Characteristics of Risk and Returnin Risk ArbitrageMARK MITCHELL and TODD PULVINO*ABSTRACTThis paper analyzes 4,750 mergers from 1963 to 1998 to characterize the risk andreturn in risk arbitrage. Results indicate that risk arbitrage returns are positivelycorrelated with market returns in severely depreciating markets but uncorrelatedwith market returns in flat and appreciating markets. This suggests that returnsto risk arbitrage are similar to those obtained from selling uncovered index putoptions. Using a contingent claims analysis that controls for the nonlinear rela-tionship with market returns, and after controlling for transaction costs, we findthat risk arbitrage generates excess returns of four percent per year.AFTER THE ANNOUNCEMENT OF A MERGER or acquisition, the target company’sstock typically trades at a discount to the price offered by the acquiringcompany. The difference between the target’s stock price and the offer priceis known as the arbitrage spread. Risk arbitrage, also called merger arbi-trage, refers to an investment strategy that attempts to profit from thisspread. If the merger is successful, the arbitrageur captures the arbitragespread. However, if the merger fails, the arbitrageur incurs a loss, usuallymuch greater than the profits obtained if the deal succeeds. In this paper,we provide estimates of the returns to risk arbitrage investments, and wealso describe the risks associated with these returns.Risk arbitrage commonly invokes images of extraordinary profits and in-credible implosions. Numerous articles in the popular press detail large prof-its generated by famous arbitrageurs such as Ivan Boesky and even largerlosses by hedge funds such as Long Term Capital Management. Overall,existing academic studies find that risk arbitrage generates substantial ex-cess returns. For example, Dukes, Frohlich, and Ma ~1992! and Jindra andWalkling ~1999! focus on cash tender offers and document annual excessreturns that far exceed 100 percent. Karolyi and Shannon ~1998! conclude* Harvard Business School and Kellogg School of Management, respectively. We are gratefulto seminar participants at the Cornell Summer Finance Conference, Duke University, HarvardUniversity, the University of Chicago, the University of Kansas, the New York Federal ReserveBank, the University of North Carolina, Northwestern University, the University of Rochester,and the University of Wisconsin-Madison for helpful comments, and to three anonymous ref-erees, Malcolm Baker, Bill Breen, Emil Dabora, Kent Daniel, Bob Korajczyk, Mitchell Petersen,Judy Posnikoff, Mark Seasholes, Andrei Shleifer, Erik Stafford, René Stulz, Vefa Tarhan, andespecially Ravi Jagannathan for helpful discussions. We would also like to thank the manyactive arbitrageurs who have advanced our understanding of risk arbitrage.THE JOURNAL OF FINANCE • VOL. LVI, NO. 6 • DEC. 20012135that a portfolio of Canadian stock and cash merger targets announced in1997 has a beta of 0.39 and an annualized return of 26 percent, almost twicethat of the TSE 300. In a similar study using a much larger sample of U.S.cash and stock mergers, Baker and Savasoglu ~2002! conclude that risk ar-bitrage generates annual excess returns of 12.5 percent.These findings suggest that financial markets exhibit systematic ineffi-ciency in the pricing of firms involved in mergers and acquisitions. However,there are two other possible explanations for the large excess returns docu-mented in previous studies. The first explanation is that transaction costsand other practical limitations prevent investors from realizing these ex-traordinary returns. The second explanation is that risk arbitrageurs re-ceive a risk premium to compensate for the risk of deal failure. In this paper,we attempt to empirically distinguish between these three alternativeexplanations.To assess the effect of transaction costs, we use a sample of 4,750 mergersand acquisitions between 1963 and 1998 to construct two different series ofrisk arbitrage portfolio returns.1The first portfolio return series is a calendar-time value-weighted average of returns to individual mergers, ignoring trans-action costs and other practical limitations ~value-weighted risk arbitragereturns are subsequently referred to as VWRA returns!. The second portfolioreturn series mimics the returns from a hypothetical risk arbitrage indexmanager ~subsequently referred to as RAIM returns!. RAIM returns includetransaction costs, consisting of both brokerage commissions and the priceimpact associated with trading less than perfectly liquid securities. RAIMreturns also reflect practical constraints faced by most risk arbitrage hedgefunds. However, unlike actively managed hedge funds, no attempt to dis-criminate between anticipated successful and unsuccessful deals is madewhen generating RAIM returns. Comparing the VWRA and RAIM returnseries indicates that transaction costs have a substantial effect on risk ar-bitrage returns. Ignoring transaction costs results in a statistically signifi-cant alpha ~assuming linear asset pricing models are valid! of 74 basis pointsper month ~9.25 percent annually!. However, when we account for transac-tion costs, the alpha declines to 29 basis points per month ~3.54 percentannually!.The second possible explanation for the extraordinary returns to risk ar-bitrage documented in previous studies is that they simply reflect compen-sation for bearing extraordinary risk. Although previous studies that reportexcess returns attempt to control for risk, they make the implicit assump-tion that linear asset pricing models are applicable to risk arbitrage invest-1The sample includes stock swap mergers, cash mergers, and cash tender offers. Construct-ing returns from individual mergers allows us to avoid the sample selection issues inherent inrecent studies that use hedge fund returns to assess the risk0reward profile of risk arbitrage.For example, Fung and Hsieh ~1997!, Ackermann, McEnally, and Ravenscraft ~1999! and Agar-wal and Naik ~1999! provide analyses of hedge fund returns. Fung and Hsieh ~2000! present adiscussion of the sample selection biases inherent in using these returns.2136 The Journal of Financements. However, this assumption is problematic if the returns to risk arbitrageare related to market returns in a nonlinear way. Building on Merton’s ~1981!work on the ability of fund managers to time the market, Glosten and Ja-gannathan ~1994! show how to evaluate the performance of