University of California Davis Jackets and Calculators Articles Questions


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Problem Set 1
Question 1: Malkiel, Shiller, and the EMH
In the Journal of Economic Perspectives Winter 2003 issue, Burton Malkiel, the author of A Random
Walk Down Wall Street, and Robert Shiller, winner of the 2013 Nobel Prize in Economics, published
competing articles about the Efficient Markets Hypothesis (EMH).1
In his article, Malkiel defends the EMH from critics, while Shiller argues in favor of a behavioral approach
to understanding markets. Read both of these articles, which have been posted on Blackboard, then
answer the following:
A. How do Malkiel and Shiller define the EMH? Are their definitions the same? If not, how do they
differ? Is it possible for one to be true while the other is false?
B. What is Shiller’s main argument against the EMH? How does Malkiel respond to that argument?
C. How does Shiller’s notion of “feedback” differ from the notion of feedback used by Hirshleifer,
Subrahmanyam, and Titman (2006)2 we discussed in class?
D. In Shiller’s assessment, what are the obstacles to “smart money” correcting the price of
mispriced assets in the market?
E. According to Shiller, what are Eugene Fama’s critiques of behavioral finance, and how does
Shiller respond to them?
F. After reading both articles, how well do you think each of the authors defended their thesis?
Which viewpoint do you find more convincing, or are the both (or neither) right? Why or why
Malkiel, Burton (2003). “The Efficient Market Hypothesis and Its Critics.” Journal of Economic Perspectives. Vol.
17, No. 1. 59-82.
Shiller, Robert (2003). “From Efficient Markets Theory to Behavioral Finance.” Journal of Economic Perspectives.
Vol. 17, No. 1. 83-104.
Hirshleifer, David, Avanidhar Subrahmanyam, and Sheridan Titman (2006). “Feedback and the Success of
Irrational Investors.” Journal of Financial Economics. 81. 311-338.
Question 2: Jackets and Calculators
In their 1981 article in Science,3 Amos Tversky and Daniel Kahneman describe two versions of a
hypothetical scenario they posed to survey groups and how they responded. These were the two
Version 1
Imagine that you are about to purchase a jacket for $125 and a calculator for $15. The calculator
salesman informs you that the calculator you wish to buy is on sale for $10 at the other branch of the
store, located 20 a minutes’ drive away. Would you make the trip to the other store?
Version 2
Imagine that you are about to purchase a jacket for $15 and a calculator for $125. The calculator
salesman informs you that the calculator you wish to buy is on sale for $120 at the other branch of the
store, located 20 a minutes’ drive away. Would you make the trip to the other store?
The authors found that substantially more people were willing to make the trip in version 1 of the story
than in version 2, even though the savings of $5 were the same each time. We are going to explore this
A. What is the total amount the individual will spend on the combined jacket and calculator combo
if he does not make the trip in each version of the story?
B. What will the individual spend on the jacket and calculator combo if he does make the trip in
each version?
C. According to expected utility theory, if an individual is willing to make the trip in version 1,
would that person necessarily make the trip in version 2? Why or why not?
D. According to prospect theory, if an individual is willing to make the trip in version 1, would that
person necessarily make the trip in version 2? Why or why not? (You may use pictures to
illustrate your point if you feel it would be helpful)
Tversky, Amos and Daniel Kahneman (1981). “The Framing of Decisions and the Psychology of Choice.” Science.
Vol. 211, No. 4481. 453-458.
Journal of Economic Perspectives—Volume 17, Number 1—Winter 2003—Pages 59 – 82
The Efficient Market Hypothesis and Its
Burton G. Malkiel
generation ago, the efficient market hypothesis was widely accepted by
academic financial economists; for example, see Eugene Fama’s (1970)
influential survey article, “Efficient Capital Markets.” It was generally believed that securities markets were extremely efficient in reflecting information
about individual stocks and about the stock market as a whole. The accepted view
was that when information arises, the news spreads very quickly and is incorporated
into the prices of securities without delay. Thus, neither technical analysis, which is
the study of past stock prices in an attempt to predict future prices, nor even
fundamental analysis, which is the analysis of financial information such as company earnings and asset values to help investors select “undervalued” stocks, would
enable an investor to achieve returns greater than those that could be obtained by
holding a randomly selected portfolio of individual stocks, at least not with comparable risk.
The efficient market hypothesis is associated with the idea of a “random walk,”
which is a term loosely used in the finance literature to characterize a price series
where all subsequent price changes represent random departures from previous
prices. The logic of the random walk idea is that if the flow of information is
unimpeded and information is immediately reflected in stock prices, then tomorrow’s price change will reflect only tomorrow’s news and will be independent of the
price changes today. But news is by definition unpredictable, and, thus, resulting
price changes must be unpredictable and random. As a result, prices fully reflect all
known information, and even uninformed investors buying a diversified portfolio at
the tableau of prices given by the market will obtain a rate of return as generous as
that achieved by the experts.
y Burton G. Malkiel is Chemical Bank Chairman’s Professor of Economics, Princeton
University, Princeton, New Jersey. His e-mail address is ?
Journal of Economic Perspectives
The way I put it in my book, A Random Walk Down Wall Street, first published in
1973, a blindfolded chimpanzee throwing darts at the Wall Street Journal could select
a portfolio that would do as well as the experts. Of course, the advice was not
literally to throw darts, but instead to throw a towel over the stock pages—that is,
to buy a broad-based index fund that bought and held all the stocks in the market
and that charged very low expenses.
By the start of the twenty-first century, the intellectual dominance of the
efficient market hypothesis had become far less universal. Many financial economists and statisticians began to believe that stock prices are at least partially
predictable. A new breed of economists emphasized psychological and behavioral
elements of stock-price determination, and they came to believe that future stock
prices are somewhat predictable on the basis of past stock price patterns as well as
certain “fundamental” valuation metrics. Moreover, many of these economists were
even making the far more controversial claim that these predictable patterns
enable investors to earn excess risk adjusted rates of return.
This paper examines the attacks on the efficient market hypothesis and the
belief that stock prices are partially predictable. While I make no attempt to present
a complete survey of the purported regularities or anomalies in the stock market,
I will describe the major statistical findings as well as their behavioral underpinnings, where relevant, and also examine the relationship between predictability and
efficiency. I will also describe the major arguments of those who believe that
markets are often irrational by analyzing the “crash of 1987,” the Internet “bubble”
of the fin de siecle and other specific irrationalities often mentioned by critics of
efficiency. I conclude that our stock markets are far more efficient and far less
predictable than some recent academic papers would have us believe. Moreover,
the evidence is overwhelming that whatever anomalous behavior of stock prices
may exist, it does not create a portfolio trading opportunity that enables investors
to earn extraordinary risk adjusted returns.
At the outset, it is important to make clear what I mean by the term “efficiency.” I will use as a definition of efficient financial markets that such markets do
not allow investors to earn above-average returns without accepting above-average
risks. A well-known story tells of a finance professor and a student who come across
a $100 bill lying on the ground. As the student stops to pick it up, the professor says,
“Don’t bother—if it were really a $100 bill, it wouldn’t be there.” The story well
illustrates what financial economists usually mean when they say markets are
efficient. Markets can be efficient in this sense even if they sometimes make errors
in valuation, as was certainly true during the 1999 – early 2000 Internet “bubble.”
Markets can be efficient even if many market participants are quite irrational.
Markets can be efficient even if stock prices exhibit greater volatility than can
apparently be explained by fundamentals such as earnings and dividends. Many of
us economists who believe in efficiency do so because we view markets as amazingly
successful devices for reflecting new information rapidly and, for the most part,
accurately. Above all, we believe that financial markets are efficient because they
don’t allow investors to earn above-average risk adjusted returns. In short, we
Burton G. Malkiel
believe that $100 bills are not lying around for the taking, either by the professional
or the amateur investor.
What I do not argue is that the market pricing is always perfect. After the fact,
we know that markets have made egregious mistakes, as I think occurred during the
recent Internet “bubble.” Nor do I deny that psychological factors influence
securities prices. But I am convinced that Benjamin Graham (1965) was correct in
suggesting that while the stock market in the short run may be a voting mechanism,
in the long run it is a weighing mechanism. True value will win out in the end.
Before the fact, there is no way in which investors can reliably exploit any anomalies
or patterns that might exist. I am skeptical that any of the “predictable patterns”
that have been documented in the literature were ever sufficiently robust so as to
have created profitable investment opportunities, and after they have been discovered and publicized, they will certainly not allow investors to earn excess returns.
A Nonrandom Walk Down Wall Street
In this section, I review some of the patterns of possible predictability suggested by studies of the behavior of past stock prices.
Short-Term Momentum, Including Underreaction to New Information
The original empirical work supporting the notion of randomness in stock
prices looked at measures of short-run serial correlations between successive stock
price changes. In general, this work supported the view that the stock market has
no memory—that is, the way a stock price behaved in the past is not useful in
divining how it will behave in the future; for example, see the survey of articles
contained in Cootner (1964). More recent work by Lo and MacKinlay (1999) finds
that short-run serial correlations are not zero and that the existence of “too many”
successive moves in the same direction enable them to reject the hypothesis that
stock prices behave as true random walks. There does seem to be some momentum
in short-run stock prices. Moreover, Lo, Mamaysky and Wang (2000) also find,
through the use of sophisticated nonparametric statistical techniques that can
recognize patterns, some of the stock price signals used by “technical analysts,” such
as “head and shoulders” formations and “double bottoms,” may actually have some
modest predictive power.
Economists and psychologists in the field of behavioral finance find such
short-run momentum to be consistent with psychological feedback mechanisms.
Individuals see a stock price rising and are drawn into the market in a kind of
“bandwagon effect.” For example, Shiller (2000) describes the rise in the U.S. stock
market during the late 1990s as the result of psychological contagion leading to
irrational exuberance. The behavioralists offered another explanation for patterns
of short-run momentum—a tendency for investors to underreact to new information. If the full impact of an important news announcement is only grasped over a
period of time, stock prices will exhibit the positive serial correlation found by
Journal of Economic Perspectives
investigators. As behavioral finance became more prominent as a branch of the
study of financial markets, momentum, as opposed to randomness, seemed reasonable to many investigators.
However, several factors should prevent us from interpreting the empirical
results reported above as an indication that markets are inefficient. First, while the
stock market may not be a mathematically perfect random walk, it is important to
distinguish statistical significance from economic significance. The statistical dependencies giving rise to momentum are extremely small and are not likely to
permit investors to realize excess returns. Anyone who pays transactions costs is
unlikely to fashion a trading strategy based on the kinds of momentum found in
these studies that will beat a buy-and-hold strategy. Indeed, Odean (1999) suggests
that momentum investors do not realize excess returns. Quite the opposite—a
sample of such investors suggests that such traders did far worse than buy-and-hold
investors even during a period where there was clear statistical evidence of positive
momentum. This is because of the large transactions costs involved in attempting
to exploit whatever momentum exists. Similarly, Lesmond, Schill and Zhou (2001)
find that standard “relative strength” strategies are not profitable because of the
trading costs involved in their execution.
Second, while behavioral hypotheses about bandwagon effects and underreaction to new information may sound plausible enough, the evidence that such
effects occur systematically in the stock market is often rather thin. For example,
Eugene Fama (1998) surveys the considerable body of empirical work on “event
studies” that seeks to determine if stock prices respond efficiently to information.
The “events” include such announcements as earnings surprises, stock splits, dividend actions, mergers, new exchange listings and initial public offerings. Fama
finds that apparent underreaction to information is about as common as overreaction, and postevent continuation of abnormal returns is as frequent as
postevent reversals. He also shows that many of the return “anomalies” arise only in
the context of some very particular model and that the results tend to disappear
when exposed to different models for expected “normal” returns, different methods to adjust for risk and when different statistical approaches are used to measure
them. For example, a study that gives equal weight to postannouncement returns of
many stocks can produce different results from a study that weights the stocks
according to their value. Certainly, whatever momentum displayed by stock prices
does not appear to offer investors a dependable way to earn abnormal returns.
The key factor is whether any patterns of serial correlation are consistent over
time. Momentum strategies, which refer to buying stocks that display positive serial
correlation and/or positive relative strength, appeared to produce positive relative
returns during some periods of the late 1990s, but highly negative relative returns
during 2000. It is far from clear that any stock price patterns are useful for investors
in fashioning an investment strategy that will dependably earn excess returns.
Many predictable patterns seem to disappear after they are published in the
finance literature. Schwert (2001) points out two possible explanations for such a
pattern. One explanation may be that researchers are always sifting through
The Efficient Market Hypothesis and Its Critics
mountains of financial data. Their normal tendency is to focus on results that
challenge perceived wisdom, and every now and again, a combination of a certain
sample and a certain technique will produce a statistically significant result that
seems to challenge the efficient markets hypothesis. Alternatively, perhaps practitioners learn quickly about any true predictable pattern and exploit it to the extent
that it becomes no longer profitable. My own view is that such apparent patterns
were never sufficiently large or stable to guarantee consistently superior investment
results, and certainly, such patterns will never be useful for investors after they have
received considerable publicity. The so-called “January effect,” for example, in
which stock prices rose in early January, seems to have disappeared soon after it was
Long-Run Return Reversals
In the short-run, when stock returns are measured over periods of days or
weeks, the usual argument against market efficiency is that some positive serial
correlation exists. But many studies have shown evidence of negative serial
correlation—that is, return reversals— over longer holding periods. For example,
Fama and French (1988) found that 25 to 40 percent of the variation in long
holding period returns can be predicted in terms of a negative correlation with past
returns. Similarly, Poterba and Summers (1988) found substantial mean reversion
in stock market returns at longer horizons.
Some studies have attributed this forecastability to the tendency of stock
market prices to “overreact.” DeBondt and Thaler (1985), for example, argue that
investors are subject to waves of optimism and pessimism that cause prices to
deviate systematically from their fundamental values and later to exhibit mean
reversion. They suggest that such overreaction to past events is consistent with the
behavioral decision theory of Kahneman and Tversky (1979), where investors are
systematically overconfident in their ability to forecast either future stock prices or
future corporate earnings. These findings give some support to investment techniques that rest on a “contrarian” strategy, that is, buying the stocks, or groups of
stocks, that have been out of favor for long periods of time and avoiding those
stocks that have had large run-ups over the last several years.
There is indeed considerable support for long-run negative serial correlation in stock returns. However, the finding of mean reversion is not uniform
across studies and is quite a bit weaker in some periods than it is for other periods.
Indeed, the strongest empirical results come from periods including the Great
Depression—which may be a time with patterns that do not generalize well.
Moreover, such return reversals for the market as a whole may be quite consistent
with the efficient functioning of the market since they could result, in part, from
the volatility of interest rates and the tendency of interest rates to be mean
reverting. Since stock returns must rise or fall to be competitive with bond returns,
there is a tendency when interest rates go up for prices of both bond and stocks to
go down, and as interest rates go down for prices of bonds and stocks to go up. If
interest rates revert to the mean over time, this pattern will tend to generate return
Journal of Economic Perspectives
reversals, or mean reversion, in a way that is quite consistent with the efficient
functioning of markets.
Moreover, it may not be possible to profit from the tendency for individual
stocks to exhibit return reversals. Fluck, Malkiel and Quandt (1997) simulated a
strategy of buying stocks over a 13-year period during the 1980s and early 1990s that
had particularly poor returns over the past three to five years. They found that
stocks with very low returns over the past three to five years had higher returns in
the next period and that stocks with very high returns over the past three to five
years had lower returns in the next period. Thus, they confirmed the very strong
statistical evidence of return reversals. However, they also found that returns in the
next period were similar for both groups, so they could not confirm that a
contrarian approach would yield higher-than-average returns. There was a statistically strong pattern of return reversal, but not one that implied an inefficiency in
the market that would enable investors to make excess returns.
Seasonal and Day-of-the-Week Patterns
A number of researchers have found that January has been a very unusual
month for stock market returns. Returns from an equally weighted stock index have
tended to be unusually high during the first two weeks of the year. The return
premium has been particularly evident for stocks with relatively small total capitalizations (Keim, 1983). Haugen and Lakonishok (1988) documented the high
January returns in a book titled The Incredible January Effect. There also appear to be
a number of day-of-the-week effects. For example, French (1980) documents
significantly higher Monday returns. There appear to be significant differences in
average daily returns in countries other than the United States (Hawawini and
Keim, 1995). There also appear to be some patterns in returns around the turn of
the month (Lakonishok and Smidt, 1988), as well as around holidays (Ariel, 1990).
The general problem with these predictable patterns or anomalies, however, is
that they are not dependable from period to period. Wall Street traders now joke
that the “January effect” is more likely to occur on the previous Thanksgiving.
Moreover, these nonrandom effects (even if they were dependable) are very small
relative to the transactions costs involved in trying to exploit them. They do not
appear to offer arbitrage opportunities that would enable investors to make excess
risk adjusted returns.
Predictable Patterns Based on Valuation Parameters
Considerable empirical research has been conducted to determine if future
stock returns can be predicted on the basis of initial valuation parameters. It is
claimed that valuation ratios, such as the price-earnings multiple or the dividend
yield of the stock market as a whole, have considerable predictive power. This
section examines the body of work based on time series analyses.
Burton G. Malkiel
Predicting Future Returns from Initial Dividend Yields
Formal statistical tests of the ability of dividend yields (that is, the ratio of
dividend to stock price) to forecast future returns have been conducted by Fama
and French (1988) and Campbell and Shiller (1988). Depending on the forecast
horizon involved, as much as 40 percent of the variance of future returns for the
stock market as a whole can be predicted on the basis of the initial dividend yield
of the market index.
An interesting way of presenting the results is shown in the top panel of Exhibit
1. The exhibit was produced by measuring the dividend yield of the broad U.S.
stock market Standard & Poor’s 500 Stock Index each quarter since 1926 and then
calculating the market’s subsequent ten-year total return through the year 2001.
The observations were then divided into deciles depending upon the level of the
initial dividend yield. In general, the exhibit shows that investors have earned a
higher rate of return from the stock market when they purchased a market basket
of equities with an initial dividend yield that was relatively high and relatively low
future rates of return when stocks were purchased at low dividend yields.
These findings are not necessarily inconsistent with efficiency. Dividend yields
of stocks tend to be high when interest rates are high, and they tend to be low when
interest rates are low. Consequently, the ability of initial yields to predict returns
may simply reflect the adjustment of the stock market to general economic conditions. Moreover, the use of dividend yields to predict future returns has been
ineffective since the mid-1980s. Dividend yields have been at the 3 percent level or
below continuously since the mid-1980s, indicating very low forecasted returns. In
fact, for all ten-year periods from 1985 through 1992 that ended June 30, 2002,
realized annual equity returns from the market index have averaged over
15 percent. One possible explanation is that the dividend behavior of U.S. corporations may have changed over time (Bagwell and Shoven, 1989; Fama and French,
2001). Companies in the twenty-first century may be more likely to institute a share
repurchase program rather than increase their dividends. Thus, dividend yield may
not be as meaningful as in the past as a useful predictor of future equity returns.
Finally, it is worth noting that this phenomenon does not work consistently with
individual stocks (Fluck, Malkiel and Quandt, 1997). Investors who simply purchase
a portfolio of individual stocks with the highest dividend yields in the market will
not earn a particularly high rate of return. One popular implementation of such a
“high dividend” strategy in the United States is the “Dogs of the Dow Strategy,”
which involves buying the ten stocks in the Dow Jones Industrial Average with the
highest dividend yields. For some past periods, this strategy handily outpaced the
overall average, and so several “Dogs of the Dow” mutual funds were brought to
market and aggressively sold to individual investors. However, such funds generally
underperformed the market averages during the 1995–1999 period.
Predicting Market Returns from Initial Price-Earnings Multiples
The same kind of predictability for the market as a whole, as was demonstrated
for dividends, has been shown for price-earnings ratios. The data are shown in the
Journal of Economic Perspectives
Exhibit 1
The Future 10-Year Rates of Return When Stocks are Purchased at Alternative
Initial Dividend Yields (D/P)
Return (%)
/P .1
/P .7
/P .1
/P .7
/P .3
/P .9
/P .6
/P .3
/P .0
Stocks Cheap
Stocks Expensive
The Future 10-Year Rates of Return When Stocks are Purchased at Alternative
Initial Price-to-Earnings (P/E) Multiples
Return (%)
P/ 16.
Stocks Cheap
Stocks Expensive
Source: The Leuthold Group
bottom half of Exhibit 1. The exhibit presents a decile analysis similar to that
described for dividend yields above. Investors have tended to earn larger longhorizon returns when purchasing the market basket of stocks at relatively low
price-earnings multiples. Campbell and Shiller (1998) report that initial P/E ratios
The Efficient Market Hypothesis and Its Critics
explained as much as 40 percent of the variance of future returns. They conclude
that equity returns have been predictable in the past to a considerable extent.
Consider, however, the recent experience of investors who have attempted to
undertake investment strategies based either on the level of the price-earnings
multiple or the dividend yield to predict future long-horizon returns. Priceearnings multiples for the Standard & Poor’s 500 stock index rose into the low 20s
on June 30, 1987 (suggesting very low long-horizon returns). Dividend yields fell
below 3 percent. Price-earnings multiples rose into the low 20s. The average annual
total return from the index over the next 10 years was an extraordinarily generous
16.7 percent. Dividend yields, again, fell to 3 percent in June 1992. Price-earnings
multiples rose to the mid-20s. The subsequent return through June 2002 was
11.4 percent. The yield of the index fluctuated between 2 and 3 percent from 1993
through 1995 and earnings multiples remained in the mid-20s, yet long-horizon
returns through June 30, 2002, fluctuated between 11 and 12 percent. Even from
early December 1996, the date of Campbell and Shiller’s presentation to the
Federal Reserve suggesting near zero returns for the S&P500, the index provided
almost a 7 percent annual return through mid-2002. Such results suggest to me a
very cautious assessment of the extent to which stock market returns are predictable
on this basis.
Other Predictable Time Series Patterns
Studies have found some amount of predictability of stock returns based on
various financial statistics. For example, Fama and Schwert (1977) found that
short-term interest rates were related to future stock returns. Campbell (1987)
found that term structure of interest rates spreads contained useful information for
forecasting stock returns. Keim and Stambaugh (1986) found that risk spreads
between high-yield corporate bonds and short rates had some predictive power.
Again, even if some predictability exists, it may reflect time varying risk premiums
and required rates of return for stock investors rather than an inefficiency. Moreover, it is far from clear that any of these results can be used to generate profitable
trading strategies. Whether such historical statistical relations give investors reliable
and useful guides to appropriate asset allocation is far from clear.
Cross-Sectional Predictable Patterns Based on Firm Characteristics
and Valuation Parameters
A large number of patterns that are claimed to be predictable are based on
firm characteristics and different valuation parameters.
The Size Effect
One of the strongest effects investigators have found is the tendency over long
periods of time for smaller-company stocks to generate larger returns that those of
Journal of Economic Perspectives
large-company stocks. Since 1926, small-company stocks in the United States have
produced annual rates of return over 1 percentage point larger than the returns
from large stocks (Keim, 1983). Fama and French (1993) examined data from 1963
to 1990 and divided all stocks into deciles according to their size as measured by
total capitalization. Decile one contained the smallest 10 percent of all stocks, while
decile ten contained the largest stocks. The results, plotted in Exhibit 2, show a
clear tendency for the deciles made up of portfolios of smaller stocks to generate
higher average monthly returns than deciles made up of larger stocks.
The crucial issue here is the extent to which the higher returns of small
companies represent a predictable pattern that will allow investors to generate
excess risk-adjusted returns. According to the capital asset pricing model, the
correct measure of risk for a stock is its “beta”—that is, the extent to which the
return of the stock varies with the return for the market as a whole. If the beta
measure of systematic risk from the capital asset pricing model is accepted as the
correct risk measurement statistic, the size effect can be interpreted as indicating an
anomaly and a market inefficiency, because using this measure portfolios consisting
of smaller stocks have excess risk-adjusted returns. Fama and French (1993) point
out, however, that the average relationship between beta and return during the
1963–1990 period was flat—not upward sloping as the capital asset pricing model
predicts. Moreover, if stocks are divided up by beta deciles, ten portfolios constructed by size display the same kind of positive relationship shown in Exhibit 2.
On the other hand, within size deciles, the relationship between beta and return
continues to be flat. Fama and French suggest that size may be a far better proxy
for risk than beta, and therefore that their findings should not be interpreted as
indicating that markets are inefficient.
The dependability of the size phenomenon is also open to question. From the
mid-1980s through the decade of the 1990s, there has been no gain from holding
smaller stocks. Indeed, in most world markets, larger capitalization stocks produced
larger rates of return. It may be that the growing institutionalization of the market
led portfolio managers to prefer larger companies with more liquidity to smaller
companies where it would be difficult to liquidate significant blocks of stock.
Finally, it is also possible that some studies of the small-firm effect have been
affected by survivorship bias. Today’s computerized databases of companies include
only small firms that have survived, not the ones that later went bankrupt. Thus, a
researcher who examined the ten-year performance of today’s small companies
would be measuring the performance of those companies that survived—not the
ones that failed.