Portfolio Management
3-228-07
Albert Lee Chun
Market Efficiency
Lecture 8
30 Oct 2007
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Brownian Motion
Albert Lee Chun
Portfolio Management
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A Little Bit of History
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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
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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...
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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...
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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
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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
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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
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There are 2 principal classes of portfolio management
strategies.
1.
2.
Passive
Active
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Why would an investor choose an active strategy over
a passive strategy, or visa versa?
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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
All information
relevant to a stock
Weak
SemiStrong
Information set
of publicly available
information
Information
set of
past prices
Strong
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Fama (1970): 3 Forms of EMH
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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...
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Weak form efficiency:
Past prices are useless!
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Semi-strong form efficiency:
Public information is useless!
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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
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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
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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
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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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Portfolio Management
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Implications of Semi-Strong Form Efficiency
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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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Portfolio Management
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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
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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
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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
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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?
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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
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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
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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
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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.
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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
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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
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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.
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Costs of Active Management: There are costs of
researching information, costs of analyzing
information, transaction costs.
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Motivation for Indexing
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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.
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Percentage of Managers that Beat the S&P 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
-t
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+t
Announcement Date
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Stock Price Reaction to CNBC Reports
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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
CNBC’s “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.
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Cumulative abnormal returns over time
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10-43
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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
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Every take out a coin.
Flip the coin 10 times.
Heads you win, tails you lose!
Count the number of heads.
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Who is our big winner?
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Now let’s repeat the exercise.
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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
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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.
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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
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