ArbitrageArbitrage

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What is Arbitrage?

Arbitrage, in its truest form, involves earning a risk-free profit without the outlay of any capital.

Arbitrage is only possible because of inefficiencies in markets, typically inefficiencies in information transfer/processing.

The typical process involves simultaneously purchasing an undervalued asset and selling an economically equivalent overvalued asset, in the process obtaining a risk-less profit on the price differential.

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Examples of True Arbitrage

An over simplified example of arbitrage would be two gold dealers located next to each other. In the first shop gold is bought and sold at $400/oz., while the second store buys and sells gold for $425/oz. An investor could make a guaranteed risk-free profit of $25/oz. by purchasing gold from the cheaper shop and selling it at the more expensive shop next door.

A common, more realistic illustration of true arbitrage is that of Triangular Currency Arbitrage. It involves a situation with three currencies that are traded in different markets. When the observed exchange rate of a currency in one market is not consistent with the cross-rate in another market, there exists a true arbitrage opportunity.

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Example: Triangular Currency Arbitrage

There are 3 currencies: $ (US Dollars), £ (pounds), € (euros)

Quoted exchange rates: New York: £/$= 1.5London: €/£=1.4

Berlin: €/$= 2 The proper €/£ cross-rate in New York is: 2/1.5= 1.33 €/£

Exploitable Mispricing = Arbitrage Opportunity

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Example: Triangular Currency Arbitrage

Reminder of FX rates: New York: £/$= 1.5 London: €/£=1.4 Berlin: €/$= 2

With € 2.1 buy $1.05 (=€ 2.1/2)in Berlin

With £1.5 buy €2.1 (£1.5x1.4) in London

Spend $1 to buy £1.5 in New York

An astute investor would recognize the arbitrage opportunity here and spend $1 to buy £1.5. They would then go to London and buy (£1.5x1.4)= €2.1. They would then go back to NY and buy (€ 2.1/2)=$1.05. In the process they have made a $0.05 risk-less profit.

Return $0.05 risk-free profit back home to New York

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Arbitrage In Today’s Market

As data flow has become quicker and cheaper, ‘true’ risk-free arbitrage investment opportunities have become a rarity and quickly disappear when they do arise.

Instead, today’s arbitrage strategies are often based upon theoretical or implied value pricing inefficiencies. These strategies usually use sophisticated models that determine when an abnormally high risk-adjusted return can be generated.

Difference: Data alone isn’t enough. One needs to process the data into information based on complex models.

The main risk in these arbitrage strategies are in the valuation model used. They can be inaccurate and are often dependant on key assumptions taken by the model’s developers.

Hedge FundsHedge Funds dominate today’s arbitrage market as they have the expertise and resources needed to develop and apply the complex strategies involved. As well, hedge funds can apply short selling and other crucial techniques needed to implement arbitrage strategies, that mutual funds cannot.

Illustration of a Real Arbitrage Opportunity

MERGER ARBITRAGE

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Merger Arbitrage

Merger arbitrage capitalizes on the differences between the terms of a proposed merger between two companies, and the relative current market prices of the companies involved in the merger.

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Daimler Benz’s Acquisition of Chrysler Corp.

Target Company: Chrysler Corp. Acquiring Company: Daimler Benz

Transaction Announced: May 6, 1998Expected Close: December 15, 1998Merger Terms: One (1) Chrysler share = 0.624 Daimler Benz shares

May 6, 1998Purchase Target Company’s StockOne (1) share Chrysler @ $59.88(closing price on May 6 = $59.88)

Sell Short Acquiring Company’s Stock 0.624 share Daimler Benz @ $106.73 = $66.60(closing price on May 6 = $106.73)

+$66.60- $59.88 $ 6.72

December 15, 1998 Exchange 1 Chrysler share for .624 Daimler shares Close out Daimler short position with the .624 Daimler shares received Rate of return in 7.3 months is 11.06% (unleveraged) plus bank interest of $6.72 Annualized rate of return = 19% (approx.)

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Economic Justification for Why Such an Opportunity Exists

Target company stock price shoots up But there is still risk: Will merger be approved by

shareholders/regulators? Will Daimler balk for some reason?

Price now reflects a probability of merger, but accurate probability requires sophisticated modeling.

Typical asset manager (e.g. Pension/Mutual Fund manager) made money, and is now unable to asses the risk-premium now built into stock.

Leave last few $ on table for Merger Arbitrageur who provides liquidity for fund managers’ exit.

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Some Other Common Arbitrage Strategies

(Each Described in Appendix 2) Asset-backed securities arbitrage Capital structure arbitrage Closed-end fund arbitrage (illustrated in Appendix 1) Convertible arbitrage Event arbitrage Fixed income arbitrage Mortgage-backed securities arbitrage Options arbitrage Statistical arbitrage

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Attractiveness of Arbitrage Strategies

Proper arbitrage strategies will also offer investors abnormal risk-adjusted returns, providing higher returns than the market, with lower risk and volatility.

Arbitrage strategies are also generally market neutral. This means that the success of the strategy is not dependant on movements in the overall market.

Arbitrage can thus provide portfolio diversification, because the majority of strategies have very low correlations with the general market.

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Historical Performance of Arbitrage Strategies

*Data from CSFB/Tremont Hedge Fund Index

Strategy Annualized Return since inception

Correlation with MSCI World ($)

Sharpe Ratio

Merger Arbitrage (since 1993)

7.89% 0.46 0.95

Convertible Arbitrage (since 1994)

8.82% 0.12 1.03

Fixed Income Arbitrage (since 1994)

6.66% 0.04 0.75

Market Neutral (multi strategy) (since 1994)

10.10% 0.36 2.1

MSCI World ($) (since 1994)

7.71% 1 0.27

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The Future of Arbitrage

The future of Arbitrage can be thought of as intertwined with the future of the hedge funds that are its main proponent.

With the increasing size, number and success of hedge funds in recent years it is likely that the use of arbitrage strategies will only increase and in the process become less foreign to the average investor.

Ironically, there is the possibility that the increased usage of arbitrage strategies will actually cause its own demise. As more and more fund managers look for arbitrage opportunities, those available will increasingly disappear and become harder and harder to find. Arbitrage takes advantage of market inefficiencies and it is not impossible to envision a time in the future when these inefficiencies will be removed and the market will hold true to the market efficiency hypothesis.

Appendix 1

Illustration of another Arbitrage Strategy

CLOSED-END FUND ARBITRAGE

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A Closed-End Fund is an exchange-listed fund that collects money from investors through an IPO and then invests in a pool of assets, usually focused on a particular security, sector or country.

Units may trade at a premium or discount to NAV in response to investor sentiment.

Profit from closing the spread between the unit’s market price and its NAV Buy units at a discount Hedge out changes in the NAV Pursue strategy to redeem at NAV

Closed-End Fund Arbitrage: NAV/PRICE

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Appendix 2

DESCRIPTIONS OF SOME OTHER ARBITRAGE STRATEGIES

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Asset-Backed Securities Arbitrage

This strategy involves the purchase of odd-lot asset-backed securities. Institutions purchase new issues in full-lot allocations, then reduce them over time by amortizing the assets. Odd lots trade at a discount to full lots because of a lack of institutional appeal, and thus present profit opportunities to the arbitrageur.

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Capital Structure Arbitrage

This strategy seeks securities within a company’s capital structure that are mispriced relative to similar or more junior securities. Typically, equity holders are more optimistic than debt holders. This creates opportunities to short over-valued equities against under-valued debt. As well, the prices of debt instruments of the same issuer and similar seniority will be affected by differences in maturities or coupons. These price differentials will be eliminated on a reorganization or bankruptcy, providing opportunities to capture the spread between them.

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Closed-End Fund Arbitrage

One CEF arbitrage strategy focuses on yield-to-maturity trades. Positions are acquired at a discount in funds that are in the process of opening or closing. The long position in a CEF is hedged with a basket of indexes and securities that are highly correlated to the CEF’s underlying portfolio. A second CEF arbitrage strategy focuses on U.S. fixed income CEFs and trades fixed income CEFs on a relative value basis. This manager buys CEFs that it believes to be trading at an extreme discount, and where it believes market forces may reduce the discount – and hedges by shorting fixed income CEFs which it believes to be trading at an extreme premium. Net duration exposure is hedged with Treasuries.

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Convertible Arbitrage

This strategy looks for mispricing between a convertible security and the underlying stock. Convertible securities have a theoretical value that is based on a number of factors, including the value of the underlying stock. When the trading price of a convertible moves away from its theoretical value, an arbitrage opportunity exists. Hedge funds focusing on convertible arbitrage would typically buy an undervalued convertible and sell the underlying stock short in anticipation of either the stock moving down in value to match the convertible, or the convertible moving up in value to match the price of the stock. The movement of either the convertible security or the underlying stock generates profit for the hedge fund when the values of the two securities move towards their intrinsic values, while the short sale of the underlying stock helps to protect against stock specific and general market risk. Certain convertible hedge fund managers make use of hedging instruments to provide additional protection against credit risk.

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Event Arbitrage

Event-Driven Arbitrage takes advantage of opportunities that arise as a result of events that could cause a change or perception of change in a security’s value: material litigation, technological breakthroughs or obsolescence, acquisitions or divestitures, new management, proposed legislation, change of research coverage, or any event that could cause a change or perception of change in a securities value.

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Fixed Income Arbitrage

Fixed Income Arbitrage involves the purchase and simultaneous short sale of fixed income or debt securities. Fixed income arbitrage strategies include mortgage-backed securities arbitrage, basis trading, international credit spread trading, calendar spread trading, yield curve arbitrage, intermarket spread trading, and rate cap hedging.

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Mortgage-Backed Securities Arbitrage

Mortgage-Backed Securities Arbitrage is a subset of fixed income arbitrage. The strategy generally involves the purchase of mortgage-backed securities and the short sale of other fixed income securities of the same term, such as government bonds.

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Option Arbitrage

Option Arbitrage commonly refers to an equity trading strategy utilizing options, such as calls, puts, and warrants. The value of an option and the way it is priced in the market is based on sophisticated pricing models involving a number of variables including volatility, share price, exercise price, time to option expiration, and the risk free rate. Volatility is a measure of the tendency of a market price or yield to vary over time. As volatility is usually the only variable not known with certainty in advance, arbitrage opportunities may arise when the theoretical and market values of volatility differ. Volatility traders profit from the difference between the volatility priced into an option and the volatility actually realized in the market. The strategy involves buying options deemed to be under priced on a volatility basis and selling overpriced options.

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Statistical Arbitrage

Short-term pricing misalignments in financial instruments occur daily. These divergences are typically small and of short duration, and the costs of execution would normally offset the potential profit. Statistical arbitrage managers use proprietary models to identify securities that are mispriced relative to other securities with similar trading characteristics. The source of return is the model’s ability to use available information efficiently while maintaining very low execution costs. By tracking a vast number of market inefficiencies simultaneously, the aim is to exploit several such inefficiencies to generate returns in excess of transaction costs.