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This interactive
dice roll allows you to see how the short term results of
the dice roll can look very different than the long term. The
law
of large numbers (also see here) states that the bell shape curve should eventually
take it's shape and the actual experimental data will look like
the theoretical prediction. However, random
drift from the expected values can last a long time. Click
about 50 times or more to see for yourself. This nicely designed
illustration is from the Public Schools Community Access Program
in Edmonton, Canada.
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| The distributions of stock returns in Figures
3-10 to 3-14 look strikingly similar to the roll of the dice in Figures 3-9 and 3-9a above. |
Figure
3-10

Figure
3-11

Figure
3-12

Figure
3-13

Figure
3-14

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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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