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Arbitrage
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 riskfree 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:
London:
Berlin:
£/$= 1.5
€/£=1.4
€/$= 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
Spend $1 to buy £1.5 in New York
Return $0.05 risk-free profit
back home to New York
With € 2.1 buy $1.05 (=€ 2.1/2)
in Berlin
With £1.5 buy €2.1 (£1.5x1.4)
in London
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.
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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 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.
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Illustration of a Real Arbitrage Opportunity
MERGER ARBITRAGE
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, 1998
Expected Close:
December 15, 1998
Merger Terms:
One (1) Chrysler share = 0.624 Daimler Benz shares
May 6, 1998
Purchase Target Company’s Stock
One (1) share Chrysler @ $59.88
(closing price on May 6 = $59.88)
+$66.60
- $59.88
$ 6.72
Sell Short Acquiring Company’s Stock
0.624 share Daimler Benz @ $106.73 = $66.60
(closing price on May 6 = $106.73)
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
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
*Data from CSFB/Tremont Hedge Fund Index
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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.
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Appendix 1
Illustration of another Arbitrage Strategy
CLOSED-END FUND ARBITRAGE
Closed-End Fund Arbitrage: NAV/PRICE
 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
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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 mortgagebacked 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.
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