Firm-Specific Risk and Equity Market Development+
Gregory Brown and Nishad Kapadia*
Abstract
We examine the increase in firm-specific risk in the U.S. stock market
which has been documented by prior research. We show that the observed
increase is due solely to new listings by riskier companies. Our results
explain why prior researchers have found that growth opportunities,
profitability, firm size, and industry composition (among other factors) are
related to increases in firm-specific risk. We also show that the previously
documented decline in average R2 of a market model is due to the new
listing effect.
May 2005
JEL: G11
Keywords: Idiosyncratic Risk, Firm-specific Risk, Market Risk
+
We thank workshop participants at Duke University and the University of North Carolina. We are also
indebted to Jennifer Conrad and Tim Bollerslev for their insightful comments.
* Both authors are from the Kenan-Flagler Business School, University of North Carolina at Chapel Hill.
Contact author is at Gregory W. Brown, CB 3490, McColl Building, Chapel Hill, NC 27599, USA. Phone:
(919) 962-9250. Email: gregwbrown@unc.edu
Firm-Specific Risk and Equity Market Development
Abstract
We examine the increase in firm-specific risk in the U.S. stock market
which has been documented by prior research. We show that the observed
increase is due solely to new listings by riskier companies. Our results
explain why prior researchers have found that growth opportunities,
profitability, firm size, and industry composition (among other factors) are
related to increases in firm-specific risk. We also show that the previously
documented decline in average R2 of a market model is due to the new
listing effect.
1. Introduction
Recent research documents an increase in firm-specific risk in U.S. equity
markets over the last few decades (Campbell, Lettau, Malkiel, and Xu , 2001, hereafter,
CLMX). This discovery is puzzling for at least two reasons. First, the U.S. economy has
become notably more stable recently, experiencing only two mild recessions in the last 20
years.1 Second, volatility of market indices has not increased notably.
Just as curious is that until recently the trend in idiosyncratic risk has gone largely
unnoticed. In part, this may be because traditional asset pricing theory concludes firmspecific, as opposed to market-wide, risk can be diversified away and therefore should
not be a priced risk factor. However, idiosyncratic risk is important for many reasons.
First, high levels of idiosyncratic risk may be the result of low correlations between
stocks and thereby increase the number of securities required to generate a welldiversified portfolio (see CLMX). Similarly, some investors cannot diversify (e.g.,
participants in employee stock option plans) and must bear idiosyncratic risk. Second,
stock option prices depend on the total volatility of the underlying stock of which
idiosyncratic volatility is the largest component. Third, a large and developing corporate
risk management literature indicates that managers at non-financial corporations carefully
manage firm-specific risks including their own equity price risk (see Kendall, 1998).
Fourth, the level of idiosyncratic risk may have important consequences for the amount
of information conveyed by stock returns (see Durnev et al., 2003). Fifth, and perhaps
most importantly, recent papers by Santa Clara and Goyal (2003) and Ang et al. (2004)
show that idiosyncratic risk may be a priced risk factor.
Following the findings of CLMX, several papers have investigated the
determinants of the increase in firm-specific risk. For example, Wei and Zhang (2004)
find that a decrease in corporate earnings and an increase in their volatility explain the
increase in idiosyncratic volatility. Malkiel and Xu (2003) determine that a NASDAQ
listing, an increase in institutional ownership, and an increase in stocks with higher
forecasted growth are all important factors for explaining the trend. Bennett and Sias
(2004) find that changing industry composition and size explain the change over time.
1
See, for example, McConnell and Mosser (1999) for a discussion.
2
Cao, Simin, and Zhao (2004) show that the trend is explained largely by changes in
growth options.
In this paper we propose a simple and unifying explanation for the increase in
firm-specific risk: Increasingly risky firms have listed publicly, thus the overall
composition of publicly traded firms has changed significantly over the last 40 years.
This “new listing effect” explains the entire increase in idiosyncratic risk. It also explains
the results documented by other researchers investigating this issue (as well as some
related issues). For example, the Wei and Zhang result can be understood as a
consequence of the change in the composition of publicly traded firms—as riskier
privately held firms have listed, the cash flows of the “average” firm have decreased and
become more volatile. This change in the fundamentals of new listings is carefully
documented by Fama and French (2004) who show that new listings in the 1980s and
1990s are more left-skewed in their profitability, are more right-skewed in their growth,
and have lower survival rates. We show that this change in fundamentals of new stocks
is reflected in their idiosyncratic risk.
Firm size is an extremely important factor in explaining the level of idiosyncratic
volatility. We show the increase in idiosyncratic risk is concentrated among newer firms
which are on average small. In contrast, the idiosyncratic volatility of the largest firms
whose combined sales constitute 50% of GDP in each year has not increased over time.
Overall, we find that newly listed firms increasingly have lower profitability, are smaller
in size, are less likely to pay dividends, have a greater fraction of intangible assets, and
are more likely to be ‘growth’ stocks. In addition, industries that have shown a greater
increase in idiosyncratic volatility have a greater number of new firms. These are all
factors that have been found in prior research to be associated with higher idiosyncratic
volatility.
We stress that our results are not related directly to firm age. In particular, our
primary finding is not that newly listed firms in general have higher idiosyncratic risk
which decays as the firm matures (suggesting that an increasing proportion of newly
listed firms could lead to an upward trend in idiosyncratic risk). Instead, we find that
firms with increasingly and persistently higher idiosyncratic risk have been listing over
the last 40 years, suggesting a fundamental change for the character of the typical
3
publicly traded firm. This discovery has some important implications for many areas of
finance and economics which we discuss subsequently.
An independent project by Fink, Fink, Grullon and Weston (2005) is perhaps the
most similar to our paper. They find the increase in idiosyncratic risk is caused by firms
listing earlier in their life cycle. We believe that this is another symptom of our result
that firms with greater idiosyncratic volatility are becoming publicly traded. We find (as
do Fama and French, 2004) that age is not the only difference between firms that list later
in our sample and those that list earlier (as noted above, newer firms are also less
profitable, have a greater fraction of intangible assets, have greater stock turnover,
etcetera). In addition, we find that the idiosyncratic volatility of firms does not diminish
with age, which it should, if age at the time of IPO was the only difference between firms
that list later in our sample and those that list earlier. Also related to our analysis and that
by Fink et al. (2005) is work by Safdar (2000) which shows that the addition of new
firms after 1980 has had a substantial impact on the trend in idiosyncratic risk.
Considerable recent research has also investigated idiosyncratic volatility
normalized by total volatility, or R2 of the market model. For example, Morck et al.
(2000) and CLMX find that the R2 of the U.S. equity market is trending downward. We
find evidence consistent with our idiosyncratic risk hypothesis that explains this decline.
More recently listed firms have lower R2 than older firms, and after controlling for the
listing year, the R2 of firms is not declining over time. This reveals that newly listed
firms have caused the decline in average R2. Durnev et al. (2003) argue that lower R2 is
the result of more informed pricing. However, we find that newer, smaller, less
profitable firms with greater leverage have lower R2. Thus, the argument of Durnev et al.
would imply the seemingly contradictory result that such firms have more informed
pricing. We therefore advocate caution when using 1-R2 as a proxy for the amount of
information contained in prices until these results are reconciled.
The remainder of the paper is organized as follows. The next section surveys the
literature. Section 3 describes our key hypothesis in greater detail, and Section 4
describes the data we use and our methodology. In Section 5 we present our key results
on the sum of squared errors. Section 6 reconciles these results with some findings from
4
recent research. In Section 7 we replicate some of the SSE results for R2. Finally,
Section 8 concludes.
2. Related Literature
Researchers have defined idiosyncratic risk either as a volatility measure (e.g., the
sum of squared errors from estimating a model such as the capital asset pricing model) or
as a proxy for firm-specific information (e.g., Deurnev at al, 2004, examine 1-R2 of a
CAPM-based market model). Although these definitions are clearly related, they have
typically been examined separately, thus forming two distinct strands in the literature.
2.1. Sum of Squared Errors (SSE) Literature
Many recent papers examine the determinants of the time trend in idiosyncratic
risk. Bennett and Sias (2004) find that the growth of small firms, the growth of ‘riskier’
industries, and a decline in within-industry concentration explain the time trend. Wei and
Zhang (2004) find that fundamental factors, such as a decrease in corporate earnings and
an increase in earnings volatility, account for the growth in idiosyncratic volatility. Wei
and Zhang also note that new firms are more volatile than old firms. Malkiel and Xu
(2003) determine that NASDAQ stocks, an increase in institutional ownership, and an
increase in stocks with higher forecasted growth are all important factors for explaining
the trend. Irvine and Pontiff (2004) as well as Massa and Gaspar (2004) find that an
increase in competition is associated with the increase in idiosyncratic risk. Massa and
Gaspar specifically find that the lower ability of firms to price above their marginal cost,
combined with greater investment in R&D and innovation, are linked to higher
idiosyncratic volatility. Cao, Simin, and Zhao (2004) find that growth options explain the
trend in idiosyncratic risk.
Other research identifies a large number of factors explaining the level of
idiosyncratic risk in the cross-section of publicly-traded U.S. stocks. Harvey and
Siddique (2004) find that a number of firm-specific factors can predict idiosyncratic
volatility in the cross-section of firms. These include return on assets (ROA), firm size,
trading volume (turnover), idiosyncratic skewness, operating leverage, and inventory
growth.
5
Pastor and Veronesi (2003) examine a related, but distinct, hypothesis about
idiosyncratic risk and uncertainty in valuation using a model where investors learn about
profitability. They show that firms with greater uncertainty in valuation have higher
idiosyncratic volatility and suggest that age is a good proxy for this uncertainty (i.e., the
profitability of younger firms is more uncertain than that of older firms). In fact, they
find that younger firms have higher idiosyncratic volatility than older firms. However,
their model does not have time-series implications. In their model, the volatility of new
firms need not increase over time while our hypothesis predicts this increase. Second,
their hypothesis predicts that the idiosyncratic volatility of a given firm should decrease
over time, as uncertainty about its profitability diminishes. Also related to these findings
is the literature studying the development of financial markets (see, for example, Henry,
2003, and Rajan and Zingales, 2003).
2.2. R2 Literature
Roll (1988) finds the success of systematic factors, industry returns, and firmspecific news announcements in explaining individual firm returns is modest. The
findings are interpreted as support for the existence of private firm-specific information
or investor irrationality. Following Roll, a number of studies interpret 1-R2 of a CAPM
style model as a proxy for the level of firm-specific information that is incorporated into
prices.
For example, Morck, Yeung and Yu (2000) find that GDP per capita of a country
is inversely related to the level of synchronicity of equity prices as measured by R2. They
interpret this result as driven by greater investor protection in countries with higher per
capita GDP. CLMX and Morck, Yeung and Yu (2000) also show that the R2 of the U.S.
equity markets has declined significantly over time. Li et al. (2004) find that R2 in a
country is associated with greater capital markets openness. Durnev et al. (2003) show
that a lower R2 is linked with a greater association between current returns and future
earnings—evidence that lower R2 leads to more informed pricing. Piotrosky and
Rousltone (2003) also use 1-R2 as a proxy for the relative amount of firm-specific
information. They find 1-R2 is directly related to insider trading, and inversely related to
6
analyst activity and the level of institutional ownership.2
Despite the relatively large number of papers that use 1- R2 as a proxy for “firmspecific information that is incorporated in prices,” we have not identified any studies
investigating the association between firm-specific characteristics and R2. Consequently,
we investigate whether characteristics that are associated with low R2 are what we expect
firms with low firm-specific information to possess.
3. Hypothesis
We propose a clear-cut, but important, alternative explanation for the findings
discussed above. Quite simply, we hypothesize that an evolving composition of publicly
held firms in the post-war period has fundamentally altered the characteristics of a typical
stock. The first and most important prediction from this hypothesis is that we should not
observe an increase in idiosyncratic risk if we control for when firms list. Second, the
idiosyncratic risk of firms that list later should remain persistently higher than firms that
list earlier.
Our hypothesis also makes predictions that explain prior findings. In general, we
expect that financial and operating characteristics associated with newly traded firms will
have significant explanatory power for the time trend in idiosyncratic risk and R2.
Consequently, we expect small firms with high growth opportunities, large investments
in research and development, few tangible assets, and low dividends to be responsible for
the increase in idiosyncratic risk. We can differentiate our hypothesis from others by
considering firm characteristics as a function of listing vintage and noting the relative
trends in the time series. For example, our hypothesis suggests a trend in profitability
only for newly traded firms. Likewise, changes in industry composition or weights
associated with the trend in idiosyncratic risk should be due to changes in the age
composition of firms in each industry.
2
Their findings can be interpreted opposite to the way they interpret them. Insiders will trade precisely
when they believe that prices are uninformed, i.e., greater insider trading is probably an indicator that
prices are uninformed. Analysts and institutions generate information, therefore prices are more informed if
these agents are involved.
7
4. Data and Methodology
We collect all available data from CRSP and CompuStat for U.S. listed stocks
(with share code 10 or 11) from 1963-2002. In order to minimize the effect of
extraordinary events such as IPOs and acquisitions, years without complete returns data
are dropped from the sample. This yields a maximum sample size of 154,723 firm-years.
We plot the number of firms in each year of the sample in Figure 1. The number of firms
increases from 1,289 in 1964 to 4,829 in 2002, with a maximum of 6,378 in 1997. The
large increase from 1972 to 1973 is due to the inclusion of NASDAQ-listed companies.
We use weekly stock returns as a basis for calculating annual estimates of
idiosyncratic risk. For each year, we estimate the three-factor Fama-French (1993) model
Rit – rf = αi + βi*(Rmt – rf) + γi*SMBt + φi*HMLt + uit
(1)
for each stock i using data for weeks t=1, 2, …, 52.3 The sum of squared errors (SSE)
and the R2 (RSQ) are our annual measures of idiosyncratic risk. The result of this
estimation is an unbalanced panel that traces the evolution of every firm’s idiosyncratic
risk over time (with the exception of the first or last year of the listing should these occur
in the sample period). We compute simple averages of these measures (called SSE-EW
and RSQ-EW) as well as market-capitalization weighted averages (called SSE-VW and
RSQ-VW) for each year.
The firm-specific characteristics we use are motivated by prior research discussed
in Section 2 and the hypothesis presented in Section 3. A description of the methodology
used to calculate these characteristics is provided in Table 1.
We use this methodology as opposed to the one proposed by CLMX, as we wish
to study the idiosyncratic risk of individual firms and relate it to firm-specific
characteristics. This is not possible with the CLMX methodology as it produces average
values of idiosyncratic risk for a set of firms (all listed firms in their paper). In the next
section, we show that our methodology produces time trends in idiosyncratic risk
consistent with those shown by CLMX. We use weekly returns in our primary
regressions as a compromise between the need to use higher frequency data to better
3
Measures of idiosyncratic volatility based on market-model regressions and Fama-French regressions are
very similar (correlation greater than 90%). Since our conclusions are identical for both of these measures,
we report results based on only the Fama-French model.
8
estimate idiosyncratic volatility and the need to avoid microstructure noise (nonsynchronous trading, bid ask-bounces and stale prices) that are likely to be present in
daily returns of the large number of small stocks in our sample. We use annual measures
of volatility since the firm characteristics (e.g., profits, assets, etc.) that we wish to relate
them to are annual. In any case, we show in the Appendix that our primary results are
robust to using daily data with monthly regressions.
5. Idiosyncratic Volatility and Listing Group
5.1.
Descriptive Analysis
Figure 2 plots the time series of the value-weighted and equal-weighted measures
of idiosyncratic risk. Panel A confirms and updates the CLMX results. The valueweighted measure, SSE-VW, increases from 2.8% in 1963, to 7.5% in 1997 (the end of
the CLMX sample). After 1997, SSE-VW spikes to a sample high of 20.9% in 2000 but
declines significantly to 10.5% by 2003. Panel B plots the equal-weighted average.
Comparing the values with those in Panel A reveals a substantial difference between the
two measures. Specifically, SSE-EW begins in 1964 at 12.2% and increases to 35.4% in
1997. This series also shoots up in 2000 to a high of 60.9% before declining to 44.6% at
the end of the sample period. Each panel of Figure 2 exhibits the upward trend
documented in CLMX. However, the trend is notably greater for the equal-weighted
measure. Taken together, these results suggest that small stocks contribute significantly
to both the absolute value of idiosyncratic risk at each point in time as well as the
increase over time. As noted previously, prior research (e.g., Bennett and Sias, 2004)
documents similar results.
Table 2 contains descriptive statistics for the time series. The results confirm that
the time trend for both measures is statistically significant at the 1% level. Both of these
series are highly autocorrelated with the SSE-EW series more so. While the high degree
of autocorrelation suggests that the series may be nonstationary, an augmented DickeyFuller test with a time trend rejects unit roots at the 1% level.
9
5.2. New Lists and Idiosyncratic volatility
In this section, we examine trends in idiosyncratic risk based on listing vintage.
We begin our analysis by classifying firms into three categories:
1. Old: A firm listed 5 or more years and originally listed in or before 1964
2. Post-64: A firm listed 5 or more years but listed after 1964
3. New: A firm that has been listed less than 5 years
We define age using Jay Ritter’s proprietary database of IPO dates.4 If the IPO date is
unavailable from Ritter we use the first date a firm appears on the CRSP files. Panel A in
Figure 3 plots the SSE-EW for these three categories. In almost all years, the SSE-EW is
higher for New firms than for Old firms, confirming that listing year (or age) impacts
idiosyncratic volatility. However, the average idiosyncratic volatility of New firms is
strongly trending up over time, consistent with our hypothesis. Specifically, the volatility
of Post-64 firms also trends up, consistent with the hypothesis that as new listings
become older their idiosyncratic volatility remains at the higher levels at which they
listed. The trend in Post-64 firms is like the trend in New firms, lagged by 5 years.
Pastor and Veronesi (2003) suggest that an increase in the number of young firms
is one possible explanation for the increase in idiosyncratic risk over time (page 1779).
Panel B of Figure 3 measures the contribution of these three classes of firms to the
average idiosyncratic volatility in a given year, by weighting the idiosyncratic volatility
of each class by the number of firms in that class. As is clear from this graph, the major
part of this increase comes from firms that have been trading 5 or more years and first
appeared in CRSP post 1964. Thus, the increase in idiosyncratic volatility seems to be
because of the increasing idiosyncratic volatility of firms that are listed post 1964. This
intuition is confirmed by statistical tests in Panel A of Table 3. The time trend for Old
firms is not significant, while it is highly significant for Post-64 and New firms. The
notably higher means for New firms and Post-64 firms are also striking.
The previous analysis could suffer from an implicit survivorship bias. The firms
that survive for a long time (Old firms) are likely to be more stable and less volatile than
younger firms. We can mitigate the survivor bias by partitioning firms into finer age
groups. We sort firms into groups of firms that were listed before 1960, from 1960-1964,
from 1965-1970, and so on, until 1995-2000. Panel C of Figure 3 presents the average
4
The authors thank Jay Ritter for kindly providing these data.
10
SSE for these groups, while the data underlying this figure are in Panel B of Table 3. The
figure is a dramatic visual confirmation of our hypothesis. Each subsequent listing group
tends to start at a higher level of idiosyncratic volatility than the previous one, confirming
that new firms are getting riskier over time. Thus, in any given year, idiosyncratic
volatility tends to increase as the new listings add riskier firms to the average. The last
row of Table 3 shows the average SSE for each listing group. The monotonically
increasing average SSE makes plain the result that newer firms are riskier.
Also consistent with our hypothesis is that there is no obvious time trend within
each listing group. These findings are confirmed by estimating the time trends for each
group statistically. The results are presented in Panel A of Table 4. The magnitudes of
the trends are small and none of the 5-year listing groups have time trends statistically
different from zero at even the 10% confidence level. Panel B in Table 4 reports results
from an additional test with a regression of firm SSE including a time trend and fixed
effects for each listing group. The time coefficient is not significantly different from zero
and the coefficients of each listing group are monotonically increasing (over time).
Therefore, these results demonstrate convincingly that the increasing trend we observe in
average SSE-EW is because of riskier firms listing over time, rather than individual firms
becoming riskier.
The hypothesis of Fink et al. (2005), that the increase in idiosyncratic risk is
caused by firms listing earlier in their life-cycle, suggests that as listed firms grow older,
their idiosyncratic risk should decrease. However, we find that that time trend for each
group is flat, which appears to be inconsistent with this hypothesis.
In order to examine whether the idiosyncratic risk of any given firm has decreased
over time in greater detail, we run regressions with firm level fixed effects on a time
trend variable. In order to ensure that we do not miss a decline in idiosyncratic volatility
because of an increase caused by extraneous events, we restrict our sample to the years
before 1997 (to exclude the internet boom period). Second, we also expect that the
idiosyncratic risk of a firm might increase just prior to delisting (either because of
financial distress or M&A activity), so we add a control variable for the two last years
that the firm is in our sample.5 These results are reported in Panel C of Table 4. The
5
We obtain similar results by simply excluding the last two years the firm is in the sample.
11
annual time trend variable is almost zero (0.03%) and not statistically significant. Thus,
after listing, the idiosyncratic risk of a given firm does not decrease over time. However,
the two dummy variables representing the last two years that a firm is in the sample are
positive, economically large and highly significant. This suggests another way in which
the listing of increasingly risky firms increases average idiosyncratic volatility. As Fama
and French (2004) show, firms that list later in the sample have lower survival rates, thus
later in our sample there are more firms that disappear with typically high levels of
idiosyncratic risk in their terminal years.
In summary, the results of this section show that there is no trend in idiosyncratic
risk for individual companies. Instead, the observed increase in average idiosyncratic
risk is simply the result of increasingly higher levels of idiosyncratic risk for new listings.
6. Relation to Prior Work and Economy-Wide Financial Risk
We now turn to reconciling the findings of prior studies with the results in the
previous section. First, we show that several firm-specific characteristics are associated
with idiosyncratic volatility. Recent research has argued that changes in these firm
characteristics have caused the increase in idiosyncratic volatility. Section 6.1 discusses
how changes in firm-specific characteristics can be seen as outcomes of our new-listing
hypothesis, 6.2 examines industry effects, while 6.3 presents evidence that the population
of (public and private) firms has not become riskier.
6.1. Listing Effects and Other Firm-Specific Characteristics
Researchers have seen the correlation between the change in some of these
fundamentals and the increase in idiosyncratic volatility and concluded that they are
responsible for the increase in idiosyncratic volatility. We do not assert that there is a
causal link between the year of listing and idiosyncratic volatility. Rather, we believe
firms with riskier fundamentals have listed over time, leading to an increase in observed
idiosyncratic volatility.
To show that the prior results are consistent with our hypothesis, we examine five
of these firm-specific characteristics that the idiosyncratic risk literature has identified as
causing the increase in idiosyncratic volatility in detail: size, market-to-book, profit
margin, asset tangibility, and dividends. Our analysis of two of the factors (size and
12
profitability) essentially replicates the findings of Fama French (2004), although we use a
slightly longer sample period (1964-2002) and we sort the data differently, to be
consistent with our previous analysis.
Figure 4 plots these variables by the three listing groups defined earlier: Old,
Post-64 and New firms. Panel A shows that as older firms have increased in size, New
firms have typically remained small and even decreased in average size in some periods.
Panel B shows that, especially after the mid-1970s, New firms have significantly greater
growth opportunities as measured by the market-to-book ratio. Panels C and D provide
very convincing evidence that new firms are listing with progressively riskier
fundamentals. Profit margins and asset tangibility are both declining significantly even
as the values for Old firms remain nearly constant. Panel E shows that New firms have
become less likely to pay a dividend even as the frequency of dividends among Old firms
remains constant. Together, these figures suggests the expected payoffs of newly listed
firms are becoming progressively further in the future and hence, are more difficult to
forecast.
We also repeat the regression of these variables on time, with fixed effects for 5year listing groups. The results are presented in Table 5. For each of these variables, the
dummy variables reveal that newer listings are changing in the direction suggested by our
hypothesis that riskier firms are increasingly likely to go public. Overall, these results
suggest the changes in firm-level characteristics are correlated with when the firm lists,
and therefore, this explains the relation between these characteristics and the increase in
idiosyncratic volatility documented by previous research.
6.2. Analysis of Industry Composition
A natural next question about the ‘newly public’ companies concerns their effect
on the overall industry composition of the U.S. equities market. Examining industry
composition may allow us to reconcile our results with the prior findings on changes in
industry composition. For example, if typically riskier industries have increased in size
because of disproportionate growth in newly issued companies, this would cause an
increase in observed idiosyncratic volatility.
Table 6 presents the top 5 industries by market capitalization at the start and end
of our sample. It shows that industry composition of the sample has changed
13
substantially in the last 40 years. Consistent with our hypothesis, safer industrial
companies, such as auto manufacturers and chemical companies, have become a smaller
share of the stock market while services and research-intensive companies are now the
largest industries. Of course, these changes are reflected in the percent of total SSE these
industries are responsible for in 1964 versus 2002 (last column of table 6). In particular,
4 of the top 5 industries in 1964 have shown a substantial reduction.
Telecommunications, which has experienced an influx of innovative informationtechnology firms, is the exception. Likewise, 4 of the top 5 industries in 2002 have seen
a substantial increases in their share of total SSE (retail is the exception).
To gain additional intuitive understanding of the importance of industry effects,
we compute average SSE keeping the industry weights constant at their 1964 levels. As
can be seen in Panel A of Figure 5, there is a slight difference between this weighting
scheme and the actual time varying weights. The difference between the two lines
increases during the internet boom of 1998-2001. The difference is about 15% of the
increase in idiosyncratic volatility from 1964. However, if we repeat this calculation
using market capitalization weights, the average SSE in 2002 is higher using 1964
weights than actual weights. This suggests that a change in the composition of firms
within an industry rather than changes in industry weights is the more important effect.
A further examination of this effect is presented in Panels B and C of Figure 5
which contain scatter plots of the average SSE in each industry against average firm age
and average number of New firms (less than 5 years old). These plots show that SSE is
inversely related to average age of firms in an industry and directly related to the
proportion of new listings. The slopes are statistically significant at the 1% level. Panel
D plots the increase in SSE (SSE in 2002 – SSE 1964) for each industry against the
average fraction of New firms in that industry. The positive relation confirms that
industries with the greatest increase in average idiosyncratic volatility have a greater
fraction of New firms.
6.3. Riskier Public Firms or Riskier Economy?
Our hypothesis is that many additional firms have become publicly traded and these
firms are inherently (and persistently) riskier than existing public firms. As discussed
above, these are likely to be smaller firms, less profitable firms, etc. To better measure
14
how firm size relates to the economy as a whole (and how the addition of the ‘newly
traded’ part of the economy contributes to average levels of idiosyncratic risk), we
stratify our sample by creating baskets of firms using the measure of total sales of listed
firms to nominal GDP.
Figure 6 plots time-series for three groups of firms. The first group is constructed
by sorting firms by total sales each year and taking the minimum number of firms with
sales totaling no less than 30% of GDP. The second group is the minimum additional
number of firms needed to generate combined sales of the next 20% of GDP. The third
group is all other publicly traded firms. Panel A in Figure 6 shows the number of firms
in each of the first two groups remains fairly stable after the early 1970s. The average
number of firms in the first group is 66 and in the second group is 209. However, the
number of smaller firms grows steadily and substantially from 426 in 1964 to over 6,000
in 1997. These newly listed firms represent sales equaling approximately 25 percent of
GDP indicating that companies representing a significant portion of economic activity
have been added to the ranks of publicly listed firms. Moreover, Panel B in Figure 6
plots SSE-EW for the different size groups over time. The graph reveals that the time
trend in idiosyncratic risk is concentrated entirely in this group of smallest firms.6 This
type of stratification can be repeated for other firm characteristics with similar results
(not reported).
Nonetheless, this evidence, along with that presented in the previous sections, is
potentially consistent with both our hypothesis as well as the hypothesis that all new
private and public firms are becoming riskier. To distinguish between these competing
hypotheses, we conduct additional tests suggesting that the observed increase in risk is a
“sampling problem” and the typical riskiness of the overall population of firms has not
increased in a meaningful way.
We first examine bankruptcy rates for all public and private firms. Panel A of
Table 7 examines the trend in business failure rates from 1964 to 1997 reported by the
Dun and Bradstreet Corporation.7 The estimated time trend is economically small and
6
There is no statistically significant time trend in either of the first two groups.
Data are from the 1997 Business Failure Record and our analysis corrects for a methodological change in
1984 that expanded the survey to include agricultural and some financial services businesses. Dun and
Bradstreet’s business failure statistics are the most comprehensive available and include all public and
7
15
statistically insignificant suggesting that as a whole the risk of business failure has not
changed meaningfully over the last 40 years.8 This is in stark contrast to increasing
failure rates for publicly traded firms reported by Fama and French (2004).
If companies as a whole have become riskier, this should be reflected in the risk
premiums charged by lenders as well as loan default measures. To investigate this
question, we examine quarterly data on commercial and industrial loan rates collected by
the Federal Reserve Board. The data are only available starting in 1986, but as shown in
Figure 2, the majority of the increase in idiosyncratic risk has occurred in the years from
1986 to 2002. Panel B of Table 7 shows that loan spreads over the Federal Funds rate
increase only by about 0.003% per quarter (or about 1 basis point per year) and this trend
is statistically marginal (p-value = 0.051). We also collect quarterly data on
nonperforming commercial loans and net loan charge-offs from FFIEC Reports of
Condition and Income for All Insured U.S. Commercial Banks from 1988 to 2002.
Panels C and D of Table 7 show these measures decline significantly over this 15 year
period. Taken together, this evidence suggests that individual borrowers have not
become riskier recently.
One criticism of these measures is that banks may have simply reduced the level
of lending in response to firms becoming riskier. In fact, lower levels of bank lending to
businesses may represent indirect evidence that firms as a whole have become riskier. To
measure the level of business lending we examine the level of commercial and industrial
loans standardized by the level of GDP. Figure 7 plots these data from 1964 to 2002 and
reveals that, while there is substantial cyclical variation, there is no time trend over this
period.9
Finally, we examine the aggregate level of corporate earnings to see if profits as a
percent of GDP have declined or have become more volatile over our sample period.
Panel A of Figure 8 plots the level of overall profitability of the business sector (after tax
with inventory valuation adjustment and capital consumption adjustment) as a percent of
private businesses that “ceased operations following assignment or bankruptcy, ceased operations with
losses to creditors after such actions as foreclosures or attachment, voluntarily withdrew leaving unpaid
debts, were involved in court actions such as receivership, reorganization or arrangement, or voluntarily
compromised with creditors.”
8
This finding is somewhat surprising since the number of new businesses formed annually has more than
quadrupled over the same time period.
9
Statistical tests (not reported) confirm this result.
16
GDP. The graph shows no significant trend over the whole sample period and increasing
profits on average over the last 20 years. Panel B of Table 8 plots the standard deviation
of corporate profits for the preceding 5 years and reveals no trend. Again, we contrast
this with the finding of Wei and Zhang (2004) that corporate profitability is decreasing
and the volatility of corporate profits is increasing for publicly traded firms.
In sum, the evidence provided in the section is (i) consistent with the hypothesis
that a larger portion of riskier firms have become publicly traded companies, and (ii)
inconsistent with the hypothesis that businesses as a whole have become riskier.
7. R2
Prior literature has documented the decline in R2 in the U.S. over time. This
decline is an almost mechanical consequence of the increase in average idiosyncratic
volatility combined with trendless systematic volatility. However, examining R2 by itself
is important for at least three reasons. If R2 is used as a metric to measure the success of
asset pricing models, then understanding the decline in R2 is key to understanding the
reasons for the declining performance of asset pricing models. Second, Morck et al.
(2000) document an inverse association between countries per capita GDP and its level of
R2 which they attribute to the degree of investor protection. Third, Durnev et al. (2003)
show that lower R2 is the result of more informed pricing. Consequently, understanding
cross-sectional differences in R2 provides insights into each of these issues.
In this section, we check whether the results documented for SSE in the previous
sections carry through for R2. We also test if a firm’s listing group is associated with R2,
if the declining trend in R2 can be explained by the presence of more new firms with
lower R2, and which firm-specific characteristics are associated with R2. Armed with this
knowledge, we then address the three issues discussed above.
7.1. Prior Results
Figure 9 plots value-weighted R2 (RSQ-VW) and equal-weighted R2 (RSQ-EW)
from 1964 to 2002. The graphs shows RSQ-VW is higher than RSQ-EW and RSQ-EW
declines over time while there is no apparent trend in RSQ-VW. These results are
confirmed by statistical tests reported (along with summary statistics) in Table 8. The
difference in the two series suggests that size, or variables correlated with size such as
17
firm age, are important in understanding both cross-sectional variation in RSQ and its
time trend.
7.2. R2 , Listing Group, and Time Trends
Figure 10 plots average R2 by the 5-year listing groups defined earlier. The chart
shows a clear age effect. In any given year, older firms have higher R2. In addition, the
R2 of any given listing group is not declining over time. This is confirmed by the time
trend statistics reported in Panel A of Table 9. These show that none of the listing groups
experience a decline in average R2 and that earlier listing groups tend to have higher
average R2. Panel B shows the results of regressing R2 on a time trend variable with
dummy variables for each listing group. The time trend coefficient is not statistically
different from zero. The coefficients on the listing group variables are reliably negative
and generally decreasing over time. In summary, these results show that the R2 for
groups of firms that list within 5 years of each other is not declining.
7.3. R2 and Firm-Specific Characteristics
The literal interpretation of R2 is the fraction of a stock’s volatility that is
‘explained’ by market volatility. Since volatility is often linked with information, some
authors interpret 1-R2 as the ratio of ‘firm-specific information’ to all value relevant
information that is incorporated into prices. The next link (which has been made
empirically by Durnev et al., 2003) is between the relative amount of firm-specific
information and ‘informed’ pricing. The relation between listing group and R2
(documented above) raises doubts about the interpretation of R2 as the degree of
information in prices. Specifically, we do not expect younger firms to have more
informed prices than older firms, yet they have significantly lower R2s. To better
understand the characteristics of firms with low R2, we now examine the cross-sectional
relation between other firm-specific factors and R2 to see if these are consistent with
expectations.
Intuitively we expect that companies with relatively more informed prices would
be larger, have more liquid shares, pay dividends, have fewer growth opportunities, be
more profitable, and have more tangible assets. Table 10 presents results from a FamaMacbeth regression of R2 on proxies for these firm-specific characteristics. Our proxies
are the same as those presented in Table 4 but we also include turnover as a proxy for
18
market liquidity. Leverage and the cash ratio (which some considered negative leverage)
are included to control for possible leverage effects documented by prior research. The
coefficients for several of the factors raise concerns about the validity of 1-R2 as a
measure of the informativeness of prices. In particular, the results indicate that large,
liquid firms with high profit margins typically have high R2—findings which are all
opposite of the predictions.
While these results are not consistent with 1-R2 being a measure of the firmspecific information in prices, they can be interpreted in the context of the model by
Pastor and Veronesi (2002). In their model, idiosyncratic volatility has two components:
the idiosyncratic volatility of profitability and the uncertainty about profitability. Small,
new firms with low profit levels are likely to have greater uncertainty about profitability
than otherwise similar firms. This is likely to raise the idiosyncratic volatility of a firm,
without affecting the volatility explained by the market, thus lowering the R2. Finally,
we note that the apparent decreasing ability of the 3-factor model to explain asset returns
over time is really a statement about the ability of the 3- factor model to explain returns
of new listings. A more accurate assessment is that the model does worse for new firms,
yet for any given listing group, average explanatory power is not declining over time.
8. Implications and Conclusions
Our findings reveal a simple, but important, mechanism driving the documented
increase in idiosyncratic risk and decrease in R2. Newly listed companies are riskier and
have lower R2 than older companies. Just as importantly, this is not the result of a higher
proportion of newly listed companies which would suggest that average idiosyncratic risk
may decline as these firms mature. Instead, there is a clear and ongoing trend toward
riskier firms becoming publicly traded.
While there are potentially many explanations for this trend, we propose one
obvious hypothesis: During our sample period, firms with higher levels of firm-specific
risk were able to publicly list because of increasing financial market development. In the
context of Rajan and Zingales (2003) this statement is almost a tautology since these
authors define financial market development as the ease of access to arms-length
financial transactions. For equity markets this implies that there will be a greater fraction
19
of the economy that is publicly held.10 In support of this hypothesis, our results indicate
that the newly-traded part of the economy is where the increase in idiosyncratic risk is
observed. Not only do these firms sample have greater idiosyncratic risk, they also have
riskier fundamentals. Thus, the increase in average idiosyncratic risk and the
deteriorating fundamentals of publicly traded firms is likely to be related to increasing
financial market development.
This reiterates the potential importance of financial development in broad
economic development. If increasing financial sophistication in the U.S. allows riskier
companies to access capital markets more easily or cheaply, this could help explain why
the U.S. has experienced such high levels of productivity and technological innovation
recently. For example, an optimal risk-sharing argument suggests that raising capital
from a large number of smaller investors is desirable. It also suggests that declines over
time in the average financial condition of public corporations may not be a sign of
economic instability but instead may represent a changing composition of publicly traded
firms. In addition, this hypothesis resolves the paradox of a U.S. economy that appears to
be getting more stable and a stock market that is getting riskier by showing that the latter
is just the result of a larger (riskier) part of economic activity being undertaken by public
companies.
Our results on firm characteristics and R2 imply that the interpretation of 1-R2 as a
measure of the informativeness of prices is likely to be flawed. The discussion above
indicates a mechanism that explains the Morck et al. (1999) synchronicity result. We
have seen that as U.S. markets have become more sophisticated, firms with more
idiosyncratic volatility (and hence lower R2) have been able to list. Thus, the number and
the riskiness of new firms is linked to the degree of development of financial markets (for
example the existence of a market like the NASDAQ). In effect, the synchronicity result
suggests the rather unsurprising conclusion that these two factors are correlated with per
capita GDP and the degree of investor protection.
In summary, the contribution of this paper can be seen as bringing to light interlinkages between four recent results in financial economics i.) CLMX, who show that
10
In fact, Rajan and Zingales use aggregate market capitalization to GDP as a measure of financial
development
20
average idiosyncratic volatility has increased over time, ii.) Fama and French (2004) who
show that new lists have riskier fundamentals, iii.) Rajan and Zingales who examine
financial market development, and iv.) Morck et al (1999) who show that synchronicity is
linked to per-capita GDP and investor protection.
21
Appendix
To check the robustness of our results we generate our estimates of SSE and RSQ
using monthly Fama-French regressions with daily returns (as opposed to annual
regressions with weekly returns). The data in this sample cover January 1964 through
December 2002 and contains all common stocks (share code 10 or 11) in the CRSP
universe (as opposed to the intersection of the CRSP and CompuStat databases). Panel A
of Figure 11 shows the increase in equally-weighted idiosyncratic volatility. This timeseries is comparable to the one displayed in Figure 2. Panel B of Figure 11 shows
idiosyncratic risk by listing group where we plot 6-month moving averages (to smooth
the data) of average monthly idiosyncratic volatility. The implications from this graph
are essentially the same as those from Panel C of Figure 3 though these plots appear
noisier. As before, visual inspection suggests that each listing group series tends to begin
at a higher value than the previous one and is trendless. This is confirmed in Table 11
which replicates Panel A of Table 4.
22
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24
Figure 1. Number of Observations
This figure depicts the number of firms in the sample. Data are annual from 1964 to 2002. The
significant increase of 1,489 between 1972 and 1973 is due to the addition of NASDAQ-listed
companies. Sample size is determined by data availability on the CRSP database. Only firms with
complete returns data for the year are included in the sample.
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
1964
1969
1974
1979
1984
1989
1994
1999
Figure 2. Idiosyncratic Risk
This figure depicts the annual average sum of squared errors from the 3-factor Fama-French
model. The model is estimated each year using weekly returns data. Panel A shows the average
weighted by year-end market capitalization (SSE-VW). Panel B shows a simple equal-weighted
average (SSE-EW).
Panel A: Value-weighted idiosyncratic risk
25%
20%
15%
10%
5%
0%
1964
1969
1974
1979
1984
1989
1994
1999
1994
1999
Panel B: Equal-weighted idiosyncratic risk
70%
60%
50%
40%
30%
20%
10%
0%
1964
1969
1974
1979
1984
1989
Figure 3. Idiosyncratic Risk by Age
This figure depicts the annual average sum of squared errors from the 3-factor Fama-French model
for 3 groups of firms representing different years of listing. For Panels A and B, each year firms
are sorted into three groups:
1. Old: firms listed 5 or more years and listed in or before 1964
2. Post-64: firms listed 5 or more years and listed after 1964
3. New: firms listed less than 5 years
Panel A shows annual average idiosyncratic volatility for each of these three groups. Panel B
shows the annual average contribution of each of these groups to average idiosyncratic volatility.
The contribution is measured as the sum of idiosyncratic volatility of all firms within a group,
divided by the sum of idiosyncratic volatility for all firms that year. In Panel C, firms are sorted
into groups based on their year of listing: before 1965, 1965-69, 70-74 and so on until 1995-1999.
The chart displays the average SSE for each of these groups.
Panel A: Average idiosyncratic risk by listing group
100%
Old
Post-64
New
SSE
75%
50%
25%
0%
1964
1969
1974
1979
1984
1989
1994
1999
Panel B: Average contribution to idiosyncratic risk by listing group
80%
Old
Post-64
New
Total
SSE
60%
40%
20%
0%
1964
1969
1974
1979
1984
1989
1994
1999
Panel C: Average SSE by 5 year Listing Group
80%
SSE
60%
40%
20%
0%
1964
1969
1974
<1965
1980-84
1979
1984
1965-69
1985-89
1989
1970-74
1990-94
1994
1975-79
1995-99
1999
Figure 4. Firm Characteristics By Age
This figure depicts firm characteristics for 3 groups of firms representing different years of listing. Each year firms are sorted into
three groups:
1. Old: firms that are 5 or more years old and were founded before 1964
2. Post-64: firms that are 5 or more years old and were founded after 1964
3. New: firms less than 5 years old
Panel A plots firm size (Real Total Assets), Panel B plots the Market-to-Book ratio, Panel C plots Profit Margin, Panel D plots
Asset Tangibility, and Panel E plots the percentage of firms paying dividends. In Panels B and C we exclude firms with M/B <0 or
>20 , PM <-5 and >1, respectively, in order to remove inconsistent data, outliers and distressed firms.
Panel B. Market-to-Book Ratio
Panel A. Real Total Assets
3,000
4.5
Old
Post-64
New
2,000
3.0
1.5
1,000
0
Old
Post-64
New
0.0
1964
1969
1974
1979
1984
1989
1994
1999
1964
1969
Panel C. Profit Margin
1979
1984
1989
1994
1999
1994
1999
Panel D. Asset Tangibility
20%
50%
0%
40%
-20%
30%
Old
Post-64
New
-40%
1974
Old
Post-64
New
20%
-60%
10%
1964
1969
1974
1979
1984
1989
1994
1999
1964
1969
1974
1979
Panel E. Dividend Payers
100%
75%
50%
Old
Post-64
New
25%
0%
1964
1969
1974
1979
1984
1989
1994
1999
1984
1989
Figure 5. Average Idiosyncratic Risk and Industry Effects
This figure depicts the annual average sum of squared errors (SSE) from the 3-factor Fama-French
model for firms grouped according to the Fama-French 30 Industry classification. Panel A plots
SSE-64, a series constructed by keeping each industry's weights (relative number of firms)
constant at their 1964 levels and the SSE-EW, with the real time-varying weights. Panels B and C
are scatter plots of the average SSE of each industry against average firm age and the fraction of
new firms (firms less than 5 years old) in that industry. Panel D is a scatter plot of the increase in
SSE (SSE in 2002 - SSE in 1964) against the fraction of new firms in that industry.
Panel A: SSE with different industry weights
75%
SSE-64
SSE
SSE-EW
50%
25%
0%
1964
1969
1974
1979
1984
1989
1994
1999
Year
Panel B: Scatter plot of average SSE with average firm age by industry
60%
SSE
40%
20%
0%
0
10
20
30
40
Years
50
Panel C: Scatter plot of average SSE with fraction of new firms by industry
60%
SSE
40%
20%
0%
0%
10%
20%
30%
% New Firms
40%
Panel D: Scatter plot of increase in SSE with fraction of new firms in each industry
100%
75%
50%
25%
0%
0%
10%
20%
30%
% New Firms 40%
Figure 6. Idiosyncratic Risk by Total Sales to GDP
This figure depicts the annual average sum of squared errors from the 3-factor Fama-French
model for 3 groups of firms representing different percentages of GDP. Each year, firms are
sorted by total sales as a percent of GDP. The first group is constructed by taking the largest
firms whose sales total the 30% of GDP. The second group consists of the next 20% of GDP,
and the third group is all other firms.
Panel A: Number of firms
10,000
Log
scale
First 30% GDP
Next 20% GDP
All Other Firms
1,000
100
10
1964
1969
1974
1979
1984
1989
1994
1999
1994
1999
Panel B: Sum of squared errors
80%
First 30% GDP
Next 20% GDP
All Other Firms
SSE
60%
40%
20%
0%
1964
1969
1974
1979
1984
1989
Figure 7. Commercial and Industrial Loans as a Percent of GDP
This figure depicts the level of commercial and industrial loans divided by the level of gross domestic
product (GDP). Loan data are measured for the end-of-quarter month and are from the Federal Reserve
Board statistical release H.8. GDP data are obtained from the U.S. Department of Commerce.
13%
12%
11%
10%
9%
8%
1964
1969
1974
1979
1984
1989
1994
1999
Figure 8. Corporate Profits
Panel A plots the level of Corporate Profits After Tax with Inventory Valuation Adjustment and Capital
Consumption Adjustment divided by the level of gross domestic product (GDP). Panel B plots a rolling
estimate of the volatility of corporate profits by taking the standard deviation of the 5 prior years of
quarterly values plotted in Panel A. Data are obtained from the U.S. Department of Commerce.
Panel A: Corporate profits (as % of GDP)
8%
7%
6%
5%
4%
3%
1964
1969
1974
1979
1984
1989
1994
1999
Panel A: Volatility of corporate profits (as % of GDP)
1.2%
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
1964
1969
1974
1979
1984
1989
1994
1999
Figure 9. R2
This figure plots the annual average R-squared from the 3-factor Fama-French model. The model
is estimated each year using weekly returns data. Panel A shows the average weighted by yearend market capitalization (RSQ-VW). Panel B shows a simple equal-weighted average (RSQEW).
Panel A: Value-weighted R2
60%
45%
30%
15%
0%
1964
1969
1974
1979
1984
1989
1994
1999 Year
1994
1999
Panel B: Equal-weighted R2
40%
30%
20%
10%
0%
1964
1969
1974
1979
1984
1989
Year
Figure 10. R2 by Age
This figure depicts the annual R-squared of the 3-factor Fama-French model for groups of firms
representing different years of listing. Firms are sorted into groups based on their year of listing:
before 1965, 1965-69, 70-74 and so on until 1995-1999.
40%
30%
20%
10%
1964
1969
1974
<1965
1980-84
1979
1965-69
1985-89
1984
1989
1970-74
1990-94
1994
1999
1975-79
1995-1999
Figure 11. Idiosyncratic Risk by Age (Monthly Data)
This figure depicts the monthly average sum of squared errors from the 3-factor Fama-French
model. The model is estimated each month using daily returns data. Panel A shows a simple equalweighted average (SSE-EW). Panel B displays average SSE for groups of firms sorted based on
their year of listing: before 1965, 1965-69, 70-74 and so on until 1995-1999.
Panel A: Equal-weighted idiosyncratic risk
12%
8%
4%
0%
1964
1969
1974
1979
1984
1989
1994
1999
Panel B: Equal-weighted idiosyncratic risk by listing group
14%
SSE
12%
10%
8%
6%
4%
2%
0%
1964
1969
1974
<1965
1985-89
1979
1965-69
1990-94
1984
1970-74
1995-99
1989
1994
1975-79
2000-
1999
1980-84
Table 1. Description of Variables
This table reports labels and descriptions for the primary variables. Financial and operating characteristics are
calculated using annual data from CompuStat.
Label
Description
Log Real Assets
Turnover
Log of Total Assets deflated by the Consumer Price Index (CPI).
Average Daily Volume over the year divided by the Number of
Shares Outstanding (times 1,000).
Market Capitalization
Number of Shares Outstanding at the end of the fiscal year times
Price at the end of the fiscal year.
Following Fama and French (1993), Book Equity is constructed
as Stockholders’ Equity plus Balance Sheet Deferred Taxes and
Investment Tax Credit (COMPUSTAT item 35) minus the Book
Value of Preferred Stock. Depending on availability,
Stockholder’s Equity is computed as COMPUSTAT item 216 or
60+130 or 6-181, in that order, and Preferred Stock is computed
as item 56 or 10 or 130, in that order. Market-to-Book is ratio of
Book Equity to Market Capitalization.
Market-to-Book Ratio
Leverage
Long Term Debt divided by Total Assets.
Profit Margin
Operating Income Before Depreciation divided by Total Sales.
Return on Equity
Operating Income Before Depreciation divided by Book Equity.
Asset Tangibility
Property Plant and Equipment divided by Total Assets.
Dividend Dummy
1 if Common or Preferred Dividends >0 during the fiscal year.
Cash Ratio
Cash (Item 1) divided by Total Assets.
Year of listing
Old Firm Dummy
If the IPO date is unavailable from Jay Ritter's database, we use
the first date a firm appears on CRSP.
1 if firm listed before 1964 and listing is more than 5 years prior.
New Firm Dummy
1 if listing is less than 5 years prior.
Post-64 Firm Dummy
1 if firm listed after 1964 and listing is greater than or equal to 5
years prior.
Table 2. Time Series Analysis of Idiosyncratic Risk
This table reports summary statistics for the value-weighted (SSE-VW) and
equal-weighted (SSE-EW) sum of squared error measures of idiosyncratic
risk. Data are annual from 1964 to 2002 (39 observations).
Mean
Standard deviation
Minimum
Maximum
Linear time-trend coefficient
Linear time-trend p -value
SSE-VW
7.2%
3.5%
2.8%
20.9%
SSE-EW
29.1%
14.6%
11.8%
60.9%
0.19%
0.005
1.00%
<0.001
Table 3. Analysis of Idiosyncratic Risk by Listing Group
Panel A reports summary statistics for equal-weighted (SSE-EW) sum of squared error measures of idiosyncratic
risk of three groups of firms representing different years of listing Each year, these groups are defined as:
1. Old: A firm that is 5 or more years old and was founded before 1964
2. Post-64: A firm that is 5 or more years old and that was founded after 1964
3. New: A firm that is less than 5 years old
Data are annual from 1964 to 2002 (39 observations). Panel B describes the annual average sum of squared
errors from the 3-factor Fama-French model for groups of firms. Firms are sorted into groups based on their year
of listing - before 1965, 1965-69, 70-74 and so on until after 1999.
Panel A: Summary statistics for equal-weighted annual average SSE
Mean
Standard deviation
Minimum
Maximum
Old
12.3%
3.4%
4.6%
19.5%
Post-64
27.9%
11.1%
11.8%
53.5%
New
38.5%
19.2%
13.4%
87.1%
Linear time trend coefficient (%)
Linear time trend p -value
0.07%
0.330
0.84%
<0.001
1.44%
<0.001
Panel B: Annual average SSE by 5-year listing group
Year
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
Average
<1965
11%
12%
12%
16%
13%
11%
16%
13%
12%
15%
20%
19%
13%
10%
11%
11%
14%
12%
12%
13%
9%
9%
12%
12%
11%
10%
17%
20%
17%
15%
12%
13%
9%
8%
12%
14%
19%
19%
18%
13.4%
1965-69
1970-74
1975-79
1980-84
1985-89
1990-94
1995-99
>1999
13%
18%
15%
14%
20%
18%
17%
24%
29%
31%
22%
15%
18%
17%
20%
18%
19%
19%
14%
14%
17%
21%
15%
14%
23%
30%
29%
19%
15%
14%
15%
15%
18%
21%
29%
21%
19%
19.2%
17%
15%
23%
25%
29%
22%
18%
20%
17%
20%
16%
18%
20%
14%
16%
19%
19%
16%
15%
39%
27%
32%
23%
14%
16%
16%
15%
21%
25%
29%
23%
17%
20.5%
35%
27%
28%
34%
45%
32%
38%
45%
29%
32%
30%
35%
27%
26%
37%
56%
58%
51%
35%
44%
38%
27%
36%
46%
49%
35%
27%
37.1%
48%
53%
53%
34%
41%
41%
48%
38%
38%
51%
60%
60%
43%
34%
41%
38%
36%
45%
52%
53%
38%
31%
44.4%
41%
45%
40%
41%
55%
68%
61%
42%
34%
34%
33%
32%
42%
48%
55%
45%
40%
44.5%
55%
52%
43%
37%
41%
42%
42%
54%
63%
59%
50%
39%
48.1%
43%
45%
78%
80%
80%
73%
57%
65.1%
103%
67%
85.0%
Table 4. Time Trends in Idiosyncratic Volatility by Listing Group
This table describes the annual sum of squared errors (SSE) from the 3-factor Fama-French model for groups of
firms. Firms are sorted into groups based on their year of listing: before 1965, 1965-69, 70-74 and so on until
after 1999. Panel A reports the results of a regression of the average SSE of each of these groups on a constant
and a time-trend variable. Panel B reports the results of a regression of SSE of each firm on time, with fixed
effects for each listing group. The p -value reported in all tables is based on t-statistics calculated using robust
standard errors. In Panel B the group of firms listed before 1960 is omitted from the regression, thus all
coefficients on dummy variables are relative to this group.
Panel A: Time trends in average SSE by listing group
Regression estimates
Group
<1965
1965-69
1970-74
1975-79
1980-84
1985-89
1990-94
1995-99
>1999
Average SSE
13.38%
19.19%
20.50%
37.11%
44.36%
44.47%
48.08%
65.14%
85.00%
Time Trend
p -value
0.04%
0.05%
0.07%
0.29%
-0.27%
-0.23%
0.33%
3.54%
0.49
0.59
0.57
0.18
0.34
0.59
0.71
0.32
Panel B: Time trends with fixed effects for each listing group
Variable
Time Trend
1960-64 dummy
1965-69 dummy
1970-74 dummy
1975-79 dummy
1980-84 dummy
1985-89 dummy
1990-94 dummy
1995-99 dummy
> 1999 dummy
Coefficient
0.02%
10.36%
11.19%
11.96%
27.95%
35.19%
36.10%
37.47%
59.85%
74.67%
p -value
0.451
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
Table 5. Firm Characteristics by Listing Group
This table describes the relation between firm-specific characteristics and the year of a firm's listing. Firms are sorted
into groups based on their year of listing: before 1965, 1965-69, 70-74 and so on until after 1999. The panels below
contain the results of different firm-level characteristics regressed on dummy variables for the listing group and a time
trend. Panel A shows size (Real Total Assets), Panel B shows the Market-to-Book ratio, Panel C shows Profit Margin,
Panel D shows Asset Tangibility, and Panel E shows the Dividend Dummy variable. In Panel B we filter out firmyears with Market-to-Book <0 or >20 , and in Panel C we filter out firm-years with Profit Margin <-5 and >1, in order
to remove inconsistent data, outliers and distressed firms. All standard errors are robust to serial correlation and
heteroskedasticity.
Panel A: Real Total Assets (log)
Coef.
t-stat
Time Trend
0.06
93.79
1960-64 dummy
-2.04 -119.43
1965-69 dummy
-2.29 -130.05
1970-74 dummy
-2.52 -155.99
1975-79 dummy
-3.93 -152.62
1980-84 dummy
-4.24 -216.67
1985-89 dummy
-4.00 -187.76
1990-94 dummy
-3.90 -180.82
1995-99 dummy
-3.98 -161.24
> 1999 dummy
-4.16
-65.48
Constant
-115.78
-89.28
p -value
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
Panel B: Market-to-Book
Coef.
t-stat p -value
Time Trend
0.006
3.64 <0.001
1960-64 dummy
0.109
1.74
0.082
1965-69 dummy
0.002
0.04
0.972
1970-74 dummy
-0.021
-0.36
0.716
1975-79 dummy
0.751
8.79 <0.001
1980-84 dummy
1.041
14.37 <0.001
1985-89 dummy
1.103
14.13 <0.001
1990-94 dummy
1.296
16.90 <0.001
1995-99 dummy
1.369
16.49 <0.001
> 1999 dummy
0.872
6.61 <0.001
Constant
-10.030
-3.15
0.002
Panel C: Profit Margin
Coef.
t-stat
Time Trend
0.002
9.65
1960-64 dummy
-0.036
-5.79
1965-69 dummy
-0.046
-8.16
1970-74 dummy
-0.043
-7.57
1975-79 dummy
-0.118
-10.09
1980-84 dummy
-0.205
-19.92
1985-89 dummy
-0.161
-16.97
1990-94 dummy
-0.192
-18.21
1995-99 dummy
-0.273
-22.64
> 1999 dummy
-0.606
-13.37
Constant
-3.071
25.11
p -value
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
Panel D: Asset Tangibility
Coef.
t-stat p -value
Time Trend
-0.105
-8.50 <0.001
1960-64 dummy
-0.131
-11.20 <0.001
1965-69 dummy
-0.139
-12.65 <0.001
1970-74 dummy
-0.106
-7.58 <0.001
1975-79 dummy
-0.151
-13.73 <0.001
1980-84 dummy
-0.202
-18.83 <0.001
1985-89 dummy
-0.209
-19.91 <0.001
1990-94 dummy
-0.249
-24.40 <0.001
1995-99 dummy
-0.280
-22.21 <0.001
> 1999 dummy
-0.448
48.45 <0.001
Constant
3.286
20.27 <0.001
Panel E: Dividend Dummy
Coef.
t-stat
Time Trend
0.003
9.09
1960-64 dummy
-0.207
-14.07
1965-69 dummy
-0.234
-17.58
1970-74 dummy
-0.282
-25.46
1975-79 dummy
-0.578
-29.10
1980-84 dummy
-0.675
-56.34
1985-89 dummy
-0.630
-50.32
1990-94 dummy
-0.688
-56.87
1995-99 dummy
-0.721
-57.71
> 1999 dummy
-0.786
-39.24
Constant
-5.337
106.51
p -value
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
Table 6. Industry Effects
This table reports summary statistics for the equal-weighted (SSE-EW) sum of squared error measures of idiosyncratic risk for the five largest industries
in 1964 and 2002 based on market capitalization. Industries are classified according to the Fama-French 30 Industry classification. Data are annual from
1964 to 2002 (39 observations).
Industry
Market Cap ($bn)
1964
2002
Number of Firms
1964
2002
SSE-EW
1964
2002
% Total SSE
1964
2002
Top 5 industries in 1964 by Market Cap
Oil
72.1
514.0
69
141
11.0%
28.0%
5.4%
1.9%
Utilities
50.4
297.1
101
115
2.0%
19.0%
1.4%
1.0%
Auto
41.1
72.8
58
47
8.0%
37.0%
3.3%
0.8%
Telecommunications
39.6
438.7
15
134
9.0%
97.0%
1.0%
6.2%
Chemicals
29.0
195.8
52
67
11.0%
33.0%
4.1%
1.1%
5.5
2,177.4
38
927
8.0%
13.0%
2.2%
5.8%
Health Care & Pharmaceuticals
14.3
1,182.8
30
488
5.0%
57.0%
1.1%
13.3%
Business Equipment
27.4
886.8
83
543
16.0%
62.0%
9.5%
16.1%
0.9
848.8
19
747
23.0%
68.0%
3.1%
24.3%
22.0
605.9
81
231
7.0%
43.0%
4.1%
4.8%
Top 5 industries in 2002 by Market Cap
Financial Services
Services
Retail
Table 7. Measures of Total Business Risk
This table presents evidence on time trends for various measures of total business risk. All estimates are
from OLS regressions with linear time trends. Panel A examines annual data on business failure rates for
1964-1997 from Dun and Bradstreet. Panel B examines quarterly data provided by the Federal Reserve
Board on commercial and industrial loan spreads over the Federal Funds rate from 1986 to 2002. Panel C
examines nonperforming loans defined as the percentage of commercial loans more than 90 days past due.
Panel D examines the level of net loan charge-offs as a percentage of total loans. Data for Panels C and D are
from the FFIEC Reports of Condition and Income for All Insured U.S. Commercial Banks for 1988-2002.
Panel A: Business failure rates
(failures per 10,000 businesses)
Time Trend
Constant
Dummy for 1984 change in methodology
Coef.
0.27
44.11
44.25
t-stat
0.43
5.51
3.45
p -value
0.672
<0.001
<0.001
Panel B: Commercial and industrial loan spreads over the federal funds rate
Coef.
0.003%
1.840%
Time Trend
Constant
t-stat
1.99
34.09
p -value
0.051
<0.001
t-stat
-6.80
15.21
p -value
<0.001
<0.001
t-stat
-3.68
14.09
p -value
0.001
<0.001
Panel C: Nonperforming commercial loans
(% of loans 90 days past due)
Time Trend
Constant
Coef.
-0.050%
3.941%
Panel D: Net loan charge-offs
(% of loans charged off each quarter)
Time Trend
Constant
Coef.
-0.008%
1.099%
Table 8. Time Series Analysis of R2
This table reports summary statistics for the value-weighted (RSQ-VW) and equal-weighted (RSQEW) R2 measures of idiosyncratic risk. Data are annual from 1964 to 2002 (39 observations).
RSQ-VW
RSQ-EW
34.9%
19.3%
8.2%
5.9%
Minimum
18.7%
11.0%
Maximum
56.7%
35.7%
Linear time trend coefficient
0.06%
-0.17%
0.440
0.101
Mean
Standard deviation
Linear time trend p -value
2
Table 9. R by Listing Group
This table describes the relation between RSQ and the year of a firm's listing. Firms are sorted into groups based on
their year of listing: before 1965, 1965-69, 70-74 and so on until after 1999. The table below contains the results of
RSQ regressed on dummy variables for the listing group and a time trend. All standard errors are robust to serial
correlation and heteroskedasticity. In Panel B the group of firms listed before 1960 is omitted from this regression,
thus all coefficients on the dummy variables are relative to this group.
Panel A: Time trends in average RSQ by listing group
Group
<1965
1965-69
1970-74
1975-79
1980-84
1985-89
1990-94
1995-99
> 1999
Regression estimates
p -value
Average RSQ Time Trend
24.62%
0.06%
0.584
21.70%
-0.07%
0.521
19.00%
0.05%
0.651
14.96%
0.10%
0.369
15.55%
0.16%
0.285
14.88%
0.14%
0.648
14.83%
0.62%
0.076
16.14%
1.01%
0.010
18.50%
Panel B: Time trends with fixed effects for each listing group
Time Trend
1960-64 dummy
1965-69 dummy
1970-74 dummy
1975-79 dummy
1980-84 dummy
1985-89 dummy
1990-94 dummy
1995-99 dummy
> 1999 dummy
Constant
Coef.
0.05%
-5.14%
-4.83%
-8.28%
-11.96%
-12.21%
-13.09%
-13.60%
-11.40%
-9.08%
25.87%
p -value
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
Table 10. R2 and Firm Characteristics in Fama-Macbeth Regressions
This table reports the results of annual cross-sectional regressions of each firm's R 2 on various firm
characteristics from 1964 to 2002. Time-series averages of estimated coefficients are reported in the
column labeled Mean . The reported t-statistics have been corrected for serial correlation using
Newey-West standard errors (for 4 lags). Reported p -values are for a two-tailed test against a null
hypothesis of zero. The coefficients for the 29 industry dummy variables are not reported. Variable
definitions are provided in Table 1.
Predicted Sign
Intercept
Mean
t-statistic
p -value
0.054
3.34
0.002
Real Assets (log)
-
0.036
15.51
0.000
Market-to-Book
+
0.007
6.52
0.000
Turnover
-
0.023
4.50
0.000
Profit Margin
-
0.027
2.58
0.015
Dividend Dummy
-
-0.005
-1.62
0.117
Asset Tangibility
-
-0.008
-1.10
0.281
Cash Ratio
?
0.035
3.48
0.002
Leverage
?
-0.052
-4.56
0.000
Table 11. Time Trends in Idiosyncratic Volatility by Listing Group
This table describes the monthly sum of squared errors (SSE) from the 3-factor Fama-French model for groups of
firms. Firms are sorted into groups based on their year of listing: before 1965, 1965-69, 70-74 and so on until after
1999. The reported results are obtained from a regression of the average SSE of each of these groups on a constant
and a time trend variable. The reported p -values are based on t-statistics calculated using Newey-West corrected
standard errors.
Regression estimates
Group
<1965
1965-69
1970-74
1975-79
1980-84
1985-89
1990-94
1995-99
>1999
Average SSE
1.34%
1.68%
1.95%
3.60%
4.76%
5.28%
5.52%
6.41%
6.05%
Time Trend x 105
0.21
-0.39
2.50
7.00
3.00
-0.04
-7.00
0.58
p -value
0.639
0.520
0.024
0.050
0.420
0.994
0.360
0.970