Daniel Schwartz FALL 2009 [email protected]

Arbitrage: A Brief Introduction

Arbitrage strategies use relative value trades to generate excess returns with attractive risk profiles. Their low betas with respect to traditional asset classes make arbitrage strategies particularly effective components of a diversified portfolio. This paper offers a brief introduction to arbitrage, including descriptions of several common strategies and an overview of their historical performance.

The information set forth herein has been obtained or derived from sources believed by AQR Capital Management, LLC (“AQR”) to be reliable. However, AQR does not make any representation or warranty, express or implied, as to the information’s accuracy or completeness, nor does AQR recommend that the attached information serve as the basis of any investment decision. This document has been provided to you solely for information purposes and does not constitute an offer or solicitation of an offer, or any advice or recommendation, to purchase any securities or other financial instruments, and may not be construed as such. This document is intended exclusively for the use of the person to whom it has been delivered by AQR and it is not to be reproduced or redistributed to any other person. This document is subject to further review and revision. PLEASE SEE IMPORTANT INFORMATION AND RISK DISCLOSURES ON THE LAST PAGE. WHAT IS ARBITRAGE? risk that the deal fails – an event that typically results in a large loss. Seen another way, arbitrageurs capture Arbitrage strategies are often defined as riskless profit a risk premium in exchange for providing liquidity to opportunities. They consist of the simultaneous those investors who no longer have a desire to hold purchase and sale of two assets that are substantially shares in a target company and bear the risk of deal similar or related, but that have different prices. By failure. being long the “cheap asset” and the “expensive asset,” an arbitrageur seeks to profit from an eventual Most mergers fall into two general categories defined price convergence. Since the real world presents very by the form of payment: cash mergers and stock few truly riskless opportunities, arbitrage strategies mergers. InBev NV’s 2008 acquisition of Anheuser- are more accurately defined as relative value trades Busch is an example of a cash merger. The day after that offer attractive risk-adjusted returns. InBev announced its intention to purchase Anheuser- Busch for $70 per share, Anheuser-Busch’s stock For investors, especially in light of the events of price rose to $66.60. The typical merger arbitrage 2008, arbitrage has another desirable characteristic: trade would be to buy Anheuser-Busch for $66.60 low with respect to traditional asset classes. and to sell Anheuser-Busch stock to InBev for $70.00 While all types of arbitrage have some risk, in most upon consummation of the merger. In addition, the cases this risk is largely independent of equity and arbitrageur would collect dividends on Anheuser- debt markets. For this reason, arbitrage strategies are Busch stock paid prior to the merger closing often referred to as “market-neutral”. Over the long date. Including $0.74/share in dividends, the spread term, these market-neutral strategies can improve a between the offer price and the market price was portfolio’s risk/return profile by reducing portfolio 6.2%. Amortizing this spread over the 126 days until volatility through market cycles. deal completion provided a potential annualized return of 19.1%.

COMMON TYPES OF ARBITRAGE Because the offer price in a cash merger is fixed, capturing the arbitrage spread can be accomplished In theory, arbitrage opportunities are possible for simply by purchasing the target stock. However, in a virtually every kind of asset, wherever price discrep- stock merger, capturing the arbitrage spread requires ancies occur. In practice, transaction costs and other the purchase of the target’s stock and the simultane- frictions limit the investable universe of arbitrage ous short selling of the acquirer’s stock. The 2008 strategies. This paper focuses on several common acquisition of Merrill Lynch (MER) by Bank of arbitrage strategies, namely: merger arbitrage, convert- America (BAC) is a recent example of a stock merger. ible bond arbitrage, and other event-driven arbitrage BAC offered 0.86 shares of its stock for each share of strategies. MER, an offer that amounted to $25.40 per share. After the announcement, MER jumped to $22.18, Merger Arbitrage leaving a deal spread of 14.5% over the following 107 days to expected completion, providing an When a merger is announced, the target company’s attractive potential annualized return of 58.7%. The stock price generally increases, but not fully to the typical arbitrage trade would be to buy MER stock price offered by the acquirer. The remaining spread and to sell short 0.86 BAC shares for each MER share reflects the risk that the merger will not be completed. purchased. Arbitrageurs who implemented this trade Arbitrageurs can earn this positive spread for deals isolated the spread between the two stock prices, and that are successful if they are willing to assume the created a market-neutral investment whose primary

2 | FOR INVESTMENT PROFESSIONAL USE ONLY Please read important disclosures at the end Exhibit 1: HFRI Merger Arbitrage Monthly Returns January 1990 – July 2009

HFRI Merger Arbitrage Monthly Returns January 1990 – July 2009

4%

2%

0%

-2%

-4% Monthly Return

-6%

-8% Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09

Source: Fund Research, Inc. © 2009, www.hedgefundresearch.com risk was that of deal failure. In this way, merger typically modest and downturns rarely last longer arbitrage is analogous to writing against than 1-3 months (see Exhibit 1). deal failure. A merger arbitrageur collects a positive spread on the many merger deals that are completed, Convertible Bond Arbitrage but faces the potential for loss when a merger fails. A convertible bond is a corporate bond that can, at By investing in a sufficiently large number of merger the option of the holder, be converted into common deals, and by employing appropriate risk controls, stock. Because of the conversion feature, a convert- the arbitrageur is able to build a portfolio that seeks ible bond is a hybrid that bundles together a to generate attractive returns with little systematic corporate bond and an equity call option. risk. However, as first demonstrated by Mitchell and Pulvino (The Journal of Finance, 2001)i, in a falling Each convertible bond has a conversion ratio which , merger arbitrage has a historical beta is the number of shares into which the bond may be of approximately 0.3. As the market declines, cash converted. The conversion price is the stock price at buyers often seek to re-negotiate the purchase price which the holder is indifferent between receiving par or terminate the merger, and thus cash mergers have value and converting the bond into common stock. a greater tendency to fail when markets decline. Therefore, the conversion price is effectively the However, the impact on merger arbitrage strategies is strike price of the embedded stock option.

FOR INVESTMENT PROFESSIONAL USE ONLY Please read important disclosures at the end |3 In theory, a convertible bond’s fundamental value is Event-driven Arbitrage Strategies simply the sum of the values of its two components, each of which can be determined in a fairly straight- Merger arbitrage and convertible bond arbitrage are forward manner. The strategy in convertible bond probably the most well-known arbitrage strategies. arbitrage is to identify situations in which the There are, however, a number of other miscellaneous convertible bond is trading at a discount to its fun- arbitrage strategies that are typically classified under damental value. When this occurs, arbitrageurs buy the broad name “event arbitrage”. A few common the convertible bond and synthetically sell the types of event arbitrage strategies are described below. embedded call option by short selling the company’s common stock. By doing so, arbitrageurs capture the Stub Trades spread (the difference between market value and fundamental value) as the bond matures, is put to the Arbitrage opportunities often arise when a publicly company, or is called by the company, bearing the traded firm has an ownership stake in a risk of a limited secondary market. By building a publicly traded subsidiary. If the value of the parent’s diversified portfolio and by employing portfolio level ownership stake in the subsidiary is large relative to credit and interest rate hedges, convertible arbi- the value of the parent firm, the value of the parent’s trageurs seek to generate excess returns that have low remaining assets can be undervalued. The arbitrage correlation with traditional asset classes. strategy is to buy the parent stock and short the subsidiary stock based on the number of subsidiary An example of a trade involves shares held by the parent firm. By undertaking this the $600 million convertible bond issue by Textron trade, the arbitrageur isolates the value of the “stub” in April 2009. Each $1,000 face value bond is assets, which if undervalued should appreciate convertible into 76.1905 shares of Textron common through time. stock. The bonds began trading in the secondary market at a price of $131.70. Based on the credit A stub-trade arbitrage opportunity occurred in spread from a Textron bond with similar maturity November 2008 when Time Warner (TWX) decided and seniority, but without the embedded call option, to split-off Time Warner Cable (TWC). As part of the the bond portion of the Textron convertible was deal, TWX would exchange 0.2496 shares of TWC worth $90.68. Furthermore, call options with the for every share of TWX. TWC closed at $17.99 on strike price and expiration date similar to the option November 20, 2008 making 0.2496 shares of TWC embedded in the convertible bond were trading at worth $4.493. TWX closed at $8.14 on the same date. $0.69 providing value of $52.491. Thus, the sum of As a stub is the value of the parent’s assets less their the components were worth $143.172 and therefore stake in the subsidiary, the implied stub price was the convertible bond was trading at an approximately $3.654. This compares to an estimate of $6.505 for 8% discount to fundamental value. Convertible the fair value of the stub and suggests that the stub arbitrageurs sought to profit from this discrepancy was trading at more than a 40% discount. Stated by buying the convertible bond, short selling the differently, the market price of $8.14 for TWX, was underlying common stock, and hedging the bond’s far less than the sum of the parts of TWX at $10.996,ii. contribution to portfolio credit and interest rate risk. To capture this price discrepancy, an arbitrageur would short 0.2496 shares of TWC for every share of TWX with the expectation that the stub would appreciate over time.

1 Conversion ratio 76.1905* Market price of option $0.69=$52.49 3 Market price of TWC $17.99 * Exchange ratio of spin-off 0.2496=$4.49 2 Value of straight bond $90.68+ Value of embedded option $52.49=$143.17 4 Market price of TWX $8.14- Value of TWC when exchanged $4.49=$3.65 5 Jefferies Equity Research, November 2008 6 Fair value of stub $6.50 + Market value of exchanged shares of TWC $4.49= $10.99

4 | FOR INVESTMENT PROFESSIONAL USE ONLY Please read important disclosures at the end When-issued Arbitrage As the stocks are traded, technical market forces can cause prices of the different classes to diverge. When When-issued arbitrage opportunities arise immedi- this occurs, a dual-class arbitrage opportunity arises ately prior to spin-offs and other corporate actions. and an arbitrageur can earn the spread between the At that point, up to four securities are traded in the two classes. The typical dual class arbitrage trade is market: Parent shares, Subsidiary shares, When-Issued to wait for the spread to become abnormally large Parent shares and When-Issued Subsidiary shares. and then buy the “cheap” class of stock and short the A “when-issued” parent share is the stock that begins “expensive” one, taking on the risk that the anticipated to trade prior to a spin-off but reflects firm assets spread reversion takes a long time to occur. after the spin-off (i.e. when-issued parent shares reflect parent shares without the subsidiary assets). This type of arbitrage opportunity arose with Royal A “when-issued” subsidiary share is simply a right to Dutch Shell in the second quarter of 2008. On April receive a subsidiary share following the spin-off. 11, Royal Dutch Shell Class-A stock closed at $66.83 When-issued subsidiary and when-issued parent while Royal Dutch Shell Class-B closed at $65.69. shares often trade at premia or discounts to the regular Arbitrageurs could have bought Class-B and shorted subsidiary and parent shares. Arbitrageurs capture price Class-A. When the stock prices did converge on discrepancies by buying and shorting shares May 2, the positions would have been sold and the of the parent, the subsidiary, and the when-issued spread realized. shares. SPACs (Special Purpose Acquisition Companies) are A when issued arbitrage opportunity occurred with publicly traded “shell” companies whose primary Altria’s spin-off of Kraft in March 2007. Altria asset is a trust account invested in low-risk securities distributed approximately 89% of Kraft’s outstanding such as Treasury bills. SPAC managers are typically shares owned by Altria to Altria shareholders. given 18-24 months to find an operating company to Specifically, for each outstanding share of Altria, purchase using the assets of the trust account. Once Altria distributed 0.7 shares of Kraft. On March 22, the SPAC managers have found a candidate company, Altria closed at $86.15 and Kraft closed at $31.85. the acquisition is presented to shareholders for a The theoretical value of the Altria “stub” (Altria ex-Kraft), vote. If the vote fails, money from the trust account was $63.857. However, the when-issued stock of is returned to shareholders on a pro-rata basis. Altria closed at $64.43. To capture this price discrep- However, even if the vote succeeds, shareholders ancy, an arbitrageur would buy Altria and short both who vote against the acquisition are allowed to Kraft and when-issued Altria (w/o-Kraft). redeem their pro-rata share of the trust account.

Dual-Class Arbitrage Under normal market conditions, SPACs trade at close to fundamental value – the value of the Dual-class stocks are different classes of common Treasury bills in the trust account. However, during stock issued by the same company. Companies issue market dislocations, SPAC prices can trade at dis- different share classes for various reasons, but it counts, creating arbitrage opportunities. Under these usually involves tax and control considerations. circumstances, arbitrageurs capture the discount by Typically, each class of stock is entitled to the same voting against acquisitions and receiving their pro-rata cash flow interest in the company, but one share class portion of the trust account, paid in cash. Assuming has superior voting rights (e.g. 10 votes per share). the opportunities are properly identified, SPACs represent a relatively low strategy.

7 Market price of Altria $86.15 - .7 Market price of Kraft $31.85 = $63.85

FOR INVESTMENT PROFESSIONAL USE ONLY Please read important disclosures at the end | 5 Exhibit 2: HFRI Index Returns January 1990 – July 2009

HFRI Merger HFRI Convertible HFRI Event S&P 500 Merrill Lynch Arbitrage Index Arbitrage Index Arbitrage Index Index 3-Month T-Bill Index Annualized Return 9.5% 8.5% 12.2% 5.4% 3.9% Volatility 4.3% 6.6% 7.0% 15.1% 0.5% Sharpe Ratio 1.24 0.69 1.14 0.1 0.0 (annual) 5.1% 4.2% 7.4% 0.0% 0.0% Beta to S&P 500 0.15 0.19 0.32 1.00 0.00

Source: Research, Inc. © 2009, www.hedgefundresearch.com

RISK AND RETURN CHARACTERISTICS ARBITRAGE AND THE DIVERSIFIED OF ARBITRAGE STRATEGIES PORTFOLIO

Arbitrage strategies have a long history of attractive To illustrate the diversification benefits of arbitrage risk-adjusted returns. Exhibit 2 shows the perform- strategies, we compare two hypothetical portfolios: ance of the HFRI Merger Arbitrage, HFRI Convertible a standard portfolio to a hypothetical enhanced Arbitrage, and HFRI Event-Driven Arbitrage Indices portfolio that includes arbitrage strategies from the compared to U.S. equity and U.S. Treasury Indices. period January 1990 through July 2009. The standard portfolio consists of 60% stocks, 30% bonds, and The alphas, or excess returns, of the arbitrage strategies 10% cash8. The modified portfolio features a 15% range from 2.5% to 7% with volatilities between 4% arbitrage component, taken equally from stocks, and 7%, substantially lower than the U.S. equity bonds, and cash and placed into the HFRI Merger market. Low betas relative to the S&P 500 and attrac- Arbitrage, Convertible Arbitrage, and Event-Drive tive Sharpe ratios are key reasons investors look to Arbitrage Indices. As shown in Exhibit 3, the inclu- diversify their portfolios with arbitrage strategies. sion of arbitrage strategies enhances returns while decreasing volatility, resulting in a much improved Sharpe ratio9.

Exhibit 3: Adding Arbitrage to a Standard Portfolio – Hypothetical Example

Standarized Portfolio Enhanced Portfolio (60% stocks, 30% bonds, 10% cash) (55% stocks, 25% bonds, 5% cash, 15% arbitrage) Annualized Return 6.01% 6.70% Volatility 9.32% 7.60% Sharpe Ratio 0.26 0.39

Source: Hege Fund Research, Inc. © 2009, www.hedgefundresearch.com

8 Stock returns are taken from the S&P 500, bond returns are taken from the Lehman Aggregate Bond Index and cash returns are taken from the Merrill Lynch 3 Month T-Bill Index. 9 Hypothetical performance has many inherent limitations and is for illustrative purposes only. No representation is being made that any fund or account will or is likely to achieve profits or losses similar to those shown herein.

6 | FOR INVESTMENT PROFESSIONAL USE ONLY Please read important disclosures at the end CONCLUSION economic crises, we have seen that arbitrage strategies generally fall less than equity markets, and, Recent history has reminded investors of the because of the convergence nature of the trades, tend importance of diversification. Many individual to recover losses following crises. For long-term arbitrage strategies have low betas with respect to investors looking to enhance risk-adjusted returns traditional investment classes and, importantly, with through market cycles, we think exposure to respect to each other. While not immune to global arbitrage strategies is a practical option.

i Mitchell, Mark and Todd Pulvino, Characteristics of Risk and Return in Risk Arbitrage, Journal of Finance, December, 2001. ii Jefferies Equity Research Report, Special Opportunities, November 20, 2008.

DISCLOSURES:

The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC its affiliates, or its employees.

The information set forth herein has been obtained or derived from sources believed by author to be reliable. However, the author does not make any representation or warranty, express or implied, as to the information’s accuracy or completeness, nor does the author recommend that the attached information serve as the basis of any investment decision. This document has been provided to you solely for information purposes and does not constitute an offer or solicitation of an offer, or any advice or recommendation, to purchase any securities or other financial instruments, and may not be construed as such. This document is intended exclusively for the use of the person to whom it has been delivered by the author, and it is not to be reproduced or redistributed to any other person.

Hypothetical performance results (e.g., quantitative backtests) have many inherent limitations, some of which, but not all, are described herein. No representation is being made that any fund or account will or is likely to achieve profits or losses similar to those shown herein. In fact, there are frequently sharp differences between hypothetical performance results and the actual results subsequently realized by any particular trading program. One of the limitations of hypothetical performance results is that they are generally prepared with the benefit of hindsight. In addition, hypothetical trading does not involve financial risk, and no hypothetical trading record can completely account for the impact of financial risk in actual trading. For example, the ability to withstand losses or adhere to a particular trading program in spite of trading losses are material points which can adversely affect actual trading results. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results, all of which can adversely affect actual trading results. Hypothetical performance results are presented for illustrative purposes only.

The arbitrage transactions described herein are strictly for educational purposes and are in no way a recommendation of specific securities or services.

There is no guarantee that these strategies will be successful.

FOR INVESTMENT PROFESSIONAL USE ONLY Please read important disclosures at the end | 7 AQR Capital Management, LLC | 2 Greenwich Plaza, Third Floor, Greenwich, CT 06830 | 203.742.3600 www.aqr.com