Arbitrage
Empirical Corporate Finance
ECON 2727
Core Concepts
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Law of One Price
Market Efficiency
Equilibrium Arbitrage
Limits to Arbitrage
Arbitrage in Real Asset Markets
Arbitrage
• An investment strategy that guarantees
a positive payoff in some state, with no
possibility of a negative payoff, no net
investment, and at arbitrary scale
 Money Machine
• Arbitrage opportunities are inconsistent
with common notions of equilibrium
Law of One Price
• Portfolios with the same payoff in every
state must have the same price
• Consequence of no arbitrage
opportunities
• Key to law of one price is perfect
substitutes (exact same payoffs)
• Underlies the MM Propositions
Efficient Markets Hypothesis
• Efficient Markets Hypothesis (EMH)
At each point in time, prices for all
securities fully reflect all available
information (Fama (1970))
• Otherwise, profit opportunities exist
(although maybe risky --- risk arbitrage)
Market Efficiency
• This notion of efficiency requires that
capital markets are competitive and
dominated by rational investors
• The strong-form of the EMH also
assumes that information and
transaction costs are zero
Equilibrium Arbitrage
• Grossman and Stiglitz (1980)
• When arbitrage is costly, prices cannot fully
reflect all information --- no incentive to bear the
cost of information gathering, if there is no
compensation for bringing information into prices
• EMH*: prices reflect information within bounds of
information and transaction costs
Limits to Arbitrage
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Imperfect information
Transaction costs
Agency
Noise traders
 Real-world “arbitrage” is both risky and
capital intensive
Limits to Arbitrage
• When there is uncertainty over the economic nature of an
apparent mispricing and it is at least somewhat costly to learn
about it, arbitrageurs may be reluctant to incur the potentially
large fixed costs of entering the business of exploiting the
arbitrage opportunity (Merton (1987))
• Uncertainty over the distribution of arbitrage returns will deter
arbitrage activity until would-be arbitrageurs learn enough
about the distribution to determine that the expected payoff is
large enough to cover the fixed costs of setting up shop.
• Even with active arbitrageurs, opportunities may persist while
the arbitrageurs learn how to best exploit them.
Limits to Arbitrage
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Imperfect information and market frictions can encourage
specialization, which limits the degree of diversification in the
arbitrageur’s portfolio and causes him to bear idiosyncratic risks for
which he must be rewarded
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Fundamental risk - a purely random chance that prices will not
converge to fundamental value will cause a highly specialized
arbitrageur to invest less and therefore make arbitrage less effective
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Financing risk - even if prices eventually converge to fundamental
values, the path of convergence may be long and bumpy. If the
arbitrageur does not have access to additional capital when security
prices diverge, he may be forced to prematurely unwind the position
and incur a loss (DeLong, Shleifer, Summers, and Waldman (1990),
Shleifer and Summers (1990), Shleifer and Vishny (1997)).
Limits to Arbitrage
• Key to SV (1997) limits to arbitrage argument is
agency relation between investors and money
manager (Performance-Based Arbitrage)
– Arbitrage is least effective when it is needed most,
and may even compound mispricing
– Financing constraint binds precisely when
opportunities are good because investors cannot
determine whether the need for more capital is
because opportunities have improved or manager is
incompetent
Liquidity & Asset Fire Sales
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When financing constraint binds, one option is to sell assets
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If assets are illiquid, a quick sale may require a discount to fundamental
value
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Moreover, if asset is specialized and natural buyers are also constrained,
then only potential buyers are outsiders who do not value asset as much
 Asset liquidity can be an important cost of leverage and therefore a
potential determinant of capital structure
 Is there a risky arbitrage opportunity buying distressed assets?
Liquidation Values and Debt Capacity
(Shleifer-Vishny (1992))
• When firms have trouble meeting debt payments and sell assets or
are liquidated, the highest valuation potential buyers of these
assets are likely to be other firms in the same industry.
• But these firms are themselves likely to have trouble meeting their
debt payments at the time assets are put up for sale if the shock
that causes the seller’s distress is industry- or economy-wide.
• Assets may have to be sold to industry outsiders who do not know
how to manage them well and fear overpaying.
• As a result, the outsider will pay a lower price for the asset than
would an industry insider.
Empirical Research
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Event Studies
Long-term Event Studies
Price Pressure
Limits to Arbitrage
Asset Fire Sales
Event Study
• What is the average wealth effect of an
event?
• Measure the “abnormal” return, or stock price
reaction, to the announcement of the event
(initial release of information)
• Either assumes or tests:
– Market Efficiency
– Model of Expected Returns E[Ri,t]
Event Study Methodology
Estimation
Window
[
Event
Window
]
(
)
0
• Market Model: E[Ri,t] = a + b E[RM,t]
• Regress Ri on RM to estimate a and b
• ARi,t = Ri,t - E[Ri,t] = Ri,t – a – b RM,t
• Sum ARi,t over event-window to get CAR
• Average over CARi
Time
Event Study
• Avg Wealth Effect = Mean CAR
• Std Error = std(CAR) / sqrt(N)
• t-statistic = mean / std error
• Campbell, Lo, MacKinlay (1997) Ch. 4
• Brown and Warner (1980, 1985)
Empirical Considerations
• Data
– Get the correct announcement dates
• Shorter the event window, less important the
model of E[R]
• 3-day E[R]  0
• Estimate parameters during a “normal” period
• Some events may have unusual pre-event periods (i.e.
mergers tend to be announced after large stock price
runups of acquirers)
Long-term Event Studies
• Don’t do it
• Long event window (3 to 5 years)
• Requires a model of 3-yr expected
returns
• Multi-year abnormal returns are not
independent
• Failure to account for positive cross-correlation
of individual abnormal returns will lead to
overstated test statistics
Bootstrapped Distribution of
mean(BHAR) for SEOs
Mean BHAR
Mitchell and Stafford 2000, “Managerial Decisions and Long-Term Stock Price Performance,” Journal of Business
Long-term Event Studies
• Buy-and-hold abnormal returns (BHAR)
• Typically assumes independence
• Provides estimate of mean multi-year abnormal
return, but statistical inference is difficult
• Calendar-Time Portfolio Approach
• Automatically accounts for cross-sectional
correlations
• Provides reliable estimates and inferences on a
feasible investment strategy
Calendar-Time Portfolios
• Identify firms that have completed an event
within the past X months
• Create a portfolio of these firms
• Weighting scheme
• Analyze performance of this portfolio
• Model of expected returns
• Variation in the time series of portfolio returns
automatically accounts for the cross-sectional
correlations of the individual securities
• Represents a realistic investment strategy
• Can you make money doing this?
Price Pressure Around Mergers
• Acquirers in cash mergers have announcement
period reactions of 0% to 1%
• Acquirers in stock mergers have announcement
period reactions of –2% to -3%
• Common explanation is information or agency
• Stock is overvalued
• Mergers are bad
• Is this really the reason?
• Are we just labeling the “error” term an information effect?
Another Story
• Merger arbitrageurs push acquirers’ stocks
down around merger announcements
– Merger arb trading around mergers:
• Always buy target
• Short-sell acquirer in stock mergers, but not in cash
mergers
• Short-selling could cause downward price pressure on
acquirer stock and partially explain negative reaction
• Information is simultaneously being released,
so hard to distinguish stories
Insight: 2 Types of Stock Mergers
• Fixed-exchange ratio stock merger
• Acquirer offers to exchange X shares for each target
share
• X is fixed and known at announcement
• Arbs short-sell X shares acquirer stock immediately for
each target share they are long
• Floating-exchange ratio stock merger
• Acquirer offers to exchange $Y worth of acquirer stock
for each target share
• X is floating until right before merger completion when it
gets fixed based on average acquirer stock price over a
several day “pricing period”
• Arbs short-sell acquirer stock during pricing period, not
at announcement
Floating-Exchange Ratio Stock Mergers
• At Announcement: 0.5%
– Looks like cash merger
– Information coming out
• During Pricing Period: -3%
– Looks like traditional stock merger
– Little information
– Lots of short selling
Are Arbs Really Responsible?
• If negative reaction partially due to arb short
selling, then short interest should follow
pattern
• Increase around announcement for fixed-exchange stock
mergers
• No change at announcement for cash and floatingexchange stock mergers
• Trading activity of other professional investors
should create price pressure
• Index funds rebalance at merger closing for certain types
of stock mergers
• No rebalancing for others
How much due to Arbs?
• Estimate roughly 50%
– Predict change in short interest due to
merger arbitrageurs
– Use predicted value as a control in a crosssectional regression of CARs
– How much does this control affect
estimate?
Implications
• Mergers not so bad
• Must be careful interpreting event
studies when event triggers trading
• More evidence on the existence of price
pressure (downward sloping short-run
demand curves)
Behind the Scenes
• Topic Selection
• Framing Paper
• Price pressure
• Mergers
• Event studies
• Data
• “Always plot the data!” (Arnold Zellner)
• Methodology
Limited Arbitrage in Equity Markets
• Negative Stub Values (a typical case)
• Parent firm carves out subsidiary and retains
80%+ ownership
– Allows for a tax-free distribution of remaining shares
to parent shareholders
• MVParent < 0.8 x MVSubsidiary
• Implies that parents “Stub” assets are negative
Limited Arbitrage in Equity Markets
• Arbitrage?
• Strong link between 2 securities (nearly perfect
substitutes)
• Is this risk free?
• Is there a capital requirement?
• Can you make money?
December 4, 1998
Creative Computer’s Market Value Balance Sheet
Stake in Ubid
Other Assets
Stub (Plug)
Assets
$352M
?
-$80M
$272M
Liabilities
Equity
$3M
$269M
Liab & Equity
$272M
Creative Computers owns 7.33M shares (80%) of
Ubid stock
 Creative Computers has 10.25M shares
outstanding
 Owner of 1 share of Creative Computers
effectively owns 0.715 shares of Ubid

Strategy:
 Buy 1 share of Creative Computers at $26.25 / shr
 Short 0.715 shares of Ubid at $48.00 / shr
($34.34)
 Requires an investment of $30.29 (50% of the
long & 50% of the short)
June 7, 1999
Creative Computer’s Market Value Balance Sheet
Stake in Ubid
Other Assets
Stub (Plug)
Assets
$249M
?
$93M
$342M
Liabilities
Equity
$3M
$339M
Liab & Equity
$342M
Creative Computers distributes shares of Ubid to
shareholders in a tax-free spinoff
 Value of long position in Creative Computers has
changed from $26.25 to $32.63
 Value of short position in Ubid has changed from
$34.34 to $24.02
Total gain of $16.70 on $30.29 initial investment
(55% return over 6 months)

Data
• 82 negative stub situations (1985-2000)
• Use 2 definitions of negative stub value
• SDC Database of IPOS, where another publicly traded
firm owned shares beforehand
• Search financial press for extreme relative value
situations (make sure it satisfies condition above)
• Need shares outstanding for both firms and
shares owned
• CRSP is usually wrong on IPO shares outstanding
• Collect from 10Ks/10Qs
Path to Convergence
Figure 1
Creative Computers/UBID Arbitrage
$160
Margin Call
Margin Call
#4, 12/23/98
$140 #3, 12/22/98
Margin Call
$120#2, 12/21/98
UBID (x .72)
$100Margin Call
#1, 12/18/98
Creative
Computers
$ per share
$80
$60 Invest
12/9/98
$40
$20
$0
12/1/98
1/1/99
2/1/99
3/1/99
4/1/99
5/1/99
6/1/99
Impediments to Arbitrage
• Link is unfavorably severed
• 30% of all situations terminate without convergence
• Path to convergence is too long
• Range from 1 day to 2,796 days
• Even with convergence, investment can underperform RF
when the path is long
• Path to convergence is too bumpy
• Mispricing can worsen before it disappears
• Returns to a specialized arb would be 50% higher if path
was smooth rather than as observed
• Imperfect Information
• What is known ex-post is not known ex-ante
Portfolio Values
Figure 2
Daily Portfolio Values of Negative Stub Investments
Rule 1 --- Buy Threshold = 1.25; Sell Threshold = 1.0
(No Maintenance Requirements)
$20
$15
$10
$5
$1 Initial Investment
MALL / UBID
Spread Widens
$0
9/12/1986
-$5
-$10
9/12/1988
9/12/1990
9/12/1992
9/12/1994
9/12/1996
11 out of 15
Spreads Widen
9/12/1998
9/12/2000
Imperfect Information
• Be careful interpreting perfect capital
market anomalies
• Consider setting up a fund to exploit
anomaly
• Uncertainty seems to be a major
impediment to arbitrage
• Large stock price reaction to the resolution of
uncertainty
Conclusions
• Significant costs limit arbitrage activity
• Tests our faith in market forces keeping
prices at fundamental values
• Market forces are working hard to keep
markets efficient, but efforts are
sometimes ineffective
Asset Fire Sales
• Pulvino (1998) “Do Asset Fire Sales Exist? An
Empirical Investigation of Commercial Aircraft
Transactions,” Journal of Finance
• Empirical test of SV (1992)
• Do financial constraints force firms with
industry-specific assets to liquidate assets at
discounts to fundamental value?
Evidence
• Capital constrained firms sell used
aircraft at substantial discounts to
estimated fundamental value
• Capital unconstrained firms purchase
used aircraft when prices are low and
refrain from purchasing when prices are
high
Priors
• Previous research examined announcement
period stock price reactions of buyers and
sellers
• Seller has negative returns before sale
• Positive reaction to announcement for both buyer and seller
• If sale is not actually completed, seller loses gain
 Asset sales represent reallocations from low to
high value users
• Positive reaction to seller seems inconsistent with a forced
sale
Comments
• Key to paper: Obtain actual transaction prices
of used aircraft sales and then compare to
estimates of fundamental value
• Estimate fundamental value with hedonic pricing model
(regress price on asset characteristics)
• Concern: Do the observed characteristics fully
capture the “quality” of the aircraft
• AGE and STAGE (engine noise level) are proxies
• What if constrained airlines cutback on maintenance, use
cheap replacement parts, and/or falsify records?
• Maybe just getting a low, but fair price for a crappy plane