A Reinvestigation of Idiosyncratic Volatility

Transcription

1 A Reinvestigation of Idiosyncratic Volatility Nicholas Wilmes Western Kentucky University May 5, 2015 Abstract In updating Campbell et al. (2001) I find evidence that the level of idiosyncratic volatility, industry-specific volatility, and market volatility have increased to their highest level in 50 years during the 21 st century. I also find evidence that the average correlation among stocks has steadily increased as well. Finally, I find that the average R-squared is increasing, opposite the findings by Fama & French (2004) and Brown & Kapadia (2007) that the average R-squared is decreasing. I would like to thank Dr. Alex Lebedinsky for his generous support and guidance through this process. I would also like to thank Dr. Brian Goff and Dr. David Beckworth for their helpful feedback and comments.

2 1 Introduction In this paper, I investigate volatility patterns in U.S. stock market by decomposing aggregate volatility into idiosyncratic, market and industry volatilities. The paper closely follows Campbell et al. (2001) updating their work with more recent data. In this paper, I focus on the effect of major market events, changing market dynamics, and unique economic and financial position in which we currently reside on idiosyncratic volatility. Since the turn of the 21 st century, investors in the United States stock market have seen their fortunes change drastically. These fifteen years encompassed not only a strong bull market, but also two cataclysmic events that will forever define the decade in history books. These two events are the technology bubble and the Great Recession. These major events wreaked havoc on the stock market and major indices declined markedly, decimating the wealth of many. While it is obvious that the returns generated by firms during times of great financial distress in a weakening economy will be below their historical levels, an important question to ask is whether the resulting volatility is systematic or idiosyncratic in nature. Systematic volatility is defined here as volatility of the market as a whole on collective risk that is common to equities in general rather than specific firms. In contrast, idiosyncratic volatility is volatility that is unique to an individual firm due to risks and information that pertain solely to that firm rather than to the market as a whole. When levels of volatility are high for equities, investors place a higher risk premium on equity securities. This reduces the assets price by further discounting future cash flows because of the high risk associated with the increase in uncertainty about the future, or investors require a larger return. Measuring volatility not only in the aggregate, but also its industry and firm specific idiosyncratic components is important for investors. Idiosyncratic volatility of individual firms may be offset by other firms in a portfolio, but not necessarily their associated industry risk. Similarly, the various stocks in a given portfolio may be diversified as to their industry-specific risk but not necessarily their firm-specific idiosyncratic risk (Campbell et al. [2001]). Lastly, the prices of derivatives such as call or put options are dependent on the price of the individual stock

3 2 for which the option pertains, and the price is affected by the total of the market risk, industryspecific risk, and idiosyncratic risk. A prominent and widely cited study by Campbell et al. (2001) showed that from 1962 through 1997 idiosyncratic firm volatility increased and had a statistically significant upward trend and that the overall market volatility did not exhibit a similar trend. Campbell et al. (2001) also found that along with an increase in idiosyncratic risk, there was a decrease in the correlation among stocks over their sample, and that the industry-level volatility, and to a lesser extent market and idiosyncratic volatility, help to forecast economic activity. This paper extends Campbell et al. (2001) work by updating the data to include the rise and fall of stocks during the technology bubble, the years of growth during the mid-2000s, the Great Recession, and the current recovery. In updating Campbell et al. (2001) I find evidence that the level of idiosyncratic volatility, industry-specific volatility, and market volatility have increased to their highest level in 50 years during the 21 st century. I also find evidence that the average correlation among stocks has steadily increased as well. Related Literature As this study intends to update Campbell et al. (2001), it is substantially based upon their work. In their paper, Campbell et al. (2001) find that idiosyncratic volatility increased from 1962 through 1997 and had a significant upward trend. However, they did not find an upward trend for industry-specific volatility or market volatility. They also found that the average R-squared of the market model was decreasing over time and as a result, the number of stocks required to diversify a portfolio had increased. The upward trend in idiosyncratic volatility reported by Campbell et al. (2001) has been disputed by some. An alternative view put forward by Brandt et al. (2010) is that the increase in idiosyncratic volatility was an episodic phenomenon concentrated in low-priced stocks with high levels of retail ownership that reversed itself in the year 2000 and was not a time trend. However, many other researchers have also found an upward trend in idiosyncratic volatility including

4 3 Irvine & Pontiff (2009), Bartram et al. (2012), Brown & Kapadia (2007), and Comin & Philippon (2006). A great deal of the literature examines what has caused the change in the level of idiosyncratic volatility and characteristics of firm s that have high levels of idiosyncratic volatility. This literature will be discussed at length in the discussion section. Empirical Analysis In this paper I use daily stock returns from The Center for Research in Security Prices (CRSP) database. The sample ranges from July 1, 1962 to December 31, 2013 and includes all firms traded on the NYSE, NASDAQ, NYSE Market, and the NYSE Arca exchanges during the period. I also obtained each firm s SIC code and market capitalization (stock price multiplied by the number of outstanding shares) from the CRSP database at monthly intervals with the observation recorded on the final trading day of the month. I used the SIC codes to assign industry codes using the Fama & French (1997) scheme. This scheme classifies firms into 49 industries, including one other category. From this monthly data I dropped any observations that had missing values for market capitalization. Finally, I obtained 1-month Treasury bill data in monthly intervals from Kenneth French s Data Library for the sample period. My data differs slightly from the data Campbell et al. (2001) because I include firms that are traded on the NYSE Arca exchange. The NYSE Arca exchange did not begin actively trading securities until 1997, the final year included in Campbell et al. (2001). Because this study includes sixteen years of trading since the NYSE Arca became active, including stocks traded on this exchange is pertinent to investigating the volatility of equities in the United States as a whole. After deleting observations containing missing values, the sample used in this paper differed slightly from Campbell et al. (2001) in the number of firms. At the beginning of the period my sample contained 2,044 firms compared to the 2,047 in Campbell et al. (2001), and in the last month of Campbell et al. (2001) sample period my sample had 9,205 firms compared to their 8,927. However, even after excluding firms that traded on the NYSE Arca exchange the number of firms did not match perfectly. Even though the sample varied slightly from Campbell et al. (2001), my results very closely resemble theirs.

5 4 Figure 1 (see appendix) plots the number of firms in my sample over the period. Figures 2 and 3 show the distribution of the size of firms within my sample. Figure 2 graphs the median market capitalization, first and third quartiles, and mean market capitalization, all adjusted for inflation. This figure shows that since the early 1970 s the real mean market capitalization has been above the third quartile. Figure 3 shows the mean and values 1.96 standard deviations above and below the mean. This figure depicts where 95% of firms would fall if the market capitalization of stocks was normally distributed. It is obvious from these figures that the size of firms within the market is heavily right-skewed. To calculate a measure of overall aggregate volatility encompassing every stock traded, a scheme must be devised to weight the returns of each firm. The simplest possible weighting scheme would be to give each firm, regardless of its size, an equal weight such that the volatility of a small start-up influences the overall volatility to the same extent that the volatility of one of the largest firms does. Campbell et al. (2001) showed that weighted average of return volatilities can be decomposed as follows = + = = + + Equation (1) shows that the firm volatility is equal to the variance of firm specific residuals multiplied by the weight of firm j in industry i in period t,, and then summed for all firms within industry i. This is then multiplied by the weight of industry i in period t,, and summed for all industries. Using this method I can decompose return volatilities into their components without estimating betas for individual stocks or industries, which may change over the sample. Following Campbell et al. (2001), and the method by which market indices weigh component stocks, I assigned weights to firms based upon their market capitalization. I

6 5 calculated a firm s weight by dividing their market capitalization by the sum of the market capitalization for all firms in the sample during a particular month. For example, to calculate weighted return in March 2013, I used market caps from February Firms were re-weighted each month based upon their market capitalization on the last day of the previous month. I then merged these monthly weights with the daily return data and I calculated market-weighted average return for each day in the sample. I then subtracted the 1-month Treasury bill rate from the average weighted returns to calculate the daily excess average returns Rms, or the returns that were earned above the risk-free rate. 2 = = From the daily excess average returns I calculated the mean excess return of the market over the sample period µm for month t. Volatility for each month was calculated with daily data for that month using equation (2) above. Note, this equation measures variation around the mean for the entire sample rather than month-specific means. Figures 4 and 5 (see appendix) graph the market volatility and the 12-month moving average of volatility over time. It is clear from these figures that since Campbell et al. (2001), market volatility increased greatly and remained high for around five years, which coincides with the technology bubble. After this period, market volatility decreased back to normal levels until the financial crisis and the ensuing Great Recession. The market volatility reaches its maximum level in the sample around the end of 2008, surpassing the second highest month in the sample which contains the 1987 stock market crash. 3 = = = As with the weights of the individual firms within the market, the weight of each firm within its respective industry is based upon the firm s market capitalization. The weight of firm j

7 6 in industry i is equal to firm j s weight within the market divided by the sum of the weights of all firms within industry i. Using these industry weights and returns for each firm in the industry, I calculate weighted average returns for each industry. From the daily average returns by industry, the 1-month Treasury bill rate is subtracted to give the excess industry returns. The volatility for each industry is then calculated following equation (4) by subtracting the excess market returns from the excess industry returns and squaring the differences, denoted, and summing the squared differences by industry for each month. Average industry volatility is calculated using individual industry volatilities and weights of industries in the market, as shown in equation (5). The industry volatility series and its 12-month moving average are shown over time in the figures 6 and 7 (see appendix.) These graphs show that during both the technology bubble and the Great Recession, average industry volatility peaks at levels that are almost double the highest level observed during the period in Campbell et al. (2001). This increased level of industry-specific volatility persisted for multiple years surrounding both of these major events. However, between the technology bubble and the Great Recession industry-level volatility fell to its previous levels. Figure 7 is perhaps more striking because it shows that level of industry volatility at its peak during the technology bubble was about 5 times greater than the highest level in Campbell et al. (2001) = + = = 9 = Finally, to compute the idiosyncratic firm volatility I subtracted the average industry return from each firm s excess returns and squared the difference, resulting in from equation (7). Then, per equation (8), I summed the squared differences for each firm by month

8 7 and multiplied each firm s total squared differences by the firm s weight within its industry to result in average idiosyncratic volatility in industry i. Next, following equation (9), I calculate average idiosyncratic volatility for the all stocks as the weighted average of, where is weight of industry i within the total market in period t. and its 12-moth moving average are depicted in figures 8 and 9, respectively. Campbell et al. (2001) found that there was an upward trend in the idiosyncratic volatility but Brandt et al. (2010) found that by 2001 this trend ceased to exist. Post 2001 there does not appear to be any upward trend in the idiosyncratic volatility Brandt et al. (2010). As with the industry volatility, the 12-month moving average of idiosyncratic volatility in figure 9 peaks during technology bubble. This peak is approximately 2.5 times greater than the largest value in the period studied by Campbell et al. (2001). During the Great Recession, the peak in idiosyncratic volatility is slightly less than double the peak in Campbell et al. (2001). To further investigate the relationship among stocks, and the systematic risk in the market, I used the rolling regression method in Campbell et al. (2001). The dependent variable in each of these regressions is each individual firm s excess return with the market excess return used as the sole explanatory variable. For each month I used all firms with complete return data for the previous 12 months and saved the R-squared of each model. I then averaged the R- squared for all firms with complete data in each month and plotted the resulting equally weighted average R-squared in figure 10 (see appendix). Campbell et al. (2001) found that the average R-squared of individual firms was decreasing and thus the systematic risk was decreasing because stocks were less correlated with one another. Campbell et al. (2001) also calculated the average correlation among stocks by calculating all pairwise correlations and then averaging the correlations for each month. Interestingly, the average correlation perfectly mirrors the equally weighted average R-squared through the sample. During their sample period both the average correlation among stocks and the average R-squared declined. Campbell et al. (2001) states that the decrease in the correlation among stocks increases the number of randomly selected stocks required to hold a relatively diversified portfolio. This finding coincides with Comin & Philippon (2006) who document a decrease in the

9 8 correlation of shocks among sectors, which they find to be decreasing the overall volatility rather than a decline in sectoral volatility. Contrary to Campbell et al. (2001) and Comin & Philippon (2006), I found that beginning right after the period in Campbell et al. (2001), the average R-squared began increasing almost constantly for the next 10 years. A rising R-squared means that the stocks are becoming more correlated and the share of the systematic risk is increasing. The average R-squared of this market model peaks at an astonishingly high 40 percent. This means that for any given firm equally weighted within the market, the average market return can explain 40% of the variation in that firm s return. However it should be noted that there has been much debate about the validity of using R-squared as a measure of idiosyncratic volatility in recent literature both with matching the empirical findings of the firm profiles with high idiosyncratic volatility and the information content in prices using 1-R-squared Brown & Kapadia (2007.) Also, a recent article by Li et al. (2014) has shown that the firm variance and R-squared are not the same and demonstrates the difficulty in directly mapping between the two metrics. The difficulty stems in the calculation of R-squared, which has two components. 1-R-sqaured is equal to the variance of the error term (idiosyncratic volatility) divided by the total variance of the stock. Thus a change in either component changes the ratio, not just a change in the idiosyncratic volatility. Discussion The literature is filled with many explanations for the changes in the idiosyncratic volatility of the stock market, some contradictory and others supplemental. While there is much debate about the trend in idiosyncratic volatility, if one exists, I want to avoid that discussion and focus on the underlying factors that drive changes in idiosyncratic volatility. I feel that developing an understanding of the reasons why idiosyncratic volatility changes over time is crucial in attempting to understanding how idiosyncratic volatility in the U.S. has changed, and whether that change is positive or not. To understand how my results fit with the current literature and put them in context, I will discuss the explanations of the causes of changes in idiosyncratic volatility in the following six categories: small and low priced stocks, how new firms differ from

10 9 older firms, a firm s investor base, research and development, industry turnover, and market development. Small and Low-Priced Stocks In attempting to explain the apparent puzzle in idiosyncratic volatilities, Brandt et al. (2010) found the price of stocks to be very important in understanding idiosyncratic volatility. More specifically, they found that the increase and reversal in idiosyncratic volatility was concentrated in stocks that had low stocks prices and a high proportion of retail ownership. In their analysis, Brandt et al. (2010) controlled for the size of the firm to see if the significance of a low stock price was really just a proxy for the size of a firm. They found that after controlling for firm size, which was statistically significant, stock price was still highly statically significant and of a much larger magnitude than firm size. To further support their notion that low stock prices significantly contribute to an increase in idiosyncratic volatility, Brandt et al. (2010) examined stock splits. Interestingly, these events, which lower the stock price by issuing additional shares and do not change firm fundamentals, were shown to increase idiosyncratic volatility Brandt et al. (2010). While stock price may be a vital component in understanding idiosyncratic volatility, Brown & Kapadia (2007) found evidence that supports Brandt et al. (2010) finding that firm size matters as well. New Firms vs. Old Firms Another topic that has gained prominence in the literature is the change in the nature of public firms. Notably Fama & French (2004) document that new firms fundamentals are different than older firms and that newer firms are more left-skewed in profitability, more rightskewed in their growth, and overall have lower survival rates. The effect of new firms is investigated in depth by Brown & Kapadia (2007). They find that the increase in idiosyncratic volatility is due solely to new listings by riskier firms. The also conclude that the decline in R- squared in their sample is due to new listings of companies with higher idiosyncratic risk, and thus lower R-squared, thereby increasingly reducing the average R-squared as these firms become more prevalent in the market.

11 10 Brown & Kapadia (2007) also document that industries with higher levels of idiosyncratic volatility are industries that have a larger number of new firms in them. Brown & Kapadia (2007) also refute the notion that newer firms have higher idiosyncratic volatility because they list earlier in their life than firms of previous decades. To support their finding, Brown & Kapadia (2007) split stocks into groups of five year intervals with each group containing all stocks that were initially listed during its intervals. They find that each successive group had a higher starting level of idiosyncratic volatility and a lower average R-squared. They argue that if newer firm s idiosyncratic volatility was higher because they listed earlier, the increased idiosyncratic volatility would decline and the average R-squared would increase over time, but they found no evidence that either of these has occurred. Brown & Kapadia (2007) also found that newer firms have declining profit margins and tangible assets, but older firms profit margins and level of tangible assets have stayed almost the same. To further support their conclusion, Brown & Kapadia (2007) also documented that idiosyncratic volatility is inversely related to the average age of firms within an industry and directly related to the proportion of firms within an industry that are newly listed. Finally, Brown & Kapadia (2007) show that the risk of doing business has not changed over time by looking at default rates, to rule out the possibility that newly listed firms are more risky because they are listing in a period of increased risk of doing business. Investor Base Another aspect of firms with high idiosyncratic volatility that differs from firms with low idiosyncratic volatility is the investor base of the firm. Brandt et al. (2010) show that both the increase and decrease in idiosyncratic volatility that they find was concentrated in stocks with low prices and stocks that had a proportion of their shares owned by retail investors. Brandt et al. (2010) also investigated the characteristics of firms which are widely held by retail investors. These firms tended to have low market capitalization, low stock prices, low institutional ownership, and high idiosyncratic volatility. Part of this is due to the fact that retail investors significantly overweight low-priced stocks in their portfolios relative to a portfolio chosen at random based upon firms market capitalization Kumar (2009). In their study, Brandt et al. (2010) found large positive or negative returns, or high turnover, events which they term attentiongrabbing events attract the attention of retail investors and volatility moves around these

12 11 events. Further, Brandt et al. (2010) found that the increase in trading surrounding attentiongrabbing events by retail traders occurs regardless of the information content. This seems to imply that retail traders may not always trade on fundamentals and may be noise traders. Brandt et al. (2010) makes this point by saying that to a retail investor, a stock with a lower level of institutional ownership may be more enticing because they may see the stock as being on a more level playing ground without institutional investors who can appear to have superior information. However, taken with the findings of Jiang & Yao (2009), institutional investors may have superior information. More likely, institutional investors can do a better job reading between the lines and understanding the true fundamentals of a business through murky disclosures and are not distracted by attention-grabbing events that do not contain news. Bartram et al. (2012) found that disclosures were negatively related with idiosyncratic volatility, so it is plausible that retail investors need disclosures to understand the firm s they are trading. Jiang & Yao (2009) found that idiosyncratic volatility is inversely related to future earnings shocks and that the return predictive power stems from information content about future earnings. Jiang & Yao (2009) also found that this predictive power from idiosyncratic volatility was related to corporate selective disclosures and was strongest among stocks with a less sophisticated investor base. This fits with the findings in Brandt et al. (2010) that retail investors trade do not always trade on fundamentals, that institutional investors have a superior ability to read between the lines (when the quality of disclosures is low), and that the noise trading by retail investors pushes prices further away from their fundamentals allow there to be predictive power of future earnings shocks in the volatility. Finally, along with their finding that volatility increases following a stock split, Brandt et al. (2010) also found that institutional holdings of firms fell following a stock split. This further connects a firm s investor base to idiosyncratic volatility. Brandt et al. (2010) also include a term in their regressions interacting firms with low stock prices and low retail ownership, which was not statistically significant. From this they conclude that retail ownership is important and that its importance isn t due to retail investor s tendency to overweight low-priced stocks. Research and Development

13 12 As Bartram et al. (2012) point out, volatility isn t necessarily a good or bad thing. Rather, high volatility can be good or bad depending on its root causes. One of the positive characteristics they found to increase idiosyncratic volatility is the number of patents. Similarly, Comin & Philippon (2006) document that idiosyncratic volatility increase in industries that experience large increases in research and development, and that current volatility has a significant impact on future research and development that peaks three periods forward. They also found that past research and development spending effects current levels of volatility five periods back, and that the sign was always positive, statistically significant, and typically larger than the contemporaneous correlations between research and development and idiosyncratic volatility. Increases in volatility because of increased spending on research and development are positive for both the companies investing their money and for all of their stakeholders. Research and development is what spurs innovation and progress. While this may cause variations in cash flows and income, it is the only way to get ahead of competitors and increase returns to shareholders. Investment in research and development is a sign of a stable market because it shows that firms are confident enough in their future that they are willing to invest in developing new products and technology. Turnover Turnover in market shares, or alternatively, more competition in product markets, is what Comin & Philippon (2006) reports to be the main cause of the increase in idiosyncratic volatility. They found that the profiting margins of the industry leaders has not changed over time, but the average length of time that a firm is an industry leader has decreased dramatically. Brown & Kapadia (2007) also found changes in the composition of firms within an industry to an important factor in explaining idiosyncratic volatility, more important than the changing of the weights of industries within the market over time. Irvine & Pontiff (2009) further confirmed the positive relationship of turnover within an industry and future idiosyncratic volatility. I believe that these findings are intertwined with research and development. Increases in research and development mean that there will be more competition in the market and more differentiated products. In this environment it is harder to stay ahead of an entire industry, thus the average duration of a

14 13 market leader declines. Since the expected duration of a firm as an industry leader has dropped drastically, there is an increased incentive to innovate and invest in new technologies in aspiration of unseating the current market leader. Thus one creates incentives for the other, but while both increase volatility they also spur innovation and progress. Market Development The increased development of a stock market also increases the level of idiosyncratic volatility Bartram et al. (2012). Bartram et al. (2012) find that part of the reason the U.S. has experienced an increase in idiosyncratic volatility is due to an increase in investor protections. This reduces the overall riskiness of investing in stocks allowing them to trade on the risk of the individual companies rather than also pricing in general risks of holding equities. Comin & Philippon (2006) states that idiosyncratic volatility increases after deregulation and in industries that issue more debt and equity. These drivers in volatility are all due to the development of the market as a whole, and how this protects investors and allows equity prices to not incorporate risks that these protections take out of the market. Interestingly, Bartram et al. (2012) did not find evidence that measures of political risk or creditor rights are important in understanding idiosyncratic volatility in their cross-country analysis. Conclusion After decomposing aggregate volatility, I found that idiosyncratic risk has been at very high levels since the turn of the 21 st century. Much of the current literature uses data that does not include the end of the Great Recession and the current recovery, periods where idiosyncratic risk is twice as high as any other period in the last 50 years. I also showed that the average R- squared of equally weighted U.S. equities has increased substantially, peaking around 40 percent, its highest level in 50 years. Based on the finding by Campbell et al. (2001) that the graph of the average R-squared perfectly mirrors the average pairwise correlation among stocks, I conclude that stocks have become much more correlated over the last 15 years. This increased correlation makes diversifying a portfolio more difficult for an investor because they have an increased level of risk common to more stocks in their portfolio that cannot be hedged away by simply holding more stocks with the same level of correlation among them.

15 14 Given the vast array of explanations in the literature for idiosyncratic risk, many of which contradict one another, there are many veins for future researchers to explore. One of these is to further explore the size of firms and stock prices, and to see if the results found by Brandt et al. (2010), Brown & Kapadia (2007), and others still hold with current data. Another area for future research is a more in-depth study of various industries to see how they evolve over time and how research and development and industry leadership lead one another. Finally, given the strong evidence by Fama & French (2004) and Brown & Kapadia (2007) that new firms differ significantly from older firms, and that the average R-squared is decreasing, a finding for which I find opposite results, further research should investigate whether this trend is still continuing. References Bartram, S., Brown, G., & Stulz, R. (2012). Why Are U.S. Stocks More Volatile? The Journal of Finance, 67(4),

16 15 Brandt, M., Brav, A., Graham, J., & Kumar, A. (2010). The Idiosyncratic Volatility Puzzle: Time Trend or Speculative Episodes? Review of Financial Studies, 23(2), Retrieved April 9, 2015, from JSTORE. Brown, G., & Kapadia, N. (2007). Firm-specific risk and equity market development. Journal of Financial Economics, 84(2), Retrieved April 9, 2015, from Campbell, J., Lettau, M., Malkiel, B., & Xu, Y. (2001). Have Individual Stocks Become More Volatile? An Empirical Exploration Of Idiosyncratic Risk. The Journal of Finance, 56(1), Retrieved January 30, 2015, from JSTORE. Comin, D., & Philippon, T. (2006). The Rise in Firm-Level Volatility: Causes and Consequences. In NBER Macroeconomics Annual 2005 (Vol. 20). MIT Press. Fama, E., & French, K. (1997). Industry costs of equity. Journal of Financial Economics, 43(2), Fama, E., & French, K. (2004). New lists: Fundamentals and survival rates. Journal of Financial Economics, 73(2), Retrieved April 20, 2015, from Irvine, P., & Pontiff, J. (2009). Idiosyncratic Return Volatility, Cash Flows, and Product Market Competition. Review of Financial Studies, 22(3), Retrieved April 9, 2015, from JSTORE. Jiang, G., Xu, D., & Yao, T. (2009). The Information Content of Idiosyncratic Volatility. The Journal of Financial and Quantitative Analysis, 44(1), Retrieved April 9, 2015, from JSTORE. Kumar, A. (2009). Who Gambles in the Stock Market? The Journal of Finance, 64(4), Retrieved April 20, 2015, from JSTORE. Li, B., Rajgopal, S., & Venkatachalam, M. (2014). R2 and Idiosyncratic Risk Are Not Interchangeable. The Accounting Review, 89(6), Appendix Figure 1

17 Number of Firms in Sample 8000 Number of Firms m8 1966m8 1970m8 1974m8 1978m8 1982m8 1986m8 1990m8 Time 1994m8 1998m8 2002m8 2006m8 2010m8 2014m8 Figure Distribution of Market Capitalization Dollars m8 1966m8 1970m8 1974m8 1978m8 1982m8 1986m8 1990m8 Time 1994m8 1998m8 2002m8 2006m8 2010m8 2014m8 Average Market Cap First Quartile Median Market Cap Third Quartile Figure 3

18 Average Real Market Capitalization Dollars m8 1966m8 1970m8 1974m8 1978m8 1982m8 1986m8 1990m8 Time Average Market Capitalization 1.96 Standard Deviations 1994m8 1998m8 2002m8 2006m8 2010m8 2014m8 Figure 4 Market Volatility Volatility m8 1966m8 1970m8 1974m8 1978m8 1982m8 1986m8 1990m8 1994m8 1998m8 2002m8 2006m8 2010m8 2014m8 Time Figure 5

19 Month Moving Average of Market Volatility.015 Volatility m8 1967m m m2 1980m4 1984m6 1988m8 1992m10 Time 1996m m2 2005m4 2009m6 2013m8 Figure 6 Industry Volatility Volatility m8 1966m8 1970m8 1974m8 1978m8 1982m8 1986m8 1990m8 Time 1994m8 1998m8 2002m8 2006m8 2010m8 2014m8 Figure 7

20 Month Moving Average of Industry Volatility.006 Volatility m8 1968m2 1972m8 1977m2 1981m8 1986m2 1990m8 Time 1995m2 1999m8 2004m2 2008m8 2013m2 Figure 8 Firm Volatility Volatility m8 1966m8 1970m8 1974m8 1978m8 1982m8 1986m8 1990m8 Time 1994m8 1998m8 2002m8 2006m8 2010m8 2014m8 Figure 9

21 Month Moving Average of Firm Volatility.02 Volatility m8 1968m2 1972m8 1977m2 1981m8 1986m2 1990m8 1995m2 1999m8 2004m2 2008m8 2013m2 Time Figure 10