Portfolio Management 3-228-07 Albert Lee Chun

1
Portfolio Management3-228-07 Albert Lee Chun
Market Efficiency

• Lecture 8

30 Oct 2007
2
Brownian Motion
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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.

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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.

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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.

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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.

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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.

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The Life of Louis

• 11 March 1870 Louis Jean-Baptiste Alphonse
  Bachelier is born in Le Havre
• 11 January 1889 Fathers death
• 7 May 1889 Mothers death
• 18911892 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,
  Theorie de la Speculation
• 19091914 Free lecturer at Sorbonne
• 1912 Publication of Calcul des Probabilites
• 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
• 19191922 Assistant professor in Besancon
• 19221925 Assistant professor in Dijon
• 19251927 Associate professor in Rennes
• January 1926 Blackballed in Dijon
• 1 October 1927 Professor in Besancon

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Efficient Market Hypothesis
Past, present, and even discounted future events
are reflected in market price. Louis Bachelier
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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.

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The 3 EMH and Their Information Sets
Weak
Semi-Strong
Strong
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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.

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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!

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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.

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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.
• Consistent with Random Walk Theory Movements in
  stock prices from day to day do not reflect any
  pattern, they are random.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Inefficient Markets

• Reasons for Inefficient Markets
• 1. Market Segmentation
• 2. Illiquidity
• 3. High Costs of Transaction and Information

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Passive Management Strategies
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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.

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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

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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.

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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.

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Motivation for Indexing

• Empirical Motivation
• 1. Individual investors under-perform the SP
  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.

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Percentage of Managers that Beat the SP 500
Source Aswath Damodaran (http//pages.stern.nyu.
edu/adamodar/)
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Active vs. Passive Index Fund
Source Aswath Damodaran (http//pages.stern.nyu.
edu/adamodar/)
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Empirical Tests of the EMH
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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.
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Event Studies

• Examine prices and returns over time

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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.

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Stock Price Reaction to CNBC Reports
Minute by minute report of stock prices of firms
featured in CNBCs Morning or Midday Call.
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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.
• Cumulative abnormal returns over
  time

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Cumulative Abnormal Returns
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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.

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

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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.

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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

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Small Firm (January) Effect
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Book-to-Market Effect
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Post-Earnings-Announcement Drift
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Mutual Fund Alphas
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Mutual Fund Performance