A Reinvestigation of Idiosyncratic Volatility
Nicholas Wilmes
Western Kentucky University
May 5, 2015
Abstract
In updating Campbell et al. (2001) I find evidence that the level of
idiosyncratic volatility, industry-specific volatility, and market volatility have
increased to their highest level in 50 years during the 21st century. I also find
evidence that the average correlation among stocks has steadily increased as well.
Finally, I find that the average R-squared is increasing, opposite the findings by
Fama & French (2004) and Brown & Kapadia (2007) that the average R-squared is
decreasing.
I would like to thank Dr. Alex Lebedinsky for his generous support and guidance through this
process. I would also like to thank Dr. Brian Goff and Dr. David Beckworth for their helpful
feedback and comments.
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Introduction
In this paper, I investigate volatility patterns in U.S. stock market by decomposing
aggregate volatility into idiosyncratic, market and industry volatilities. The paper closely follows
Campbell et al. (2001) updating their work with more recent data. In this paper, I focus on the
effect of major market events, changing market dynamics, and unique economic and financial
position in which we currently reside on idiosyncratic volatility.
Since the turn of the 21st century, investors in the United States stock market have seen
their fortunes change drastically. These fifteen years encompassed not only a strong bull market,
but also two cataclysmic events that will forever define the decade in history books. These two
events are the “technology bubble” and the Great Recession. These major events wreaked havoc
on the stock market and major indices declined markedly, decimating the wealth of many. While
it is obvious that the returns generated by firms during times of great financial distress in a
weakening economy will be below their historical levels, an important question to ask is whether
the resulting volatility is systematic or idiosyncratic in nature. Systematic volatility is defined
here as volatility of the market as a whole on collective risk that is common to equities in general
rather than specific firms. In contrast, idiosyncratic volatility is volatility that is unique to an
individual firm due to risks and information that pertain solely to that firm rather than to the
market as a whole.
When levels of volatility are high for equities, investors place a higher risk premium on
equity securities. This reduces the assets’ price by further discounting future cash flows because
of the high risk associated with the increase in uncertainty about the future, or investors require
a larger return. Measuring volatility not only in the aggregate, but also its industry and firm
specific idiosyncratic components is important for investors. Idiosyncratic volatility of individual
firms may be offset by other firms in a portfolio, but not necessarily their associated industry risk.
Similarly, the various stocks in a given portfolio may be diversified as to their industry-specific
risk but not necessarily their firm-specific idiosyncratic risk (Campbell et al. [2001]). Lastly, the
prices of derivatives such as call or put options are dependent on the price of the individual stock
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for which the option pertains, and the price is affected by the total of the market risk, industryspecific risk, and idiosyncratic risk.
A prominent and widely cited study by Campbell et al. (2001) showed that from 1962
through 1997 idiosyncratic firm volatility increased and had a statistically significant upward
trend and that the overall market volatility did not exhibit a similar trend. Campbell et al. (2001)
also found that along with an increase in idiosyncratic risk, there was a decrease in the correlation
among stocks over their sample, and that the industry-level volatility, and to a lesser extent
market and idiosyncratic volatility, help to forecast economic activity. This paper extends
Campbell et al. (2001) work by updating the data to include the rise and fall of stocks during the
technology bubble, the years of growth during the mid-2000s, the Great Recession, and the
current recovery.
In updating Campbell et al. (2001) I find evidence that the level of idiosyncratic volatility,
industry-specific volatility, and market volatility have increased to their highest level in 50 years
during the 21st century. I also find evidence that the average correlation among stocks has
steadily increased as well.
Related Literature
As this study intends to update Campbell et al. (2001), it is substantially based upon their
work. In their paper, Campbell et al. (2001) find that idiosyncratic volatility increased from 1962
through 1997 and had a significant upward trend. However, they did not find an upward trend
for industry-specific volatility or market volatility. They also found that the average R-squared of
the market model was decreasing over time and as a result, the number of stocks required to
diversify a portfolio had increased.
The upward trend in idiosyncratic volatility reported by Campbell et al. (2001) has been
disputed by some. An alternative view put forward by Brandt et al. (2010) is that the increase in
idiosyncratic volatility was an episodic phenomenon concentrated in low-priced stocks with high
levels of retail ownership that reversed itself in the year 2000 and was not a time trend. However,
many other researchers have also found an upward trend in idiosyncratic volatility including
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Irvine & Pontiff (2009), Bartram et al. (2012), Brown & Kapadia (2007), and Comin & Philippon
(2006). A great deal of the literature examines what has caused the change in the level of
idiosyncratic volatility and characteristics of firm’s that have high levels of idiosyncratic volatility.
This literature will be discussed at length in the discussion section.
Empirical Analysis
In this paper I use daily stock returns from The Center for Research in Security Prices
(CRSP) database. The sample ranges from July 1, 1962 to December 31, 2013 and includes all
firms traded on the NYSE, NASDAQ, NYSE Market, and the NYSE Arca exchanges during the
period. I also obtained each firm’s SIC code and market capitalization (stock price multiplied by
the number of outstanding shares) from the CRSP database at monthly intervals with the
observation recorded on the final trading day of the month. I used the SIC codes to assign
industry codes using the Fama & French (1997) scheme. This scheme classifies firms into 49
industries, including one “other” category. From this monthly data I dropped any observations
that had missing values for market capitalization. Finally, I obtained 1-month Treasury bill data in
monthly intervals from Kenneth French’s Data Library for the sample period.
My data differs slightly from the data Campbell et al. (2001) because I include firms that
are traded on the NYSE Arca exchange. The NYSE Arca exchange did not begin actively trading
securities until 1997, the final year included in Campbell et al. (2001). Because this study includes
sixteen years of trading since the NYSE Arca became active, including stocks traded on this
exchange is pertinent to investigating the volatility of equities in the United States as a whole.
After deleting observations containing missing values, the sample used in this paper differed
slightly from Campbell et al. (2001) in the number of firms. At the beginning of the period my
sample contained 2,044 firms compared to the 2,047 in Campbell et al. (2001), and in the last
month of Campbell et al. (2001) sample period my sample had 9,205 firms compared to their
8,927. However, even after excluding firms that traded on the NYSE Arca exchange the number
of firms did not match perfectly. Even though the sample varied slightly from Campbell et al.
(2001), my results very closely resemble theirs.
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Figure 1 (see appendix) plots the number of firms in my sample over the period. Figures
2 and 3 show the distribution of the size of firms within my sample. Figure 2 graphs the median
market capitalization, first and third quartiles, and mean market capitalization, all adjusted for
inflation. This figure shows that since the early 1970’s the real mean market capitalization has
been above the third quartile. Figure 3 shows the mean and values 1.96 standard deviations
above and below the mean. This figure depicts where 95% of firms would fall if the market
capitalization of stocks was normally distributed. It is obvious from these figures that the size of
firms within the market is heavily right-skewed.
To calculate a measure of overall aggregate volatility encompassing every stock traded, a
scheme must be devised to weight the returns of each firm. The simplest possible weighting
scheme would be to give each firm, regardless of its size, an equal weight such that the volatility
of a small start-up influences the overall volatility to the same extent that the volatility of one of
the largest firms does. Campbell et al. (2001) showed that weighted average of return volatilities
can be decomposed as follows
= + ∈
∈
= + + 1 = + + Equation (1) shows that the firm volatility is equal to the variance of firm specific
residuals multiplied by the weight of firm j in industry i in period t, , and then summed
for all firms within industry i. This is then multiplied by the weight of industry i in period t, ,
and summed for all industries. Using this method I can decompose return volatilities into their
components without estimating betas for individual stocks or industries, which may change over
the sample.
Following Campbell et al. (2001), and the method by which market indices weigh
component stocks, I assigned weights to firms based upon their market capitalization. I
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calculated a firm’s weight by dividing their market capitalization by the sum of the market
capitalization for all firms in the sample during a particular month. For example, to calculate
weighted return in March 2013, I used market caps from February 2013. Firms were re-weighted
each month based upon their market capitalization on the last day of the previous month. I then
merged these monthly weights with the daily return data and I calculated market-weighted
average return for each day in the sample. I then subtracted the 1-month Treasury bill rate from
the average weighted returns to calculate the daily excess average returns Rms, or the returns
that were earned above the risk-free rate.
2 = = − " ∈
From the daily excess average returns I calculated the mean excess return of the market
over the sample period µm for month t. Volatility for each month was calculated with daily data
for that month using equation (2) above. Note, this equation measures variation around the
mean for the entire sample rather than month-specific means. Figures 4 and 5 (see appendix)
graph the market volatility and the 12-month moving average of volatility over time. It is clear
from these figures that since Campbell et al. (2001), market volatility increased greatly and
remained high for around five years, which coincides with the technology bubble. After this
period, market volatility decreased back to normal levels until the financial crisis and the ensuing
Great Recession. The market volatility reaches its maximum level in the sample around the end
of 2008, surpassing the second highest month in the sample which contains the 1987 stock
market crash.
3 = + 4%
= ∈
5'()*+, = %
As with the weights of the individual firms within the market, the weight of each firm
within its respective industry is based upon the firm’s market capitalization. The weight of firm j
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in industry i is equal to firm j’s weight within the market divided by the sum of the weights of all
firms within industry i. Using these industry weights and returns for each firm in the industry, I
calculate weighted average returns for each industry. From the daily average returns by industry,
the 1-month Treasury bill rate is subtracted to give the excess industry returns. The volatility for
each industry is then calculated following equation (4) by subtracting the excess market returns
from the excess industry returns and squaring the differences, denoted , and summing the
squared differences by industry for each month. Average industry volatility is calculated using
individual industry volatilities and weights of industries in the market , as shown in equation
(5).
The industry volatility series and its 12-month moving average are shown over time in the
figures 6 and 7 (see appendix.) These graphs show that during both the technology bubble and
the Great Recession, average industry volatility peaks at levels that are almost double the highest
level observed during the period in Campbell et al. (2001). This increased level of industry-specific
volatility persisted for multiple years surrounding both of these major events. However, between
the technology bubble and the Great Recession industry-level volatility fell to its previous levels.
Figure 7 is perhaps more striking because it shows that level of industry volatility at its peak
during the technology bubble was about 5 times greater than the highest level in Campbell et al.
(2001).
6 = + 7/
= ∈
8/
= ∈
9234 = Finally, to compute the idiosyncratic firm volatility I subtracted the average industry
return from each firm’s excess returns and squared the difference, resulting in /
from
equation (7). Then, per equation (8), I summed the squared differences for each firm by month
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and multiplied each firm’s total squared differences by the firm’s weight within its industry to result in /
– average idiosyncratic volatility in industry i. Next, following equation (9), I
calculate average idiosyncratic volatility for the all stocks as the weighted average of /
, where
is weight of industry i within the total market in period t. 234 and its 12-moth moving
average are depicted in figures 8 and 9, respectively.
Campbell et al. (2001) found that there was an upward trend in the idiosyncratic volatility
but Brandt et al. (2010) found that by 2001 this trend ceased to exist. Post 2001 there does not
appear to be any upward trend in the idiosyncratic volatility Brandt et al. (2010). As with the
industry volatility, the 12-month moving average of idiosyncratic volatility in figure 9 peaks during
technology bubble. This peak is approximately 2.5 times greater than the largest value in the
period studied by Campbell et al. (2001). During the Great Recession, the peak in idiosyncratic
volatility is slightly less than double the peak in Campbell et al. (2001).
To further investigate the relationship among stocks, and the systematic risk in the
market, I used the rolling regression method in Campbell et al. (2001). The dependent variable
in each of these regressions is each individual firm’s excess return with the market excess return
used as the sole explanatory variable. For each month I used all firms with complete return data
for the previous 12 months and saved the R-squared of each model. I then averaged the Rsquared for all firms with complete data in each month and plotted the resulting equally
weighted average R-squared in figure 10 (see appendix). Campbell et al. (2001) found that the
average R-squared of individual firms was decreasing and thus the systematic risk was decreasing
because stocks were less correlated with one another.
Campbell et al. (2001) also calculated the average correlation among stocks by calculating
all pairwise correlations and then averaging the correlations for each month. Interestingly, the
average correlation perfectly mirrors the equally weighted average R-squared through the
sample. During their sample period both the average correlation among stocks and the average
R-squared declined. Campbell et al. (2001) states that the decrease in the correlation among
stocks increases the number of randomly selected stocks required to hold a relatively diversified
portfolio. This finding coincides with Comin & Philippon (2006) who document a decrease in the
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correlation of shocks among sectors, which they find to be decreasing the overall volatility rather
than a decline in sectoral volatility.
Contrary to Campbell et al. (2001) and Comin & Philippon (2006), I found that beginning
right after the period in Campbell et al. (2001), the average R-squared began increasing almost
constantly for the next 10 years. A rising R-squared means that the stocks are becoming more
correlated and the share of the systematic risk is increasing. The average R-squared of this
market model peaks at an astonishingly high 40 percent. This means that for any given firm
equally weighted within the market, the average market return can explain 40% of the variation
in that firm’s return. However it should be noted that there has been much debate about the
validity of using R-squared as a measure of idiosyncratic volatility in recent literature both with
matching the empirical findings of the firm profiles with high idiosyncratic volatility and the
information content in prices using 1-R-squared Brown & Kapadia (2007.) Also, a recent article
by Li et al. (2014) has shown that the firm variance and R-squared are not the same and
demonstrates the difficulty in directly mapping between the two metrics. The difficulty stems in
the calculation of R-squared, which has two components. 1-R-sqaured is equal to the variance
of the error term (idiosyncratic volatility) divided by the total variance of the stock. Thus a change
in either component changes the ratio, not just a change in the idiosyncratic volatility.
Discussion
The literature is filled with many explanations for the changes in the idiosyncratic volatility
of the stock market, some contradictory and others supplemental. While there is much debate
about the trend in idiosyncratic volatility, if one exists, I want to avoid that discussion and focus
on the underlying factors that drive changes in idiosyncratic volatility. I feel that developing an
understanding of the reasons why idiosyncratic volatility changes over time is crucial in
attempting to understanding how idiosyncratic volatility in the U.S. has changed, and whether
that change is positive or not. To understand how my results fit with the current literature and
put them in context, I will discuss the explanations of the causes of changes in idiosyncratic
volatility in the following six categories: small and low priced stocks, how new firms differ from
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older firms, a firm’s investor base, research and development, industry turnover, and market
development.
Small and Low-Priced Stocks
In attempting to explain the apparent puzzle in idiosyncratic volatilities, Brandt et al.
(2010) found the price of stocks to be very important in understanding idiosyncratic volatility.
More specifically, they found that the increase and reversal in idiosyncratic volatility was
concentrated in stocks that had low stocks prices and a high proportion of retail ownership. In
their analysis, Brandt et al. (2010) controlled for the size of the firm to see if the significance of a
low stock price was really just a proxy for the size of a firm. They found that after controlling for
firm size, which was statistically significant, stock price was still highly statically significant and of
a much larger magnitude than firm size. To further support their notion that low stock prices
significantly contribute to an increase in idiosyncratic volatility, Brandt et al. (2010) examined
stock splits. Interestingly, these events, which lower the stock price by issuing additional shares
and do not change firm fundamentals, were shown to increase idiosyncratic volatility Brandt et
al. (2010). While stock price may be a vital component in understanding idiosyncratic volatility,
Brown & Kapadia (2007) found evidence that supports Brandt et al. (2010) finding that firm size
matters as well.
New Firms vs. Old Firms
Another topic that has gained prominence in the literature is the change in the nature of
public firms. Notably Fama & French (2004) document that new firms’ fundamentals are
different than older firms and that newer firms are more left-skewed in profitability, more rightskewed in their growth, and overall have lower survival rates. The effect of new firms is
investigated in depth by Brown & Kapadia (2007). They find that the increase in idiosyncratic
volatility is due solely to new listings by riskier firms. The also conclude that the decline in Rsquared in their sample is due to new listings of companies with higher idiosyncratic risk, and
thus lower R-squared, thereby increasingly reducing the average R-squared as these firms
become more prevalent in the market.
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Brown & Kapadia (2007) also document that industries with higher levels of idiosyncratic
volatility are industries that have a larger number of new firms in them. Brown & Kapadia (2007)
also refute the notion that newer firms have higher idiosyncratic volatility because they list
earlier in their life than firms of previous decades. To support their finding, Brown & Kapadia
(2007) split stocks into groups of five year intervals with each group containing all stocks that
were initially listed during its intervals. They find that each successive group had a higher starting
level of idiosyncratic volatility and a lower average R-squared. They argue that if newer firm’s
idiosyncratic volatility was higher because they listed earlier, the increased idiosyncratic volatility
would decline and the average R-squared would increase over time, but they found no evidence
that either of these has occurred. Brown & Kapadia (2007) also found that newer firms have
declining profit margins and tangible assets, but older firms’ profit margins and level of tangible
assets have stayed almost the same. To further support their conclusion, Brown & Kapadia
(2007) also documented that idiosyncratic volatility is inversely related to the average age of
firms within an industry and directly related to the proportion of firms within an industry that are
newly listed. Finally, Brown & Kapadia (2007) show that the risk of doing business has not
changed over time by looking at default rates, to rule out the possibility that newly listed firms
are more risky because they are listing in a period of increased risk of doing business.
Investor Base
Another aspect of firms with high idiosyncratic volatility that differs from firms with low
idiosyncratic volatility is the investor base of the firm. Brandt et al. (2010) show that both the
increase and decrease in idiosyncratic volatility that they find was concentrated in stocks with
low prices and stocks that had a proportion of their shares owned by retail investors. Brandt et
al. (2010) also investigated the characteristics of firms which are widely held by retail investors.
These firms tended to have low market capitalization, low stock prices, low institutional
ownership, and high idiosyncratic volatility. Part of this is due to the fact that retail investors
significantly overweight low-priced stocks in their portfolios relative to a portfolio chosen at
random based upon firms’ market capitalization Kumar (2009). In their study, Brandt et al. (2010)
found large positive or negative returns, or high turnover, events which they term “attentiongrabbing events” attract the attention of retail investors and volatility moves around these
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events. Further, Brandt et al. (2010) found that the increase in trading surrounding “attentiongrabbing events” by retail traders occurs regardless of the information content. This seems to
imply that retail traders may not always trade on fundamentals and may be noise traders. Brandt
et al. (2010) makes this point by saying that to a retail investor, a stock with a lower level of
institutional ownership may be more enticing because they may see the stock as being on a more
level playing ground without institutional investors who can appear to have superior information.
However, taken with the findings of Jiang & Yao (2009), institutional investors may have
superior information. More likely, institutional investors can do a better job reading between
the lines and understanding the true fundamentals of a business through murky disclosures and
are not distracted by “attention-grabbing events” that do not contain news. Bartram et al. (2012)
found that disclosures were negatively related with idiosyncratic volatility, so it is plausible that
retail investors need disclosures to understand the firm’s they are trading. Jiang & Yao (2009)
found that idiosyncratic volatility is inversely related to future earnings shocks and that the return
predictive power stems from information content about future earnings. Jiang & Yao (2009) also
found that this predictive power from idiosyncratic volatility was related to corporate selective
disclosures and was strongest among stocks with a less sophisticated investor base. This fits with
the findings in Brandt et al. (2010) that retail investors trade do not always trade on
fundamentals, that institutional investors have a superior ability to read between the lines (when
the quality of disclosures is low), and that the noise trading by retail investors pushes prices
further away from their fundamentals allow there to be predictive power of future earnings
shocks in the volatility.
Finally, along with their finding that volatility increases following a stock split, Brandt et
al. (2010) also found that institutional holdings of firms fell following a stock split. This further
connects a firm’s investor base to idiosyncratic volatility. Brandt et al. (2010) also include a term
in their regressions interacting firms with low stock prices and low retail ownership, which was
not statistically significant. From this they conclude that retail ownership is important and that
its importance isn’t due to retail investor’s tendency to overweight low-priced stocks.
Research and Development
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As Bartram et al. (2012) point out, volatility isn’t necessarily a good or bad thing. Rather,
high volatility can be good or bad depending on its root causes. One of the positive characteristics
they found to increase idiosyncratic volatility is the number of patents. Similarly, Comin &
Philippon (2006) document that idiosyncratic volatility increase in industries that experience
large increases in research and development, and that current volatility has a significant impact
on future research and development that peaks three periods forward. They also found that past
research and development spending effects current levels of volatility five periods back, and that
the sign was always positive, statistically significant, and typically larger than the
contemporaneous correlations between research and development and idiosyncratic volatility.
Increases in volatility because of increased spending on research and development are
positive for both the companies investing their money and for all of their stakeholders. Research
and development is what spurs innovation and progress. While this may cause variations in cash
flows and income, it is the only way to get ahead of competitors and increase returns to
shareholders. Investment in research and development is a sign of a stable market because it
shows that firms are confident enough in their future that they are willing to invest in developing
new products and technology.
Turnover
Turnover in market shares, or alternatively, more competition in product markets, is what
Comin & Philippon (2006) reports to be the main cause of the increase in idiosyncratic volatility.
They found that the profiting margins of the industry leaders has not changed over time, but the
average length of time that a firm is an industry leader has decreased dramatically. Brown &
Kapadia (2007) also found changes in the composition of firms within an industry to an important
factor in explaining idiosyncratic volatility, more important than the changing of the weights of
industries within the market over time. Irvine & Pontiff (2009) further confirmed the positive
relationship of turnover within an industry and future idiosyncratic volatility. I believe that these
findings are intertwined with research and development. Increases in research and development
mean that there will be more competition in the market and more differentiated products. In
this environment it is harder to stay ahead of an entire industry, thus the average duration of a
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market leader declines. Since the expected duration of a firm as an industry leader has dropped
drastically, there is an increased incentive to innovate and invest in new technologies in
aspiration of unseating the current market leader. Thus one creates incentives for the other, but
while both increase volatility they also spur innovation and progress.
Market Development
The increased development of a stock market also increases the level of idiosyncratic
volatility Bartram et al. (2012). Bartram et al. (2012) find that part of the reason the U.S. has
experienced an increase in idiosyncratic volatility is due to an increase in investor protections.
This reduces the overall riskiness of investing in stocks allowing them to trade on the risk of the
individual companies rather than also pricing in general risks of holding equities. Comin &
Philippon (2006) states that idiosyncratic volatility increases after deregulation and in industries
that issue more debt and equity. These drivers in volatility are all due to the development of the
market as a whole, and how this protects investors and allows equity prices to not incorporate
risks that these protections take out of the market. Interestingly, Bartram et al. (2012) did not
find evidence that measures of political risk or creditor rights are important in understanding
idiosyncratic volatility in their cross-country analysis.
Conclusion
After decomposing aggregate volatility, I found that idiosyncratic risk has been at very
high levels since the turn of the 21st century. Much of the current literature uses data that does
not include the end of the Great Recession and the current recovery, periods where idiosyncratic
risk is twice as high as any other period in the last 50 years. I also showed that the average Rsquared of equally weighted U.S. equities has increased substantially, peaking around 40 percent,
its highest level in 50 years. Based on the finding by Campbell et al. (2001) that the graph of the
average R-squared perfectly mirrors the average pairwise correlation among stocks, I conclude
that stocks have become much more correlated over the last 15 years. This increased correlation
makes diversifying a portfolio more difficult for an investor because they have an increased level
of risk common to more stocks in their portfolio that cannot be hedged away by simply holding
more stocks with the same level of correlation among them.
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Given the vast array of explanations in the literature for idiosyncratic risk, many of which
contradict one another, there are many veins for future researchers to explore. One of these is
to further explore the size of firms and stock prices, and to see if the results found by Brandt et
al. (2010), Brown & Kapadia (2007), and others still hold with current data. Another area for
future research is a more in-depth study of various industries to see how they evolve over time
and how research and development and industry leadership lead one another. Finally, given the
strong evidence by Fama & French (2004) and Brown & Kapadia (2007) that new firms differ
significantly from older firms, and that the average R-squared is decreasing, a finding for which I
find opposite results, further research should investigate whether this trend is still continuing.
References
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Appendix
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m
20 8
14
m
8
Number of Firms
16
Number of Firms in Sample
10000
8000
6000
4000
2000
Time
Figure 2
Distribution of Market Capitalization
500000
400000
300000
200000
100000
0
Time
Average Market Cap
First Quartile
Figure 3
Median Market Cap
Third Quartile
19
62
m
19 8
66
m
19 8
70
m
19 8
74
m
19 8
78
m
19 8
82
m
19 8
86
m
19 8
90
m
19 8
94
m
19 8
98
m
20 8
02
m
20 8
06
m
20 8
10
m
20 8
14
m
8
Volatility
19
62
m
19 8
66
m
19 8
70
m
19 8
74
m
19 8
78
m
19 8
82
m
19 8
86
m
19 8
90
m
19 8
94
m
19 8
98
m
20 8
02
m
20 8
06
m
20 8
10
m
20 8
14
m
8
Dollars
17
Average Real Market Capitalization
6000000
4000000
2000000
0
-2000000
-4000000
-6000000
Time
Average Market Capitalization
1.96 Standard Deviations
Figure 4
Market Volatility
.06
.05
.04
.03
.02
.01
0
Time
Figure 5
19
62
m
19 8
66
m
19 8
70
m
19 8
74
m
19 8
78
m
19 8
82
m
19 8
86
m
19 8
90
m
19 8
94
m
19 8
98
m
20 8
02
m
20 8
06
m
20 8
10
m
20 8
14
m
8
Volatility
19
63
m
8
19
67
m
19 10
71
m
1
19 2
76
m
19 2
80
m
19 4
84
m
19 6
88
m
8
19
92
m
19 10
96
m
1
20 2
01
m
20 2
05
m
20 4
09
m
20 6
13
m
8
Volatility
18
12-Month Moving Average of Market Volatility
.02
.015
.01
.005
0
Time
Figure 6
Industry Volatility
.012
.01
.008
.006
.004
.002
0
Time
Figure 7
19
62
m
19 8
66
m
19 8
70
m
19 8
74
m
19 8
78
m
19 8
82
m
19 8
86
m
19 8
90
m
19 8
94
m
19 8
98
m
20 8
02
m
20 8
06
m
20 8
10
m
20 8
14
m
8
Volatility
Time
Figure 9
20
13
m
20
08
m
20
04
m
19
99
m
19
95
m
19
90
m
19
86
m
19
81
m
19
77
m
19
72
m
19
68
m
19
63
m
2
8
2
8
2
8
2
8
2
8
2
8
Volatility
19
12-Month Moving Average of Industry Volatility
.008
.006
.004
.002
0
Time
Figure 8
Firm Volatility
.04
.03
.02
.01
0
Time
Figure 10
20
13
m
20
08
m
20
04
m
19
99
m
19
95
m
19
90
m
19
86
m
19
81
m
19
77
m
19
72
m
19
68
m
19
63
m
2
8
2
8
2
8
2
8
2
8
2
8
Volatility
20
12-Month Moving Average of Firm Volatility
.025
.02
.015
.01
.005
0