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					       Arbitrage

Empirical Corporate Finance
        ECON 2727
             Core Concepts
•   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
•   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
•   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

•   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

•   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
•   When financing constraint binds, one option is to sell assets

•   If assets are illiquid, a quick sale may require a discount to fundamental
    value

•   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
•   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                Event
          Window                  Window
    [                    ]        (       )
                                      0           Time
• 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
            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 floating-
        exchange 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 cross-
    sectional 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            $352M      Liabilities          $3M
Other Assets                 ?      Equity             $269M
Stub (Plug)              -$80M
Assets                   $272M      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             $249M      Liabilities        $3M
Other Assets                  ?      Equity           $339M
Stub (Plug)                $93M
Assets                    $342M      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)
            Margin Call
         $100
                 #1, 12/18/98                                                                   Creative
               $80                                                                              Computers
$ per sh are




               $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
                                                      MALL / UBID
                                                      Spread Widens
                   $1 Initial Investment
 $5


 $0
 9/12/1986   9/12/1988    9/12/1990    9/12/1992   9/12/1994   9/12/1996   9/12/1998   9/12/2000

 -$5
                                                          11 out of 15
                                                          Spreads Widen
-$10
      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

				
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