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.

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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 firm-

specific, 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 well-

diversified 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.

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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

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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

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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.

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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 firm-

specific 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

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analyst activity and the level of institutional ownership.2

Despite the relatively large number of papers that use 1- R2 as a proxy for “firm-

specific 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.

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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.

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estimate idiosyncratic volatility and the need to avoid microstructure noise (non-

synchronous 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 value-

weighted 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 Dickey-

Fuller test with a time trend rejects unit roots at the 1% level.

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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.

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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.

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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

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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 5-

year 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

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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 information-

technology 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

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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. 7 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

16

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.

17

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

18

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 Fama-

Macbeth 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

19

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 firm-

specific 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

20

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 inter-

linkages 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

21

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.

22

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 time-

series 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.

23

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Figure 1. Number of Observations

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

1964 1969 1974 1979 1984 1989 1994 1999

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.

Figure 2. Idiosyncratic Risk

Panel A: Value-weighted idiosyncratic risk

Panel B: Equal-weighted idiosyncratic risk

0%

5%

10%

15%

20%

25%

1964 1969 1974 1979 1984 1989 1994 1999

0%

10%

20%

30%

40%

50%

60%

70%

1964 1969 1974 1979 1984 1989 1994 1999

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).

Figure 3. Idiosyncratic Risk by Age

Panel A: Average idiosyncratic risk by listing group

Panel B: Average contribution to idiosyncratic risk by listing group

0%

25%

50%

75%

100%

1964 1969 1974 1979 1984 1989 1994 1999

OldPost-64New

SSE

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 yearsPanel 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.

0%

20%

40%

60%

80%

1964 1969 1974 1979 1984 1989 1994 1999

OldPost-64NewTotal

SSE

Panel C: Average SSE by 5 year Listing Group

0%

20%

40%

60%

80%

1964 1969 1974 1979 1984 1989 1994 1999

<1965 1965-69 1970-74 1975-791980-84 1985-89 1990-94 1995-99

SSE

Figure 4. Firm Characteristics By Age

Panel A. Real Total Assets Panel B. Market-to-Book Ratio

Panel E. Dividend Payers

Panel D. Asset TangibilityPanel C. Profit Margin

0

1,000

2,000

3,000

1964 1969 1974 1979 1984 1989 1994 1999

OldPost-64New

0.0

1.5

3.0

4.5

1964 1969 1974 1979 1984 1989 1994 1999

OldPost-64New

10%

20%

30%

40%

50%

1964 1969 1974 1979 1984 1989 1994 1999

OldPost-64New

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 oldPanel 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.

-60%

-40%

-20%

0%

20%

1964 1969 1974 1979 1984 1989 1994 1999

OldPost-64New

0%

25%

50%

75%

100%

1964 1969 1974 1979 1984 1989 1994 1999

OldPost-64New

Figure 5. Average Idiosyncratic Risk and Industry Effects

Panel A: SSE with different industry weights

Panel B: Scatter plot of average SSE with average firm age by industry

0%

25%

50%

75%

1964 1969 1974 1979 1984 1989 1994 1999 Year

SSE-64

SSE-EWSSE

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.

0%

20%

40%

60%

0 10 20 30 40 50Years

SSE

Panel C: Scatter plot of average SSE with fraction of new firms by industry

Panel D: Scatter plot of increase in SSE with fraction of new firms in each industry

0%

20%

40%

60%

0% 10% 20% 30% 40%% New Firms

SSE

0%

25%

50%

75%

100%

0% 10% 20% 30% 40%% New Firms

Figure 6. Idiosyncratic Risk by Total Sales to GDP

Panel A: Number of firms

Panel B: Sum of squared errors

10

100

1,000

10,000

1964 1969 1974 1979 1984 1989 1994 1999

First 30% GDPNext 20% GDPAll Other Firms

Log scale

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.

0%

20%

40%

60%

80%

1964 1969 1974 1979 1984 1989 1994 1999

First 30% GDPNext 20% GDPAll Other Firms

SSE

Figure 7. Commercial and Industrial Loans as a Percent of GDP

8%

9%

10%

11%

12%

13%

1964 1969 1974 1979 1984 1989 1994 1999

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.

Figure 8. Corporate Profits

Panel A: Corporate profits (as % of GDP)

Panel A: Volatility of corporate profits (as % of GDP)

3%

4%

5%

6%

7%

8%

1964 1969 1974 1979 1984 1989 1994 1999

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1964 1969 1974 1979 1984 1989 1994 1999

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.

Figure 9. R2

Panel A: Value-weighted R2

Panel B: Equal-weighted R2

0%

15%

30%

45%

60%

1964 1969 1974 1979 1984 1989 1994 1999 Year

0%

10%

20%

30%

40%

1964 1969 1974 1979 1984 1989 1994 1999 Year

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 year-end market capitalization (RSQ-VW). Panel B shows a simple equal-weighted average (RSQ-EW).

Figure 10. R2 by Age

10%

20%

30%

40%

1964 1969 1974 1979 1984 1989 1994 1999

<1965 1965-69 1970-74 1975-791980-84 1985-89 1990-94 1995-1999

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.

Figure 11. Idiosyncratic Risk by Age (Monthly Data)

Panel A: Equal-weighted idiosyncratic risk

Panel B: Equal-weighted idiosyncratic risk by listing group

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 equal-weighted 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.

0%

2%

4%

6%

8%

10%

12%

14%

1964 1969 1974 1979 1984 1989 1994 1999

<1965 1965-69 1970-74 1975-79 1980-841985-89 1990-94 1995-99 2000-

SSE

0%

4%

8%

12%

1964 1969 1974 1979 1984 1989 1994 1999

Label Description

Log Real Assets Log of Total Assets deflated by the Consumer Price Index (CPI).Turnover 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.Market-to-Book Ratio 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.

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 If the IPO date is unavailable from Jay Ritter's database, we use

the first date a firm appears on CRSP.Old Firm Dummy 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 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.

Table 2. Time Series Analysis of Idiosyncratic Risk

SSE-VW SSE-EWMean 7.2% 29.1%Standard deviation 3.5% 14.6%Minimum 2.8% 11.8%Maximum 20.9% 60.9%

Linear time-trend coefficient 0.19% 1.00%Linear time-trend p -value 0.005 <0.001

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).

Old Post-64 New Mean 12.3% 27.9% 38.5%Standard deviation 3.4% 11.1% 19.2%Minimum 4.6% 11.8% 13.4%Maximum 19.5% 53.5% 87.1%

Linear time trend coefficient (%) 0.07% 0.84% 1.44%Linear time trend p -value 0.330 <0.001 <0.001

Year <1965 1965-69 1970-74 1975-79 1980-84 1985-89 1990-94 1995-99 >19991964 11%1965 12%1966 12% 13%1967 16% 18%1968 13% 15%1969 11% 14%1970 16% 20%1971 13% 18% 17%1972 12% 17% 15%1973 15% 24% 23%1974 20% 29% 25%1975 19% 31% 29%1976 13% 22% 22% 35%1977 10% 15% 18% 27%1978 11% 18% 20% 28%1979 11% 17% 17% 34%1980 14% 20% 20% 45%1981 12% 18% 16% 32% 48%1982 12% 19% 18% 38% 53%1983 13% 19% 20% 45% 53%1984 9% 14% 14% 29% 34%1985 9% 14% 16% 32% 41%1986 12% 17% 19% 30% 41% 41%1987 12% 21% 19% 35% 48% 45%1988 11% 15% 16% 27% 38% 40%1989 10% 14% 15% 26% 38% 41%1990 17% 23% 39% 37% 51% 55%1991 20% 30% 27% 56% 60% 68% 55%1992 17% 29% 32% 58% 60% 61% 52%1993 15% 19% 23% 51% 43% 42% 43%1994 12% 15% 14% 35% 34% 34% 37%1995 13% 14% 16% 44% 41% 34% 41%1996 9% 15% 16% 38% 38% 33% 42% 43%1997 8% 15% 15% 27% 36% 32% 42% 45%1998 12% 18% 21% 36% 45% 42% 54% 78%1999 14% 21% 25% 46% 52% 48% 63% 80%2000 19% 29% 29% 49% 53% 55% 59% 80%2001 19% 21% 23% 35% 38% 45% 50% 73% 103%2002 18% 19% 17% 27% 31% 40% 39% 57% 67%

Average 13.4% 19.2% 20.5% 37.1% 44.4% 44.5% 48.1% 65.1% 85.0%

Panel B: Annual average SSE by 5-year listing group

Table 3. Analysis of Idiosyncratic Risk by Listing Group

Panel A: Summary statistics for equal-weighted annual average SSE

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 oldData 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: Time trends in average SSE by listing group

Group Average SSE Time Trend p -value<1965 13.38% 0.04% 0.49

1965-69 19.19% 0.05% 0.591970-74 20.50% 0.07% 0.571975-79 37.11% 0.29% 0.181980-84 44.36% -0.27% 0.341985-89 44.47% -0.23% 0.591990-94 48.08% 0.33% 0.711995-99 65.14% 3.54% 0.32>1999 85.00%

Panel B: Time trends with fixed effects for each listing group

Variable Coefficient p -valueTime Trend 0.02% 0.451

1960-64 dummy 10.36% <0.0011965-69 dummy 11.19% <0.0011970-74 dummy 11.96% <0.0011975-79 dummy 27.95% <0.0011980-84 dummy 35.19% <0.0011985-89 dummy 36.10% <0.0011990-94 dummy 37.47% <0.0011995-99 dummy 59.85% <0.001> 1999 dummy 74.67% <0.001

Table 4. Time Trends in Idiosyncratic Volatility by Listing Group

Regression estimates

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.

Coef. t-stat p -value Coef. t-stat p -valueTime Trend 0.06 93.79 <0.001 Time Trend 0.006 3.64 <0.0011960-64 dummy -2.04 -119.43 <0.001 1960-64 dummy 0.109 1.74 0.0821965-69 dummy -2.29 -130.05 <0.001 1965-69 dummy 0.002 0.04 0.9721970-74 dummy -2.52 -155.99 <0.001 1970-74 dummy -0.021 -0.36 0.7161975-79 dummy -3.93 -152.62 <0.001 1975-79 dummy 0.751 8.79 <0.0011980-84 dummy -4.24 -216.67 <0.001 1980-84 dummy 1.041 14.37 <0.0011985-89 dummy -4.00 -187.76 <0.001 1985-89 dummy 1.103 14.13 <0.0011990-94 dummy -3.90 -180.82 <0.001 1990-94 dummy 1.296 16.90 <0.0011995-99 dummy -3.98 -161.24 <0.001 1995-99 dummy 1.369 16.49 <0.001> 1999 dummy -4.16 -65.48 <0.001 > 1999 dummy 0.872 6.61 <0.001Constant -115.78 -89.28 <0.001 Constant -10.030 -3.15 0.002

Coef. t-stat p -value Coef. t-stat p -valueTime Trend 0.002 9.65 <0.001 Time Trend -0.105 -8.50 <0.0011960-64 dummy -0.036 -5.79 <0.001 1960-64 dummy -0.131 -11.20 <0.0011965-69 dummy -0.046 -8.16 <0.001 1965-69 dummy -0.139 -12.65 <0.0011970-74 dummy -0.043 -7.57 <0.001 1970-74 dummy -0.106 -7.58 <0.0011975-79 dummy -0.118 -10.09 <0.001 1975-79 dummy -0.151 -13.73 <0.0011980-84 dummy -0.205 -19.92 <0.001 1980-84 dummy -0.202 -18.83 <0.0011985-89 dummy -0.161 -16.97 <0.001 1985-89 dummy -0.209 -19.91 <0.0011990-94 dummy -0.192 -18.21 <0.001 1990-94 dummy -0.249 -24.40 <0.0011995-99 dummy -0.273 -22.64 <0.001 1995-99 dummy -0.280 -22.21 <0.001> 1999 dummy -0.606 -13.37 <0.001 > 1999 dummy -0.448 48.45 <0.001Constant -3.071 25.11 <0.001 Constant 3.286 20.27 <0.001

Coef. t-stat p -valueTime Trend 0.003 9.09 <0.0011960-64 dummy -0.207 -14.07 <0.0011965-69 dummy -0.234 -17.58 <0.0011970-74 dummy -0.282 -25.46 <0.0011975-79 dummy -0.578 -29.10 <0.0011980-84 dummy -0.675 -56.34 <0.0011985-89 dummy -0.630 -50.32 <0.0011990-94 dummy -0.688 -56.87 <0.0011995-99 dummy -0.721 -57.71 <0.001> 1999 dummy -0.786 -39.24 <0.001Constant -5.337 106.51 <0.001

Table 5. Firm Characteristics by Listing Group

Panel A: Real Total Assets (log) Panel B: Market-to-Book

Panel C: Profit Margin Panel D: Asset Tangibility

Panel E: Dividend Dummy

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 firm-years 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.

Industry 1964 2002 1964 2002 1964 2002 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%

Top 5 industries in 2002 by Market Cap

Financial Services 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%

Services 0.9 848.8 19 747 23.0% 68.0% 3.1% 24.3%

Retail 22.0 605.9 81 231 7.0% 43.0% 4.1% 4.8%

Table 6. Industry Effects

Market Cap ($bn) Number of Firms SSE-EW % Total SSE

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).

Table 7. Measures of Total Business Risk

Panel A: Business failure rates

(failures per 10,000 businesses) Coef. t-stat p -valueTime Trend 0.27 0.43 0.672Constant 44.11 5.51 <0.001Dummy for 1984 change in methodology 44.25 3.45 <0.001

Panel B: Commercial and industrial loan spreads over the federal funds rate Coef. t-stat p -value

Time Trend 0.003% 1.99 0.051Constant 1.840% 34.09 <0.001

Panel C: Nonperforming commercial loans

(% of loans 90 days past due) Coef. t-stat p -valueTime Trend -0.050% -6.80 <0.001Constant 3.941% 15.21 <0.001

Panel D: Net loan charge-offs

(% of loans charged off each quarter) Coef. t-stat p -valueTime Trend -0.008% -3.68 0.001Constant 1.099% 14.09 <0.001

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.

Table 8. Time Series Analysis of R2

RSQ-VW RSQ-EW

Mean 34.9% 19.3%

Standard deviation 8.2% 5.9%

Minimum 18.7% 11.0%

Maximum 56.7% 35.7%

Linear time trend coefficient 0.06% -0.17%

Linear time trend p -value 0.440 0.101

This table reports summary statistics for the value-weighted (RSQ-VW) and equal-weighted (RSQ-EW) R2 measures of idiosyncratic risk. Data are annual from 1964 to 2002 (39 observations).

Group Average RSQ Time Trend p -value<1965 24.62% 0.06% 0.5841965-69 21.70% -0.07% 0.5211970-74 19.00% 0.05% 0.6511975-79 14.96% 0.10% 0.3691980-84 15.55% 0.16% 0.2851985-89 14.88% 0.14% 0.6481990-94 14.83% 0.62% 0.0761995-99 16.14% 1.01% 0.010> 1999 18.50%

Coef. p -valueTime Trend 0.05% <0.0011960-64 dummy -5.14% <0.0011965-69 dummy -4.83% <0.0011970-74 dummy -8.28% <0.0011975-79 dummy -11.96% <0.0011980-84 dummy -12.21% <0.0011985-89 dummy -13.09% <0.0011990-94 dummy -13.60% <0.0011995-99 dummy -11.40% <0.001> 1999 dummy -9.08% <0.001Constant 25.87% <0.001

Regression estimates

Panel B: Time trends with fixed effects for each listing group

Table 9. R2 by Listing Group

Panel A: Time trends in average RSQ 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.

Predicted Sign Mean t-statistic p -value

Intercept 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 10. R2 and Firm Characteristics in Fama-Macbeth Regressions

This table reports the results of annual cross-sectional regressions of each firm's R2 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.

Group Average SSE Time Trend x 105 p -value<1965 1.34% 0.21 0.639

1965-69 1.68% -0.39 0.5201970-74 1.95% 2.50 0.0241975-79 3.60% 7.00 0.0501980-84 4.76% 3.00 0.4201985-89 5.28% -0.04 0.9941990-94 5.52% -7.00 0.3601995-99 6.41% 0.58 0.970>1999 6.05%

Table 11. Time Trends in Idiosyncratic Volatility by Listing Group

Regression estimates

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.