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Market Efficiency - Download as PowerPoint

VIEWS: 31 PAGES: 88

									Market (In)Efficiency



       Introduction to Quantitative
          Portfolio Management
            Professor Matthew Rothman




               NBA 516 - Introduction to Quantitative
                     Portfolio Management               1
Bill Miller at Legg Mason
 What is your belief about why Bill Miller has been “the market” in each of the
 past 15 years? Is this a “violation” of efficient markets?




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Definition of Market Efficiency

      Definition:
       A market is efficient if all available information is used in pricing
       securities (“informational efficiency”).

      Types of available information:
           Weak form efficiency - Historical prices
           Semi-strong form efficiency – Publicly available information
           Strong form efficiency - All available information (including private
            information)




                               NBA 516 - Introduction to Quantitative
                                     Portfolio Management                           3
The Efficient Market Hypothesis (EMH)
and the “joint hypothesis problem”
      The hypothesis that markets are efficient is called the efficient
       market hypothesis (EMH).


      All statements about market efficiency are conditioned on an asset
       pricing model used to test efficiency. That is, any test of efficiency
       is a joint test of efficiency and the asset-pricing model.

      Given a particular pricing model, you might find evidence against
       market efficiency. Another explanation, however, is that the market
       is efficient and you are using the wrong pricing model. This is a
       common dilemma in testing joint hypotheses.




                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                          4
The Efficient Market Hypothesis (EMH)
and the “joint hypothesis problem”
     For example, let‟s say you find that a particular trading strategy allows
      you to make profits above and beyond that predicted by the CAPM.


     Two possibilities:
        One: The market is inefficient but the CAPM is the right pricing
         model for all securities.

          Two: The market is efficient but the CAPM does not describe the
           right pricing model for all securities




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                                   Portfolio Management                           5
The Joint-Hypothesis Problem

             “It is a disappointing fact that,
              because of the joint-hypothesis
              problem, precise inferences
              about the degree of market
              efficiency are likely to remain
              impossible … Rationality is
              not established by the existing
              tests … and the joint-
              hypothesis problem likely
              means that it cannot be
              established.”
Market Efficiency & “Making Money”

     There have been (and still are) many misconceptions about EMH
        “Market efficiency implies that you cannot make any money.”

        “Market efficiency implies that stock prices are random walks.”

        “If stock prices are random walks, then markets are efficient.”

        “Market efficiency implies that stock prices are not predictable.”

        All these statements are wrong!




                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                        7
“You cannot “make money” if markets
are efficient.”
      Not True! Counter Example:
         The CAPM is a model of an efficient market

         In the CAPM, investors expect to make money by holding risky
          assets
         The expected return on a risky asset is determined by the risk-
          free return, the beta of the asset, and the risk premium of the
          market portfolio. Remember: E(ri) = rf + i [ E(rm) - rf ].




                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                      8
Correct Definition of A Random Walk

     Definition:
        A series is a random walk if future changes are i.i.d. (that is,
         independently and identically distributed) and are unpredictable.

     Illustration:
          Pt is the price of a stock at time t.
          If Pt is a random walk then [Pt+1 - Pt] is unpredictable.
          If Pt is a random walk then [Pt+1 - Pt] / Pt is unpredictable.

     Implications:
        The future value of the price can be arbitrarily large
        Returns are not serially correlated.




                              NBA 516 - Introduction to Quantitative
                                    Portfolio Management                     9
Common Misconception of Random
Walks
     Many practitioners use the term „random walk‟ to mean the lack of
      serial correlation in returns.

     This is not the correct usage of the term
        Random walks imply the lack of serial correlation

        But the lack of serial correlation does not imply random walks, if
         returns are not normally distributed.




                           NBA 516 - Introduction to Quantitative
                                 Portfolio Management                         10
Are Stock Prices Random Walks?

     Empirically:
        Stock returns have little serial correlation
           This is an implication of random walks
           This was found in the early literature on market efficiency
             (Fama (1965))
           This evidence was used to “prove” that markets are efficient


          Stock returns are not normally distributed
             Lack of serial correlation does not imply random walk


          Stock returns have predictable volatility changes
             The recent finance literature has found ARCH, GARCH
               models fit the data (Engle‟s Nobel Prize in 2003).
             This means that stock prices are NOT random walks.



                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                     11
Do Random Walks Imply Efficiency?

      The following statement is true:
         Even if stock prices follow random walks, that says nothing
          about market efficiency

           For example, expected returns could be time-varying.




                    So how do you test for efficiency?!?




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Tests of Weak form Market Efficiency

     Technical analysis refers to methods for detecting recurrent patterns in prices.
        Using only price histories - chartists, moving average, oscillators, Elliot Wave
          Theory.
        Sentiment indicators: TRIN, Sentiment Surveys.
        Academics believe that EMH implies technical analysis has no merit.
        Some practioners believe technical analysis gives the term “analysis” a bad name.


     Empirical evidence
        The weak form of market efficiency is sometimes rejected, but the magnitudes of
         the inefficiencies are very small relative to transactions costs. A variety of filter
         rules, price-volume rules, moving average rules and other technical analysis
         strategies generally fail to find exploitable inefficiencies in the US stock market.
         (See Fama and Blume (1966), Brock, Lakonishok and LeBaron (1992)). However,
         there is some evidence of technical strategies working in foreign exchange markets,
         suggesting foreign exchange markets are weakly inefficient (See Arnott and Pham
         (1993), Chang (1996).)

          Short term momentum and long-term reversal results are still debated. For
           example, Short-term seasonalities like time-of-day, holiday and day-of-week
           effects, January effect, and momentum. We discuss these later.

                                  NBA 516 - Introduction to Quantitative
                                        Portfolio Management                                     13
Tests of Semi-Strong form Market Efficiency

   Most Common Test is the Event Study

   • Examine market reaction (abnormal reaction) when new news are
     announced.
   • We need to define “Normal” versus “abnormal” returns.
   • Collect different events where similar news is introduced to eliminate
     idiosyncratic influences.
   • Place returns in “event time”.




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                                 Portfolio Management                         14
Event Study Methodology
  1.   Define the event you want to study! Have a research question and a
       hypothesis. Define
           Examples include: share splits; dividend initiations and eliminations;
            expirations of IPO lockups; share repurchases; company name
            changes; M&A activity; earnings announcements; etc.
           Clearly define what the announcement date is.
                  Need to understand first public announcement
                  Need a database of historical news reports
           Select an event window say T days
  2.   Estimate what is the expected return of the stock during the announcement
       period. Want to understand ABNORMAL returns.
             Market Model approach:
                   a. Rt = at + btRmt + et
                   b. Excess Return = (Actual - Expected)
                      et = Actual - (at + btRmt)
                             NBA 516 - Introduction to Quantitative
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Event Study Methodology

  3. Calculate the abnormal returns and statistical significance
         AR = Actual Returns – Expected Returns
             = Abnormal returns (average excess returns for each date)

        Line up the returns in event time (surrounding announcement dates) across
        firms. Announcement date is event day 0

        Calculate average abnormal return for that date in the announcement
        window.
        •     This your mean return for that date.
        •     Standard error is the standard error of the announcement return.
        •     Then see if statistically significant.

        Also people look at CARs: Cumulative Abnormal returns (start at first date
        of announcement window and add up abnormal returns throughout event
        study)
                             NBA 516 - Introduction to Quantitative
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NBA 516 - Introduction to   17
 Quantitative Portfolio
Event Study Methodology Example:
IPO Lockup expirations
      The company and the underwriter negotiate the terms of the lockup.
         Example: Healtheon

         registered 5,658,184 shares.

         Insiders (pre-IPO investors such as management and VCs) restricted
          for 180 days. After this period float gradually increases to
          52,254,368 shares.

      Underwriters can release earlier.
      Company rules not to sell around earnings announcements.
      Company may conduct an SEO.




                            NBA 516 - Introduction to Quantitative
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Event Study Methodology Example:
IPO Lockup expiration
  Brav and Gompers (2003, Review of Financial Studies)

     Collect a sample of 2,794 IPO firms conducted over the period 1988 to
      1996
          What is the event day?
          What is the period over which we shall determine what “normal” expected
           return is for every firm in our sample?




                               NBA 516 - Introduction to Quantitative
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Histogram of Lock-Up Days

    1400
    1200

    1000
    800

    600
    400

    200
       0
           45   91   150    183        225       360       395      450   548   730

                           NBA 516 - Introduction to Quantitative
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Event Study Methodology Example:
IPO Lockup expiration
     Suppose that we were to estimate the market model with daily data for
      every IPO firm over the period t-110 through t-10, where t denotes the
      day in which the lock up expires.
     End up with 2,794 estimates of at and bt
     What do these estimates look like?




                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                         21
                       Intercept (at), in %      Slopes (bt)
     Average                  0.08                  0.74
     Median                   0.08                  0.68
Standard Deviation            0.48                  0.98




                     NBA 516 - Introduction to                 22
                      Quantitative Portfolio
Resulting Abnormal Returns (averaged across firms)




                  NBA 516 - Introduction to      23
                   Quantitative Portfolio
Cumulative Abnormal Returns




       NBA 516 - Introduction to   24
        Quantitative Portfolio
Buy and Hold Abnormal Returns




        NBA 516 - Introduction to   25
         Quantitative Portfolio
Event Studies (Continued)

     The manner with which abnormal returns are calculated can make a big
      difference. For example, the choice of the CAPM or the Fama French 3 factor
      model. But it has been argued that in practice for short-run event studies, how
      you control for risk does not matter. Why?
          Because for a short run event study, the amount of systematic risk on a day or two
           is tiny relative to the size of the event. For example, if the market risk premium is
           8% per year and there are 250 trading days then the daily premium is .00032, or a
           little more than 3/100 of a percent a day (3 basis points)

     Hence, the joint hypothesis problem is really not an issue and the favorable
      evidence form short-run event studies has been hailed as supportive of market
      efficiency.
          “Evidence tilts … toward the conclusion that prices adjust efficiently firm specific
           infortmation.”
          Do you agree? What does Thaler say?
     For long-run event studies, however, the choice of the asset pricing model is
      crucial.


                                  NBA 516 - Introduction to Quantitative
                                        Portfolio Management                                       26
The Adjustment Of Stock Prices To New
Information, Fama, Fisher, Jensen, Roll (1969)




                 NBA 516 - Introduction to Quantitative
                       Portfolio Management               27
Tests of Strong Form Efficiency

     Strong form strategies assume you have information that the market
      does not have.

     Existence of Insider trading tell us that private information is valuable.
        Jaffee (1974): insiders can profit but so can outsiders from
         watching insiders
        Seyhun (1986): insiders can profit but not outsiders

        Difference is due to use of CAPM. Most of it occurs in small firms
         where we know the CAPM is not a good model.

     In general when an insider buy‟s her own stock this is a signal of good
      future performance. Sales is really complicated though!


                             NBA 516 - Introduction to Quantitative
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Tests of Strong Form Efficiency

     Do Investment Professionals Have Private Information? Can Mutual
      Fund managers “Beat The Market”?
        Most evidence supports the view that net of expenses, they cannot.

            Critical though what your pricing model is: CAPM vs FF 3
             factor vs 4 factor.
        Greatest predictor of future performance is fees. Low fee
         funds outperform; high fee funds underperform!
        Performance is not repeatable but can be highly profitable: fund
         flows. In other words, investors think it is repeatable.
        Surprisingly, fees are quite sticky. Bad performing funds do not
         lower fees and high performing funds do not raise them. Indeed,
         funds close – failure of the “price” system.


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Caveats

     Tests of market efficiency has to consider:

          The Magnitude Issue: Statistical power. It is simply hard to detect small
           and economically important deviations from market efficiency

          The Selection Bias Issue: If someone discovered a great money making
           scheme, they would not publicize it. We are not likely to find out about
           schemes that work. If I really thought I had discovered a money
           machine, do you think I‟d publish it or start a hedge fund myself?

          The Lucky Find Issue: If you flip a fair coin 50 times, you expect to see
           50% heads. If 10,000 people each flip a fair coin 50 times we expect to
           get at least two of them getting 75% heads. Now, suppose any bet can
           beat the market 50% of the time. Similarly, suppose 10,000 traders each
           make 50 bets. We expect to get at least two traders beat the market in
           75% of their bets!



                                NBA 516 - Introduction to Quantitative
                                      Portfolio Management                             30
Bill Miller at Legg Mason

     What is your belief about why Bill Miller has been “the
      market” in each of the past 15 years?

         Risk return adjustment: Is it enough for him to have simply
          “outperformed” the S&P?

         Could it be luck?




                              NBA 516 - Introduction to Quantitative
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Bill Miller at Legg Mason: Risk
      Risk return adjustment: Is it enough for him to have simply “outperformed” the
       S&P? What‟s the Beta for his fund? Is loading up on high beta stocks skill?
      We know CAPM doesn‟t fully explain returns. What is abnormal return relative
       to the 3 or 4 factor model?




                            NBA 516 - Introduction to Quantitative
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Bill Miller at Legg Mason: Risk
     Characteristics of His Major Holdings

  Ticker   Stock                   Weighting        Beta     Price/Book           Trailing P/E   Market Cap ($ Mil)
  S        Sprint Nextel            6.4%            1.38        2.13                 28.9                  69,997
  UNH      United Health Care       5.7%            2.55        4.38                 22.7                  73,137
  AMZN     Amazon                   5.6%            1.50        62.28                42.9                  15,575
  TYC      Tyco                     5.3%            2.13         N/A                 15.8                  51,953
  GOOG     Google                   4.4%            2.00        11.1                 68.3                 105,237
  AES      The AES Corporation      4.2%            2.76        7.88                 20.4                  11,327
  JPM      JP Morgan Chase          3.8%            1.68        1.35                 17.2                 143,443
  EBAY     eBay                     3.4%            1.85        5.36                 48.5                  54,500
  AET      Aetna                    3.3%            0.31        3.13                 18.4                  29,173
  Q        Qwest                    3.2%            3.14         N/A                  N/A                  11,795
  MCK      McKesson                 2.9%            0.87        2.79                 20.8                   8,057
  EK       Eastman Kodak            2.8%            1.15         4.1                  N/A                   8,057
  HNT      Healthnet                2.7%            0.52        3.49                 24.4                   5,501
  CFC      Countrywide Financial    2.5%            1.71        1.63                   8.4                 20,689
  IACI     IAC                      2.5%            1.47        1.07                 12.1                   9,571
  C        Citigroup                2.5%            1.28        2.09                 10.0                 231,447
  YHOO     Yahoo!                   2.5%            2.77        5.01                 23.7                  45,131
  EXPE     Expedia                  2.3%            0.55        1.12                 28.4                    6,370
  ERTS     Electronic Arts (EA)     2.1%            1.32        4.66                 62.3                  15,747

           Miller Portfolio                                     4.08                  28.6
           S&P 500                                              2.82                 17.44
           Large Cap Growth                                     4.12                 20.89

           Number of Funds                     19   68.0%
           Number of Funds                     12   51.0%


                                         NBA 516 - Introduction to Quantitative
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Bill Miller at Legg Mason: Risk
  Stated Investment Objective
    Portfolio Mix
    • The fund, with 41 holdings, is invested primarily in large-capitalization stocks (93.72%)
    • 5.85% of the fund’s assets are invested in mid-capitalization stocks
    • 61.77% of the fund’s net assets are invested in the Consumer Discretionary, Healthcare and
    Financials sectors
    • The fund’s largest overweight positions relative to the S&P 500 are in the Telecommunication
    Services and Consumer Discretionary sectors
    • The fund’s largest underweight positions are in the Financials, Industrials and Consumer
    Staples sectors with no exposure to the Materials or Energy sectors

    Investment Philosophy
    We seek to generate excess returns by owning securities that have been priced by the market at
    significant discounts to their intrinsic value by our multi-factor valuation analysis. Our analytical
    approach is not based on traditional, accounting-based valuation measures. We focused on cash earnings
    – namely, the present value of future cash flows of a company. Shareholder value is the result of cash, not
    accounting, earnings. In this way, we believe we differ from most value managers. Traditional valuation
    measures miss many mispriced stocks because those measures do not focus on the value of a business.

    Primary Risks of this Fund
    •            Market Risk - The risk that prices of securities will go down because of the
    interplay of market forces, may affect a single issuer, industry or sector of the economy or may
    affect the market as a whole.
    •            Value-Style Risk - The value approach to investing involves the risk that those
    stocks deemed to be undervalued by the portfolio

                                      NBA 516 - Introduction to Quantitative
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Bill Miller at Legg Mason: Luck?
  • There were approximately 8,044 mutual funds being run at the
  end of 2004. Of these, 4,600 are U.S. equity mutual funds.

  • There are approximately 6,500 “dead” U.S. equity mutual funds.
  So in total, some 11,100 mutual funds have ever existed.

  • There is a 50% chance of “beating market” as most people define
  it each year.

  • Given that, we have had 11,100 mutual funds exist, and have had
  40 of funds existing, what number should we expect to have beaten
  the market for 15 years in row, by pure chance? 5

  •There should be more Bill Miller’s out there! Why aren’t there?



                         NBA 516 - Introduction to Quantitative
                               Portfolio Management                   35
The impossibility of informationally efficient
markets: Grossman and Stiglitz (1980)

      Go through the following logical steps:
           If markets are perfectly informationally efficient,
           Then, informed investors cannot profit by analyzing securities‟
            fundamentals
           If it is costly to analyze then informed investors will stop analyzing
            because they lose money on average
           But, if they stop analyzing information there will be no guarantee that
            publicly available information is incorporated into prices. Thus, the market
            won‟t be informationally efficient
           Hence, need some expected profit to attract informed investors. These are
            normal returns to their investments. An efficient amount of inefficiency in
            the market!




                                 NBA 516 - Introduction to Quantitative
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The impossibility of informationally efficient
markets (continued)

      Is the GS argument consistent with passive investment strategies such
       as indexing?
      Should we all buy and hold the S&P500? How many investors indexing
       is too many?
      Why do people buy stocks anyway? devices?




                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                         37
Where Do Anomalies Come From?

     Why might market inefficiencies exist and persist?
          Human beings are not rational information processors. They systematically
           make errors in judgment, use heuristics to help them in decision make
           processing, and are subject to the follies of greed and fear.
               Work of Kahneman and Tversky
               Vernon Smith and others


          Institutional / Structural Reasons:
               Short sales constraints
               Erisa / Prudent Man Laws


          Limits of Learning / Limits of Arbitrage

          Data Mining: they don‟t exist, rather you have found quirks in the data

                                 NBA 516 - Introduction to Quantitative
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Market Anomalies (Selected…)
   1.    The January effect and the Small Firm Effect.
   2.    Predictability in Asset Returns.
   3.    Predictability in Asset Volatility.
   4.    Very short horizon (1 month) Price Reversal.
   5.    Post earnings announcement drift (PEAD).
   6.    Short horizon (3 to 12 month) price momentum.
   7.    Long horizon (3-5 year) price reversal and B/M effect.
   8.    Long term performance subsequent to a variety of corporate events
         (e.g., IPO, SEOs, Repurchases, dividend initiations and omissions).
   9.    Brokerage Analysts' Earnings Estimates.
   10.   Accounting Accruals
   11.   Institutional Ownership
   12.   Abnormal Trading Volume
   13.   Measures of Normalized Earnings
                           NBA 516 - Introduction to Quantitative
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The Small Firm Effect

      Banz (1981) found that small firms tend to outperform large firms in
       total and risk-adjusted basis
         Divide all NYSE stocks into 5 quintiles according to firm size

         The average annual return of the firms in the smallest-size quintile
           was 4.3% higher than the average return of the firms in the
           largest-size quintile
      This is called the Small Firm Effect.




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                                   Portfolio Management                          40
Average Annual Returns By Period

   30%

   25%
   20%
   15%

   10%
   5%

   0%

   -5%
  -10%                                          Large Cap             Small Cap
  -15%
         1926-30




                   1931-40




                             1941-50




                                           1951-60




                                                            1961-70




                                                                              1971-80




                                                                                        1981-90




                                                                                                  1991-98
                               NBA 516 - Introduction to Quantitative
                                     Portfolio Management                                                   41
The Small-Firm January Effect

      Keim (1983), Reinganum (1983), Blume and Stambaugh (1983)
       found that the small firm effect primarily occurs in January.
      Potential explanations:
          Tax loss selling in December
          Small firms are neglected by large institutional traders
          Small firms have lower liquidity.




                               NBA 516 - Introduction to Quantitative
                                     Portfolio Management               42
Average Stock Return By Month: 1926-82

   8%


   6%                                      Large Cap    Small Cap



   4%


   2%


   0%


   -2%
         Jan   Feb   Mar   Apr       May      Jun       Jul     Aug       Sep   Oct   Nov   Dec




                                 NBA 516 - Introduction to Quantitative
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Average Stock Return By Month: 1983-98

   6%


   4%                                      Large Cap      Small Cap



   2%


   0%


  -2%


  -4%
        Jan   Feb   Mar   Apr       May       Jun       Jul      Aug     Sep   Oct   Nov   Dec



                                NBA 516 - Introduction to Quantitative
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Predictability in Asset Returns

      Variables that help to predict stock returns:
         dividend yield
         spread between long-term and short-term government bonds
         spread between Moody‟s Baa and Aaa corporate bonds
         spread between treasury bill rates and inflation rate


      The R² is low, typically less than 10%

      Explanations:
         market inefficiency
         time varying risk premium, e.g. Ferson and Harvey (1991)
         data mining




                             NBA 516 - Introduction to Quantitative
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Stock Return Regression: 1965-91

              Dependent Variable: S&P-Tbill

       Explanatory Variable                      Coeff        T-stat
       Constant                                -0.0165       -1.4131
       Dividend Yield (Lag 1)                   0.0010        0.3013
       Moody's Baa-Aaa (Lag 1)                  0.0124        1.7044
       Treasury 10y-3m (Lag 1)                  0.0088        1.7139
       Tbill-CPI (Lag 1)                        1.1086        1.2388

       R2                                       0.0430


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Predicting Stock Returns: 1970-99

      Strategy 1: Tactical Asset Allocation
         If the S&P-T-bill is predicted to be positive, hold the S&P

         Otherwise hold T-bill.



      Strategy 2: Buy and hold S&P.

      We simulate the returns of these two strategies starting with $100 in
       December 1969. Here are the average annual return for 1970-99:

                             Period        Strategy 1 Strategy 2
                            1970-79          13.5%       7.0%
                            1980-89          18.4%      17.6%
                            1990-99           8.8%      17.7%

                             NBA 516 - Introduction to Quantitative
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Predictability in Asset Volatility

      At daily and weekly intervals, stock return volatility is predictable:
         there is volatility clustering

         high volatility days tend to be followed by high volatility days

         low volatility days tend to be followed by low volatility days

         volatility reverts back to a normal level



      Models of volatility:
         Engle‟s (Econometrica, 1982) ARCH model

         Bollerslev‟s (J. of Econometrics, 1986) GARCH model

         Hsieh (J. of Finance, 1991)

         Bollerslev, Chou, and Kroner (J. of Econometrics, 1992)




                              NBA 516 - Introduction to Quantitative
                                    Portfolio Management                        48
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                                            n   -5
                                                   8
                                         Ja
                                            n   -6
                                                   1
                                         Ja
                                            n   -6
                                                   4
                                         Ja
                                            n   -6
                                                   7
                                         Ja
                                            n   -7
                                                   0
                                         Ja




      Portfolio Management
                                            n   -7
                                                   3
                                         Ja
                                            n   -7
                                                   6




NBA 516 - Introduction to Quantitative
                                         Ja
                                            n   -7
                                                   9
                                         Ja
                                            n   -8
                                                   2
                                         Ja
                                                                                                 S&P500 Daily Returns: 1928-99




                                            n   -8
                                                   5
                                         Ja
                                            n   -8
                                                   8
                                         Ja
                                            n   -9
                                                   1
                                         Ja
                                            n   -9
                                                   4
                                         Ja
                                            n   -9
                                                   7
49
S&P500 Rolling 20-day Historical Volatility

     120%



     100%



     80%



     60%



     40%



     20%



       0%
                8             3             8             3             8             3             8             3             8             3             8             3             8             3             8
         n   -2        n   -3        n   -3        n   -4        n   -4        n   -5        n   -5        n   -6        n   -6        n   -7        n   -7        n   -8        n   -8        n   -9        n   -9
      Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja            Ja




                                                                            NBA 516 - Introduction to Quantitative
                                                                                  Portfolio Management                                                                                                                  50
S&P Monthly Returns: 1928-99

     50%

     40%

     30%

     20%

     10%

        0%

    -10%

    -20%

    -30%

    -40%
           7



                      2



                                 7



                                            2



                                                       7



                                                                  2



                                                                             7



                                                                                        2



                                                                                                   7



                                                                                                              2



                                                                                                                         7



                                                                                                                                    2



                                                                                                                                               7



                                                                                                                                                          2



                                                                                                                                                                     7
        -2



                   -3



                              -3



                                         -4



                                                    -4



                                                               -5



                                                                          -5



                                                                                     -6



                                                                                                -6



                                                                                                           -7



                                                                                                                      -7



                                                                                                                                 -8



                                                                                                                                            -8



                                                                                                                                                       -9



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     ec



               ec



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    D



               D



                          D



                                     D



                                                D



                                                           D



                                                                      D



                                                                                 D



                                                                                            D



                                                                                                       D



                                                                                                                  D



                                                                                                                             D



                                                                                                                                        D



                                                                                                                                                   D



                                                                                                                                                              D
                                                           NBA 516 - Introduction to Quantitative
                                                                 Portfolio Management                                                                                    51
Monthly Standard Deviation of U.S. Stocks




               NBA 516 - Introduction to Quantitative
                     Portfolio Management               52
Predicting Asset Volatility

      Very strong evidence of volatility clustering in daily returns
      Much weaker evidence of volatility clustering in monthly returns
      Exchange rates, commodity prices, and bond prices also exhibit this
       type of behavior

      Uses:
         Short term risk management (Value-at-risk)




                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                       53
Very Short Horizon Reversals

     Jegadeesh (J. of Finance, 1990) has found that:

      At the beginning of each month from 1934 to 1987, divide all stocks into 10
      deciles based on their previous month‟s return
        Decile 1 has the worst performing stocks
        Decile 10 has the highest performing stocks.


      Now look at the return for the current month
        Decile 1 has the best performance!
        Decile 10 has the worst performance!


     Likely due to microstructure effects (bid-ask bounce) and probably hard to
      trade on.




                               NBA 516 - Introduction to Quantitative
                                     Portfolio Management                           54
Monthly Return of Decile Portfolios Ranked
On Previous Month’s Performance: 1934-87
                     1.50%


                     1.00%


                     0.50%
   Monthly Returns




                     0.00%


                 -0.50%


                 -1.00%


                 -1.50%
                             1   2   3           4         5             6        7   8   9   10
                                                               Deciles




                                         NBA 516 - Introduction to Quantitative
                                               Portfolio Management                                55
Post-Earnings-Announcement Drift
(PEAD)
     Ball and Brown (1968), Foster, Olsen, Shevlin (1984), Bernard and
      Thomas (1990)
        stocks with large positive (negative) earnings surprises have a
          positive (negative) price jump on the announcement day and
          continue to increase (decrease) in price for 13 weeks.




                           NBA 516 - Introduction to Quantitative
                                 Portfolio Management                      56
PEAD Standard Methodology

     Bernard and Thomas (1990)
        1974-1986 period

        Firms are assigned to one of 10 portfolios based on standardized
         unexpected earnings (SUE)
     SUE Calculation
        We need a proxy for expected earnings

        Regress current earnings on earnings four quarters ago with a drift
         term. A seasonal random walk model
                                EPSt = a + b EPSt-1 + et
          We can write down more elaborate time-series models
          Conduct the regression firm by firm.




                            NBA 516 - Introduction to Quantitative
                                  Portfolio Management                         57
PEAD Standard Methodology

     SUE Calculation
        Expected earnings are therefore:
                              E(EPSt) = a + b EPSt-1
        Then, the surprise is the realized EPS (before extraordinary items
         and discontinued operations) less E(EPSt).
        The last step is to scale by the estimation standard deviation of the
         forecast errors to get SUE:
         SUE = (EPS-EEPS)/(s.d.(error))
        Why is it necessary to scale by s.d.(error)?
     SUE Grouping
        Take SUE for each firm and group into deciles.
        Abnormal returns are cumulated beginning the day after the
         earnings announcement to get the post-earnings announcement
         drift.


                             NBA 516 - Introduction to Quantitative
                                   Portfolio Management                          58
PEAD Standard Methodology




   Source: Bernard and Thomas (1989)

                                       NBA 516 - Introduction to Quantitative
                                             Portfolio Management               59
PEAD Standard Methodology




   Source: Bernard and Thomas (1990)

                                       NBA 516 - Introduction to Quantitative
                                             Portfolio Management               60
PEAD: Results

     SUE(10) – SUE(1) earns an abnormal return of 8.6 percent.

     About a half of average abnormal return is concentrated in the first 60
      days following the announcement.

     In the previous graph Bernard and Thomas sort firms by size into
      large (top 30% NYSE/AMEX), medium (middle 40%) and small
      (bottom 30%)
        For small and medium-sized firms, the effect is even greater: 10%
        The cumulative returns are about 2/3 as large as the cumulative
          returns during the quarter up to and including the earnings
          announcement.




                             NBA 516 - Introduction to Quantitative
                                   Portfolio Management                         61
PEAD: Results

     About 25% of the effect is concentrated during the next four earnings
      announcement periods.

     Stocks held by institutions tend to have less of a drift (controlling for size).

     Since earnings surprises tend to include both permanent and temporary
      components, a portion of the initial earnings surprise (about 40%) persists as
      earnings surprise a quarter later, with progressively smaller amounts later on.

     The anomaly has been remarkably stable over time and it is not explained, for
      example, buy either the size or book/market factors (Fama and French (1993)).

     But now it looks like SUE / PEAD has declined in the 1990s if not dead!




                                 NBA 516 - Introduction to Quantitative
                                       Portfolio Management                              62
Brokerage Analysts' Recommendations

     Does the market            incorporate           the       information   in   analysts‟
      recommendations?

         Womack (1996). Extreme recommendation changes
              For Buy (Sell) recommendations event-day abnormal returns are 3% (-4.7%)
              Post recommendation drift for Buys is significant but short-lived with size-
               adjusted return of +2.4% over the first post-event month. For Sells, the post-
               event drift lasts for 6 months and equals -9.1%

         Barber, Lehavy, McNichols, and Trueman (1999, 2003). Implement
          various trading strategies focusing on changes in consensus
          recommendations.




                                NBA 516 - Introduction to Quantitative
                                      Portfolio Management                                      63
Do Analysts’ Recommendations Have
Investment Value? Womack (1996)




             NBA 516 - Introduction to Quantitative
                   Portfolio Management               64
Womack (continued)




             NBA 516 - Introduction to Quantitative
                   Portfolio Management               65
Can Investors Profit from the Prophets? Security Analysts
Recommendations and Stock Returns,
Barber, Lehavy, McNichols, and Trueman (1999, 2003)




                       NBA 516 - Introduction to Quantitative
                             Portfolio Management               66
Barber, Lehavy, McNichols, and Trueman
(1999, 2003)




                NBA 516 - Introduction to Quantitative
                      Portfolio Management               67
Bernstein: Earnings Surprise Alphas




             NBA 516 - Introduction to Quantitative
                   Portfolio Management               68
Analyst Earnings Revisions




             NBA 516 - Introduction to Quantitative
                   Portfolio Management               69
Monthly Return of Decile Portfolios Ranked
On Previous Month’s Performance: By Cap




                NBA 516 - Introduction to Quantitative
                      Portfolio Management               70
Short Horizon Price Momentum

     Jegadeesh and Titman (J. of Finance, 1993) have found that:
      Over a 3- to 12-month horizon, stock returns have “momentum”:
        Good recent performance tends to persist
        Bad recent performance tends to persist


     Each quarter from 1965 to 1989, rank stocks in deciles based on the previous
      L (=3,6,9,12) months‟ performance
        Go long the highest decile and hold for H (=3,6,9,12) months
        Go short the lowest decile and hold for H months


     These long/short portfolios generate abnormal returns! (mainly on the short
      (losers) portfolio).




                              NBA 516 - Introduction to Quantitative
                                    Portfolio Management                             71
Jegadeesh & Titman (1993) Average
Monthly Returns from Buys-Sells




              NBA 516 - Introduction to Quantitative
                    Portfolio Management               72
Jegadeesh & Titman (continued)




              NBA 516 - Introduction to Quantitative
                    Portfolio Management               73
Country Momentum Strategies




             NBA 516 - Introduction to Quantitative
                   Portfolio Management               74
Fama & French, Long Horizon Autocorrelations
       Table 1. Summary of Multiperiod Autocorrelations (1926-1985): Return Horizons (years 1-6, 8, 10)
   Portfolio       Year 1     Year 2      Year 3      Year 4    Year 5      Year 6     Year 8     Year 10
   Food             -0.01       -0.24      -0.34       -0.36      -0.34      -0.15        0.01        0.08
   Apparel          -0.08       -0.18      -0.20       -0.27      -0.30      -0.21       -0.21       -0.27
   Drugs            -0.02       -0.14      -0.18       -0.12      -0.13      -0.06       -0.09       -0.22
   Retail           -0.01       -0.17      -0.30       -0.32      -0.33      -0.18       -0.10       -0.02
   Durables          0.02       -0.14      -0.26       -0.33      -0.30      -0.09        0.02        0.13
   Autos            -0.05       -0.22      -0.36       -0.42      -0.35      -0.13       -0.04       -0.02
   Construction     -0.01       -0.13      -0.27       -0.41      -0.42      -0.21        0.16        0.24
   Finance          -0.01       -0.17      -0.26       -0.25      -0.15       0.07        0.22        0.35
   Misc             -0.02       -0.13      -0.25       -0.35      -0.37      -0.18        0.00        0.12
   Utilities        -0.05       -0.16      -0.27       -0.22      -0.02       0.24        0.14        0.10
   Transportation -0.10         -0.20      -0.26       -0.33      -0.32      -0.18       -0.09        0.02
   Bus. Equipment 0.01          -0.22      -0.39       -0.41      -0.36      -0.19        0.05        0.13
   Chemicals        -0.04       -0.33      -0.43       -0.38      -0.37      -0.19        0.01        0.12
   Metal Prod.       0.01       -0.20      -0.38       -0.49      -0.52      -0.37       -0.16       -0.05
   Metal Ind.       -0.08       -0.27      -0.36       -0.36      -0.35      -0.17        0.18        0.28
   Mining           -0.09       -0.29      -0.37       -0.44      -0.48      -0.28        0.02        0.08
   Oil              -0.02       -0.23      -0.29       -0.42      -0.40      -0.20        0.17        0.27
   Average          -0.03        -0.2       -0.3       -0.34      -0.32      -0.14        0.02        0.08



                                      NBA 516 - Introduction to Quantitative
                                            Portfolio Management                                             75
Long Horizon (3-5 year) Price Reversal
and the B/M effect.
      DeBondt and Thaler‟s (1985) evidence. Past long-term losers earn
       higher future returns than long-term winners with most of the excess
       return earned in January

      Lakonishok, Shleifer and Vishny (1994)
           We have already discussed these findings and the possible interpretations




                                NBA 516 - Introduction to Quantitative
                                      Portfolio Management                              76
Long-Term Performance of Repurchasing
Firms
      Ikenberry, Lakonishok, and Vermaelen, 1995, “Market underreaction
       to open market share Repurchases”, Journal of Financial Economics.
           Why would firms repurchase their stock?
           Signaling Hypothesis: Asymmetric information firm‟s insiders and
            investors. Repurchase announcement is a credible signal. With rational
            expectations investors should respond immediately in an unbiased
            manner.
           Underreaction Hypothesis: Less than fully rational reaction which
            subsequently leads to positive abnormal returns.
           Data: All repurchases over the period 1980-1990.
           The benchmark portfolios are i) equal-weighted index, ii) value weighted
            index, iii) size-based, and iv) size and book-to-market based benchmark.
           How should we calculate the test statistics? Cumulative abnormal returns
            or buy and hold returns?
           Key long-term results: Unconditionally, investing in repurchasing firms
            leads to positive abnormal returns. Moreover, abnormal return is
            increasing in the firms‟ book-to-market ratios.


                               NBA 516 - Introduction to Quantitative
                                     Portfolio Management                              77
Ikenberry, Lakonishok, and Vermaelen, 1995




                NBA 516 - Introduction to Quantitative
                      Portfolio Management               78
Abnormal Performance Subsequent to
Dividend Initiations and Omissions
     Price Reactions to Dividend Initiations and Omissions: Overreaction or Drift?
      By Michaely, Thaler, and Womack (1995)
          Consistent with the prior literature find that short run price reactions to omissions
           are greater than for initiations (-7.0% vs. +3.4% three day return)
          Controlling for the change in the magnitude of dividend yield (which is larger for
           omissions), the asymmetry shrinks or disappears, depending on the specification
          In the 12 months after the announcement (excluding the event calendar month),
           there is:
                a significant positive market-adjusted return for firms initiating dividends of +7.5% and
                a significant negative market-adjusted return for firms omitting dividends of -11.0%
                However, the post dividend omission drift is distinct from and more pronounced than that
                 following earnings surprises
                A trading rule employing both samples (long in initiation stocks and short in omission
                 stocks) earns positive returns in 22 out of 25 years
     Do firms that omit (initiate) dividends perform as expected given their
      characteristics?


                                      NBA 516 - Introduction to Quantitative
                                            Portfolio Management                                             79
Summing up...
     Three definitions of market efficiency:
          Markets incorporate various levels of information into security prices.
     Random walks and market efficiency.
     The impossibility of informationally efficient markets: Grossman and Stiglitz
      (1980).
     Anomalies. There are still other anomalies we did not cover…
          Turn of the Month Effect: Stocks consistently show higher returns on the last day
           and first four days of the month.
          The Monday Effect
           Monday tends to be the worst day to be invested in stocks.
          Merger related underperformance: Acquiring firms that complete stock mergers
           underperform while firms that complete cash tender offers do not. One
           interpretation is that acquirers who use their stock may use it because they believe
           it to be overvalued.




                                 NBA 516 - Introduction to Quantitative
                                       Portfolio Management                                       80
Anomalies or Data Mining?

     Are these real anomalies?
     Are these data mining?
          Data mining:
           The same data are massaged over and over again. It is not surprising to
           find something that will “predict” returns.
     Final point: Most money managers do not beat the market
          Malkiel article
               So, if managers do not beat the market, what does that say about market
                efficiency?




                                  NBA 516 - Introduction to Quantitative
                                        Portfolio Management                              81
But why it is hard to settle these issues?
1) Statistically: No “power”

   • We cannot just compare current prices to a reliable
     fundamental value model to determine the existence of a
     financial anomaly.




                        NBA 516 - Introduction to Quantitative
                              Portfolio Management               82
But why it is hard to settle these issues?
2) Research design: Returns-Based approach

      The central theme of financial economics has been to assume the
       existence of capital market equilibrium under some model
      Then test whether the average returns, covariability, and predictability
       (or lack of) of returns is consistent with that model.
           Don‟t actually try to “price” assets.
           Just look to see if price “changes” are behaving according to posited
            models.




                                 NBA 516 - Introduction to Quantitative
                                       Portfolio Management                         83
Financial Economists Reject “Fundamental
 Value”; Embrace Returns Based Research

                  “Financial economists … work
                   only with hard data and are
                   concerned with the
                   interrelationships between the
                   prices of different financial
                   assets. They ignore what seems
                   to many to be the more important
                   question of what determines the
                   overall level of asset prices. …
                   [There is] a deep distrust of
                   research purporting to explore
                   fundamental valuations.”
But Such Tests Have Very Low Power

                        “This paper argues that
                         existing evidence does not
                         establish that financial
                         markets are efficient in the
                         sense of rationally reflecting
                         fundamental values. It
                         demonstrates that the types
                         of statistical tests which
                         have been used to date have
                         essentially no power …”
               NBA 516 - Introduction to Quantitative
                     Portfolio Management               85
Lessons From Market Efficiency Tests


 Can Time Series/Cross Sectional Tests or Volatility
 Studies Establish Market Efficiency or
 Inefficiency?
                                                                      NO

 Can Long Run Event Studies Establish Market
 Efficiency or Inefficiency?                                          NO


 Can Short Run Event Studies Establish Market                 MAYBE. ALWAYS
 Efficiency or Inefficiency?                                  ABOUT REACTION
                             NBA 516 - Introduction to Quantitative
                                   Portfolio Management                    86
Market Efficiency Tests: Bottom Line

   • We cannot rely on returns-based tests to tell us
     whether prices are efficient or not.

   • Such tests may reject market efficiency when
     prices are efficient because we are using the
     wrong model of market equilibrium (consider
     FF three-factor model)

   • Such tests may fail to reject market efficiency
     because they assume a model that attributes
     returns to rational factors (consider same)
                     NBA 516 - Introduction to Quantitative
                           Portfolio Management               87
Concluding Comments

     BKM, Chapter 12:

      “We conclude that markets are very efficient, but
      that rewards to the especially diligent, intelligent,
      or creative may in fact be waiting.” (page 405)




                         NBA 516 - Introduction to Quantitative
                               Portfolio Management               88

								
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