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					     Divisible Good
        Auctions
Dr Orly Sade

Hebrew University
   Issuing Securities - Mechanisms
                    Primary Markets



      Book Building                Auctions



           Stocks
                                Auction Specific
Corporate Bonds                 Mechanism

 Treasury Bonds
     Auctions of Financial assets
   Divisible good units:
     Many
     Identical
     Thecombination is not important
     Sum and price

   Initial sale of - Treasuries, Muni’s,
    Corporate Bonds and Equity
                    Motivation
 Treasury auctions are probably the largest primary
  markets in the world

 Countries with well-developed financial markets use
  auction procedures to sell debt instruments

 The  common mechanisms are: discriminatory and
  uniform

 Ina global financial world – mechanism choice may play
  an important role
Commonly Employed Mechanisms

1.   Discriminatory – Each accepted bid is
     filled at the price specified by the bidder.

2.   Uniform Price – All accepted bids are
     filled at a common price – the equilibrium
     price.
   Uniform-Price Example
   Quantity = 26, Intrinsic Value (resale value) = 20
                  Bidders                   Demand         Cumulative
                                                             Demand
PRICE   A    B      C        D        E

   20   11   0      5        0        0       16              16
   19   5    0      3        2        8       18              34
   18   5    0      8        6        10      29              63
   17   5    26     10       18       8       67              130


                         A        B          C        D              E
Alloca            13.8            0         6.7      1.1            4.4
   tion
 Profit 13.8*(20-19) =            0 6.7*(20-19) 1.1*(20-     4.4*(20-
                    13.8                  = 6.7      19)          19)
                Discriminatory-Price Example

Quantity = 26, Intrinsic Value (resale value) = 20
                        Bidders              Demand           Cumulative
                                                                Demand
 PRICE     A      B       C       D    E

    20     11      0      5       0    0          16             16
    19     5       0      3       2    8          18             34
    18     5       0      8       6    10         29             63
    17     5      26      10      18   8          67             130



                         A        B          C           D              E
Allocati               13.8       0         6.7         1.1            4.4
     on
  Profit 11*0+2.8*1               0 5*0+1.7*1=     1.1*1=1.    4.4*1=4.
                       =2.8                1.7           1           4
           International Survey
   Brenner Galai and Sade (2009)

   Our sample consists of countries from different
    continents, different population, and economic size

   Argentina, Austria, Australia, Bangladesh, Belgium,
    Brazil, Cambodia, Canada, Colombia, Cyprus, Ecuador,
    Fiji, Finland, France, Germany, Ghana, Greece,
    Hungary, Ireland, Israel, Italy, Jamaica, Japan, Korea,
    Latvia, Lithuania, Luxembourg, Macedonia, Malta,
    Mauritius, Mexico, Mongolia, Norway, New Zealand,
    Poland, Portugal, Sierra Leon, Singapore, Slovenia,
    Solomon Islands, Sweden, Switzerland, Trinidad and
    Tobago, Turkey, United Kingdom, U.S.A, Venezuela
         Mechanism choices
 50%, use a discriminatory price
  mechanism to issue government debt
 19% use a uniform price auction
 19% use both mechanisms depending on
  the type of debt instruments being issued
 The rest of the countries, about 12%, use
  a pricing format that is different than the
  two conventional ones
                               Discriminatory       Uniform               Both
                                   (N=24)            (N=9)               (N=9)
       % of civil law               83%               44%                43%
    Avg Stock Market                38%                97%                54%
  Capitalization % of GDP        (std=32%)          (std=69%)          (std=42%)
   Median Stock Market              28%               101%               42%
  Capitalization % of GDP
         Avg GDP                   2.49E+11          1.43E+12           5.54E+11
                               (std= 5.80E+11)   (std = 3.56E+12)   (std = 6.36E+11)
 Percentage of Indebtedness         67%               33%                44%
       Classification
Avg Ranking of Ease of Doing         56                25                 62
         Business
 Median Ranking of Ease of           52                11                 70
     Doing Business
 Avg Ranking of Corruption           61                33                 44
          Index
Median Ranking of Corruption         51                17                 40
          Index
Average ranking of Economics         55                39                 51
       Freedom Index
    Median Ranking Of                44                30                 42
 Economics Freedom Index
Uniform Versus Discriminatory

                         1          2          3            4

    CONSTANT          -2.572**    -0.503     -0.110      -1.535
                      (-2.995)   (-0.765)   (-0.154)    (-1.233)
     Cap / GDP        0.030 **   _______    _______     0.025**
                      (2.579)                            (2.075)
Dummy (Indebtedness   _______     -1.069    _______     _______
 Classification)                 (-1.085)
        GDP           _______    3.66e-13   7.60e-13    _______
                                  (0.847)    (1.459)
 Dummy (Civil Law)    _______    _______    -1.823 **     -1.140
                                             (-2.020)   (-1.071)




     Pseudo R2         0.096      0.106      0.088       0.126
    Prob > chi(n)     0.023**     0.069*     0.115       0.057*
        Bidders Preferences
 Survey
 The participants were asked to imagine
  that the market consists of 10 participants,
  and each participant can decide in which
  auction mechanism to participate.
         Survey Parameters
 There were 26 units issued.
 The resale value of each unit at the end of
  the auction was Fr. 20.
 The possible price levels were Fr. 17, Fr.
  18, Fr. 19, and Fr. 20.
                  Participants
   Survey during 2004 and 2005 in 6 different countries
    getting a varying rate of response.
   Our final sample consists of 220 participants. (USA
    (43.2%), Israel (22.7%), Switzerland (8.2%),
    Luxembourg (12.3%), Norway (7.7%) and South
    Africa (5.9%).
   The participants: financial professionals from one of
    the leading financial institutions in Israel, bankers
    from South Africa that attended a risk management
    course, Executive MBA students from Israel and
    Norway, advanced MBA students from the USA,
    Israel, Luxemburg and Switzerland and advanced
    business undergraduates from the USA.
              Participants
 On average 2.33 years of experience in
  the financial markets (the maximum is 25
  and the minimum is zero).
 11.4% of them had direct previous
  experience with financial assets auctions.
 21.8% of the sample are female.
    Participants           Month and     Number     %               %              %
                             Year                 Uniform     Discriminatory   Indifferent
Executive MBA and
Executive Courses
   Israel-Hebrew U-         June 2004      18      55.56%            38.89%      5.56%
  Executives MBA-              And
        Finance             April 2005
 South Africa-Bankers       June 2004      13      46.15%            30.77%      23.08%
 Norway – Executive         May 2005       17      76.47%            17.65%       5.88%
       MBA at BI
MBA
Luxemburg - School of       February       27      70.37%            25.93%      3.70%
        Finance               2004
                           and January
                              2005
      Switzerland -         May 2004       18      50.00%            33.33%      16.67%
Lausanne-MBA finance
  Israel – Hebrew U –       November       10      40.00%            60.00%      0.00%
    Advanced MBA -            2004
         Finance
 NYU- -MBA 2-3 year         December       24      66.67%            20.83%      12.5%
     part time MBA            2004
NYU- full time 2nd year     December       40      62.50%            32.50%      5.00%
           MBA                2004
           nd
 NYU- 2 year MBA-           December       19      52.63%            31.58%      15.79%
  investment banking,         2004
Business & law School
Advanced
Undergraduate
     NYU-Business           December       12      41.67%            33.33%      25.00%
    Undergraduate- –          2004
          Seniors
Professionals
Financial Professionals      January       22      63.64%            36.36%      0.00%
from a leading financial      2005
   institution in Israel

        TOTAL                             220               90.91%               9.09%
        TOTAL                             220      59.55%            31.36%      9.09%
        Main Survey Results
  91% of the participants are not indifferent
  to the pricing rule of the auction
  mechanism
 Most of those that have a preference for a
  specific price mechanism (65.5 percent)
  have chosen to participate in a uniform
  price mechanism.
    Participants            Month and     Number      %               %              %
                              Year                 Uniform     Discriminatory   Indifferent
Executive MBA and
Executive Courses
   Israel -Hebrew U -        June 2004      18      55.56%            38.89%       5.56%
   Executives MBA -             And
         Finance             April 2005
 South Africa -Bankers       June 2004      13      46.15%            30.77%      23.08%
  Norway – Executive         May 2005       17      76.47%            17.65%       5.88%
       MBA at BI
MBA
Luxemburg - School of        February       27      70.37%            25.93%       3.70%
         Finance               2004
                            and January
                               2005
       Switzerland -         May 2 004      18      50.00%            33.33%      16.67%
Lausanne -MBA finance
  Israel – Hebrew U –        November       10      40.00%            60.00%       0.00%
    Advanced MBA -             2004
          Finance
 NYU - -MBA 2 -3 year        December       24      66.67%            20.83%       12.5%
     part time MBA             2004
NYU - full time 2 nd year    December       40      62.50%            32.50%       5.00%
            MBA                2004
            nd
 NYU - 2 year MBA -          December       19      52.63%            31.58%      15.79%
  investment banking,          2004
Business & law School
Advanced
Undergraduate
     NYU -Business           December       12      41.67%            33.33%      25.00%
    Undergraduate - –          2004
          Seniors
Professionals
Financial Professionals       January       22      63.64%            36.36%       0.00%
from a leading financial       2005
   institution in Israel

        TOTAL                               220              90.91%                9.09%
        TOTAL                               220     59.55%            31.36%       9.09%
           Uniform Price Experiment




Based on Sade, Schnitzlein and Zender (2006a, 2006b)
               Tradeoff
 Discriminatory – Winner Curse  affect
  bidding
 Uniform  game theory  potential
  collusion that is an equilibrium
                  Parameters
   There were 26 widgets available to all players.
   The resale value of each widget at the end of the
    auction was Fr. 20.
   The possible price levels were Fr. 17, Fr. 18, Fr.
    19, and Fr. 20.
   Once all schedules were submitted, price
    and quantity were set:
     Uniform
     Discriminatory
       Subjects and Incentives
 MBAs, Graduates and Undergraduates –
  mixed sample– (Incentives = money)
 Prerequisites – finance, econ and stat
 2 types of professionals (incentives =
  pride):
     Bank of Israel – Monetary department
     Mutual fund investment managers
Expected Equilibria According to the
Theory in The Experimental Setting
   Uniform
     can  support equilibrium at any of the prices
     17 is coalition proof

   Discriminatory
     can   support equilibrium at price of 19
Proposition 1: There exists a coalition-proof symmetric
Nash equilibrium of the uniform-price auction with fixed
supply where all bidders submit demand for 5 units at a
price of 20 and 21 units at a price of 17
(If A bids 26units@18, profits declines to 12)
                               Bidders

    PRICE       A        B        C       D        E

          20     5       5        5        5       5
          19     0       0        0        0       0
          18     0       0        0        0       0
          17    21      21       21       21      21
Summary of the Main Experimental
            Results

 Different bidding behavior than predicted
  by the theory
 Revenue: Uniform > Discriminatory
 Symmetry of allocations: Discriminatory >
  Uniform
Revenue and Experience Effect
                                         Pane l A: Re ve nue

485

480

475

470

465                                                                                                       UF
                                                                                                          UR
460
                                                                                                          D
455

450

445
      1-14

             2-14

                    3-14

                           4-14

                                  5-14

                                         6-14

                                                7-14

                                                       8-14

                                                              9-14

                                                                     10-14

                                                                             11-14

                                                                                     12-14

                                                                                             13-14

                                                                                                     14
                                         Data Grouping
When Less (Potential Demand) is More
            (Revenue)

   Introducing asymmetry – some traders
    have limited bidding ability
     Will this affect the auction results?
     If yes, how?
          Future Research
 Link between auctions and other markets
 Uncertainty

				
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