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In
the language of statistics, the distributions seen above are
the result of the Central Limit Theorem. The central limit
theorem is one of the most remarkable results of the theory
of probability. In its simplest form, the theorem states that
the sum of a large number of independent observations from
the same distribution has, under certain general conditions,
an approximate normal distribution. The approximation steadily
improves as the number of observations increases. The theorem
is considered the heart of probability theory, although a better
name would be normal convergence theorem.
Suppose an ordinary coin is tossed 100 times and the number of
heads is counted. This is equivalent to scoring one for a head
and zero for a tail and computing the total score. The total number
of heads is the sum of 100 independent, identically distributed
random variables. The central limit theorem states the distribution
of the total number of heads will be, to a very high degree of
approximation, normal. This is illustrated graphically by repeating
this experiment many times. The results of this experiment are
displayed in a diagram. The percentage computed over the number
of experiments is arranged along the vertical axis, and the total
score or the number of heads is arranged along the horizontal axis.
After a large number of repetitions, a curve appears that looks
like the normal curve.
It has been empirically observed that various natural phenomena,
such as the heights of individuals, daily returns of the S&P
500, the managers who fall in the top fifty percent of all managers,
and the students who correctly guess the outcome of a coin flip,
follow approximately a normal distribution, as seen below.
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For
more examples of randomness in the market, see below
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A suggested
explanation is that these phenomena are sums of a large
number of independent random effects, like the daily news
that moves the market, and hence are approximately normally
distributed by the central limit theorem.
Source: stattucino.com
From the
transcript of the PBS Nova Special, The
Trillion Dollar Bet, Boston University Professor of Economics,
Zvi Bodie (Bodie
research) put it this way, "In flipping a coin, if
you flip it long enough, there may be a long run of heads,
which doesn't at all imply that the person flipping it had
the ability to make it come up heads. It could just be the
luck of the toss."
Narrator:
This strange view arose from an unexpected discovery. After
the stock market crash of 1929, economists decided to find
out whether traders really could predict how prices moved by
looking at past patterns. They decided to run a series of experiments.
In one of them they simply picked stocks at random. They threw
darts at the Wall Street Journal while blindfolded. At the
end of the year, this random choice outperformed the predictions
of top traders. This was a revelation: prices must be moving
totally at random, and although patterns came and went, they
were there by chance alone and had no predictive value. The
economists arrived at a devastating conclusion: it seemed just
as plausible to attribute the success of top traders to sheer
luck rather than skill.
Zvi
Bodie: "When some individual made a fortune in the
stock market, we have a tendency to assume that that was
because he knew something, and of course the individual himself
is happy to reinforce that belief - yes, I was a genius,
or I was very clever, or I always said Microsoft was going
to make me rich. But what you don't see are the thousands,
hundreds of thousands, perhaps millions of people who are
going, I always said that ABC company was going
to make me rich, and ABC company went bust."
WHAT IS
GOING ON HERE?
The
answer was first given over 100 years ago, on March 29, 1900,
by Louis Bachelier, in his landmark study on the Theory
of Speculation. This has since been documented by hundreds
of other researchers. Investors are either too lazy, uninterested
in learning, or else they rely on some "stock market expert."
They operate like gamblers in Vegas, hoping that their skill,
which is really just luck, will lead them to market beating
returns. As shown below, studies show the average investor
only gets eighteen percent of the market returns.
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3.3.7
Stock Pickers are Style Drifters
One of the most difficult
problems in confirming stock pickers’ skill is that they are
constantly changing the criteria, ownership rules or style of their
investments. Since their style is constantly changing, it is very difficult
to track and compare them to the proper index. In fact, one study found
that 40% of mutual funds are invested outside of their stated styles.
This will alter their performance and result in different risk and
return characteristics, which is sort of like changing the number of
dice in the dice roll example.
Table
3-3
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In fact, every portfolio
that differs from the stated benchmark or style will result in a different
return. Since these portfolios that have drifted from a benchmark have
no long-term characteristics, investors have no idea what to expect
from the manager’s newly created style. In the absence of expectations,
an investor becomes a speculator, and the expected return of speculation
is zero. Style drifters are further discussed in Step 6.
3.3.8
Stock Pickers are Looking for a Needle in a Haystack

John
Bogle accurately described stock picking as looking for a needle in
a haystack. The top 10 stocks perform 20 times better in their first
three years than they do in the following three years, according to
a study by Ibbotson and Associates. Stock pickers are often surprised
when they purchase what they think have been winners, only to be grossly
disappointed in the period after purchase.
Many investors invest in blue chip companies, believing they are reliable
and true blue. See Table 3-3 for less than favorable
outcomes of 10 of these blue chip companies.
The solution is to buy the haystack rather than pick and choose certain
stocks. This will guarantee market returns at a much lower cost. The
only valid question is: Which haystack or index, and in what proportions?
3.3.9
Stock Pickers Play a Zero Sum Game
All
financial markets are zero sum games. This is a mathematical fact.
In any financial market it is mathematically impossible for the average
investor in that market to outperform the average of the market. This
is because in any market, the pre-cost returns earned by good, bad,
and average stock pickers combined together must be the same as the
total market return. The after-cost returns will be less than the total
market return. All investors as a group are mathematically obligated
to underperform the market by the amount of their costs of investing.
There are occasional active investors who outperform a given market,
even after costs and taxes. The market-beating returns they generate
must then counterbalance the inferior returns of those who underperform
the market. That is, the amount of the outperformance must be offset
to the same degree as the amount of the underperformance for reasons
none other than simple arithmetic!
3.3.10
Stock Pickers in International Markets
Many
investors agree that the U.S. financial markets are highly efficient.
But are other markets outside the United States efficient? Are there
profitable investments that can be made that might outperform their
respective index? Many investors believe that these “underdeveloped” markets
are inferior to our own, and that analysts are better at choosing stocks
in international markets that outperform the appropriate index. Evidence
shows that this is not the case.
Several studies have proven that the indexes of these smaller markets,
on average, will perform better than an active fund. If one investment
manager has an idea about an international country or company, it would
only be logical to have numerous other firms investigating the profitable
possibilities, with only one conclusion available—that none of
the firms will outperform the index average over any lengthy period of
time.
In fact, there have been studies that show higher costs associated with
international investing make it even harder for active investors to beat
their benchmarks. In a research paper by Garret Quigley and Rex Sinquefield
titled “Performance of UK Equity Unit Trusts,” the authors
concluded that UK money managers were unable to outperform markets in
any meaningful sense.
Meanwhile, a study by Cambridge Associates looked at U.S. Small-Cap manager
performance form 1995 to 2004. Specifically, the survey looked at the
persistence of U.S. small-cap manager performance across two five-year
periods: 1995 to 1999 and 2000 to 2004. Of the managers in the top quintile
of performance in the first period, 59% landed in the bottom quintile
in the following period. A full 97% ended up in the bottom two quintiles.
In addition, more than half of the managers in the second best quintile
in the 1995 to 1999 period dropped to the bottom two quintiles in 2000
to 2004. The point: there is no evidence to suggest consistency in manager
performance. A couple of managers post great performance over an extended
period of time. But, the reason is most certainly luck.
3.3.11
Stock Pickers in Small-Cap Markets
Many
people are led to believe that active managers can provide a greater
advantage and higher value to investors in the small-cap versus large-cap
market, thus resulting in a larger alpha. A large alpha infers that
the stock or mutual fund has performed better than would be expected
based on its volatility or risk, suggesting that active management
is the reason for the better than expected performance.
Richard M. Ennis and Michael D. Sebastian of Ennis Knupp + Associates,
one of the 10 largest pension consulting firms, published a paper titled
“The Small-Cap-Alpha Myth,” in September 2001. In the study,
the firm constructed a sample of 128 small-cap managers from the Mobius
Group M-Search database, a small-cap database of institutional commingled
funds and composites of separate accounts. The researchers concluded
that this so-called small-cap-alpha advantage is actually the “small-cap-alpha
myth.” At first blush, it appears that a small-cap- alpha advantage
does exist. But when looking at the 10-year period ending June 30, 2001,
their research showed that the median portfolio in their sample outperformed
the Russell 2000 Index by 4.04%. A more accurate picture formed when
they delved deeper.
When three important performance evaluation methods were considered,
the alpha diminished to virtually zero. These performance evaluation
errors include (1) neglecting to account for management fees, (2) comparing
the portfolio to an inappropriate benchmark, and (3) overlooking survivorship
bias.
Error #1: Ninety percent of the products in the sample reported performance
before fees. When fees were included in the equation, the stock picker’s
advantage dropped from 4.04% to 3.09%.
Error #2: To derive an accurate net return, appropriate benchmarks must
be used for comparison. A single index, such as the Russell 2000, cannot
be used for proper comparison if the portfolios being compared are not
exactly the same in style and make-up as that index. Ennis and Sebastian
created effective style mixes (ESMs) for the products being studied.
Based on a type of multiple regression, ESMs are a more precise way to
benchmark. Now accounting for errors #1 and #2, the adjusted alpha dropped
from 4.04% to 1.2%.
Error #3: Many databases do not include the records of stock pickers
that went out of business, which hyper-inflates the performance reports
of active managers and funds. This survivorship bias does not accurately
reflect the true performance of all managers that started at the beginning
of the period.
When considering all three performance evaluation errors, Ennis and Sebastian
concluded that the true median alpha in their sample is “likely
to be zero or negative, not 4%.” In conclusion they found “no
support for the claim that active management of small-cap portfolios
is any more fruitful than it is for large-cap portfolios.” In other
words, forget about it! Focus on the only important question of investing:
What allocation of index funds is most appropriate for you?
Stock
Picking Academic Research
Countless
studies show that individual and professional investors consistently
underperform market averages. A visit to our article
database of research studies will demonstrate the vast
amount of research in this area,
1. The
case against active management is clearly and logically
spelled out by Nobel
Laureate William Sharpe, see The
Arithmetic of Active Management.
2. Trading
Is Hazardous to Wealth: The Common Investment Performance
of Individual Investors. See this exhaustive study of
66,465 individual trading accounts, by Terrance
Odean (ssrn)
and Brad
Barber (ssrn).
It should cure the investor of any desires to trade their
own account. From 1991 to 1996, those investors that traded
the most, earned an annual return of 11.4%. In the same time
period, the market returned 17.9%. The simple conclusion: Active
investment strategies will underperform passive [indexed]
investment strategies. Overconfident investors will overestimate
the value of their private information, causing them to trade
too actively and to earn below-average returns. The average
household underperformed a risk adjusted benchmark by 3.7%
annually, before the additional cost of federal and state
taxes. The top twenty percent of active investors underperformed
by 5.5%. The results of individuals are remarkable similar
to mutual funds, which also underperform a simple market
index (Jensen 1969
and Malkiel 1995).
Mutual funds trade often and trading hurts their performance
(Carhart
1997). Carhart's conclusion: The results do not support
the existence of skilled or informed mutual fund portfolio
managers.
3. In another study, Elton, Gruber,
Hlavka and Das studied all 143 Equity Mutual Funds that
survived from 1965-1984. These funds were compared to a
set of index funds comprised of large cap, small cap, and
fixed income, that most closely matched the actual investment
choices of the funds. The result: on average these funds
underperform the index funds by a whopping 1.6% per year,
before federal and state taxes. Not a single fund generated
a positive performance that was statistically significant.
4. A far more comprehensive study of 1,892 funds that existed
in any period between 1961 and 1993, became the dissertation
of Mark
Carhart, at the University of Chicago. The result:
Carhart found that when adjusted for the common factors
in returns, an equal-weighted portfolio of the funds underperformed
the proper benchmark by 1.8% per year, before federal and
state taxes.
5. In the first
major study of bonds funds, Blake, Elton,
and Gruber examined
361 bonds funds for the period starting in 1977. They compared
the actively managed bond funds to a simple index alternative. The
result: the actively managed bond funds underperform the
proper benchmark by 0.85% per year, before federal and
state taxes.
6. Security
Analysts may be the ultimate stock pickers. Their embarrassing
results were tallied and presented in PROPHETS
AND LOSSES: REASSESSING THE RETURNS TO ANALYSTS STOCK
RECOMMENDATIONS by Barber, Lehavey,
et al.
7. Investment Clubs don't do any better. In fact, they do quite
poorly. Review this extensive
study by Barber and Odean that
explains how too many cooks can spoil the profits. (see summary
of data below)
8. In the
study below, DFA looked at 31 institutional pension plans
with $70 billion in total assets. They found that when the
returns were properly risk adjusted using the Fama French
Three-Factor model, 97% of the returns were explained by
the three risk factors, and the value added
by active management was statistically insignificant,
even before fees.
9.In
a study by Nobel Laureate William F. Sharpe, ASSET
ALLOCATION: MANAGEMENT STYLE AND PERFORMANCE
MEASUREMENT, An Asset class factor model can
help make order out of chaos, the
following conclusions were stated. The graph
is taken directly from the online
version of the article.
"Figure
18 shows the distribution of the average tracking
errors obtained from the style analyses of 636
stock, bond and balanced funds. Each value is
the average error term value obtained from a
style analysis using returns for one fund covering
the period from January 1985 through December
1989. Note that the distribution is roughly normal,
with a mean of -0.074 (-7.4
basis points per month). This is roughly
consistent with the hypothesis that the average
mutual fund cannot "beat the market" before costs,
because such funds constitute a large (and presumably
representative) part of the market. Annualized,
the mean underperformance is approximately 0.89%
per year -- an amount that, if anything, may
be slightly less than the non-transaction costs
incurred by a typical mutual fund."
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