13
CFA Institute Why Company-Specific Risk Changes over Time Author(s): James A. Bennett and Richard W. Sias Source: Financial Analysts Journal, Vol. 62, No. 5 (Sep. - Oct., 2006), pp. 89-100 Published by: CFA Institute Stable URL: http://www.jstor.org/stable/4480775 Accessed: 15/04/2010 23:40 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=cfa. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. CFA Institute is collaborating with JSTOR to digitize, preserve and extend access to Financial Analysts Journal. http://www.jstor.org

Bennett Sias 2006

Embed Size (px)

Citation preview

Page 1: Bennett Sias 2006

CFA Institute

Why Company-Specific Risk Changes over TimeAuthor(s): James A. Bennett and Richard W. SiasSource: Financial Analysts Journal, Vol. 62, No. 5 (Sep. - Oct., 2006), pp. 89-100Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4480775Accessed: 15/04/2010 23:40

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/action/showPublisher?publisherCode=cfa.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

CFA Institute is collaborating with JSTOR to digitize, preserve and extend access to Financial AnalystsJournal.

http://www.jstor.org

Page 2: Bennett Sias 2006

Financial Analysts Journal Volume 62. Number 5

?2006, CFA Institute

Why Company-Specific Risk Changes over Time

James A. Bennett, CFA, and Richard W. Sias

Company-specific risk climbed steadily between 1962 and 1999 in the U.S. market butfell sharply between 2000 and 2003. This article explores the hypothesis that three factors are primarily responsiblefor observed changes in company-specific risk: changes in the market weights of "riskier" industries, changes in the relative role of small-capitalization stocks in the market, and measurement error associated with changes in within-industry concentration. Empirical tests reveal that each factor contributes to changes in company-specific risk over time and that, combined, these three factors largely explain changes in company-specific risk over the past 40 years.

A number of recent studies [e.g., Campbell, Lettau, Malkiel, and Xu 2001 (henceforth, CLMX); Morck, Yeung, and Yu 2000; Goyal and Santa-Clara 2003] have demonstrated

that, although market and industry risk remained relatively stable in the U.S. market between the early 1960s and the late 1990s, company-specific risk climbed steadily throughout the period. In addition, as we demonstrate in this study, company-specific risk has exhibited a secular decline since the market peak in 2000.

Changes in company-specific risk over time affect portfolio managers for a number of reasons. First, company-specific risk is directly related to portfolio diversification: Active managers attempt- ing to achieve some given level of company-specific risk need to hold larger portfolios, all else being equal, during periods of high company-specific risk. This aspect is especially important in light of recent research revealing that diversification requires portfolio sizes much greater than previ- ously believed. For example, we have demonstrated (see Bennett and Sias 2006) that in recent years, one in five investors holding a randomly selected equal- weighted 50-stock portfolio averaged an annual company-specific shock of 16 percent. Not surpris- ingly, we reported that value-weighted portfolios (corresponding closely to most portfolios held in practice) exhibited even greater levels of company- specific risk. Second, the level of company-specific risk is directly related to both tracking error versus an index and the cross-sectional dispersion of active

portfolio returns (De Silva, Sapra, and Thorley 2001; Bennett and Sias 2006). When company-specific risk increases, managers have a greater likelihood of obtaining returns that differ (positively or nega- tively) from both indices and peers. Third, recent evidence (Goyal and Santa-Clara 2003; Jiang and Lee 2004) suggests that the aggregate level of company-specific risk is positively related to future market returns. Hence, the recent decline in company-specific risk portends lower future mar- ket returns if this pattern continues. Fourth, arbi- trageurs' ability to exploit security mispricing is directly related to levels of company-specific risk; because the difficulty of forming arbitrage portfo- lios increases with an increase in company-specific risk, mispricings can persist longer during periods of high company-specific risk. Thus, for an informed active manager, the payoff from investing in an undervalued stock may take longer to realize when company-specific risk levels are high.

Previous researchers have argued that changes in company-specific risk over time may reflect fun- damental changes in the economy and/or markets, such as decreases in operational diversification as companies narrow their product/market focus (CLMX), an increase in the use of stock options as executive compensation (CLMX), systematic increases in the volatility of return on equity or growth opportunities (Wei and Zhang 2006; Cao, Simin, and Zhao 2005), a decline in financial report- ing quality (Rajgopal and Venkatachalam 2005), an increase in the role of institutional investors in the market and their tendency to herd (Xu and Malkiel 2003), increases over time in levels of informed trading (Morck, Yeung, and Yu 2000; Durnev, Morck, and Yeung 2004), an increase in capital market openness (Li, Morck, Yang, and Yeung 2004), and an increase in competition between com- panies (Irvine and Pontiff 2005).

James A. Bennett, CFA, is assistant professor offinance at the University of Southern Maine, Portland. Richard W. Sias is a professor and Gary P. Brinson Chair of Investment Management at Washington State Univer- sity, Pullman.

September/October 2006 www.cfapubs.org 89

Page 3: Bennett Sias 2006

Financial Analysts Journal

In the study reported here, we tested a simpler explanation than previously proposed for changes in aggregate company-specific risk over time. To understand how our explanation differs from previ- ous explanations, consider the following: The (value- weighted) average company-specific risk, FIRMt, for the Njt securities in the market at time t is simply the product of each security j's company-specific risk at time t, c2(j,t), and its time t weight in the market portfolio, wjt, summed across securities:

Njt

FIRM, = w W11& (jt) - (1) j=1

Previous explanations for changes in FIRMt focused on factors influencing the company-specific risk of individual securities, such as increased use of stock options, increased herding by institutional investors, or increased competition between compa- nies. Our explanation focuses on changes in the weights of individual securities, which, in turn, determine the relative importance of industries and small-cap stocks in the market and also affect errors in estimates of company-specific risk.1 Specifically, we propose that three key changes in the composi- tion of the market explain changes in company- specific risk over time: * changes in the relative importance of industries

containing above-average levels of company- specific risk,

* changes in the relative importance of small companies in the market, and

* changes in measurement error induced by changing within-industry concentration.

Distinguishing between these explanations is important in practice because our analysis suggests that changes in company-specific risk faced by a given manager are a function of the changes in that manager's portfolio. For example, as long as the manager does not have great exposure to small- capitalization stocks, the rise in aggregate company- specific risk attributed to the growth of small-cap stocks in the market will not affect that manager. In other words, according to our explanations, manag- ers can control their exposure to time-varying aggre- gate company-specific risk through industry and security selection. Previous explanations suggested that changes in company-specific risk are pervasive, so a manager can do little to manage such risks.

Company-Specific Risk over Time CLMX demonstrated that by aggregating over all securities in the market, one can generate an esti- mate of company-specific risk without estimating

individual securities' betas. Following CLMX, we estimated the company-specific return for stock j in industry i on day s as the daily deviation between the stock's return and its industry's return; we used the 49 industries defined by Fama and French (1997). We then computed the estimated monthly company-specific risk for stock j in month t as the sum of the squared daily deviations over all days in month t:

(52(Ijiit) = is -Ris) S(2) set

where Rjs is security j's return on day s in month t and Ri, is the value-weighted industry return on day s.2

Aggregate company-specific risk in month t is the weighted average company-specific risk across all securities:

Nj,

FIRM, = Wjta (it) (3) j=l

Using Equations 2 and 3, we estimated company-specific risk for each month between August 1962 and December 2003 for all NYSE, Amex, and NASDAQ securities in the CRSP data- base. Figure 1 graphs the estimated annualized (i.e., monthly variance estimate times 12) value- weighted company-specific volatility in the sam- ple period.

Figure 1 reveals, as previously documented by CLMX, an upward trend in company-specific risk in the 1962-99 period. At approximately the market peak in 2000, however, company-specific risk went into a sharp decline. Following CLMX, we com- puted a linear trend coefficient (i.e., the coefficient from a time-series regression of aggregate company-specific risk on time) and a trend t-statistic that is robust to serial correlation (the Vogelsang t -PST t-statistic).3 Estimates for the entire sample period (1962-2003), the period with generally rising company-specific risk (1962-1999), and the period with generally falling company- specific risk (2000-2003) are reported in Table 1.

The results in Table 1 reveal no evidence of a statistically significant trend in company-specific risk over the entire sample period, but company- specific risk displays a statistically significant uptrend in the 1962-99 period followed by a statis- tically significant downtrend during the 2000-03 period. In fact, company-specific risk has declined so sharply since the market peak that it was lower in 2003 than the average company-specific risk over the 1970s.4

90 www.cfapubs.org ?2006, CFA Institute

Page 4: Bennett Sias 2006

Why Company-Specific Risk Changes over Time

Figure 1. Value-Weighted Company-Specific Risk, 1962-2003

Value-Weighted Company-Specific Risk (%)

50

45-

40-

35-

30-

25-

20-

15

10

62 67 72 77 82 87 92 97 03

Note: Updated monthly.

Table 1. Descriptive Statistics and Tests for Linear Trends in Company-Specific Risk

1962-2003 1962-1999 2000-2003 Measure (n = 497 months) (n = 451 months) (n = 46 months)

Mean risk (%) 7.954 7.085 16.084

Standard deviation (%) 5.362 3.507 10.556

Autocorrelation (lst order) 0.802 0.665 0.803

Linear trend x 105 1.624 1.195 -51.605

T-PS 1 t-statistic (5%) 1.443 3.180** -3.328**

-PS' t-statistic (10%) 1.689 3.381* -3.701*

Notes: Company-specific risk was computed monthly as the sum of the squared daily deviations between the stock's return and the value-weighted industry return weighted by the market value of the stock. These variance estimates were annualized by multiplying by 12. The critical values for the 10 percent and 5 percent levels for Vogelsang's t - PST- t-statistic are, respectively, 1.720 and 2.152. The linear trend for each risk measure was calculated from a regression of the monthly risk measure on time.

*Significant at the 10 percent level. **Significant at the 5 percent level.

Why Does Company-Specific Risk Change over Time? As demonstrated in Figure 1 and Table 1, company- specific risk exhibited a secular uptrend between 1962 and 1999. As a result, most explanations for changes in company-specific risk focus on explain- ing the rise in company-specific risk over time (e.g., increased herding by institutional investors). The results in Figure 1 and Table 1 suggest, however, that any explanation for changes in company- specific risk over time should explain both the

increase over the 1962-99 period and the subsequent decline. In addition, most previous explanations implicitly assumed that changes in value-weighted average company-specific risk are driven by changes in the return-generating process itself (i.e., that the distribution of company-specific shocks for each security changes over time) rather than changes in weighting. Equation 1, however, shows that given different levels of company-specific risk among securities, changes in weighting will cause aggregate company-specific risk to change over time. Therefore, we next present evidence that the

September/October 2006 www.cfapubs.org 91

Page 5: Bennett Sias 2006

Financial Analysts Journal

three factors associated with changes in weighting largely explain the changes in company-specific risk over time.

Changes in Industry Weights. In August 1962 (the first month in our sample period), the four largest industries-petroleum and natural gas, util- ities, telecommunications, and automobiles- accounted for 44 percent of aggregate market cap- italization. By December 2003, those industries accounted for only 14 percent of market capitaliza- tion. Similarly, the four largest industries at the end of the sample period-banking, business services, pharmaceuticals, and trading-accounted for 36 percent of the market capitalization in December 2003 but only 5 percent of the aggregate market capitalization in 1962. As long as industries have different levels of company-specific risk, changes in industry weights will lead to changes in the weighted average company-specific risk over time. For example, company-specific shocks arising from a change in technology will affect a greater fraction of the market in today's environment than previ- ously because the relative value of technology com- panies has increased over time.

To examine the possibility that changes in industry weights help explain changes in company- specific risk, we assigned each of the 49 industries to one of two groups-"Risky" or "Safe." Specifi-

cally, we computed the value-weighted average company-specific risk of securities within each industry over the August 1962-July 1964 period and then defined those industries with median and above-median company-specific risk as Risky and those with below-median company-specific risk as Safe. We then calculated, each month, the ratio of the total capitalization of Risky industries to the total capitalization of Safe industries. Figure 2 graphs this ratio, as well as aggregate company-specific risk, over time. The pattern is clear: Aggregate company- specific risk rises (falls) as riskier industries become a larger (smaller) part of the market.

As a formal test that changes in industry weights help explain changes in aggregate company-specific risk, we computed the correla- tion between realized aggregate company-specific risk and a hypothetical forecast of company-spe- cific risk calculated by assuming that company- specific risk within each industry remains constant over time but industry weights vary over time. We began by computing the value-weighted company- specific risk in each industry over the first two years in the sample period as the (constant) estimate of the company-specific risk for each industry in the future. For each month subsequent to the first two years in the sample, we computed the "forecast" of company-specific risk as the sum (across indus-

Figure 2. Ratio of Market Value of Risky Industries to Market Value of Safe Industries Compared with Company-Specific Risk over Time, 1962-2003

Total Capitalization of Risky Industries to Value-Weighted Company-Specific Risk (%) Total Capitalization of Safe Industries

50 1.0

45 . 0.9

40 0 Company-Specific Risk2 08 40 - ~~~~~~(left axis) -

0.

35 0.7

30 0.6

25 F Risky Industries/Safe Industries

20:(right axis) 0

15 0.3

62 67 72 77 82 87 92 97 03

Note: Updated monthly.

92 www.cfapubs.org ?2006, CFA Institute

Page 6: Bennett Sias 2006

Why Company-Specific Risk Changes over Time

tries) of the products of each industry's actual weight at time t and the constant estimate of com- pany-specific risk for that industry. That is, although we updated the industry weights each month, the estimate of company-specific risk in each industry was held constant at its average value over the first two years in the sample period. The time- series correlation between actual aggregate com- pany-specific risk and this monthly forecast of com- pany-specific risk based solely on changing industry weights was found to be 51.47 percent and statistically significant at the 1 percent level.

Company Size. The number of small compa- nies in the sample grew dramatically over time as the sample size increased from 2,039 securities in August 1962 to a peak of 9,146 securities in Decem- ber 1997. The number of small companies subse- quently declined as the number of companies fell from the 1997 peak to 6,690 securities in December 2003. Although aggregate company-specific risk is a value-weighted measure, the dramatic rise and subsequent fall in the number of securities in the sample suggests that changes in the relative impor- tance of small-cap stocks in the market may help explain observed changes in aggregate company- specific risk over time.

We began to examine this relationship by parti- tioning stocks into two groups each month: "Large" (the largest-cap stocks that, in total, accounted for

half of the total market capitalization at time t) and "Small" (the remaining stocks, which also accounted for half of market capitalization). Figure 3 graphs the ratio of number of Small to number of Large and repeats the graph of aggregate company- specific risk over time. Figure 3 reveals a strong positive relationship between this ratio and value- weighted company-specific risk. At the beginning of the sample period, there were approximately 37 small-cap stocks for every large-cap stock. The ratio closely tracked the pattern in aggregate value- weighted company-specific risk. The ratio rose to more than 100 small-cap stocks for every large-cap stock by the end of 1999. By year-end 2003, however, the ratio had fallen to 57 small-cap stocks for every large-cap stock.

Similar to our analysis of changes in industry weights, we generated a formal test of the hypoth- esis that the rise and subsequent fall in the relative role of small-cap stocks in the market helps explain changes in aggregate company-specific risk by computing the correlation between realized aggre- gate company-specific risk and a hypothetical fore- cast of company-specific risk designed to isolate the impact of changes in the weight of small-cap stocks over time. We ranked the 2,039 securities in the first month of the sample period (August 1962) by size and placed them in size deciles. Each of the first nine deciles contained 204 stocks; the remaining 203 stocks were placed in the bottom decile (smallest

Figure 3. Ratio of Number of Small Companies to Number of Large Companies Compared with Company-Specific Risk over Time, 1962-2003

Value-Weighted Company-Specific Risk (%) Ratio of Small to Large

50 120

45-

100 40-

Number of Small Companies/ 80 Number of Large Companies 30 ~~~~(right axis)

25 60

20

15

10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1

- ~~~~~~~Company-Specific Risk (left axis) 0 A,I A A 0

62 67 72 77 82 87 92 97 03

Note: Updated monthly.

September/October 2006 www.cfapubs.org 93

Page 7: Bennett Sias 2006

Financial Analysts Journal

companies). Then, holding the number of securities in each of the top nine deciles constant at 204 in each subsequent month, we placed all remaining securi- ties into the bottom decile. That is, each month, the first nine deciles contained the largest 1,836 securi- ties (9 x 204) and the final decile contained all remaining securities. We then estimated each decile's weighted average company-specific risk over the first two years in the sample period as our constant estimate of company-specific risk for that size decile in the future. In each subsequent month (excluding the first two years), we computed the forecast of company-specific risk as the sum (across size deciles) of the products of each decile's time t market weight and the constant estimate of company-specific risk for that decile. Thus, as in our industry analysis, although the size-decile weights were updated each month, the estimate of company-specific risk within each decile was held constant at its average over the first two years in the sample period. As a result, changes in the level of the forecasted weighted average company-specific risk over time were completely a result of changes in the relative weights of the size deciles. The time- series correlation between this monthly forecast of company-specific risk and actual aggregate company-specific risk was found to be 24.88 percent and statistically significant at the 1 percent level.

In summary, despite the fact that the company- specific risk metric is value weighted, we found that the growth and subsequent decline of small-cap securities in the market play a substantial role in accounting for the changes in aggregate company- specific risk over time.

Changes in Within-industry Concentration. The analysis thus far has demonstrated that changes in market weights affect aggregate company- specific risk by changing both the relative impor- tance of industries with high versus low levels of company-specific risk and the relative importance of small-cap versus large-cap stocks. The impact on weighted average company-specific risk caused by these changes in weights may be considered a "direct" effect.

Changes in security weights also have a more subtle, "indirect" effect on estimated company- specific risk, however, because of the estimation of company-specific returns as the difference between security and industry returns. All else being equal, including returns themselves, the estimated company- specific risk for a particular security (and thus the aggregate company-specific risk for a given indus- try and the overall market) will vary with the distri- bution of market capitalization among companies within an industry. Specifically, assuming returns

are generated by a linear factor model in which securities within each industry have homogeneous factor sensitivities (i.e., homogeneous betas), the estimated value-weighted average company- specific risk of companies in the industry is given by (proof available from authors upon request):

a2( (f(i,t) - i 2t (jit) a2 (i~=a2(i.~w2.aji j) (4) jcri

where c2(fiit) is the true (unobservable) weighted average company-specific risk in industry i and ca2(i it) is the estimated weighted average company- specific risk in industry i.5

The first term on the right-hand side of Equation 4 is the "true" weighted average company-specific risk in the industry. The second term, however, demonstrates that estimated company-specific risk will depend on the distribution of within-industry weights; therefore, the second term represents a potential source of bias.6

Two intuitive examples will demonstrate that this bias is likely to cause estimated company-specific risk to increase (decrease) when within-industry concentration declines (increases). First, consider the extreme case of industry concentration-an industry consisting of a single company.7 In this situation, industry returns will equal the company's returns and esti- mated company-specific returns (and risk) will equal zero, even if the company truly does expe- rience company-specific shocks.8

Or consider a less extreme example, one in which the true variance of company-specific shocks is some constant, C, across all securities within an industry; that is,

a2 (jit)=

C (5)

for all securities in industry i. In such a case, Equa- tion 4 simplifies to the industry's true average company-specific risk, C, times 1 less the industry portfolio's Herfindahl index; that is,9

2 (JC(j i2 (6)

In other words, when securities in an industry have the same level of company-specific risk, an increase in industry concentration leads to an increase in the downward bias in estimated company-specific risk. In addition, the magnitude of the bias will be mini- mized when market capitalizations are equal across companies in the industry. Although not all securi- ties in an industry are likely to possess equal levels of company-specific risk, Equation 4 demonstrates that the negative bias in estimated company-specific risk for any industry is maximized when industry

94 www.cfapubs.org ?2006, CFA Institute

Page 8: Bennett Sias 2006

Why Company-Specific Risk Changes over Time

concentration is maximized: As the weight of any company within an industry approaches 1, esti- mated company-specific risk for the industry approaches 0.

In general, however, the set of weights wjit that minimizes the bias term (i.e., the second term in Equation 4) will depend on the specific values of the true company-specific risk, 2(ijit), across companies. The question of how concentration affects changes in estimated company-specific risk over time is ultimately an empirical one, and it cannot be ignored unless concentration is either very low or constant over time.

Empirically, U.S. market concentration is both high and variable over time; less than half of 1 percent of securities, for example, made up the top quarter of the market's capitalization, on average, between 1962 and 2003. Over time, however, mar- kets have become somewhat less highly concen- trated. Figure 4 graphs the weighted average within-industry Herfindahl index and aggregate company-specific risk over time.10 The graph reveals a steady downtrend in within-industry concentration between 1962 and 1999 followed by a slight increase in concentration since then, which is consistent with the hypothesis that estimation error induced by changes in within-industry con-

centration contributes to changes in estimated company-specific risk over time.11 In the absence of such a bias, this negative relationship between industry concentration and estimated company- specific risk may be counterintuitive. One might expect that as industry profitability declines, the industry will consolidate (i.e., concentration will increase) and company-specific risk will increase because of greater uncertainty (i.e., a positive rela- tionship exists between concentration and company-specific risk).12

In our study, we next performed a simple examination of the potential role that changing industry concentration plays in explaining changes in company-specific risk over time. Using only returns from the first month in the sample period and holding the role of small companies and industry weights constant, we examined whether realized changes in industry concentra- tion, by themselves, help explain changes in company-specific risk over time. We began by computing industry weights and company- specific risk measures based on the sample of 2,039 securities in 48 industries in August 1962.13 We then identified the number of companies in each industry and ranked each security in its industry

Figure 4. Industry Concentration Compared with Company-Specific Risk over Time, 1962-2003

Industry Concentration Value-Weighted Company-Specific Risk (%) (Herfindahl Index)

50 0.25 Weighted Average Within-Industry Concentration Index

45 (right axis)

40 0.20

35

30 01

25

20 01

15 :

a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ i

10 0.05

.^--:--. .-: * *--- Company-Specific Risk (left axis) 0 A . 0

62 67 72 77 82 87 92 97 03

Note: Updated monthly.

September/October 2006 www.cfapubs.org 95

Page 9: Bennett Sias 2006

Financial Analysts Journal

based on its capitalization at the beginning of August 1962. Thus, in August 1962, the company- specific portion of company j's return was esti- mated as

Nth Nth R lj,iJ,se8/62 - Rji,se8/6 E

Nth NI

Nth Nth (7) = Rj,ise8162 - Wjit 11Rj,i,se8162'

,j=l

where Ni securities were in industry i in August 1962 and RN.th is the return on the Nth largest-

j, i, S E8/62

cap security in industry i on day s in August 1962. For August 1962, with is security j's weight in its industry for that month and security j is the Nth largest-cap security in its industry.

We repeated this procedure each month and used updated security weights only in the calcula- tion of the industry return (i.e., within-industry weights from time t were used to compute Ri S E8/62).

For all other calculations, weights were held con- stant at August 1962 values. Thus, in September i962,wNth in Equation 7 was computed as the cap- italization of the Nth largest-cap security in indus- try i divided by the total capitalization of the Ni largest-cap securities in industry i in September 1962. As we moved forward through time, the num- ber of securities in most industries grew as small companies were added. By limiting the sample to the Ni largest-cap securities in each industry each month, we eliminated the changes in company- specific risk resulting from changes in the number of small companies in the sample.14

We then computed the estimate of company- specific risk for a given company in the same fash- ion as before, by summing the squared differences between the August 1962 daily returns and the time-varying industry return computed with August 1962 returns but time t industry concentra- tion (i.e., company weights at time t were used to compute industry concentration). The weighted average company-specific risk across companies within an industry was then calculated by using August 1962 market values to control for changes in company-specific risk arising from direct effects of changing weights, and the weighted average of company-specific risk for the market was com- puted by using August 1962 industry weights to control for changes in company-specific risk result- ing from the growth of riskier industries. The time- series correlation between aggregate company- specific risk and the forecast of company-specific risk that was fully driven by changing industry concentration was found to exceed 55 percent (sta- tistically significant at the 1 percent level).

In summary, the definition of company-specific returns as the difference between a company's return and an index that includes the company's return induced a dependency between estimated company-specific risk and the distribution of weights across companies. As a result, measurement error associated with changing industry concentra- tion contributed to changes in estimated aggregate company-specific risk over time.

Controlling for the Three Factors The analysis thus far reveals that three factors (changes in the relative role of riskier industries, changes in the relative role of small companies in the sample, and changes in within-industry concentra- tion) contribute to changes in company-specific risk over time. In this section, we examine the relation- ship between company-specific risk and time while controlling for all three factors simultaneously.

We took two approaches to these tests. First, we reestimated company-specific risk over time while attempting to directly control for the three factors. Second, we included variables proxying for each of the factors in the regression of company- specific risk on time.

Controlling the Sample. We examined changes in company-specific risk over time while controlling for the three factors by holding industry weights, within-industry concentration, and sample sizes constant at August 1962 levels. We began by limiting our sample in all months to stocks with a price of at least $1.00.15 This step reduced the num- ber of securities in August 1962 from 2,039 to 1,989.

We then computed company-specific risk for August 1962 as previously described, based on Equations 2 and 3. For subsequent months, we lim- ited the sample to the Ni largest companies in industry i (to control for changes in the number of small-cap stocks in the market) and computed company-specific returns for the Nth largest-cap security in industry i at time t as

^Nth = RNth Nth Nth

where Ni is the number of securities in industry i in Nth

August 1962 and RJNth is the return for the Nth largest-cap security (security j) in industry i on day s. To control for changes in industry concentration, we used 1962 within-industry weights (i.e.,

Nth= 8/62 is the August 1962 industry weight of the Nth largest-cap security in industry i).16

We then estimated company-specific risk for each subsequent month on the basis of August 1962 within-industry weights (which also controlled for

96 www.cfapubs.org 02006, CFA Institute

Page 10: Bennett Sias 2006

Why Company-Specific Risk Changes over Time

changing industry concentration) and August 1962 industry weights (to control for changing industry weights over time):

48 [N. F Nth 21 Wi,t=8/62 WJ,t=8/62 j (9)

Thus, FIRM*, graphed over time in Figure 5, denotes estimated company-specific risk after con- trol for changes in the role of small-cap stocks, riskier industries, and the bias induced by chang- ing industry concentration.

The results in Figure 5 reveal little evidence of a systematic rise in company-specific risk after we controlled for the three factors over the 1962-99 period. In addition, the rise in idiosyncratic risk during the technology/media/telecommunica- tions (TMT) bubble is much more muted than in Figure 1. Nonetheless, even when the three factors were controlled for, company-specific risk can be seen to have increased during the bubble period and then to have declined.

To quantify the difference between Figures 1 and 5, we estimated trend coefficients for the mea- sure of company-specific risk after controlling for all three factors (FIRM*) for both the period of gen- erally rising company-specific risk (1962-1999) and the period of generally falling company-specific risk (2000-2003) and compared these trend coeffi- cients with those estimated for the same periods for the unrestricted estimate of company-specific risk

(FIRM); that is, we compared the trend coefficients for the estimates in Figure 1 with the trend coeffi- cients for the estimates in Figure 5. We then esti- mated the fraction of the unrestricted trend that was accounted for by the three factors as

%Trend resulting from size, industry, and concentration

Trend FIRM* (10) =1-

Trend FIRM

We found that the three factors accounted for 63 percent of the trend coefficient during the period of rising company-specific risk (1962-1999) and 56 percent of the trend coefficient during the period of falling company-specific risk (2000-2003). Thus, even given the tremendous rise in company-specific risk around the TMT bubble, the results suggest that changes in the relative roles of small-cap stocks, riskier industries, and estimation error induced by changing industry concentration accounted for a majority of the trend in both the periods.

Regression Tests: Controlling for Size, Industry, and Concentration Effects. We next estimated the effect of these factors by controlling for them in the regressions of value-weighted company-specific risk on proxies for each factor and time. We used the ratio of the capitalization of Risky industries to Safe industries as a measure of changes in the role of riskier industries (as graphed in Figure 2). We measured the role of small compa- nies in the samole at time t as the ratio of the

Figure 5. Company-Specific Risk after Controlling for Size, Industry Weights, and Concentration, 1962-2003

Company-Specific Risk (%) 50

45-

40

35-

30-

25-

20-

15-

10

5

0

62 67 72 77 82 87 92 97 03

Note: Updated monthly.

September/October 2006 www.cfapubs.org 97

Page 11: Bennett Sias 2006

Financial Analysts Journal

number of companies accounting for the bottom half of the market's total time t capitalization to the number of companies accounting for the top half (as graphed in Figure 3). We accounted for changes in within-industry concentration by calculating, for each month, the weighted average (across indus- tries) of each industry's Herfindahl index (as graphed in Figure 4).

We estimated regressions of value-weighted company-specific risk (FIRMt from Equation 3) on time, the ratio of Small to Large, the value- weighted within-industry Herfindahl index, and the ratio of the total capitalization of securities in Risky industries to the total capitalization of secu- rities in Safe industries. Because of the serially correlated nature of volatility (see Table 1), we also repeated the analysis with lagged company- specific risk included as an additional variable. Regression coefficients and associated t-statistics (based on Newey-West 1987 standard errors with six lags) are reported in Table 2.

Table 2. Regression of Value-Weighted Company-Specific Risk on Sample Characteristics and Time, 1962-2003 (t-statistics in parentheses)

Variable Regression 1 Regression 2

Intercept (xlO) 0.520 0.285 (1.50) (1.52)

Lagged company-specific risk 0.522 (5.52)***

Time (x103) -0.287 -0.143 (-3.81)*** (-3.24)***

Small/Large (x102) 0.194 0.091 (5.90)*** (4.08)***

Industry concentration -0.620 -0.315

(-3.48)*** (-2.92)*** Risky/Safe 0.230 0.114

(3.58)*** (2.88)***

N (months) 496 496 Adjusted R2 58.4% 69.8%

Notes: The second regression included lagged company-specific risk as a control variable. The t-statistics are based on Newey- West standard errors with six lags.

Significant at the 1 percent level.

Table 2 reveals statistically significant coeffi- cients on the size, concentration, and industry risk variables, and these variables have the expected signs: Value-weighted company-specific risk increases as the role of small companies in the sample increases, as the relative importance of risk- ier industries grows, and as industries become less concentrated. The results held regardless of whether we accounted for the serial correlation in

company-specific risk. In addition, the coefficient on time is negative, suggesting that once these factors have been accounted for, the overall trend in company-specific risk is down. Moreover, the negative coefficient on time was not driven by the decline in company-specific risk following the TMT bubble; limiting the sample to the 1962-99 period yielded qualitatively identical results.

Other Explanations for Changes in Company-Specific Risk over Time. As noted in the introduction, previous researchers proposed a number of explanations for the systematic rise in the volatility of individual securities over the 1962-99 period, including a reduction in conglomerates, an increase in executive stock options, a systematic rise in the volatility of return on equity or growth oppor- tunities, an increase in herding by institutional investors, an increase in the level of informed trad- ing, greater capital market openness, a decline in financial reporting quality, and an increase in com- petition between companies.

Our results are not necessarily inconsistent with many of the previous explanations. For exam- ple, changes in the relative importance of small-cap stocks and riskier industries over time will cause changes in the average volatility of return on equity and financial reporting quality over time.

In addition, nearly all the other explanations for changes in company-specific risk have attempted to explain only the uptrend in company- specific risk in the 1962-99 period, not the decline in company-specific risk since 2000. In contrast, our results suggest that the role of small companies, riskier industries, and changes in industry concen- tration contributed to the dramatic rise and fall of aggregate company-specific risk around the TMT bubble. However, although the rise and fall of company-specific risk around the TMT bubble in Figure 5, which reflects control for the three factors we suggest, is much more muted than in Figure 1, Figure 5 still documents a rise in company-specific risk around the TMT bubble. Therefore, Figure 5 suggests that other factors played a role in the rise and fall of company-specific risk at the time of the TMT bubble. Brandt, Brav, and Graham (2005) pro- vided an additional likely explanation-namely', that excessive speculation at that time contributed to the rise in aggregate company-specific risk in the late 1990s and its subsequent decline since 2000.

Previous researchers have noted that the num- ber of small companies (which typically have higher levels of company-specific risk than large companies) increased over the 1962-99 period. Pre- vious work, however, largely discounted the pos- sibility that these securities played an important role in changes in the value-wleighted measure of company-specific risk.

98 www.cfapubs.org X)2006, CFA Institute

Page 12: Bennett Sias 2006

Why Company-Specific Risk Changes over Time

No other study has considered the influence of changing industry weights or changes in estimation error induced by changing industry concentration on estimates of value-weighted company-specific risk. In this work, we demon- strated that both of these factors play an important role in explaining the observed changes in company-specific risk over time.

Conclusion Aggregate company-specific risk exhibited a steady upward trend over the 1962-99 period and a steep decline in the 2000-03 period. Because changes in company-specific risk affect the number of securities needed to achieve a given level of diversification, tracking error, cross-sectional return dispersion across managers, and the ability of arbitrageurs to exploit mispricing and because company-specific risk may be priced, an under- standing of how and why company-specific risk changes over time is important.

Previous work suggested that changes in company-specific risk are driven by fundamental changes in markets or the retum-generating pro- cess. We posited that changes in company-specific

risk reflect changes in the composition of securities used to estimate company-specific risk. Distin- guishing between these explanations is important in practice because our explanation suggests that managers can control their exposure to time- varying company-specific risk through industry and security selection. If changes in company- specific risk are pervasive (driven by changes in the company-specific risk of individual securities), however, a manager can do little to control the risks.

Our empirical tests support our hypotheses: Changes in the relative importance of riskier industries, changes in the relative importance of small companies in the market, and changes in estimated company-specific risk associated with estimation error related to changes in industry concentration largely drive changes in company- specific risk over time.

We thank Tim Vogelsang for kindly providing Gauss code. We thank seminar participants at the University of Montana, the University of New Hampshire, and the 2004 Financial Management Association meetings for helpful comments.

This article qualifies for 1 PD credit.

Notes 1. Although we focus on changes in weights, we do not assume

company-specific risk for individual securities to be constant over time. In a recent working paper, Fink, Fink, Grullon, and Weston (2005) argued that the increase in the number of young companies going public largely explains the steady rise in company-specific risk over time (i.e., that changes in weights arising from an increase in the number of young companies, rather than changes in risk itself, are responsible for the increase in company-specific risk over time).

2. Following CLMX, using beginning-of-month capitalizations, we computed monthly industry returns as the value- weighted average return for all securities within the industry.

3. The calculation of the Vogelsang t-statistic depends on the desired significance level. See Vogelsang (1998) for details.

4. The long uptrend (1962-1999) and subsequent downtrend (2000-2003) reported in Table 1 were not driven by outliers. Specifically, in unreported tests, we excluded October 1987 from the analysis and limited the uptrend period to August 1962 through December 1998 (i.e., excluding the spike in company-specific risk in calendar year 1999). The linear trend coefficient fell only 18 percent (from the 1.195 reported in Table 1 to 0.976) and remained statistically significant at the 5 percent level. Similarly, when we excluded the first six months of calendar year 2000 from the downtrend period, the coefficient magnitude fell 13 percent (from -51.605 to -44.876) and was statistically significant at the 10 percent level.

5. The weighted average estimated company-specific risk in the market (FIRMt) is simply the sum of Equation 4 across the 49 industries weighted by industry capitalization.

6. All variables in the second term of Equation 4 are positive, so this term will induce a downward bias in estimated company-specific risk. This bias does not influence total risk, only how risk is partitioned among market, industry, and company-specific risk.

7. More generally, consider an industry with many companies but only one of them is contained in the CRSP database while the rest are either private or foreign listed.

8. The idea that industry concentration affects estimates of company-specific risk is informally recognized in a number of studies. For example, authors of studies of international data (which usually include markets with even greater con- centration than found in the U.S. markets) commonly esti- mate company-specific risk for securityj as security j's return less the average return on all stocks other than j (e.g., Li et al. 2004). Note, however, that as shown in Equation 4, such an adjustment will not generally result in an unbiased estimate.

9. The Herfindahl index, a measure of industry concentration, is calculated as the sum of the squared within-industry weights; therefore, it has a maximum value of 1. For exam- ple, if an industry contains only two securities of equal size, the Herfindahl index is 0.52 + 0.52.

10. The weighted average within-industry Herfindahl index is the Herfindahl index in each industry weighted by the industry's market weight at the beginning of the month.

11. Declining concentration reduces the negative bias in esti- mated company-specific risk (under the assumption that securities within an industry have similar company-specific risk) and is thus associated with an expected increase in estimated company-specific risk.

12. We thank an anonymous referee for pointing this out.

September/October 2006 www.cfapubs.org 99

Page 13: Bennett Sias 2006

Financial Analysts Journal

13. No companies were classified as in the "health care" indus- try in August 1962.

14. For a few industries, sample sizes at some point in time were smaller (i.e., there were fewer securities in the industry at time t than the Ni securities in the industry in August 1962). In those cases, we simply computed the company-specific portion of the return based on the remaining securities. For example, if there were 100 securities in the industry in August 1962 and only 99 in September 1962, within-industry weights were based on the sample of 99 securities (and still summed to 1).

15. As discussed later, we used security weights based on August 1962 levels but returns from time t. Without this constraint, a stock with a very low price at time t could be assigned a relatively large weight in a shrinking industry.

For example, in 2002, a single low-price security (Tramford International) had a 1,600 percent one-day return as its price went from 2 cents on 8 August to 33.91 cents on 9 August.

16. If an industry had more securities in a future month than in August 1962, we implicitly assigned the additional securi- ties a weight of zero. If the industry had fewer securities in a future month, we scaled the assigned weights from August 1962 to sum to 1; we used these weights to calculate the month t industry return. Once company-specific risk was calculated for each security, we returned weights to their unscaled August 1962 values and gave the smallest security the "missing" weight. This approach was equiva- lent to assuming the missing securities had the same risk as the smallest security in a shrinking industry.

References Bennett, J., and R. Sias. 2006. "How Diversifiable Is Firm-Specific Risk?" Working paper, University of Southern Maine and Washington State University.

Brandt, M., A. Brav, and J. Graham. 2005. "The Idiosyncratic Volatility Puzzle: Time Trend or Speculative Episodes?" Working paper, Duke University.

Campbell, J., M. Lettau, B. Malkiel, and Y. Xu. 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk." Journal of Finance, vol. 56, no. 1 (February):1-43.

Cao, C., T. Simin, and J. Zhao. 2005. "Can Growth Options Explain the Trend in Idiosyncratic Risk?" Working paper, Pennsylvania State University.

de Silva, H., S. Sapra, and S. Thorley. 2001. "Return Dispersion and Active Management." Financial Analysts Journal, vol. 57, no. 5 (September/October):29-41.

Durnev, A., R. Morck, and B. Yeung. 2004. "Value-Enhancing Capital Budgeting and Firm-Specific Stock Return Variation." Journal of Finance, vol. 59, no. 1 (February):65-105.

Fama, E., and K. French. 1997. "Industry Costs of Equity." Journal of Financial Economics, vol. 43, no. 2 (February):153-194. Fink, J., K. Fink, G. Grullon, and J. Weston. 2005. "IPO Vintage and the Rise in Idiosyncratic Risk." Working paper, James Madison University and Rice University.

Goyal, A., and P. Santa-Clara. 2003. "Idiosyncratic Risk Matters!" Journal of Finance, vol. 58, no. 3 (June):975-1007.

Irvine, P., and J. Pontiff. 2005. "Idiosyncratic Return Volatility, Cash Flows, and Product Market Competition." Working paper, University of Georgia and Boston College.

Jiang, X., and B. Lee. 2004. "On the Dynamic Relation between Returns and Idiosyncratic Volatility." Working paper, University of Northern Iowa and University of Houston.

Li, K., R. Morck, F. Yang, and B. Yeung. 2004. "Firm-Specific Variation and Openness in Emerging Markets." Review of Economics and Statistics, vol. 86, no. 3 (August):658-669.

Morck, R., B. Yeung, and W. Yu. 2000. "The Information Content of Stock Markets: Why Do Emerging Markets Have Synchronous Stock Price Movements?" Journal of Financial Economics, vol. 58, no. 1 (October):215-260.

Newey, W.K., and K.D. West. 1987. "A Simple, Positive Semi- Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." Econometrica, vol. 55, no. 3 (May):703-708.

Rajgopal, S., and M. Venkatachalam. 2005. "Financial Reporting Quality and Idiosyncratic Return Volatility over the Last Four Decades." Working paper, University of Washington and Duke University.

Vogelsang, T. 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation." Econometrica, vol. 66, no. 1 (January):123-148.

Wei, S., and C. Zhang. 2006. "Why Did Individual Stocks Become More Volatile?" Journal of Business, vol. 79, no. 1 January):259-292.

Xu, Y., and B. Malkiel. 2003. "Investigating the Behavior of Idiosyncratic Volatility." Journal of Business, vol. 76, no. 4 (October):613-644.

100 www.cfapubs.org 02006, CFA Institute