiicantly correlated with the market return in a lat or rising market. Using contingent claims analysis produces an estimated annual excess return o 6.3%, which is less than the 11.88% return derived when CAPM, and10.27% return when Fama-French three actor models are used as the base expected return model or our sample. 2. Strategy II portolios, which involve delta hedging, also exhibit a strong non-linear risk return relationship: positively correlated with the market return in a severely declining market (market excess return less than 2.29% 9 ) and are not signiicantly correlated with the market return in a lat or rising market. Using contingent claims analysis produces an annual excess return o 22.7%. With CAPM and FF model, risk arbitrage portolio produces excess returns o 9.25% and 8.6% respectively or our sample. The remainder o this paper is organized as ollows. Section I describes the sample used in this paper. Section II presents the cross sectional analysis and the empirical results. Section III describes time series analysis and the empirical results. Section IV explores the impact o market return on the outcome o a deal. Section V concludes. 8 The threshold 3.7% is estimated empirically rom the piecewise regression. 9 The threshold 2.29% is estimated empirically rom the piecewise regression. 6

9 I Data Description We irst obtain a list o 641 collar oers announced and completed between 1994 and 2003 rom Securities Data Company (SDC) database. Second, we exclude 373 transactions because either the target or the acquirer o those deals is not listed in CRSP. Then, we obtain detailed deal inormation including oer price, exchange ratio, collar type rom merger news inormation in Lexis-Nexis. We deleted an additional 81 transactions because news inormation revealed that the deal consideration did not contain a collar structure. Our inal sample contains 187 collar oers, 126 were FV collars, 61 were FEX collars. SDC also mentions revisions in the description o the deal consideration. Only 13 or 7% o our sample are listed as revised or amended. However, we couldn t ind detailed inormation about most o the revision rom Lexis-Nexis to validate SDC reports. Accordingly, we choose not to close or adjust positions or the revised deals because the detailed inormation about the price revision is not available and the proportion o revised deal is small. Table I Panel A shows a summary o the 187 mergers used in this study, broken down by announcement year and collar type. Table I Panel B shows a summary o descriptive statistics on the continuous variables that are utilized in the cross sectional analysis: arbitrage spread, deal duration and the acquirer s return volatility 10. II. Cross sectional analysis o the arbitrage spread. Arbitrage spreads are calculated by taking the percentage dierence between the bid price and market price two days ater the initial announcement. This variable exhibits 10 Descriptive statistics on the categorical variables are presented in panel A. 7

10 a positive mean o 9.03%, with an average cross-sectional variation o 7.35% (standard deviation). We investigate the inluence o our variables on the arbitrage spreads: acquirer s return volatility, the duration o the deal, the outcome o the deal and whether the deal is challenged or not. We hypothesize the ollowing: H1. Acquirer s volatility is positively correlated with the arbitrage spread. The intuition behind this hypothesis is straightorward. The higher the volatility o the acquirer s stock, the more likely the reerence price is to move beyond the collar limits, thus the more uncertain is the inal bid price and the greater the arbitrage spread needed as the compensation or the greater risk. H2. Deal duration is positively correlated with the arbitrage spread. The argument is as ollows: the deal duration is positively correlated with the opportunity cost o risk arbitrage. The longer the expected duration, the greater the spread needs to be in order to justiy the investment. Thus we hypothesize a positive correlation between the deal duration and the arbitrage spread. H3. Arbitrage spreads are lower or successul deals than or ailed deals. I the market successully anticipates the outcome o the deal, we expect the arbitrage spreads or successul deals to be less than the arbitrage spreads or ailed deals. A dummy variable (1 or success, 0 or ailure) is utilized as a proxy or deal s outcome. H4: Arbitrage spreads are lower or challenged deals than or unchallenged deals. I a deal is challenged by a another bidder ( who normally oers a higher price), then very oten, the original bidder will raise the oer to match the competing bid. Thus i the market anticipates a competing bid, then the target price oten goes above the initial 8

11 oer price, thus, we hypothesize that the initial arbitrage spreads to be less or challenged deals than or unchallenged deals. We model arbitrage spreads as a unction o the acquirer s return volatility, deal duration, the deal s outcome, and the challenged deal, expressed as equation [1]. Arb _ spread = β 0 + β1σ A + β 2duration + β 3 * deal' s outcome + β 4 * challenged + ε [1] Where deal s outcome is 1 or successul deals, 0 or ailed deals. Challenged is 1 or challenged deals, 0 or ailed deals. The empirical results are reported in Table II. Arbitrage spreads have signiicant positive correlations with both the volatility o the acquirer s stock (a coeicient o 1.328) and the deal duration (a coeicient o ); signiicant negative correlations with the deal s outcome (a coeicient o ) and the dummy variable or challenged deals ( a coeicient o ). The results support our hypotheses. III Time Series Analysis o Risk Arbitrage on Collar Oers Construction o the Arbitrage Portolio We adopt the approach utilized by Baker and Savasoglu. A deal is included in the risk arbitrage portolio starting two days ater the takeover announcement and removed when the deal is consummated or withdrawn. In this way, extraordinary abnormal returns around the announcement are excluded (Jensen and Ruback, 1983). Daily returns are irst calculated or each individual deal. For example, the return or a FV collar oer i on day t is equal to the return on the target on day t: r Tit, which is obtained rom CRSP. The return or a FEX collar oer i on day t has three sources: the return on the target, the return rom a short position in acquirer shares, and the risk ree rate earned on the proceeds rom the short sale, calculated as ollows: 9

12 PAit rit = rtit ( rait rt ) δ P 1 Tit 1 Where r r are the returns on the target and the acquirer on date t respectively. Tit, Ait r t is the daily risk ree rate on date t, obtained rom DataStream. δ is the number o shares o the acquirer s stock that are sold short. P, P Tit 1 Ait 1 are the t-1 closing stock prices o the target and the acquirer s respectively. Then the daily returns are averaged across all the available active deals on day t to obtain the daily portolio return. Finally, the monthly portolio returns are obtained by compounding the daily portolio return. T R = + t= 1 N t r it i= 1 [1 ] N t where N i denotes number o active deals or day t. T denotes number o trading days in a month. A deal that is active only or part o the month is dropped out o the calculation or the remainder o the month. Models Three asset-pricing models are utilized to analyze the risk return relationship o risk arbitrage strategy: 10

13 1. CAPM: Where R r = α + β ( R r ) [2] Risk Arb Mkt Mkt R Risk Arb is the monthly return to a risk arbitrage portolio. RMkt is the return to the value-weighted market index rom CRSP. R is the monthly risk ree rate on three months treasury bill, obtained rom DataStream. 2. Fama-French three actor model: Where R r = α + β ( R r ) + β SMB+ β HML [3] Risk Arb Mkt Mkt SMB HML R Risk Arb, R Mkt, R are as speciied with CAPM. SMB is the return on a portolio o small stocks minus that on large stocks. HML is the dierence in returns on portolios o high book to market stocks and low book-to-market. Data or SMB, HML are obtained rom Kenneth French s Data Library. 3. A piecewise linear CAPM-type model is utilized to estimate the parameters o the contingent claim analysis. (e.g. Mitchell and Pulvino 2001) R r = α + β ( R r threshold) i R r threshold [4] Risk Arb Rising Mkt Mkt Mkt > R Risk Arb r = α + β ( R r threshold) i R r threshold [5] Declining Mkt Mkt Mkt Where R Risk Arb, R Mkt, R are as speciied with the irst two models. β Rising Mkt denotes the market coeicient in an up market. 11

14 β Declining Mkt denotes the market coeicient in a down market. A piecewise linear regression model speciied by equations [4] and [5] allows the variation in the market coeicients conditional on the market returns, as illustrated in igure 2. [Insert Figure 2 about here] Empirical Results and Contingent Claim Analysis Strategy I. Using CAPM as our base model, strategy I portolio produces a signiicant monthly excess return o 94 basis point, corresponding to a 11.88% annualized excess return (Panel B, table III). In addition, the risk arbitrage portolio returns are ound to be strongly positively correlated with the market returns. The intercept rom the Fama- French (FF) model indicates a signiicant monthly excess return o 82 basis point, (10.30% annualized return) (Panel C, table III), which is a little less than that derived rom CAPM. The use o FF model also indicates that the risk arbitrage portolio is exposed to the high minus low risk actor, with a signiicant coeicient o Piecewise regression indicates a strong nonlinear risk return relationship or the risk arbitrage portolio (Panel A, Table III, Figure 3): a beta o when the market excess return is less than 3.7% (the threshold 3.7% is estimated empirically rom the piecewise regression); a beta, which is not signiicantly dierent rom zero when the market excess return is greater than 3.7%. This is consistent with Mitchell and Pulvino, The argument is as ollows: in a declining market, a deal has a greater probability to ail and thereby is more likely to cause losses or the risk arbitrageurs. Thus risk 12

15 arbitrage returns may be positively correlated with the market return when that return is signiicantly negative. In a lat or rising market, a deal has a much greater chance to succeed and thus the arbitrage return is largely determined by the arbitrage spread and is likely to be uncorrelated with the market 11. Given the nonlinear risk return relationship that we have ound, the intercept in the piecewise linear regression cannot be explained as excess returns. Contingent claims analysis may be a better approach. With a contingent claims analysis [e.g. Mitchell and Pulvino (2001)], a portolio consisting o a risk ree bond and index options is constructed in such a way that it generates the same expected payo matrix as the trading strategy o interest (e.g. $100 investment in risk arbitrage), regardless o market conditions. A comparison o the cost o replicating the portolio or that trading strategy will provide us with an estimate o the excess returns. In our case, based on the empirical results rom the piecewise regression, the monthly payo to a $100 investment in the risk arbitrage portolio can be replicated by a portolio consisting o a long position in a risk ree bond, and a short position in βdeclining Mkt index puts. The risk ree bond has a ace value o $100*(1 + r + α), where r is the monthly risk ree rate. The strike price or the put is equal to $100*(1 + threshold + r ). Assuming the parameter estimates rom Table III and Black-Scholes option pricing model, the cost o the replicating portolio is equal to: Where 100 * ( r 1 + r ) * Put( X, S, r _ annual r is the monthly risk ree rate, 0.34% (sample average)., σ, T t) 11 We developed a logistic regression to investigate the eect o market returns on the probability o deal ailure and did ind supportive results. 13

16 Put( X, S, r _, σ, T t) is price or the put option rom Black-Scholes option annual pricing model. X is the strike price: $100*( )=$96.7. S is $100. r annual is the annual risk ree rate, 4.1% (sample average) σ is the market volatility 0.16 (monthly volatility o the market * 12 ). T-t is a month. Using those parameters indicates that the cost o replicating portolio is $100.51, which corresponds to a 51 basis points o monthly excess return, or a 6.3% annualized excess return. Comparing the three models, we conclude that CAPM and Fama-French model ail to account the nonlinear risk return relationship or strategy I and their use as the base model lead to mis-estimation o the excess returns. Strategy II. With CAPM, the risk arbitrage portolio using a delta hedging strategy produces a monthly excess return o 74 basis points and non-signiicant correlation with the market returns (Panel B, Table IV). With FF model, the arbitrage portolio produces a monthly excess return o 69 basis points, non-signiicant correlations with the market and the high-minus-low risk actor and a signiicant correlation with the small minus big actor (Panel C, Table IV). With a piecewise linear regression, we ind a similar nonlinear risk return proile as or strategy I: signiicantly positive correlation ( β o ) with the market in a declining market (market excess return less than 2.29%) and a non-signiicant 14

17 correlation in a rising market. (Panel A, Table IV, Figure 4). We apply contingent claims analysis to analyze the excess return or delta hedging as well. Assuming the parameter estimates rom Table IV and Black-Scholes option pricing model, the cost o the replicating portolio is equal to: Where 100 * ( r 1 + r ) * Put( X, S, r _ annual, σ, T t) r is the monthly risk ree rate, 0.34% (sample average). Put( X, S, r _, σ, T t) are price or the put option rom Black-Scholes option pricing model. annual X is the strike price: $100*( )=$ S is $100. r annual is the annual risk ree rate, 4.1% (sample average) σ is the market volatility 0.16 (monthly volatility o the market * 12 ). T-t is a month. Using those parameters indicates that the cost o replicating portolio is $101.72, which corresponds to a 1.72% monthly excess return, 22.7% annualized excess return. IV Eect o Market Returns on the Probability o a Deal to Succeed We utilize a logistic regression model to estimate the probability o a deal to ail as a unction o the market return in the month that the deal closes (either ails or succeeds), and two lagged monthly market returns. 15

18 P( Failure) = 1 + exp ( β + β Mkt + β Mkt β Mkt ) 0 1 t t 1 Table V shows the empirical results. All the three coeicients or the market returns are positive, which means when market return decreases, the denominator o the model decreases, thus the probability o ailure increases. Thereore, the increase in market beta in depreciating markets is caused, partially at least, by the increased probability o deal ailure ater a severe market downturn. 3 t 2 V Conclusion In this paper, we examine the risk return characteristics o risk arbitrage on stock swap oers containing collars. Using cross sectional analysis, we ind that arbitrage spreads are signiicantly positively correlated with both the acquirer s stock return volatility and with the deal s duration. We also ind that arbitrage spreads are signiicantly lower or successul deals than or ailed deals, lower or challenged deals than or unchallenged deals. Those reports support the proposition that market has a rational expectancy o the uture target price and the deal duration. Using time series analysis, we identiy a signiicant non-linear relationship in the risk return proile or risk arbitrage portolios: 1. Risk arbitrage with strategy I (long the target or the ixed value collar oers; long the target and short the acquirer or the ixed ratio collar oers) is strongly positively correlated with the market return in a severely declining market and are not signiicantly correlated with the market return in a lat or rising market. Using contingent claim analysis as our base model produces an estimated annual excess return o 6.3%, which is less than the 11.88% return or CAPM or10.27% return or Fama- French three actor models. 2. Risk arbitrage with strategy II, which involves delta 16

19 hedging exhibit a similar nonlinear risk return pattern: strongly positively correlated with the market return in a severely declining market and are not signiicantly correlated with the market return in a lat or rising market. Using contingent claims analysis as our base model indicates an annual excess return o 22.7%. Using CAPM and FF as our base models, strategy II portolio produces excess returns o 9.25% and 8.6% respectively. 17

20 Figure 1.1. Target Payo with a ixed value collar oer. Deal Between BioShield Technologies Inc. and AHT Corp. I BioShield (the acquirer) s average closing price or the pricing period is between $6 and $8, AHT shareholders will receive $1.75 worth o BioShield common stock or each AHT share. I the reerence price is above $18, AHT shareholders will receive 1.75/18= BioShield shares. I the reerence price is below $6, AHT shareholders will receive 1.75/6= BioShield shares. Figure 1.2. Target Payo or a ixed exchange ratio collar oer. Deal Between First Union (FU) and BancFlorda Financial (BFF). I FU (the acquirer) s average closing price or the pricing period is between $ and $44.875, BFF shareholders will receive shares o FU common stock or each BFF share. I the reerence price is above $44.875, BFF shareholders will receive 0.669*44.875=$30 worth o FU shares. I the reerence price is below $41.875, BFF shareholders will receive 0.669*41.875=$28 worth o FU shares. 18

21 Replication o a FV Collar Structure Payo o the replicating Portolio Acquirer's Average Price Combined Short Put Long Call Figure 1.3 Replication o a FV Collar Structure 'Replication' o a FEX Collar Structure 6 Payo o the Replicating Portolio Acquirer's Average Price Long Call Short Call Combined Figure 1.4 Replication o a FEX Collar Structure 19

22 R Risk Arb R β Declining Mkt α β Rising Mkt Threshold R Mkt R Figure2. This igure illustrates the piecewise linear regression model speciied by equation [3] and [4]. β Rising Mkt is the market coeicient when market excess return ( R Mkt R ) is greater than the threshold. β is the market coeicient when market Declining Mkt excess return is less than the threshold. α denotes the intercept rom the regression. 20

23 21 Figure3: This igure plots risk arbitrage return against market return or strategy I: long the target or FV collar oers; long the target and short the acquirer or FEX collar oers. Fitted line rom a piecewise linear regression is also shown. Risk Arbitrage: Strategy I Fitted Piecewise Regression Market Return Minus Risk Free Rate -0.2 Risk Arbitrage Return Minus Risk Free Rate Risk Return Proile or Strategy I

24 22 Figure4: This igure plots risk arbitrage return against market return or strategy II-Delta Hedging: long the target or FV collar oers; long the target and short the acquirer or FEX collar oers. Fitted line rom a piecewise linear regression is also shown. Risk Arbitrage: Strategy II-Delta Hedging Fitted Piecewise Regression Market Return Minus Risk Free Rate -0.2 Risk Arbitrage Return Minus Risk Free Rate Risk Return Proile: Strategy II - Delta Hedging

25 Table I. Descriptive Statistics This table represents a summary o the mergers used in this paper. Three criteria are used to screen out the sample: 1. Deal is recorded in SDC. 2. Both target and acquirer are available in CRSP dataset. 3. Deal consideration only involves stocks or a combination o stock and cash. (e.g. cash plus warrants is omitted). 4. Collar inormation is available rom Lexis- Nexis. Transaction duration is measured as the number o trading days rom the announcement to the closing o the deal. Arbitrage spread is deined as the percentage dierence between the target market price two days ater the merger announcement and the oer price. Acquirer s return volatility is estimated using the historical return data over the 250 days prior to merger announcement. Year 2003 only includes the deals that are announced and completed in Panel A. Distribution o the sample by outcome and collar type. Year Number o Deals Completed Challenged Fixed Ratio Fixed Value Total Panel B. Descriptive Statistics on deal duration, arbitrage spread, acquirer s return volatility Variable Mean Std. Deviation Min. Max. Deal Duration Arbitrage Spread 9.03% 7.35% -8.07% 44.26% Acquirer s Return Volatility 2.73% 2.46% 0.99% 9.32% 23

26 Table II. Cross sectional analysis comparing the initial arbitrage spreads with the acquirer s volatility, the deal duration, and the deal s outcome. This table presents the empirical results rom the ollowing model: Arb _ Spread = β 0 + β 1 * σ A + β 2 Deal Duration + β 2 Deal Outcome + β 3Challenged + ε Where: Arb _ Spread is deined as the percentage dierence between the target market price two days ater the announcement and the oer price. σ A is the acquirer s return volatility, estimated using historical return data over the 250 trading days prior to the merger announcement. Deal Duration is the number o days between the deal announcement and the deal completion. Deal Outcome is a dummy variable: 1 or successul deals, 0 or ailed deals. Challenged is a dummy variable: 1 or challenged deals, 0 or unchallenged deals. Intercept Acquirer s Volatility Deal Duration Deal Outcome Challenged Adj. R Square *** 1.328*** *** *** *** (0.0249) (0.361) ( ) (0.0195) ( ) *** indicate signiicance at the level o ** indicate signiicance at the level o * indicate signiicance at the level o

27 Table III Time Series Analysis o Risk Arbitrage on Collar Oers Strategy I With strategy I, we long the target or the ixed value collar oers, long the target and short the acquirer or the ixed exchange ratio collar oers. This table represents empirical results rom the ollowing three models. 1. Piecewise Linear Regression Model RRisk Arb r = α + β Rising Mkt ( RMkt r threshold) i RMkt r > threshold R Risk Arb r = α + β ( R r threshold) Declining Mkt Mkt i R Mkt r threshold 2. CAPM R R = α + β ( R R ) riskarb mkt mkt 3. Fama-French Three Factor Model R R = α + β ( R R ) + β R + β R riskarb mkt mkt SMB SMB HML HML Where R riskarb is the monthly return on the equal weighted risk arbitrage index, Rmkt is the value weighted CRSP index, R SMB is the Fama-French small minus big monthly return series, R HML is the Fama-French high book-to-market return series. Standard errors are reported in parentheses. Panel A. Dependent Variable Arb. Index Returns Panel B. Dependent Variable α (0.0106) α β Declining Mkt Rising Mkt (0.2921)** β Adj- R Mkt β Threshold Adj- R (0.1325)** (0.0177)** Arb. Index Returns ( )** (0.082)*** Panel C Dependent Variable α β Mkt β SMB β HML Adj- R 2 Arb. Index Returns ( )** ( )*** *** indicates statistical signiicance at the 0.01 level. ** indicates statistical signiicance at the.05 level (0.1031) (0.0869)***

28 Table IV Time Series Analysis o Risk Arbitrage on Collar Oers Delta Hedging This table represents results rom the ollowing three models. 4. Piecewise Linear Regression Model RRisk Arb r = α + β Rising Mkt ( RMkt r threshold) i RMkt r > threshold R Risk Arb r = α + β ( R r threshold) Declining Mkt Mkt i R Mkt r threshold 5. CAPM R R = α + β ( R R ) riskarb mkt mkt 6. Fama-French Three Factor Model R R = α + β ( R R ) + β R + β R riskarb mkt mkt SMB SMB HML HML Where R riskarb is the monthly return on the equal weighted risk arbitrage index, Rmkt is the value weighted CRSP index, R SMB is the Fama-French small minus big monthly return series, R HML is the Fama-French high book-to-market return series. Standard errors are reported in parentheses. Panel A. Dependent Variable α β Declining Mkt Rising Mkt β Threshold Adj - R 2 Arb. Index Returns (0.0064)** (0.1934)** (0.1463) (0.0139) Panel B. Dependent Variable α β Adj - R Mkt 2 Arb. Index Returns (0.0034)** (0.0034) Panel C Dependent Variable α β Mkt β SMB β HML Adj - R 2 Arb. Index Returns (0.0034)** (0.0762) *** indicates statistical signiicance at the 0.01 level. ** indicates statistical signiicance at the.05 level (0.0964)** (0.0813)

29 Table V Impact o Market Returns on the Outcome o a Deal This table reports results rom the ollowing logistic regression model: 1 Prob(Failure) = 1 + exp( β + 0 β mkt 1mkt + + t β 2mktt 1 β 3 t 2 Where: Prob(Failure) denotes the probability o a deal to ail. mkt denotes the market return or the month that a deal closes. t mkt denotes the one month lagged market return. t 1 mkt denotes the two months lagged market return. t 2 Intercept mkt mkt 1 mkt 2 t t ) t *** * (0.3099) (4.6742) *** indicates statistical signiicance at the 0.01 level. ** indicates statistical signiicance at the.05 level. * indicates statistical signiicance at the 0.1 level (5.5525) *** (6.1085) 27

30 Reerences: Branch, B and T.W. Yang, 2001, Merger arbitrage: evidence o proitability, Journal o Alternative Investments. Branch, B and T.W. Yang, 2003, Predicting successul takeovers and risk arbitrage, Journal o Quarterly Business and Economics. Baker, Malcolm and Serkan savasoglu, 2002, Limited arbitrage in mergers and acquisitions, Journal o Financial Economics. Dukes, William, Cheryl Frohlich and Christopher Ma, 1992, Risk arbitrage in tender oers: Handsome rewards and not or insiders only, Journal o Portolio Management. Fama, Eugene and Ken French, 1993, Common risk actors in the returns on stocks and bonds, Journal o Financial Economics. Hsieh, Jim and Ralph Walkling, 2003, Determinants and implications o arbitrage holdings in acquisitions, Journal o Financial Economics (orthcoming). Jensen, M., Ruback, R.S., 1983, The market or corporate control: the scientiic evidence. Journal o Financial Economics. Jindra, Jan and Ralpha Walkling, 1999, Arbitrage spreads and the market pricing o proposed acquisitions, Journal o corporate inance (orthcoming). Mitchell, Mark and Todd Pulvino, 2001, Characteristics o Risk and Return in Risk Arbitrage, Journal o Finance. Mitchell, Mark, Todd Pulvino and Erik Staord, 2004, Price pressure around mergers Journal o Finance. Oicer, Micah, 2003, The market pricing o implicit options in merger collars, Journal o Business (orthcoming). 28