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									        Portfolio Management
               3-228-07
               Albert Lee Chun

              Market Efficiency


                  Lecture 8
30 Oct 2007                       0
                  Brownian Motion




Albert Lee Chun    Portfolio Management   1
                  A Little Bit of History
    The Roman Lucretius's scientific poem On the Nature
     of Things (c. 60 BC) : "Observe what happens when
     sunbeams are admitted into a building and shed light
     on its shadowy places. You will see a multitude of
     tiny particles mingling in a multitude of ways... their
     dancing is an actual indication of underlying
     movements of matter that are hidden from our sight...
     It originates with the atoms which move of
     themselves”
    Jan Ingenhousz had described the irregular motion of
     coal dust particles on the surface of alcohol in 1785.


Albert Lee Chun        Portfolio Management                    2
                  A Little Bit of History
    Brownian motion is traditionally regarded as
     discovered by the botanist Robert Brown in 1827. It
     is believed that Brown was studying pollen particles
     floating in water under the microscope .
    The first person to describe the mathematics behind
     Brownian motion was Thorvald N. Thiele in 1880 in
     a paper on the method of least squares.
    This was followed independently by Louis Bachelier
     in 1900 in his PhD thesis "Théorie de la spéculation",
     in which he presented a stochastic analysis of the
     stock and option markets.

Albert Lee Chun       Portfolio Management                    3
                     Louis Bachelier
      Louis Bachelier, in his Ph.D. thesis (Théorie de la
      spéculation) at the Sorbonne in 1900, wrote: “Past,
        present, and even discounted future events are
                  reflected in market price.”




Albert Lee Chun       Portfolio Management                  4
          Louis Was Way Ahead of His Time...
    The tragic hero of financial economics was the
     unfortunate Louis Bachelier.
    In his 1900 dissertation written in Paris, Theorie de la
     Spéculation (and in his subsequent work, esp. 1906,
     1913), he anticipated much of what was to become
     standard fare in financial theory: random walk of
     financial market prices, Brownian motion and
     martingales.
    Bachelier's work on random walks predated Einstein's
     celebrated study of Brownian motion by five years.

Albert Lee Chun        Portfolio Management                     5
          Louis Was Way Ahead of His Time...
    His innovativeness, however, was not appreciated by
     his professors or contemporaries. His dissertation
     received poor marks from his teachers and,
     consequently blackballed, he quickly dropped into the
     shadows of the academic underground.
    After a series of minor posts, he ended up obscurely
     teaching in Besançon for much of the rest of his life.
    Virtually nothing else is known of this pioneer - his
     work being largely ignored until the 1960s.



Albert Lee Chun       Portfolio Management                    6
                                   The Life of Louis
    11 March 1870 Louis Jean-Baptiste Alphonse Bachelier is born in Le Havre
    11 January 1889 Father‟s death
    7 May 1889 Mother‟s death
    1891–1892 Military service
    1892 Student at Sorbonne
    October 1895 Bachelor in sciences at Sorbonne
    July 1897 Certificate in mathematical physics
    29 March 1900 Bachelier defends his thesis, Th´eorie de la Sp´eculation
    1909–1914 Free lecturer at Sorbonne
    1912 Publication of Calcul des Probabilit´es
    1914 Publication of Le Jeu, la Chance et le Hasard
    9 September 1914 Drafted as a private in the French army
    31 December 1918 Back from the army
    10 December 1919 A member of the French Mathematical Society
    1919–1922 Assistant professor in Besan¸con
    1922–1925 Assistant professor in Dijon
    1925–1927 Associate professor in Rennes
    January 1926 Blackballed in Dijon
    1 October 1927 Professor in Besan¸con
    1937 Professor Emeritus
    1 October 1937 Retirement
    1941 His last publication
    28 April 1946 Louis Bachelier dies in Saint-Servan-sur-Mer; and is buried in Sanvic near Le Havre
    1996 The Bachelier Finance Society is founded

Albert Lee Chun                        Portfolio Management                                              7
                  Efficient Market Hypothesis

              “Past, present, and even discounted future events
               are reflected in market price.” Louis Bachelier




Albert Lee Chun            Portfolio Management                   8
                Portfolio Management Strategies
    There are 2 principal classes of portfolio management
     strategies.

           1.      Passive
           2.      Active

    Why would an investor choose an active strategy over
     a passive strategy, or visa versa?

    The answer depends on the beliefs of the investors on
     whether or not the market is efficient.
Albert Lee Chun          Portfolio Management                9
             The 3 EMH and Their Information Sets

                         All information
                        relevant to a stock
     Weak                  Information set
                        of publicly available
                             information
                            Information
 Semi-                         set of
 Strong                      past prices



    Strong




Albert Lee Chun        Portfolio Management         10
                  Fama (1970): 3 Forms of EMH
      Weak form efficiency: The past behavior of prices
       cannot help us predict future movements in prices.
       Price changes over time are statistically
       independent.
      Semi-strong form efficiency: There is no public
       information that can help us predict future
       movements in prices. Prices quickly reflect new
       value-changing information.
      Strong form efficiency: Even the „private‟
       information of experts and insiders cannot help us
       predict future movements in prices. Professional
       managers are unable to accurately forecast the
       future prices of individual stocks.
Albert Lee Chun          Portfolio Management               11
                      In other words...
      Weak form efficiency:
       Past prices are useless!

      Semi-strong form efficiency:
       Public information is useless!

      Strong form efficiency:
       All available information, including „private‟
       information is useless!



Albert Lee Chun        Portfolio Management             12
                  Efficient Market Hypothesis
 Assumptions for Efficient Market Hypothesis:

    The number of participants in the market is large and
    that they are profit maximizing. Think of large banks,
    hedge funds, institutional investors...
  Investors rapidly adjust the prices of securities

 to reflect any new information.
  New information here is defined as a surprise -
    something random and unpredictable.


Albert Lee Chun         Portfolio Management                 13
          Implications of Weak Form Efficiency
    Implications of Weak Form Efficiency:
       Past trading data contains no relevant information
        about future prices.
       Best guess of the future price is the current price
        plus the expected return on the stock.

 Pt 1  Pt  Expected Return  Random Number
         Consistent with Random Walk Theory:
          Movements in stock prices from day to day do not
          reflect any pattern, they are random.


Albert Lee Chun         Portfolio Management                  14
                  A Note on the Weak Form
    Technical analysis is useless if this is true! Technical
     analysis looks for patterns in past prices, as opposed
     to fundamental analysis which looks for fundamental
     value.
    Even if there are patterns in the market, the presence
     of a few smart investors would be cause them to
     profit from these patterns for a while, but once the
     market recognizes the pattern it will disappear.




Albert Lee Chun        Portfolio Management                     15
                  Empirical Evidence on EMH
       Tests on aggregate stock indices (TSX and NYSE)
        support weak form efficiency.
       However, momentum strategies provide a
        counterexample to the weak form of the EMH.
        Momentum strategies are based on the momentum
        of stock returns, i.e. past performers would
        outperform past losers.




Albert Lee Chun         Portfolio Management              16
        Implications of Semi-Strong Form Efficiency

    Implications of Semi-Strong Form Efficiency:
       Analysis of financial statements such as income
        statements and balance sheets will not reveal any
        relevant information about future prices.
       Financial analysts cannot identify mis-priced
        stocks from financial statements.
       Fund managers who try to beat the market by
        selecting stocks could do no better than earn an
        average return.


Albert Lee Chun       Portfolio Management                  17
                  Empirical Evidence on EMH
       Research has found that fund managers on average
        do not beat the market. It is really hard to find a
        fund manager who beats the market consistently.
       Passive index-tracking funds perform as well as
        managed funds.




Albert Lee Chun         Portfolio Management                  18
             Implications of Strong Form Efficiency

    Implications of Strong Form Efficiency
       Insider information and insider trading is not
        useful.
       There will be no gradual information leakage.




Albert Lee Chun         Portfolio Management             19
                  Empirical Evidence on EMH
       Insider trading is the trading of a corporation's
        stock or other securities by corporate insiders such
        as officers, directors, or holders of more than ten
        percent of the firm's shares. Illegal insider trading
        refers to trading a security based on nonpublic
        information about the security.
       Research has shown that insider information is
        valuable and one can profit from insider trading.




Albert Lee Chun         Portfolio Management                    20
                  Insider Trading Example
         In 2002, a Martha Stewart was charged with
          insider trading regarding the sale of 3,928 shares in
          pharmaceutical company ImClone, days before its
          application for a new drug was denied. According
          to SEC allegations, she avoided a loss of $45,673
          by selling all 3,928 shares of her ImClone stock.
          Stewart was a friend of ImClone cofounder
          Samuel Waksal. The day following her sale, the
          stock value fell 16%. Over the next month, the
          price of the shares dropped 70%.


Albert Lee Chun          Portfolio Management                     21
                  Quick Review of Market Efficiency

    Weak Form Efficiency: Prices reflect the information
     set comprising past market trading data (i.e. prices,
     volume, dividends, etc.)
    Semi-Strong Form Efficiency: Prices reflect the
     information set comprising past market trading data
     plus all other currently available public information.
    Strong Form Efficiency: Prices reflect all public and
     private information.




Albert Lee Chun           Portfolio Management                22
                  Is the Market Efficient?
    There is little reason to believe markets are strong
     form efficient.
    There seems to be compelling reason to believe that
     markets are weak-form efficient.
    A compromise: some prices, some of the time, might
     not reflect all publicly available information, but most
     assets, most of the time, do reflect this information.




Albert Lee Chun        Portfolio Management                     23
                   Implication of EMH
    Competitive forces in the capital markets drive the
     market prices of securities to their fundamental
     values.
    The more competitive a market, the more efficient it
     is.
    If the markets are efficient, the price of a security
     today is the best predictor of its fundamental value.




Albert Lee Chun       Portfolio Management                   24
                   Implication of EMH
    Efficiency does not imply that the observed prices
     reflect the fundamental value of the stock at all times.
     It implies only that deviations from it's fundamental
     value are random and unpredictable.
    If the markets are not efficient, security prices may
     deviate from their fundamental value. This implies
     that there exist strategies for beating the market.




Albert Lee Chun        Portfolio Management                     25
                   Inefficient Markets
 Reasons for Inefficient Markets

     1. Market Segmentation
     2. Illiquidity
     3. High Costs of Transaction and Information




Albert Lee Chun       Portfolio Management          26
                  Passive Management Strategies




Albert Lee Chun          Portfolio Management     27
        Active vs. Passive Strategy and Efficient
                        Markets
    Investor A: Believes the market is efficient and that it
     is not possible to beat the market and finds it optimal
     to follow a passive strategy by holding the market
     index.

    Investor B: Believes the market is not efficient and
     that it is possible to beat the market, and thus seeks to
     follow an active strategy.




Albert Lee Chun        Portfolio Management                      28
                  Active and Passive Strategies
    Passive equity portfolio management
       Long-term buy-and-hold strategy

       Usually tracks an index over time

       Designed to match market performance

       Manager is judged on how well they track the
        target index
    Active equity portfolio management
       Attempts to outperform a passive benchmark
        portfolio on a risk-adjusted basis


Albert Lee Chun          Portfolio Management          29
                   Passive Strategy
 1. Buy and Hold: Form a portfolio based on certain
    criteria and hold for a predetermined period.

 2. Portfolio Indexation: Replicate the performance of a
    market index. The strategy does not try to look for
    undervalued or overvalued stocks, nor does it try to
    predict movements in the market.




Albert Lee Chun      Portfolio Management                  30
                  Motivation for Indexing


    Theoretical motivation: According to the CAPM, the
     market portfolio is the portfolio tangent to the
     efficient portfolio, and it is not possible obtain higher
     returns for any level of risk using another portfolio.

    Costs of Active Management: There are costs of
     researching information, costs of analyzing
     information, transaction costs.


Albert Lee Chun        Portfolio Management                      31
                  Motivation for Indexing
    Empirical Motivation:

 1. Individual investors under-perform the S&P 500.
    Barber and Odean (1997, 1998, 2000)

 2. Institutional investors (who have lowers transactions
    costs and access to better information) do not
    outperform the market: Jensen(1968), Malkiel (1995),
    Cahart (1997). This is also true when you adjust for
    the price of risk using CAPM or a multifactor model.


Albert Lee Chun       Portfolio Management                  32
            Percentage of Managers that Beat the S&P 500




  Source: Aswath Damodaran (http://pages.stern.nyu.edu/~adamodar/)

Albert Lee Chun               Portfolio Management                   33
                     Active vs. Passive Index Fund




  Source: Aswath Damodaran (http://pages.stern.nyu.edu/~adamodar/)

Albert Lee Chun               Portfolio Management                   34
Albert Lee Chun   Portfolio Management   35
Albert Lee Chun   Portfolio Management   36
Albert Lee Chun   Portfolio Management   37
                  Empirical Tests of the EMH




Albert Lee Chun        Portfolio Management    38
                        Event Studies
 If security prices reflect all available information, then
    price changes must reflect new information.

 Suppose that the single index model holds
                  Rt = a + bRmt + et

 Abnormal return et = (Actual - Expected)
           et = Rt - (at + btRmt)
 Abnormal Returns are those beyond what would be predicted
               by market movements alone.
Albert Lee Chun         Portfolio Management                  39
                      Event Studies

      Examine prices and returns over time




 -t                              0           +t

                    Announcement Date

Albert Lee Chun       Portfolio Management        40
         Stock Price Reaction to CNBC Reports
    Response of 172 firms in which a controlling
     shareholder offered to buy out the minority
     shareholders.
    Acquiring shareholders pay a premium over current
     market prices. So an announcement should cause
     prices to jump!
    This is evidence of an efficient market in that prices
     fully reflect the new information within minutes of
     the announcement.
     A positive report gets digested by the market within
     5 minutes, whereas a negative report takes on average
     12 minutes to digest.
Albert Lee Chun       Portfolio Management                    41
         Stock Price Reaction to CNBC Reports




   Minute by minute report of stock prices of firms featured in
            CNBC’s “Morning” or “Midday Call.”
Albert Lee Chun        Portfolio Management                       42
                  Cumulative Abnormal Returns
     Leakage of information occurs when information regarding a
         relevant event is released to a small group of investors
         before the official public release.
     The price might start to increase days or weeks before the
         announcement and calculating the abnormal return on the
         announcement date may not best measure the impact of the
         new information. One should calculate cumulative returns.




     -t                            0                       +t
                   Cumulative abnormal returns over time
                                                                10-43

Albert Lee Chun            Portfolio Management                         43
                  Cumulative Abnormal Returns




Albert Lee Chun          Portfolio Management   44
                  Are the Markets Efficient?
 Magnitude Issue
  How efficient are the markets? Stock prices are very
  close to efficient values, and only managers of very
  large portfolios can profit from mis-pricings.

 Selection Bias Issue
 Would you publish your successful money making
   strategy? No. Only those who fail will publish their
   results to the world. Pre-selection in favor of failed
   strategies.


Albert Lee Chun         Portfolio Management                45
                   The Lucky Event Issue
    Every take out a coin.
    Flip the coin 10 times.
    Heads you win, tails you lose!
    Count the number of heads.

    Who is our big winner?

    Now let‟s repeat the exercise.

    Are successful winners able to repeat! Most likely not! Is it
     skill or merely luck? It is purely luck.


Albert Lee Chun           Portfolio Management                       46
                         Weak Form Tests
 •    Serial Correlation
     Positive or negative serial correlation is evidence that stock
      returns are related to past returns. Evidence: Over very short
      time horizons evidence of weak price trends. Not enough to
      suggest the existence of trading opportunities.

 •    Momentum Effect
     Good or bad performance continues over time for the best and
      worst recent performers. Evidence: Over 3-12 month holding
      periods, there is some evidence of positive momentum

 • Returns over Long Horizons (over multiyear periods)
 Evidence: pronounced negative correlation, evidence on
   reversals. Reversal Effect: Winners become losers and losers
   become winners.
Albert Lee Chun            Portfolio Management                        47
                  Semi-Strong Form Tests
 Fundamental analysis calls on a much stronger range of
    information than does technical analysis
 Tests of fundamental analysis are more difficult to
    evaluate.
 We will review a number of anomalies – evidence that
    seems inconsistent with the efficient market
    hypothesis.
 - Small firm in January Effect
 - Book to Market Ratios
 - Post Earnings Price Drift

Albert Lee Chun       Portfolio Management                48
                  Small Firm (January) Effect




Albert Lee Chun         Portfolio Management    49
                  Book-to-Market Effect




Albert Lee Chun      Portfolio Management   50
            Post-Earnings-Announcement Drift




Albert Lee Chun      Portfolio Management      51
                  Mutual Fund Alphas




Albert Lee Chun     Portfolio Management   52
                  Mutual Fund Performance




Albert Lee Chun        Portfolio Management   53

								
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