f5. Ann“. .».1.nw_nuyu I s in. a .umfiua. u 3: 1.1.3.!!! u" :s 3.3. q. gin tnttl. . .5an is! . x. . I, . l. x. i . .31 2.. (c. vixfie {x 5.3“. .. 4 a; uh. £323.. .. 3‘ .r “K . a t): I l- 3:05:31 t... Cu. 6 .I. .3: :5: ..,..v Ms lizt ,4 3|, 3.3 :1... .» xiv I . . .4... . Ti...» .31... 4.2;» y : . “fl .1. ET... " - '33 *3: u {ex-xii. 1. 12:2..3: uma THESIS 53V -, . LIBRARY Michigan State University This is to certify that the dissertation entitled EXPLORATIONS INTO IDIOSYNCRATIC RISK presented by NADEJDA VOZLIOUBLENNAIA has been accepted towards fulfiliment of the requirements for the Ph.D. degree in Finance (Luigi $741,, T 'Miijor Wrofessor’s Signature M 01.44 /0 ,fi Z5) 07 0 Date MSU is an afl'innative-action, equal-opportunity employer PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 6/07 p:/C|RC/DateDue.indd-p.1 EXPLORATIONS INTO IDIOSYNCRATIC RISK B y Nadejda Vozliouhlennaia A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR. OF PHILOSOPHY Department of Finance ‘2007 ABSTRACT EXPLORATIONS INTO IDIOSYNCRATIC RISK By Nadejda Vozlioubleimaia Following a study by Campbell, Lettau, Malkiel, and Xu (2001), which documents an upward trend in idiosyncratic volatility that lasted for nearly for decades, not only the interest in idiosyncratic risk has been renewed, but it became a highly researched topic in finance literature. Numerous papers propose explanations of the dynamics of idiosyncratic volatility or consider its consequences and implications. We choose to look at the behavior of idiosyncratic risk from three different perspectives reflected in the three essays, which comprise this dissertation. The first essay proposes an explanation of the observed empirical patterns in the average it‘liosyncratic volatility initially documented by Campbell, Lettau, Malkiel, and X11 (2001). In particular we show that idiosyncratic volatility is driven (at least in part) by market value concentration. In a more concentrated market, it is easier to forecast movements in the aggregate market index, and hence, the relative use— fulness of analysis that relate individual stock price movements to aggregate market movements (i.e., the Market Model) is greater. Investors will therefore place greater emphasis on such analysis in more concentrated markets, which will exhibit less id- iosyncratic volatility than markets in which value weights are more closely centered around %. Our empirical analysis suggests that the two variables are cointegrated and that a larger dispersion of market capitalization weights results in higher idiosyncratic volatility. The second essay provides a firm-by—firm estimation of trends in idiosyncratic volatility. By doing so we can identify the follmving sources that contribute to the trend in the market average idiosyncratic risk (Campbell, Lettau, hlalkiel, and Xu (2001)): new issues. delistings. and existing firms with positive, negative, or no volatil- ity trends. This identification is crucial because the relative importance of each source has drastically different investment implications. Unlike the current literature, we show that many firms ex1_)erience positive or negative volatility trends, and their dy- namic combination leads to increases or decreases in the market average idiosyncratic risk. Our approach of firm-by—firm estimation of trends further allows us to pinpoint the factors that are behind the fluctuations in idiosyncratic risk and examine the relative importance of existing interpretations including (1) firm fundamentals (Wei and Zhang (2006) and Irvine and Pontiff (2005)), (2) institutional ownership (Malkiel and Xu (2003)). and (3) speculative trading (Brandt, Brav, and Graham (2005)). Several authors proposed that growing institutional ownership share can explain the idiosyncratic risk puzzle (Malkiel and X11 (2003), Dennis and Strickland (2005)). In the third essay we argue that the causality in this relationship may run in the opposite direction as well. i.e. when changes in idiosyncratic risk induce Changes in institutional ownership. This assertion is consistent with Merton (1987) limited infor— mation model, which predicts that. investors are forced to hold (part of) idiosyncratic volatility in their portfolios. Provided that institutions have better abilities to diver- sify then iion-institiitional investors, companies with growing idiosyncratic risk also have increasing share of institutional owners. Therefore, observed trend in average idiosyncratic volatility in the US. financial market can be a reason of increasing in- stitutional ownership share. Our (’rausality tests in VECM specification support this l‘iypothesis. ACKNOWLEDGMENTS I would like to express the deepest appreciation to my adviser, Professor Geoffrey Booth, who taught me to have patience to search for the truth and an open mind to see it. Without. his guidance and help this dissertation would not have been possible. I wish to thank my committee members, Professor Long Chen, Professor Richard Baillie, and Professor Stephen Dimmock, for valuable comments and fruitful discus- sions. I am extremely grateful for the assistance and advice I received from Professor Charles Hadlock. I also thank other faculty members and doctoral students of Finance Department at Michigan State University for support during my graduate studies. Additionally, I would like to thank Professor Glenn Boyle of New Zealand Institute for the Study of Competition and Regulation, Professor Chunchi W'u of the Univer- sity of Missouri, and Professor Vedat Akgiray of Bogazici University for insightful comments and suggestions on the first essay of this dissertation. Finally. I’d like to thank my family: my sons, Alexander and Paul - for their patience, my husband Radu - for inspiration. my parents, Anatoliy and Lyudmila, and my sister Vera, — for their support, and my aunt. Lidiya - for help and encouragement. i v TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES 1 Structure of Idiosyncratic Risk: An Insight into Market Model Error 1.1 Introduction ................................ 1.2 Relevant literature ............................ 1.3 Structure of Market Model error variance ................ 1.4 Testing, data, and results ......................... 1.4.1 Analysis of market. average idiosyncratic volatility ....... 1.4.2 Analysis of industry average idiosyncratic volatility ...... 1.4.3 Analysis of the selected average idiosyncratic risk ....... 1.4.4 Analysis of the idiosyncratic volatility of individual securities . 1.5 Conclusions ................................ 2 Cross-Section of Tmnds in Firm-Specific Risk 2.1 Introduction ................................ 2.2 Gross sectional variation of trends in idiosyncratic risk ........ 2.2.1 Data construction ......................... 2.2.2 Analysis of results ........................ 2.3 Factors that. explain cross-section of trends in it'liosyncratic risk 2.3.1 Explaining probabilities of a trend ................ 2.3.2 Robustness checks ........................ 2.3.3 Explaining magnitudes of trend coefficients ........... 2.4 Conclusions and discussion ........................ 3 On causality of the relationship between institutional ownership and idiosyncratic risk 3.1 Introduction ................................ 3.2 Data, test construction. and i’nain result ................ 3.3 Future work ................................ APPENDICES A Tables and Figures for Essay 1 B Tables and Figures for Essay 2 vii ix oor—tI-i 10 17 17 23 26 27 29 31 31 35 35 36 41 41 50 52 54 57 57 60 64 67 67 78 C Tables and Figures for Essay 3 BIBLIOGRAPHY vi 93 98 LIST OF TABLES A.1 Descriptive statistics ......................... A.2 Correlation matrix ........................... A.3 Augmented Dickey-Fuller unit root tests ............. A4 Johansen cointegration tests ..................... A.5 Estimated cointegrating coefficients ................ A.6 VEC model for various measures of idiosyncratic risk ..... A.7 Cointegration tests with fundamentals .............. A.8 ADF unit root and Cointegration tests by industry ...... A.8 Continued ................................ A.9 VECM and cointegrating equation coefficients by industry A.10 VECM for selected average idiosyncratic risk .......... A11 The Market Model with GARCH(1,1) errors .......... A.11 Continued ................................ 8.1 Trends in idiosyncratic volatility of individual securities . . . B.2 Descriptive statistics of firm characteristics ........... B.3 'I‘i'end in idiosyncratic risk versus trend in firm characteristics 33 Continued ................................ B3 Continued ................................ B4 Multinomial logit regressions .................... B5 Sub-sample multinomial logit regressions ............. B5 Continued ................................ B.6 Regressions on trend coefficients .................. C1 Augmented Dickey-Fuller unit root tests ............. C2 Rolling cointegration and VEC model estimates ........ vii 68 68 69 69 69 70 71 71 72 74 74 75 79 79 80 86 94 94 C3 VEC model for idiosyncratic risk and institutional ownership 95 viii A1 A2 A3 A4 B1 B2 B3 B4 B5 B6 B7 B8 B9 C1 C2 C3 C4 LIST OF FIGURES : Idiosyncratic volatility ....................... : Quasi-Herfindahl Index ....................... : Idiosyncratic fundamental volatility ............... : Total number of securities ..................... : Market composition effect ..................... : Market average risk with positive trends removed. ..... : Market average risk with negative trends removed. ..... : Idiosyncratic volatility of the NASDAQ firms ......... : Idiosyncratic volatility of the non-NASDAQ firms ...... : Idiosyncratic volatility of the new firms ............ : Idiosyncratic volatility excluding new firms .......... : Idiosyncratic volatility of the 1980 firms ............ : Institutional ownership ....................... : Idiosyncratic risk adjustments to shock in VECM ...... : Institutional ownership adjustments to shock in VECM . . : Idiosyncratic volatility ....................... : Institutional ownership ....................... ix 76 77 77 87 88 89 90 90 91 91 92 92 96 96 97 97 CHAPTER 1 Structure of Idiosyncratic Risk: An Insight into Market Model Error 1 . 1 Introduction Finance factor models, though intuitively appealing, often perform poorly when con- fronted with the economic data (see, for example, Banz (1981), Bhandari ( 1988), Stattman (1980), Fama and French (1992)).1 For instance, Roll (1988) poses the following question: how well do the various factors proposed by theory explain the realized changes in securities prices when the factors are tested on US. data? The answer is quite disappointing. At best, only one-third of the ex-post observed re- turns can be accounted for by the major known factors, or in other words, the model R—squared is quite small, leaving a significant part of the return in the form of an unexplained error. Siii’iilar patterns hold international1y (see Morck, Yeung, and Yu (2000)) Additional intriguing evidence regarding Market Model error appears in Campbell, 1By " factor models" we refer to those that. employ market-wide factors to explain stock returns. They include such models as the Arbitrage Pricing Theory (APT), Capital Asset Pricing Model (CAPM), or multivariate CAPM. The empirical representation of these models in terms of realized returns is referred to as the " Market Model”. Note. however. that our analysis applies only to those models that include the market index along with other factors. Lettau, I\’lalkiel, and Xu (2001) (henceforth, CLMX). CLMX find that the "ctl‘l‘dllcc of the model residual steadily increased over the last four decades (although Brandt, Brav, and Graham (2005) report it fell abruptly after 2000). Thus, not only is a large portion of returns unexplained, but the error has a distinct time-series structure. Morck, Yeung, and Yu (2000) present evidence on the cross-sectional correlation between a country's average idiosyncratic volatility and level of GDP. They are unable to explain this relationship by the fundamentals. The above discussion suggests that factor models fail to account for a certain phenomenon present in the market. Some insight into the nature of this phenomenon can be gained by looking at the structure of market model error. The purpose of the present study is to provide theoretical justification for the existence of a non-random, non-Gaussian error in the market model and to identify the economic forces behind it. Based upon the evidence in Campbell, Lettau, Malkiel, and Xu (2001), we are concerned with those variables that are able to explain the behavior of market model error variance.2 In this study we make several simplifying assumptions regarding investors’ be- havior. Our primary interest lies in the outcomes of this behavior (as reflected in realized returns), not in its motives. This means we consider assumptions suitable for modeling purposes as long as they are useful in explaining behavioral outcomes even if the agents themselves believe they follow a different strategy from the one we use in our investigation. we start by assuming that investors rely on the Market Model in security evalu- 2Note that the primary focus of this investigation is average idiosyncratic risk (or average return correlations) in the economy. This is not the same as average return dispersion. For instance, a large return dispersion over a specific time period may imply either near-zero or high negative return correlations. If all returns are moving in perfect unison they could be either very dispersed or very concentrated. Of course, some information about return variation can still be supplied by the return dispersion as discussed in Connolly and Stivers (2006). ation.3 The attractiveness of factor models lies in the simplicity of their application. Specifically. one does not need to know all available information about cross-return correlations in order to price a. security; rather, it is enough to know how the se- curity’s price varies with respect to a market-wide index (or factor portfolios). The idea is that it is reasonable for investors to complement information about one stock by their knowledge about the market as a whole and its influence over the security. For instance, investors may use the market index and the one-factor model to gain additional insight. The problem with factor models such as the CAPM is that. they assume investors optimize their portfolios using data on returns distributions. This in turn implies that the resulting market. portfolio is efficient. In this case it becomes optimal for all investors to use the factor model along with the market portfolio in security evaluation instead of using (costly to collect) information about returns distributions. But this contradicts the initial assumption the CAPM makes, rendering the market portfolio possibly irmfiicient. How can the equilibrium be. sustained in this situation? It is also worth pointing out that. using the market portfolio in security analysis is not as straightforward as it may seem. First, it is hard to measure such a portfolio (Roll (1977)). Further, there are errors in the model equation, which can render the evaluation results imperfect or incorrect. Distribution analysis cannot, therefore, be completely discarded. Indeed, the latter is superior (in accuracy) to the Market Model if the distribution characteristics were fully observable. Since this is not the case, however, distribution analysis is also imperfect. In this paper we consider the case in which investors combine the two approaches to make a more efficient evaluation of security returns. Consider the following example of how the information in the market index can be used in the analysis of returns. Imagine an investor who knows little about stock :‘Some survey studies indicate that factor models are actually used (mite often by corporate n'ianz-rgers in the analysis of the cost of capital: see. for instance, Gitinan and \v’andenberg (2000). A. we want. to determine the best prediction about the return on this security if the investor knows that on average the returns on the market will increase. Most likely, the investor would think that. the return on A will increase as well. Assume that. market index behavior is more forecastable (with respect to accuracy and effort) if much of its value is concentrated in fewer stocks (market leaders). Such concentration increases the effectiveness of the factor models as predictors of an individual stocks return relative to other sources of information (such as analysts’ forecasts or indi- vidually collected information on the company). Thus. if a significant proportion of investors expect a stock to behave in a certain way, its price will adjust. in equilibrium accordingly. The existence of market favorites, i.e., firms that have attracted a majority of investors attentirm, is suggested by the fact that the 30 stocks of the Dow Jones Industrial Index are often referred to as ”the market". This argument has even more appeal if we take into account the fact that ”the market" actually consists of several thousands of stocks and the Dow accounts for only one-fifth of its value. Much broader indexes are available (e. g, Wilshire 5000, NYSE Composite or NASDAQ Composite), but they are not as popular with investors. Beneish and Gardner (1995) Show that the Dow stocks are more widely followed by analysts and hence have more available information than other companies. Also, as Merton (1987) suggests, each investor confines his attention to a small portion of the universe of available securities. What happens, however. to those stocks that are not as widely followed? We suggest that their future returns are evaluated (at least. in part) based 011 the evaluations of the major market players. \Ve assume that the market index‘s predictability depends on the influence of its major constituent stocks and therefore on market concentration. But the concentra- tion can be affected by the new companies in the market in addition to changes in the relative value of existing companies. \Vhile an iiitj'i‘easing number of securities may be expected to increase the effect of the law of large numbers on the accuracy of evaluation (assuming the securities are independent). we do not. consider this effect. l'lCI‘G. The total number of stocks in the market increased from about 2000 to 7000 during the period under analysis. l‘lowever, the effect of the law of large numbers fully applies to a sample of between 50 and 70 stocks. after which point. increasing the sample size does not make much of a difference. Admittedly, though, in the case of only a few securities, the overall evaluation effect. can be non-linear or otherwise different from our analysis. Investors’ partial reliance on the market index is not irrational given that collect- ing and processing information is costly, that. is, it is an efficient way to deal with information constraints. First, use of the market index reduces investor-specific costs of collecting information (minus. of course, losses due to reduced forecast accuracy). Second. investors can share the costs for market index analysis, since large securities are widely followed by the press (information spillover effect). Finally, the well de- veloped CAPM, which relates the market as a whole and its individual components, can be efficiently used as an aid in security evaluation. One may be inclined to think that the above arguments should only reinforce the validity of the Market. Model. But this is not necessarily the case. For example, the traditional C APM derives implications of investors choosing stock prices given the distributions and correlations of the underlying cash flows. The model does not account for the fact that investors may be using the CAPM itself to price individual stocks.4 This imposes limits 011 the models explanatory power and implies a particular structure for its error. This structure can be linked to the relative concentration of market value in the economy because a higher dispersion of value limits the ability of investors to rely on the market index and the factor models. If the market consists of "This does not necessarily imply endogeneity of the model. though it does imply, as we will see later. that the variance of the market index is related to the model error. That said, the index and the error can still be uncorrelated. and the regular model still holds in terms of expectations. a few large and many small companies (i.e.. concentrated), the large stocks are used to predict the behavior of the small, generating correlations across securities that are over and above the correlations based upon their fundamentals. For example, consider a market. that consists of two companies, A and B, which use the same supplier of raw materials. Because their performance, and therefore stock returns, are linked to the performance of this supplier, the part of their returns that are determined by fundamentals (e. g., earnings) is correlated. Suppose now that. A is a big company and is considered by investors to be a market index measure, whereas B is a small company. Investors will pay close attention to A’s performance, evaluating its stock based on collected information. In contrast, due to the costs of collecting information, B will not be researched as intensively, in which case the agents will price stock B (in part.) according to the expectation that its return follows the return of the large company, which in turn will increase correlation between the returns of A and B. In a dispersed market, on the other hand, every stock is its own trend—setter. and the relative gain of relying on the market index as opposed to gathering firm-specific information is small. The Market Model residual behaves more like a random Gaussian error in this case, as is usually expected. We introduce a new variable, the ”Quasi-Herfindahl Index" (7t), which measures market value concentration and captures the ability of investors to rely on a market- wide index. Our empirical tests show that "ft accounts for part of the observed Market Model error variance. fluctuations for various measures of idiosyncratic risk. The results suggest that. lower market value concentration increases idiosyncratic risk. Additionally we find that ”it is unrelated to several other market—wide variables with the camability of explaining fluctuations in idiosyncratic \V'olatility (eg, the total number of securities on the market and the idiosyncratic volatility of fundamentals). The idea that concentration may be related to stock returns has also been re— cently explored in the literature. Specifically, Hou and Robinson (2006) suggest. that concentration is inversely related to risk. This relationship arises if firms in highly concentrated industries are insulated from distress risk or are under lower pressure to engage in risky innovaticms. Alternatively, our explanation of this relationship is based on investors" evaluation of security returns.5 Our findings have several implications. First, it immediately follows that Mar- ket. Model error variance is non-Gaussian and that it is related to an economy-wide variable. This means that. statistical methods other than the least squares regression may better estimate the model. For instance. modeling the error variance in a certain framework may be (.lesirable in empirical research. The results also emphasize the importance of idiosyncratic variance as an indicator of investors’ knowledge about future returns, as discussed by Durnev, Morck, Yeung, and Zarowin (2003). Finally, this paper advocates the existence of an additional link between idiosyncratic variance and level of information about return distributions available to investors: consistent with the literature, it. suggests that. a higher l\llarket Model error variance implies more informative prices.6 The remainder of the paper is structured as follows. Section 2 summarizes the relevant literature. Theoretical derivations are presented in Section 3. Section 4 de- scribes empirical testing methods, data, and results. Finally, conclusions and possible extensions are discussed in Section 5. 5A concern may arise with respect. to the relationship between concentration and average idiosyn— cratic risk, in view of the recent evidence that suggests idiosyncratic risk and liquidity are negatively correlated in the cross—section of securities (see Spiegel and Wang (2006)). If small stocks are less liquid and are the source of an increase in average market liquidity, liquidity and concentration may be related, which would translate into a relationship between concentration and idiosyncratic risk. We argue that this is not likely to be the case, however. since smaller stocks are allowed to be in the market as long as they provide sufficient. liquidity. In other words. adding small securities to the market does not. necessarily change the average liquidity level and hence the liquidity does not need to be related to the market value concentration. 6This paper is also related to cross—sectional studies of the average idiosyncratic risk in the economy and its link to Gross Domestic Product (see Morck. Yeung, and Yu (2000), Jin and Myers (2004)). It is not the purpose of this study to investigate the connection between a country’s level of development. and its information efficiency. But. if we assume that investors are better aware of return distrilmtions in more advanced econon'iies. such countries should have. a higher average idiosyncratic risk. as found in the literature. 1 .2 Relevant literature Campbell, Lettau, Malkiel. and Xu (2001), Campbell and Lettau (1999), Morck, Yeung. and Yu (2000). Malkiel and Xu (1999) and Billio and Pelizzon (2003), among others. document empirical regularities in the behavior of idiosyncratic risk. These papers indicate that on average idiosyncratic volatility has increased over time in various industries and countries. moving in the direction opposite that of the business cycle and recording lower values in less developed economies. In contrast, Ham-do, Mei, and X11 (2003) find that idiosyncratic risk is pro-cyclical in Japan. They attribute this puzzling evidence to the uniqueness of the Japanese market, where most firms are members of business groups. which increases the correlation of their fundamentals and as a result the correlation of their returns. Campbell, Lettau. Malkiel. and X11 (2001) suggest. several factors that can poten— tially account for their findings: conglomerate breakups. early IPOs, executive stock option compensation, emerging new markets for derivative instruments, more volatile betas. and higher institutional ownership. \Vith respect. to conglomerates, they argue that such firms are themselves diversified portfolios of various production units. all combined into one stock. Vi'hen split. into several companies, a number of stocks are created. each with its own price, decreasing average correlation of stock prices on the market. Similarly, Campbell. Lettau, Malkiel, and Xu (2001) argue that early II’O‘S can also increase average estimated firm-specific risk. Their rationale is that. firms issue equity early in life. when their fundamentals are highly volatile. and the volatility of fundamentals translates into a higher volatility of equity returns. Executive stock option compensation. which has grown in popularity over time, may also induce higher return volatility. The argument is based on the fact that. own- ers of stock options benefit from increases in the underlying stock volatility. Managers therefore may be inclined to choose projects that are likely to increase stock price fluc- tuations. To the extent that more managers own stock options. the average volatility of stock returns is higher. Turning to emerging new derivative markets, Campbell, Lettau. Malkiel, and Xu (2001) posit that in principle, they can also increase volatility of returns by reducing the inforn‘iation content of stock prices. This would happen, for instance, when the introduction of a new derivative market encourages trading by informed speculators, as less informative stock prices result in more volatile returns. Next, higher volatility of betas are argued to affect the volatility of stock prices and hence returns via the effect on the discount rates. Finally, institutional owners, whose judgment is relatively homogeneous and who possibly rely on only a few common fac— tors, may be responsible for an increase in the average firm-specific risk. The evidence suggests that the share of institutional investors’ holdings has grown at the same time the average idiosyncratic volatility of returns has increased. Some of the more recent findings in the literature support these predictions. Co- hen. Hall. and Viceira (2000) find a. positive relationship between executive option holdings and a firm’s idiosyncratic risk. Malkiel and Xu (1999) demonstrate that institutional ownership is able to forecast. stock volatility for industry portfolios. And Morck, Yeung, and Yu (2000) suggest that increased reliance on external financing, which implies more securities are present in the market, may be able to explain the increase in the average idiosyncratic volatility. A number of studies propose additional explanations for increased return volatil- ity. For instance, Schwert (2001), Agrawal, Bharath, and Viswanathan (2004), and Mazzucato (2002) show that higher demand uncertainty translates into higher equity volatility. Malkiel and Xu (2003) attribute the trend in average idiosyncratic risk to an increase in institutional ownership and expected earnings growth. and they con- firm earlier evidence that exclusion of NASDAQ firms from the sample reduces the magnitude of the observed trends. Jin and Myers (2004) relate the trend in return volatility to the opaqueness of firms to outside investors. asserting that. less transparent. companies, which have both 9 informed and uninformed equity holders, have a larger volatility of stock returns. Fama and French (2004) suggest that the rise in idiosyncratic risk in the US. mar- ket can be partly explained by an increased dispersion of profitability among the new lists. Pastor and Veronesi (2003) also point out that economic fundamentals (i.e., volatility of profitability) can account for empirical regularities in idiosyncratic risk. Additionally, they propose that the market learns about a firm’s behavior over time, since younger firms have higher stock volatility than older companies. The rela- tionship between idiosyncratic volatility and firm maturity is also explored by Pink, Fink, Grullon, and W'eston (2005), who argue that changes in the market’s average idiosyncratic risk are solely attributed to the influence of newly listed securities, which exhibit high firm-specific return variation. Irvine and Pontiff (2005) are able to explain the trend by an increase in idiosyn- cratic volatility of sales, earnings. and cash flows, while W'ei and Zhang (2006) claim that the ("lownward trend in returns on equity combined with an upward trend in its volatility resolves the puzzle. Rajgopal and Venkatachalam (2007) attribute the trend to the decreased quality of earnings reports and as a result an increase in the dispersion of analysts‘ forecasts, which in turn may translate into a higher average idiosyncratic risk. Guo and Savickas (2007) propose the surge in the number of pub— licly traded companies as a likely explanation. F inally, Brandt, Brav, and Graham (2005) suggest that periods of large idiosyncratic variance mark episodes of a rise in speculation in financial markets. 1.3 Structure of Market Model error variance In the previous section we describe several of the numerous factors that appear to be related (intuitively and empirically) to the behavior of Market Model error variance. The fact that. so many relevant factors exist suggests that these studies may only 10 be proof that in an economy. "everything is related to everything”. The following (-lerivations provide a theoretically justified structure for the changes in idiosyncratic volatility. The CAPM error decomposition in this section is based on several assump- tions about investors. forecasting and uncertainty about the returns distributions. The goal is to determine how this uncertainty and investors” reliance on the Market Model (to resolve it) affects the observed error of the original model. In the model of asset prices derived by Sharpe (1964) and Lintner (1965), investors are assumed to know the expected value of discounted future cash flows and their co— variance structure. Using this knmvledge and portfolio diversification principles they evaluate the present value of individual stocks. The current prices of securities adjust to reflect investors evaluation so that the following relationship holds in equilibrium: EM) = 31503111), (H) where r,- is the (excess) return on stock 1', rm is the (excess) return on the market. ('(n'(7',' .rm) PM” ) . Since at any given moment actual returns are not equal IN. index. and .3, : to their mean values. this relationship yields (mean zero) errors ((3, and am), given as follows: 1‘" = [3(7'1') + cit. (1.2) Tint : [3(7‘171) + 6m!~ (1-3) and "n = 23211111 + (W — ‘-3I€IIIf) = JH'mt + 'Izr- (191) where 77,-, 2 "it — 3,67,”. Assume that based on individually collected information about security 2'. each investor k makes her evaluation of return i. E(r,-) + 24"}. where uh; is evaluation er— ror (idiosyncrt-itic infm‘mation source). Each investor is assumed to have a different 11 evaluation error. but on average these errors are zero (F (125) = 0) across investors and across time. Also assume for simplicity that all evaluation errors have the same variance (level of uncertainty in the economy). So far the above assumptions do not. change the nature of the Market Model relationship, which still holds in terms of the averages (Lintner (19653)). Additionally, assume that an investor can use her evalua- A. mt~ and the beta to evaluate individual securities (“fat tion of the market index, rmt+zx is the evaluation error. similar to ”fir and the two are assumed to be uncorrelated). These two pieces of information can be combined to form investor k‘s evaluation of a security return as follows: r5 = 01mm + at) + <1 — atWrm +14%) <15) -_— af'(l€(r,-) + 1%,) + (1 - (differ — 7M + 3i'ffnl = “fl/3(7)) + Vi?) + (1 — ohm») +3167!” +.<3wf{,t) E("I‘,') + Girl/if + (1 - afiifhkhnt + VA? ) mt The expected value of this forecast is E (r,) and its mean squared error (assuming .._, ,., k, ,7-.2‘2 ,.‘2.‘2 2 2 ..,. 2__ no (orrtlation l)( tween Vi, and (mt ) 1s (1’. 0m- + (1 -— 0,) ,3,- (0m + awn), “litre 0m- —— carp/l") 02 — curb/k ) and (72 — rar(e ) \Iinimi'iin ' this ex )ression with 7 If 1 Vin — ' ,nf,7 ( In — ' 'Int ‘ L ‘ g ' ‘ ‘I L‘ i . .. . k .- ,.-.8 respect to ”i. g1\ es. , ‘2 2 2 2 I; f,‘ (”m + 01/71).) .‘i,’ (i, = 2 3,2 2 2 = 02 = (U. (1.6) 0m + " 1‘, (gm + 011m.) m + 32 052+017m In the above expression all investors arrive at the same alpha for stock '2'. because we assumed that investors have equal abilities of collecting information about returns . . 9 . . and the market 1ndex, 1.e. 0;)» and 05m are the same across Investors. If we allow TThis assunmtion implies that the mean evaluation error is not related to the deviations of rm, around its mean value. ”The main result will follow as well if we minimize some concave function of this expression instead of the mean squared error. Such function can be chosen based on the assumed utility of the agents. these variances to change over time. equation (1.6) becomes: The above assumptions add another dimension to the model (or to the model error9). As we can see from equation (1.7), the magnitude of a” depends on the ratio of the error variances. which gives the relative advantage of using the market. index information versus the stock-specific information to evaluate the returns. Assume further that the observed returns on the market are the average return evaluations across agents plus an error term:10 1 k - - 1 k 1 A- W = X Z: 734M511 = “itEirél+(1‘0itl‘3z‘"rlit+9it+aitF Z Vjt+(1‘ait)7\7 2 WM- k k k (1.8) Given that evaluation errors are zero on average, the last two terms are negligible for large K (number of investors), therefore, we ignore them in the remaining derivations. The above equation can be rewritten as: "it = 5(1)) + ((1 — aifljiemt +511) = Efl‘i) + fitt- (1.9) Since we need to have cm, 2 2, "true”, together with above equation this condition 21 “3151'! 1"21 ”Nil—”irl‘ji E (r1) and E (rm). we can derive the relationship for the, observed market returns by implies that (2,,” 2 Since the original CAPM holds in terms of substituting equations (1) and (3) into (8): m = 3:"m + (UtCz’t + (5m (1-10) , ”132‘ 21 “'iitlz’t (1‘2;“’zfrl.1“'ztl.5lzl' where (it : Therefore. Market Model error consists of two parts: 'h’t : (WC-tr + (5,1. (1-11) 9The term is related to the model uncertainty discussed. for example. in C'ao. \Vang. and Zhang (200:3). 1“Here we assume that investors arrive at average return via trade. 13 We do not attempt. here to analyze the second part, instead, we‘ll concentrate our attention on the first, since we are able to make certain statements about behavior of alpha. This part of the error is smaller if the investors use the IVIarket Model in security evaluation decisions. Its magnitude depends on how noisy is the idiosyncratic 2 source of information. From equation (1.6) a.“ converges to one as am- converges to 22. converges to infinity zero (idiosyncratic source is fully informative) and to zero as 0V. (idiosyncratic source is very noisy). In the former case, cry-t = 1 and the model’s error takes the form: 77,} : Cit + (SI-f. Investors use only their (precise) estimates of security returns as there is no need to rely on aggregate market data. If, on the other hand, little information is present. to evaluate stock 2', investors rely exclusively on the Market. Model. In this case a” = O and the Market Model error is just 61¢, i.e., the deviations from the CAPM ermililniurn are smaller because market participants set. their expectations according to the Market Model. The resulting returns behave as the investors expected, and according to the Market Model equation. The idiosyncratic risk in this case will also appear to be smaller in magnitude. The variance of the (first part of) error in this modified Market Model is thus a 2 function of the r3110 7—:47—7 ‘vhich is not. qulte empirically tractable. We therefore (T (7" mt I/mf need an additional proposition. Assume that 012m and 012/“ are roughly constant over a. short period of time. The remaining variable in the. above ratio (dam) is the variance of the error of the adepted measure of market index. Its large values indicate that the true index is not measured well. We hypothesize that when market value is concentrated in a fewer number of securities conventional measures such as DJIA or S&P500 are better proxies of the market. index. Additionally. even if the market. index is exactly measured, it is easier 2 to access its value if market is highly concentrated. Therefore, the magnitude of aumt is smaller. In this case investors place greater emphasis (1 — a) on the Market Model source of information. thereby decreasing variance of the model error. A natural 14 measure of this effect is the concentration of market value. which is computed similar to the Herfendahl index. and is therefore referred to here as the "Quasi-Herfendahl Index” :1 I "ft = 211%. (1.12) i: where “7"th is the market value weight of security 71. Based on the above discussion we, can determine the relative gain of using firm- specific versus market index information: —,——'—.2—— = mi). (1.13) where f () is some function of 7,. For tractalnlity we assume a linear relationship of the form: K) 0'“. V1 . . 2——2—— : 07,, (1.14) all! + (Tl/Tilt where i) is positive. Therefore. the Market Model becomes: .32 ‘L ._ _ ,. i . ‘, r 711 “.~j1.’rlit+ I)” +5891 + Oil" (1'10) I From equation (1.15) we can see. that Market Model error fluctuations are smaller when market value is more concentrated, because it is easy to evaluate stock returns using the index. This task is simplified further when a stock is not very sensitive to the market’s movements (i.e.. its beta is relatively small). The opposite is also true: when the market has dispersed weights and the beta of a given security is large, it does not pay off to rely on the Market. Model in evaluation of individual securities. Some addititmal intuition can be gained if we consider the analogy to the theory of gravitational attraction: objects with non—zero masses attract each other. The attraction force is stronger the greater the mass of the objects. Imagine a region of space filled with interstellar dust. If the dust particles are evenly spread the attraction among them is weak. If the particles are arranged into clusters (with large masses) 11In the economic literature. the llerfendahl Index measures the degree of cmnpetition and is computed as the. sum of the squared market shares of the firms in an industry or market. 15 they are more likely to attract each other and the surrounding dust. Suppose now that mass is the market capitalization weight. and particles are traded securities. When in\.«'estors form their expectations about. stocks by looking at.- the behavior of a set. of large stocks, they create a. ”gravitational field“ among securities (over and beyond their fundamental co-mm'cments) similar to the one observed in nature. This field is stronger in a more concentrated market. The variable “it is a measure of the strength of this field. Suppose the market (which consists of thousands of stocks) has a well-defined cluster of large companies. It is easier in this case to anticipate the movements of the market. index as you only need to know the behavior of the few main companies. Investors know that all returns follow the 1\Iarket Model. Further, the model has better predictive power. and is more useful to investors, while collecting information about. individual companies is still costly. Investors therefore rationally decide to form their evaluations of returns based more on the Market Model than on individual security information. But in equilibrium the returns of the stocks adjust according to investors expectations. This creates additional correlations among stock returns in the market. Equation (1.15) suggests that idiosyncratic volatility depends upon a macroeco- nomic variable that measures the degree of market pzn'ticipants" reliance on a market. index in the evaluation of future returns. To the extent. that this variable records low variability in a short. period of time (e. g., one month), the measured idiosyncratic volatility should be its function. In fact. it is cowl/frond] idiosyncratic risk that. is being picked up in the monthly idiosyncratic risk measure, where “,1 is the relevant information set. Taking a linear approximation of the cocflicicnt on 1],, with parame- ters (10 and (11 (and assuming that 3,: is constant). we have the following expression for the conditional idiosyncratic risk of security i: ”in = 0’10 + mm. (1516) 16 where ”10 and ”‘il are some constants. If idiosyncratic risk am “it are integrated variables, they should have a long-run equilibrium relationship. Averaging across stocks we obtain a similar expression for the average conditional idiosyncratic risk: 1R1: 00+a‘1’7’t, (1.17) where the coefficients are the cross-stock coefficient averages. This analysis suggests that individual as well as average idiosyncratic variances should be cointegrated with 7f and this relationship should not depend on the set. of stocks included in the measure of the average idiosyncratic volatility. 1.4 Testing, data, and results Under several reasonable assumptions we establish in the previous section that. the concentration of market. value is related to changes in the idiosyncratic risk of in- dividual securities and to changes in the markets average idiosyncratic risk. These propositions are easily tested empirically. The tests that. follow are divided into four groups according to the level of aggregation of the average risk: the market average idiosyncratic risk, industry average risk, selected average risk, and individual security idiosyncratic risk. 1.4.1 Analysis of market average idiosyncratic volatility In the first group of tests we use five methods to estimate idiosyncratic volatility in an effort to ensure. that the results are not affected by differences in the estimation 1:)1‘ocedures. \Vith robustness established. we continue to use only the first method in the remaining three groups of tests. The estimation Ill(‘lll()(.lb‘ are: 1. CLMX procedure using the etmally weighted market index (LIRCE), 17 2. CLMX procedure using the value weighted market index (LIRCV), 3. the Market Model (one-factor) residual volatility (LIR). 4. the Fama and French three—factor model residual volatility (LIRFF). a. the Market. Model residual volatility estimated using five-year interval regres- sions (LIRSY). The first method, described in detail in Campbell, Lettau, Malkiel. and Xu (2001), is appealing since it does not. require estimation of betas. Assuming zero cross- correlation among betas the monthly idiosyncratic risk is constructed as follows: 71. j 11 [at z 3; Z 20,-. — 7",...) (1.18) i=1 3:1 where r}... is the return on security 2? on day s in month t, rms is the market return on day s in month t, j is the number of firms in a. given month. and n is the number of days in a given month. All other volatility measures are monthly averages of the residuals. so the time series consists of monthly data for the July 1963 to December ‘2004 period. The original data set includes daily data for all the stocks traded on NYSE, NASDAQ, and AMEX during the specified period (obtained from the Center for Research in Security Prices (CRSP) database). The measure of the concentration of market value. is the same in all of the tests and is constructed using monthly data. on market capitalization weights (wit) of all the securities in the sample: J 2 “,1 : 201'”). (1.19) i=1 All variables in this study are converted into logarithms following the convention adopted in the literature. The empirical analysis in this paper implies testing for the existence of a linear relationship between two time-series \V'ariables. If these variables are non-stationary. 18 we need to rely on the concept. of cointegration. The first step. therefore, is to establish stationarity properties of the variables of interest. An Augmented Dickey- Fuller procedure is used for this purpose. The next step is cointegration analysis, in the event both of the variables in the tested relationship are non-stationary. we apply the Johansen methodology (Johansen (1991) and Johansen (1995)). The specification we use allows the series to have linear trends. The likelihood ratio trace statistic is computed as follows: 1 en = 4210.41 — A1). (1.20) i=0 where A; is the i-th largest eigenvalue. It is the test. of H(0), no cointegrating equa- tions, against H (1). one cointegrating equation. The critical values for the test. are obtained from ()sterwald-Lenum (1992). After cointegration is established, we es- timate a vector error correction model (VECM) to infer the direction of causality among the variables. Our model predicts that idiosyncratic volatility is endogenous in this relatitmship. The VECM estimated for idiosyncratic risk and 7t, respectively. is the following: Amt = 9901+v5‘llflRt—1‘07’t—1)+P12A1Rt—1+93115AlRt—2+9914A7f—1+9915A'7t—2» (1.21) and A)? = 7902+93‘21URt—1— r“11—1)+»922A/Rt—1+¢23AlRt—2+9324A71—1+¢2FAfirt—2~ (1.22) where IR, is a measure of idiosyncratic risk. an is the market concentration index, and (Hit — 051.11) is the error correction term (ECT).13Tlre significance of the coefficients on the ECT in each equation can tell us which variable in the system is exogenous. \N’e expect that a," is exogenous and $521 is insignificant. 12In untal.)ulated tests (available upon request). specifical ions with a. different number of lags yield similar results. 19 As we mention earlier. idiosyncratic volatility of economic fundamentals (earnings and cash flows) is shown to be related to average idiosyncratic variance (see, for instance. Irvine and Pontiff (2005)). \Ve need to make sure that the variable of interest (71) does not proxy for this measure. These robustness checks are included in the first group of tests. \Ve reconstruct the three measures of the idiosyncratic volatility of fundamentals (sales. earnings. and cash flows) following Irvine and Pontiff (2005) and test whether they are related to the concentration of market value. The three measures are obtained using the following algorithm (applied in Irvine and Pontiff (2005)). Sales per share, earnings per share, and cash flows per share are computed using COR-IPUSTAT data items 2, 5, 1-1, 15, and 19 (quarterly data). Specifically. earnings per share is item 19. cash flows per share is item 5 plus item 19. and sales per share is item 2 divided by item 15. All the variables are divided by the price (item 11) and ranked into 100 groups by this ratio. If an observation has the highest rank, it is being assigned the maximum value from the previous rank group. If an observation has the lowest rank. it is being assigned the minimum value from the. previous rank group. This procedure is introduced by Irvine and Pontiff (2005) to correct for outliers. The variablts are then multiplied back by the price. Next, shocks to the fundamentals are computed as the errors from the following regression: Eu - Err—-4 = 0' + 31(511—1 - Ems) + 132(511—2 - E'f—G) + ‘fiifEit—3 — Bit—7) + mt. (1.23) where [7,) is the firm—level earnings. cash flows. or sales at. quarter t. The (quarterly) residuals of this regression are then converted into daily data by assigning the same value to each day of a given quarter. The market index for each of the fundamental measures is the moving average of the index computed using the equally weighted av- erage across the firms. The idiosyncratic fmrdamental volatility measures are monthly averages (across firms) of the deviation of these errors from the moving average index. 20 Empirical results Our data set consists of the five measures of idiosyncratic risk, the Quasi—Herfindahl Index (11)), the three measures of idiosyncratic fundamental volatility constructed using sales, cash flows, and earnings (LIS, LICF, and LIE, respectively), and the total number of securities on the market (LNS). Table A.1 contains descriptive statistics for all these variables. The. five idiosyncratic risk measures are virtually identical in their major statistical indicators and are highly correlated (Table A2). Figure A.1 depicts the first measure of idiosyncratic volatility (LIRCV) as a function of time. The trend found in various studies for the years 1963 to 2000 is clearly visible. Note also the sharp decline in volatility after 2000, as pointed out in several recent. papers (see, for example, Brandt, Brav, and Graham (2005)). The time series of the concentration measure is plotted in Figure A.2. Unlike idiosyncratic volatility, it is decreasing over time. All measi’u'es of idiosyncratic volatility are. correlated with "it (cm-relation coefficient is about. ~07). supporting our hypothesized relationship. Different idiosyncratic fmrdamental volatility measures vary in the major statis- tical indicators (Table A1), though all are correlated with the average coefficient of 0.7. They are plotted (against the time line) in Figure A3. All three have a slight positive trend. consistent with. Irvine and Pontiff (2005). Idiosyncratic volatility of sales and cash flows are not highly correlated with 7) (correlation coefficient is about —0.3), in contrast. to the volatility of earnings (correlation with 71 is -—0.57), which may potentially account for the relationship between ”)1 and idiosyncratic risk (in case it is cointeg‘ated with 71). All measures of fundamental idiosyncratic volatility are correlated with idiosyncratic risk, with coefficients between —0.5 and —0.8, sug- gesting the existence of a relationship. The last variable (number of securities in the market.) also trends upwards and is (i‘cn'related. with "it for each of the measures of idiosyncratic risk (see Figure Axel). Thus. it. can potentially account for the changes in idiosyncratic risk. Note that we use the munber of securities in the market in the 21 robustness checks to ensure that “,1 does not proxy for this variable. Augmented Dickey—Fuller unit root tests indicate that all of the considered vari- ables are non-stationary. as we are unable to reject the unit root hypothesis (Table A3) Results of Johansen cointegration tests for each of the measures of idiosyn- cratic risk and the market concentration are summarized in Table A.4. Likelihood ratio statistics indicate the existence of a cointegrating equation at the 5% level for each of the measures of idiosyncratic risk. The estimated coefficients in the cointe- grating equation (Table A.5) confirm the direction of the relationship predicted by the theory (negative). The normalization variable is idiosyncratic risk, as the theory suggests it is the endogeneous variable in the system. Whether this is indeed the case will be studied next in the analysis of the error correction model. Table A.6 contains estimates of the VECM for each of the five idiosyncratic volatil- ities. The results do not vary much across the volatility measures. The coefficients on the error correction term (ECT) in equation (1.21) are highly significant (1‘. ratios are slightly over 4.0 for all five measures), while coefficients on this rcgressor in equation (1.22) are insignificant (f, statistics are about —0.8). This indicates that 7t is not af— fected by the deviations in the relationship between concentration and idiosyncratic risk, i.e., it is exogenous. Applying similar logic. we conclude that idiosyncratic risk is endogenous in this relationship. i.e., the concentration measure evolves independently, while idiosyncratic risk adjusts to concentration in equilibrium. Note as well the significance of some of the lagged variables: lagged changes in idiosyncratic risk are significant in equation (1.21). while both the first and second lags of the past changes in 1:) are insignificant. The importance of the lagged variables may be an indication that the relationship between on and idiosyncratic risk accounts only for a part of the overall dynamics of the latter. Other factors may also explain the changes in idiosyncratic risk, as documented in recent research (such as breaking up conglomerates. increased institutional mvnership, volatility of betas. et.c..; see Section 2). The significance of the lags of idiosyncratic risk is consistent. with the GARCH framework and with the significance of the "GARCH" parameters in the variance equation (see Section 4.4). Next, we want to make sure that the variable 7)., which appears to drive the changes in idiosyncratic risk, is not just a proxy for changes in fundamentals or in the number of securities. “’8 use the three measures of fundamental volatilities suggested in Irvine and Pontiff (2005), namely, the average idiosyncratic volatility of earnings, sales, and cash flows. to test whether each is cointegrated with 7t (Table A.7). In most cases the idiosyncratic fundamental volatility and the total number of firms are (.frtiintegrarted (at least at the 5% level) with the measures of idiosyncratic risk, as expected. The measure of the fundamental volatility using earnings is cointegrated only with the LIE and not with the other measures of average idiosyncratic risk. None of the fundamental volatilities nor the number of securities is cointegrated with ”)1. suggesting that. these variables cannot account for the cointegration between the latter and the average idiosyncratic risk. 1.4.2 Analysis of industry average idiosyncratic volatility The theoretical derivations suggest that it should not matter for the results which securities are included in the average idiosyncratic risk. The conclusions should hold, therefore. for an individual industry (i.e., when the average firm-specific variance measure is computed within each industry). we proceed with the second set of tests by grouping the securities into industries according to the industry classification in Fama and French (1997).13 We also construct 1.") within each industry to compare its influence on "the industry average idiosyncratic risk to that. of the total market crmcentration. Although the theory predicts that idiosyncratic risk is related to the 13They define :18 industries; the SIC codes not accounted by this classification are combined into industry =19. total market concentration measure, looking at. the industry-specific concentration may be an interesting exercise as it can reveal the potential importance of stock Iiiarket industry segmentation since there is no industry factor included in the Market Model. To the extent that the within-industry 7t determines the dynamics of its average idiosyncratic risk, each industry can itself be treated as a market. This can arise, for example, if certain barriers to cross-industry investment exist or when within—industry inforn'iation dominates the influence of the outside world. Empirical results The results are summarized in Table A.8. Columns 3 and 5 contain the statistics of the ADF unit root test for each variable. The last two columns report cointegration tests for industry average idiosyncratic risk and both the within-industry and the market total 71’s. we can only test for cointegration between the variables that are 1(1). There are 35 such pairs among the 49 industries. Thirty of these 35 pairs record a significant cointegrating relationship at the 5% level (at least) with industry ”it or the market “#3 14 (15) industries are cointegrated with the market. "it at 1% (5%) level, and for industry ’7; the corresponding number is 6 (15). Only five industries do not exhibit any relationship with either the within-industry or the market-wide value conceittration: pharmaceuticals, precious metals, utilities, banking, and real estate. For the remaining 30 we proceed with the estimation of the cointegrating equation and the VECM. Table A9 contains the estimated coefficients on the concentration of market value in the cointegrating equation (coefficient on idiosyncratic risk is nm'malized to -1), and the 1, statistics for the error correction term in the equations of dynamics for both of the variables. As before, we expect to find an inverse relationship, i.e., that the cointegrating equation coefficient on 1., (7" ) is negative. Additicmally, we. expect that the 1‘. statistic is significant in the equation for the changes in idiosyncratic risk ‘24 and insignificant. in the equation for the changes in ’71. The results confirm these expectations whenever the total market measure of value concentration is used. All of the y; coefficients are negative (ranging from -1.042 to —0.441) and the t statistics on the error correction term in the equation for changes in idiosyncratic risk are significant (at least) at 1% level, indicating that idiosyncratic risk is the endogeneous variable in the relationship. All except one of the t statistics for the equation of the ctmcentration dynamics are insignificant at. the 1% level (the Fabricated Products industry has a t statistic of 2.12, which is significant at the 5% level), suggesting that )t is exogeneous. However, the results are. not quite as expected when the within-industry measure of market concentration is used in the analysis. Ten out of 21 industries record a positive sign on the 7, in the cointegrating equation. All of the t statistics in the idiosyncratic risk dynamics equation are significant, but seven of the industries also have a significant t in the equation for the ":"t dynamics. This points to the possibility that. both concentration and idiosyncratic risk are endogenous, i.e., the causality runs in either (,lirection. This evidence can partly explain the ”wrong" Sign in the cointegrating equation: in five cases a positive sign in the equation coincides with the significance of the t statistics. One reason could be that the influence of “It on idiosyncratic risk outweighs that of idiosyncratic risk on "/1, thereby changing the Sign of the relationship. The results indicate that both witbin—industry 7, and market-wide “,1 have an effect on the industry average idiosyncratic volatility, the second being somewhat stronger. As the evidence suggests. in certain industries local value concentration appears to affect industry average idiosyncratic risk. This can be the case if, for example, investors rely primarily on witltin-industry (along with the. market—wide) factors in security evaluation. Additionally. the data suggest that there are cases in which a. relatitimship exists between ",1 and the idiosyncratic risk of different indus- 25 tries (results are not. reported), which could mean that factors in one industry affect security evaluation in another. 1.4.3 Analysis of the selected average idiosyncratic risk So far we have established that average idiosyncratic risk and a measure of the con- centration of total market value are related in the predicted manner. This result is not driven by changes in the fundamental idiosyncratic volatility or in the number of securities in the market. There is the possibility, however, that the resulting rela— tionship between the concentration of market value and average idiosyncratic risk is driven by changes in market security composition (even if the average idiosyncratic risk is measured as a simple average). For instance, adding small stocks with high idiosyncratic volatility may affect both the average idiosyncratic risk and 7t. T0 ad- dress this concern we use the third group of tests, in which an average idiosyncratic risk measure is constructed using only those securities that existed in the market for the entire time span considered in the paper.MBy construction, this index cannot be affected by changes in market. composition. To address this issue further, in the next. section we check whether the connection exists at an individual security level for the 30 companies from the Dow Jones Industrial Index. The cointegration analysis cannot be applied directly to the average idiosyncratic risk of the securities that existed for the whole sample period. The problem is this variable appears to be stationary (while “It is non-stationary, as before). This fact does not. imply that these two variables cannot. be related. Suppose idiosyncratic risk consists of two parts, both of which are rion-static!iary, while their sum is stationary. If one of these parts is cointegrated with '71, idiosyncratic risk and the market value cotreentration are related. but the deviations from their (linear) combination may 1"This test relies on the assumption that these returns are independent from the returns of the other companies in the market. 26 not 1’1ecessarily be stationary. \Ve apply the VECM framework to test whether the dynamics of idiosyncratic volatility is affected by the errors in the idiosyncratic risk - concentration relaticmship (EC'T). The testable hypothesis is the significance of the ECT in the regression for the dynamics of selected average idiosyncratic risk. Empirical results The results are summarized in Table A10. The ECT is obtained from the regression of the selected average idiosyncratic risk on W’t- This term is significant at the 1% level in the regression of changes in idiosyncratic risk, while it is insignificant in the regression of changes in “,1, indicating that there is a relationship between the two variables and that it. is 7.1 that is causing changes in idiosyncratic volatility in the long run, as expected. A concern still exists that the distribution of the estimated standard errors for the coefficient. on the error correction term may be non-Normal (since the deviations from the concentration—idiosyncratic risk relationship are possi- bly non-stationary). To address this issue we add non-parametric bootstrap estimated standard errors, which appear on the line below the regularly estimated errors in Ta- ble A10. The bootstrap standard errors do not change any of the significance levels on the error correction terms and therefore confirm previous results. 1.4.4 Analysis of the idiosyncratic volatility of individual se- curities The arguments in the previous section suggest. that. the concentration of market value should affect the variance of i\-=larket Model error for an individual security as well. In the last group of tests we verify this hypothesis using the GARCH framework (see Bollerslev (1986)), which allows us to directly model the effect. of concentration on the Market Model Variance. We assume that Market Model error follows a GARCH 27 process: Tit : w'0 + Critirrnf + 'L’fllrsmbt + t'02rlnnlt + Cit: (124) and t t. 2 . . hit = wi +lt~'1hit—l + L"2(z.,it_1 + 9371+ 8m (125) where 1'5..th and "hmlt are the two Fania-French factors, fit is distributed as (0.12”), and hit is the conditional variance of the error term. we are interested in the sig- nificance and the sign on the coefficient 1453, which indicates whether ’Yt affects the variance in the hypothesized direction. we estimate the model by Quasi-Maximum Likelihood. Analysis of individual securities is performed on the sample of 30 stocks that comprise the Dow Jones Industrial Index as of December 2005. Empirical results The idiosyncratic risk of the Dow Jones Industrial securities appears to be stationary (results are not. reported). We therefore omit the cointegration analysis and instead use the GARC H model to test whether market concentration affects the variance of each individual security as predicted. It. is expected that concentration should enter the variance equation with a negative and significant sign. Table A.1l contains the results for all 30 companies. In 19 out of 30 cases, 1th appears significant (at the 5% level at. least) in the variance equation and has the expected nevative sign. In five cases the variable is significant but the sign is reversed. The inclusion of the concentration measure does not render either of the $1 or r22 coefficients insignificant, indicating that on does not proxy for the ARCH effects. The analysis therefore suggests that the market concentration affects Market. Model error variance directly and not as a result of the averaging of idiosyncratic risk. 28 1 .5 Conclusions The results in this study show that in general Market Model residual variance is in- versely related to the concentration of total market value, which measures the ability of investors to rely on the market index to evaluate individual securities. The rela- tionship between these two variables emerges both when the Market Model is used by market participants to price individual securities and when a higher market value concentration increases its usefulness. In particular, we find that. a decrease in a measure of the concentration of market value (7')) can at least in part explain the recently discovered trend in the average idiosyncratic. volatility in the U.S. market. This variable is also often able to account for changes in firm-specific risk averaged by industry. An index of withill-industry concentration of market value is also shown to be related to industry average idiosyncratic volatility, although not always in the way that is expected. Finally, the idiosyncratic risk of individual securities in the sample of the 30 Dow Jones Industrial Index companies also exhibits the predicted relation with respect to the concentration of market value. Analysis of the error correction model indicates that causality runs in the direction of idiosyncratic volatility, confirming our model predictions. Various measures of fundamental idiosyncratic volatility and the total munber of securities in the market do not account for the observed relationship. This paper considers general consequences of investors relying on the Market. Model to evaluate individual securities. To ensure enmirical tractability we use the market value conti'entration index as a measure of the usefulness of this source of information. Other measures may be ccmsidered in future research. For example, one could use models in which forecasts of the market index are based on the values of certain macroeconoinic variables (e.g., interest rates or GDP) or on the past values of the index itself. Additionally, the market value ctmccntration and its influence on stock return correlations can be measured using something other than the suggested 29 index. Measures can be constructed that account for such factors as the distance between the companies or whether they operate in the same industry. Finally, one could consider further intra—industry information spillovers and their effect on the present analysis. 30 CHAPTER 2 Cross-Section of Trends in Firm-Specific Risk 2.1 Introduction There has been a considerable debate in the literature during the last few years related to findings in Campbell, Lettau. l\‘Ialkiel, and Xu (2001) (henceforth CLMX). C LMX demonstrates the evidence that average idiosyncratic risk in the US economy has been steadily lIl('l'(-‘d5111g for over four decades. The authors suggest their findings have important portfolit') implications, i.e. investors nowadays need to hold a larger number of securities in their portfolios to achieve reasonable diversification effects. More recent research though indicates that the trend has reversed in the last. several years (see Brandt, Brav, and Graham (2005)). This issue has quickly gained popularity in the finance literature and 'currently is one of the most actively researched asset pricing puzzles' according to Brandt, Brav, and Graham (2005). l\lechanically. the trends of market. average. idiosyncratic volatility can only be caused by a combination of the following sources: new listings. delistings, and existing firms with positive, negative, or no trends. These difference sources, however, have drastically different investment implications. If only new issues contrilmte to an increasing average idiosyncratic risk, investors do not need to adjust their portfolios 31 of existing securities in order to keep the level of portfolio risk constant. 011 the other hand, if most firms experience a positive trend in idiosyncratic risk, then. as CLMX argue, the number of securities included in the portfolio needs to be increased to achieve the same level of diversification. Further. if some firms experience positive volatility trends but some other experience negative trends, then the implication on diversification will be quite different depending on the stocks included in the portfolio. Therefore, it is crucial to determine exactly which of the specified sources contributes to the dynamics of average idiosyncratic risk. we estimate the firn‘i-l.)y-firm trends in securities’ idiosyncratic risk. By doing so we can identify precisely the contribution of the above sources to the market average idiosyncratic volatility. we have two major findings in this regard. First, we confirm the finding by some studies (e.g., Brown and Kapadia (2006), Fink, Fink, Grullon, and \Veston (200:3), \‘Vei and Zhang (2006)), Bennett and Sias (2005)) that new listings are an important factor driving the variation of market average volatility. However, different. from this studies, we. show that new listings are far from being the only driver. For example, we show that. a subsample of firms existing since 1980 exhibit very similar trends of average volatility as those of the whole market. That is, the average volatility trends are. also observed in existing firms. Second, while existing securities on average show the same patterns as the full sample (including new listings), it does not mean that most existing firms follow the same trends. Rather, there is a rich cross—section of the trends of idiosyncratic risk. We find that. during the period with an increase of average voltility, about 30% of firms have a significantly positive trend, while about 20% have a significantly negative trend. These two groups can cancel each other in the market average. This in part explains why previous studies which concentrated on the analysis of the various market averages of idiosyncratic risk rather then individual companies, concluded that the trends in idiosyncratic risk of the existing securities are. negligible. We 32 demonstrate further that the two groups relative contrilmtion to the market average it‘liosyncratic risk changes from period to period. In 1986 - 1990 the influence of the trends in existing firms came largely from the group with a positive trend in firm specific risk, while. after 2002 the negative trend group played the dominant role. \Ve further depart from the current literature by exploring the factors that cause the cross-sectional difference in volatility trends. We achieve this task by comparing firm-by-firm volatility trends to firm—by-firm trends in firm characteristics such as earnings, earnings volatility, institutional ownership, price level, and trading volume. This exercise allows us to test three. main interpretations in the current literature. 1. Fundamentals. Wei and Zhang (2006) and Irvine and Pontiff (2005) suggested that the trend can be attributed to the behavior of fundamentals (i.e. earnings, sales or cash flows). Our evidence confirms that fundamentals play a significant. role. in the explanation of trends. In particular. we find that firms with increasing earnings and decreasing earnings volatility are more likely to have a decreasing risk. 2. Institutional ownership. Malkiel and X11 (2003) linked the increase in id- iosyncratic risk to the growing share of institutional ownership. \Ve first confirm their results using our sample, and then show that. this link exists because in- stitutional ownership serves as a proxy for other firm characteristics. When more firm characteristics are considered, a significantly negative relation be- tween firm-specific volatility trend and firm-specific institutional ownership is observed. That is, relative to other firms. those with increasingly more institu- tional ownership are more likely to experience a decrease in volatility. 3. Speculative trading. Brandt. Brav. and Graham (2005) argued that bursts in idiosyncratic volatility were temporary phenomena associated with increased speculative trading concentrated in lmv-priced stocks. \Yc. find that trends in 33 stock price do account for the cross-sectional variation of trends in risk. Similar to results in Brandt. Brav, and Graham (2005) we observe that a firm with increasing risk is likely to have a decreasing price of equity. On the other hand we find that a positive trend in security turnover implies a negative trend in idiosyncratic risk. Therefore, at least for most stocks, increased trading does not lead to increase in stock volatility. Our findings contribute to an increasingly large literature that studies aver- age volatility trends, including among others, Rajgopal and Venkatachalam (2007), Arena, Haggard, and Yan (2005), Cao, Simin, and Zhao (2006), Guo and Savickas (2007), and Kelly (2005). Most of these papers have studied variously composed av- erages of idiosyncratic risk. None so far, to the best of our knowledge, has used a firm-by-firm estimation of idiosyncratic risk. This approach does allow to distinguish among the three sources of changes in the market average which we have mentioned earlier. ()ur contribution therefore lies in precise identification of the sources of the trend in average idiosyncratic risk. Our paper also has direct implications on studies that investigate whether idiosyn- cratic risk is priced (such as Ang, Hodrick, Xing, and Zhang (2006), Spiegel and W’ang (2006)). The cross-sectional difference of volatility trends suggests interesting time series dynamics of cross-sectional expected returns related to volatility. We explore these issues in future studies. The paper is structured as follows. Section 2 provides the analysis of the trends in idiosyncratic risk at the security level and the contribution of each type of security to the average idiosyncratic risk in the economy. In section 3 we relate the trends in the firm characteristics to the trends in firm specific risk and investigate the relative role of the three proposed hypothesis. Section -1 concludes with a discussion. 34 2.2 Gross sectional variation of trends in idiosyn- cratic risk In this section we will precisely (.letermine the mechanical sources of the trend in the average idiosyncratic risk. These sources are important. to know given their dra— matic portfolio implications. Only firm-l.)__v-firm estimation would allow us to identify contribution of each firm to the total changes in idiosyncratic risk. We first. divide the market into groups of securities with different trends (positive, negative, and in- significant) and then examine contribution of each group to the changes in the overall market average idiosyncratic risk. 2.2. 1 Data construction Our data. consists of the universe of daily returns of all the traded securities on NYSE, AMEX and NASDAQ markets for the period of July 1963 till December 2005. This time span is larger then the one originally considered in CLMX and allows us to track any differences between this period and the later years. The idiosyncratic risk is estimated for each security as the monthly average vari- ance of the residual from the F ama and French three factor model estimated month- l_)y-1nonth: (m - 1‘ft) = 01‘. + ,Jzi('7‘«rnt — Tftl + Ahtsntbt + dab-Wt + 6m (2-1) 1 t 11%. = 7:16.... (22) S: where r,-, is return of stock i in period t, rm) is the market. return, if, is the risk— free rate. smb; and hmlf are the Fama and French factor portfolios. We. require for statistical accuracy at least ten daily return observations for each firm in a given month for the monthly estimate of idiosyncratic risk to be included in the analysis. 35 We then estimate the trend for the life span of each security and require that. at least two years of monthly idiosyncratic risk data to be available for each stock. As Table. 13.1 indicates there are 21860 firms which meet these requirements for the period July 1963- December 2005. We run least squares regressions of idiosyncratic risk on the time trend to obtain the estimates of the trend coefficients and their t statistics for each security: IR" = of) + o'fl't + 12,-) (2.3) CLMX suggested that. due to large autocorrelation in idiosyncratic risk the least squares estimates from such regressions may not provide a good measure of the trend coefficient. As a robustness check we re-run our results with the procedure they suggested for estimation of trend and find no significant difference from our original results (the sample size in this case is further reduced since the test. requires inclusion of lagged values of idiosyncratic risk, as the result fewer firms have. enough monthly data to obtain reasonable estimates). 2.2.2 Analysis of results Proportions of positive, negative, and no—trend securities Table 8.] reports relative proportions of positive, negative. and zero-trend securities in various time periods on US market. The first row of Table B.1 indicates that about 31% of the total sample of stocks exhibit positive significant trend (at least at 5‘7? level) in firm-specific risk, while about 25% have negative significant trend. This leaves 71-41% of the market. with no significant. trend at the firm level. These proportions may vary over time. Brandt, Brav. and Graham (2005) for instance suggest that market average idiosyncratic risk shows periods of "bubbles’. \Ve therefore investigate the possibility of changes in these proportions over time. CLMX and post-CLMX periods 36 \Ve first split. our sample into CLMX and post-CLMX periods. The trends are estimated separately for each of the two sub—samples. During CLMX period the proportions of the firms in each of the category are close to the ones observed in the total sample: 31% of stocks have positive trend, 21% have negaive trend, the rest have no significant trend. The post—CLMX sample (1997-2005), which is characterized by decreasing id- iosyncratic risk (see Brandt. Brav, and Graham (2005)), is different. Only 12% of the stocks have positive trend, while 46% have negative trend. Thus the proportion of the firms with no trends is roupgly the same as in the previous sample, but the proportions of the positive and negative trends in securities changed in favor of the latter. This in part explains the decline in the average idiosyncratic risk on the market in the last. several years. Ten years intervals We further split. our sample into four time intervals of about. ten years each. The last four rows of Table 8.1 contain the estimation results. The proportion of firms in each category varies from period to period. Positively trending securities had the largest share in the period 1963-1975 (39%), their share was the smallest during the last ten years (only 20%). Conversely, proportion of securities with negative trends was the largest in the last period (33%) and the smallest in the first period (about 6%). Overall Table 13.1 indicates that changes in proportions of the firms with positive and negative trends could be responsible for the changes in the average idiosyncratic risk in the economy. But the contribution of each group to the avemge risk depends on the relative. magnitudes of the. trend coefficients in addition to the influence of the proportions of each category. Therefore in the remainder of this section we quantify more. rigorously the effects of each category on the market average idiosyncratic risk. Relative contribution of positive versus negative trends A. New lists versus existing securities in the total average idiosyncratic risk First let us separate contribution of the trends in existing firms from that of the new lists to the trend in the total average. For this purpose we use the following procedure: all securities in the sample, which appear to have significant positive or negative trend, are assigned (to all the subsequent periods of their life) the value of idiosyncratic risk that they had at the time they were first listed. We therefore assume the idiosyncratic risk was constant (at the initial level) for each of these securities. The procedure removes the trends in idiosyncratic risk in existing firms along with the variation in the idiosyncratic risk around the trend line.1 We then compute the average (across firms) of such constructed measure of idiosyncratic risk and compare it to the total average. The resulted series are depicted in Figure 8.1. The solid line is the average idiosyncratic risk with trends in idiosyncratic risk at the firm level removed (let us call it ’listing average”), so the only contribution to the changes in the average risk comes from the new listing or delisting of securities. As expected, this variable does not trend upward as much as the total average id- iosyncratic risk. Comparing the. slopes of the two trend lines we can conclude that about 70 % of the trend in the total average is due to the new firms, the remaining is due to the trends in the existing securities (Wei and Zhang (2006) provide similar conclusions using a different estimation method). Also observe that before 1988 the two averages move very closely together, while after this date they diverge. For period 1988-1998 the listing average is below the total average, while after 2002 the inequality is reversed. These results suggest that for the first period the total average risk was increasing due. to both addition of the 1If the variation of risk around the trcnd line is preserved, i.e. trend emfff‘icicnt multiplied by the trend is subtracted from idiosyncratic risk, some. of the risk observations become negative. which has no meaning in the present context. 38 new high idiosyncratic risk securities to the market and because a high proportion (or large trend coefficient magnitudes) of existing securities had a positive trend in their it‘liosyncratic risk. After 2002 the total average risk has decreased partly due to the addition of low idiosyncratic risk securities, and partly because the proportion of the existing securities with negative trends in their risk has increased (or magnitudes of the tend coefficients have decreased). B. Positive versus negative trends in existing securities The next two graphs (Figures B2 and B3) decompose further the effect of trends in existing securities into positive and negative trends. Figure B2 compares the total average risk and the one where only positive trends at the firm level have been removed. For period 1088-1008 this new average mimics the listing average from the 1:)revious picture. This observation suggests that the effect of the trends in existing securities on the total average for this period came for the most. part from the securities with positive trends. Figure B3 plots the total average risk and the one where only negative trends have been removed. Connmriug Figures 8.1 and 33 we conclude (using similar logic.) that. the effect of the existing trends on the total average was caused mostly by the negatively trending stocks after year 2002. Together graphs Bl, B2 and B3 show that in different periods one of the effects (of positive or negative trends) in existing securities dominated in influence on the total avemge. Therefore the changing proportions of negative and positive trends in existing securities caused fluctuations around the trend line in the market. average idiosyncratic risk. C. Robustness checks 0 Several studies (CLMX including) indicate that the observed trend is the most pronounced in the sample of the NASDAQ securities. We conduct a robust- ness analysis of our previous results by repeating Figure B.1 for the sub—samples of the NASDAQ and non-NASDAQ securities (Figures Bi and B5). The con- 39 clusions are effectively unchanged although the trend lines are more pronounced in the NASDAQ sub-sample, as expected. Taking out the trends in existing securities and comparing the resulting average to the total average idiosyncratic risk is just. one way to quantify contribution of the trends in existing securities. Let us now consider an alternative approach. Figure 8.6 shows the average risk constructed on only the new firms in each month. It. is gradually increasing, indicating that the new lists contribute to the observed trend in the average. Figure 8.7 shows the average idiosyncratic risk when the new firms are excluded in each month. This graph exhibits similar trend patterns as the simple average idiosyncratic risk, suggesting that. the trend in the total average risk cannot. be fully explained by the new lists. Finally. we take a sample of the firms that were first listed in January 1980 and trace their average idiosyncratic risk over time (Figure 8.8). The graph clearly shows the same patterns as observed before: increasing risk until last several years. falling afterwords to its original level. This pattern therefore cannot be solely due to the addition of the new companies to the market over time. D. Discussion Our analysis in this section su Wests that the contribution of the new lists thou )‘h . O 7 considerable. cannot fully explain the observed behavior of the average idiosyncratic risk. The existing securities do exhibit significant trends in risk at the firm level. These trends affect non-trivially the total market average. About half of the firms in our sample have significant trends in idiosyncratic risk, 30 (X. with positive and 20 (7c with negative trend coefficients. These proportions change from period to period, causing changes in the relative contribution of each group to the total average. During period 1988—1998 the. total average idiosyncratic risk is considerably higher due to the increased proportion of the firms with positive trends. Conversely after 2002 the total 110 average risk is much lower due to a larger proportion of negatively trending securities on the market. This evidence suggests that there may be some economy wide factors behind observed fluctuations in average idiosyncratic risk. This proposition is also supported by the results in CLMX that. average idiosyncratic risk is related to the business cycle. Possibly, the market is less restrictive during some, periods about. the permissible quality of the stocks. This allows firms with high idiosyncratic risk to enter the market as well as existing companies to have higher risk of equity. Our evidence suggests that this process (if exists) is not monotonic in time. After the market downturn in 2001 we observe that majority of the new lists start having lower idiosyncratic risk, while existing securities are nrore likely to have a decreasing risk. In other words, it appears that the market. have becorrre more restrictive about the risk of its securities. 2.3 Factors that explain cross-section of trends in idiosyncratic risk 2.3.1 Explaining probabilities of a trend We found out in the previous section that. idiosyncratic risk in cross-section of secu- rities may have positive, negative trend or no trend at. all. The trend in the average idiosyncratic risk on US financial market. is the result. of the effects of the newly listed or delisted securities in every period, as well as the trends at the levels of the exist— ing securities. The latter centribrrtion is min-negligible, even though the influence of the trends at existing securities is not easily observable in the average due to partial cancellation of positive and negative trends. The existence of statistically significant trends at the firm level has implications not only for the behavior of the average idiosyncratic risk in the economy but also for portfolio strategies, which we discussed earlier in the paper. Therefore it is of research and practical interest to know what. #11 other characteristics distinguish the firms with positive, negative, or zero trend and what. are the economic factors which explain this cross—section. In this section we ask the following question: given the obser table data on firm clraractcristics, which of them can explain the presence of trends in the firms’ idiosyn- cratic risk? Since constantly increasing (or decreasing) risk is likely due to constantly increasing (or decreasing) firm characteristics, we compare (in the analysis that fol- lows) appearance of trends in idiosyncratic risk of each security to the appearance of trends in its characteristics in the cross section of traded securities. Data construction and methodology The data is obtained from COMPUSTAT (quarterly frequency firm characteristics), CRSP (monthly frequency returns) databases and 13(F) filings (quarterly frequency institutional ownership). We include in the analysis the following characteristics, which are most commonly used in the literature related to this topic: firm size (mea- sured as the log of the market value of the firm adjusted by the level of inflation (CPI), the market. value of equity is computed as the closing end of period price of security multiplied by the munber of shares outstanding); book-to—market value (the book value of equity is computed (following Fama and French (1992)) as the COM- PUSTAT data item 60 (if available, otherwise data 59+ 55 or 44-54, in this order) plus data 52 minus data 55); cash ratio (cash ratio is data. 36 over the total assets (data 4-1)); earnings per share and its volatility (the. volatility of firms’ earning per share is computed using the five year rolling estimates of the variance): leverage (the leverage ratio is equal to the book value of long-term debt (data 51) divided by the total book value of assets (data 44)); turnover; R.&D expenditure; institutional ownership share; return and price (adjusted for inflation). Table B2 contains the rrrairr statistical indicators of the major firrrr clraracteris- tics. Trends in firm characteristics at the security level are estimated using the same 42 approach as we used in estimation of trends in idiosyncratic risk. Analysis of the results A. Univariate analysis for each characteristic First we would like to compare the appearance of trends in firm characteristics versus trends in risk separately for each characteristic. Results are summarized in Table B.3. Each entry of the table represents the number of securities in the sample that have statistically significant trends both in the corresponding characteristic and in the risk. The sample shares (in (Z) are given in parenthesis and sum to 100% (total sample) for each characteristic. The last line of the table summarizes uncondi- tional appearance of each type of trend in the firm characteristic (similar to entries in Table B2 for idiosyncratic risk). The line before last. presents the correlation co- efficients between the dummy for trends (positive. negative. and insignificant) in the firm characteristic and the dummy for trends in risk. Observe from Table 8.3 that a significant portion (60-70 (X) of firms have statis- tically significant (at least at 5 (Z) level) trends in firm characteristics. These trends therefore have, a potential to explain the appearance of trends in idiosyncratic risk. Positive trends are more common then negative ones with a couple of exceptions (cash ratio and volatility of earning per share). Let. us now consider how often trends in each characteristic coincide with the trends in the security’s idiosyncratic risk. For example, firms in our sample have positive trends in earning per share in 44% of the cases. but. only in 10% of the sample securities have positive trends in both earnings and the risk. For negative trends this share is even smaller (2%). The trend in earning therefore is not very likely to explain the trends in idiosyncratic risk. This conjecture is confirmed further by an almost zero correlation coefficient of the durrnrries for the appearance of these two trends. Of all the firm characteristics that we consider the largest (in magnitude) correla- tion coefficient belongs to the institutional ownership share (—0.127). Therefore trend in this variable is a good candidate for an explanatory factor of the idiosyncratic risk trends. The remaining variables have on average correlation coefficient of magnitude 0.05. Trend dummies for institutional ownership, price, return, and size are nega- tively correlated with the durrrrrry for the trends in risk, meaning that positive trend in these characteristics is likely to imply a negative trend in idiosyncratic risk. On average positive (or negative) trend in a firm characteristic coincides with positive (or negative) trend in risk in 20-30 % of the cases. According to the univariate analysis the least. explanatory power with respect to trends in idiosyncratic risk can be attributed to earnings, turnover, earnings’ volatil- ity and R&D expenditure. The RSJD variable may appear insignificant in part due to a poor availability of data. The final conclusions though about the role of each characteristic in appearance of trends in idiosyncratic risk cannot be made before we conduct. a multivariate analysis since influence of one characteristic can obscure or enhance influence of another in the unconditional distributions, changing the conclu- sions. B. Multivariate analysis We proceed with the multivariate cross-sectional analysis of the trends in firm characteristics versus trends in idiosyncratic risk. The advantage of this approach is that now we can derive the conditional influence of every variable on the probability of observing a. trend in risk, i.e. the influence of each characteristic holding other variables constant. Table 8.4 reports the results of multinomial logit regressions of the dummy for trends in idiosyncratic risk on the dummies for trends in each of the characteristics. The. test specifics are the following. The dependent variable takes the values +1.0. or -1 depending on whether a positive, insignificant. or rregz-rtive trend is observed in the idiosyncratic risk during the life of the security. The base case in no trend, therefore we consider a model of two equations for the probabilities of trends in risk: one for the ratio of probabilities of positive versus insignificant trend, and one for the ratio of probabilities of negative versus insignificant trend. Each of the characteristics is assigned two dummy variables: one that takes the value 1 if a positive significant. trend is observed and 0 otherwise, and one that. takes the value 1 if negative trend is observed and O otherwise.2 Let us discuss in turn fundamentals, institutional ownership, and speculative trad- ing hypothesis. 1. Results on fundamentals suggest that firms with increasing idiosyncratic risk are deteriorating in quality, while firms with decreasing idiosyncratic risk are improving in quality. For example, according to Table 8.4 a growing firm is more likely to have a decreasing risk. while a firm with a decreasing total market value (possibly in distress) is more likely to have an increasing idiosyncratic risk (all size CORffiCient-s are. significant at least at 1 ‘76). Earnings and and their volatility are significant in these regressions (in con- trast to the univariate analysis. possibly because some other firm characteristics obscure their influence in the unconditional distribution). Firms with contin- uously increasing earnings per share are likely to have a negative trend in it'liosyncratic risk and are unlikely to have a positive trend. The opposite holds for the companies with decreasing earnings per share (all coefficients are sig- nificant at 1 O/(). Increasing volatility of earnings implies higher probability of observing an increasing idi(_)syncratic risk and a lower probability of observing a. decreasing risk. The evidence on earning and their volatility is consistent 2\\'e define two dummies (instead of one) for the firm characteristics since we do not wish to assume that the coefficients on positive and on negative trend are equal or related. Therefore. in our model the influence of say positive trend in a firm characteristic can be different from the influence of the negative trend in this characteristic. The reported standard errors are robust to the presence of heteroskedastisity. 45 with the findings in \Vei and Zhang (200(5) (among others), which indicate that. idiosyncratic risk and earnings are negatively related, while idiosyncratic risk and volatility of earnings are positively related. Firms with increasing book—to—market are less likely to have a decreasing id- iosyncratic risk. Increasing amount of available cash per dollar of the firms’ assets implies a larger probability of a. positive trend and a smaller probability of a negative trend in the firm’s idiosyncratic volatility. The opposite is true for the negative trend in cash ratio. More available cash in this case may be associated with an increasing risk of equity returns since managers of the firms with higher risk tend to hold more cash. Firms with a growing leverage ratio are more likely to have an increasing risk. Decreasing leverage ratio diminish the probability of a negative trend in risk, but does not affect that. of a positive trend. Additionally. firms with a positive trend in returns are less likely to have an increasing idiosyncratic risk, while those with negative trend in returns are more likely to have increasing risk. Finally any trend (positive or negative) in RSJD is likely to reduce probability of a negative trend in risk. Therefore. our results suggest. that. firms with increasing idiosyncratic risk are also likely to diminish in size and returns, have decreasing earnings along with increasing earnings’ volatility, leverage, and cash ratio. Conversely, companies which have decreasing idiosyncratic risk are more likely to grow in value, returns and earnings, have decreasing volatility of earnings, leverage, and cash. Institutional ownership as well has an effect. on the probalnlity of trends in risk. A growing ownership share of institutions implies we are less likely to observe an increasing idiosyncratic risk and more likely to observe a decreasing risk. A (.lecr'easing share of institutions implies a higher probability of a. positive trend in risk, but. does not affect probability of a negative tend. Therefore 1.16 institutions seem to abstract from securities with an increasing risk. This is contrary to what was suggested in Malkiel and Xu (2003), i.e. increasing average idiosyncratic risk in the US markets is due to the growing average institutional ownership share, and in correspondence with the suggestions in Brandt, Brav, and Graham (2005) that larger institutional ownership share may imply lower idiosyncratic risk. In order to trace the difference of our results from those of Wei and Zhang (2006) we repeat their panel regressions on our sample. The original regression in Wei and Zhang (2006) determines the effects of size and institutional ownership on idiosyncratic risk. The estimates of their model on our sample are the following: 13,-, = 0.0044 —0.0006 sized +0.0002 27-773,, (——46.45) (1.83) In this paper we use more control variables then V'Vei and Zhang (2006). As it turns out adding some of them to the regression changes the Sign of the coefficient on institutional ownership. Specifically, adding earnings per share or volatility of earnings does not. have an effect, but book—to—market, cash ratio, leverage, turnover, or research and development does. The regression results for the full set of controls are the following: 1H,,=0.0043 —0.0005*sizeI-t —0.0021*»,in5,, (—32.34) (—19.47) ——0.0003 >1: epsit —1.13 * 10—5 * ’L‘f’.p8,ft +0.0003 * bmit +0.0006 * cashrit (—6.-"12) (—0.31) (8.21) (6.77) ——0.0009 * lee” +0.0018 * turn” +0014? * rndit (——7.81) (28.73) (21.53) As we. can see the ownership appears with significant negative sign in the last regression. This result. also highlights importance of 111111ti\-'a.riate versus uni- variate analysis for this issue. Speculative trading. Brandt, Brav, and Graham (2005) propose that the increasing market average idiosyncratic risk could be due to speculative trading .17 in low—priced stocks. In our context. this implies that if a security is becoming cheaper we should observe an increasing idiosyncratic risk as more speculators are attracted to this stock. Therefore a negative trend in security’s price should correspond to a positive trend in its risk. At the same time since more spec- ulators are being attracted, the security’s turnover should increase, causing a larger volatility. Estimated regression coefficients on price dummy confirm this conjecture. Negative trend in price is likely to increase probability of a positive trend in risk and decrease probability of a negative trend. Positive trend in price has the opposite effect on trends in risk. The evidence on the turnover ratio though is not: in agreement with this intuition. Positive trend in turnover increases probability of a negative trend in idiosyncratic volatility while its effect on appearance of a positive trend is insignificant. We repeat our analysis with either price dummy or turnover dummy excluded from the regression (third and forth models in table B3) to account for the possibility that a relationship between these two variables cause the effect or either one appear insignificant or change the sign. This manipulation does not affect. any of our previous comrlusions, which are therefore robust. As can be concluded from the panel regression of idiosyncratic risk on our main characteristics turnover enters with the positive sign, as indicated in Brandt, Brav, and Graham (2005) (results not reported). This regression though and the multinomial logit model may give apparently contradicting results since they show different effects: short-run (panel regression) and long-run (multivariate logit) changes in idiosyncratic risk. Our first-stage trend estimation implies that: mm, = aim + my? (2.4) 48 Alum” = q/{At + A6317." (2.5) In terms of the panel regression the effect of changes in turnover on changes in idiosyncratic risk is the following (assuming At = 1): .' 1R __.A”"~ I _1_:a_ (,6) Aturnit 7i + Aegprn . This ratio combines the effect. of the difference. in signs of trend coefficients ((15 and )i) and the effect of short—run deviations around the trends (A653 and Aefé‘m). In our sample the second effect is much larger than the first since estimated tend coefficients in the first stage are very small in magnitude. We are. s1_)ccifi(.:ally interested though in the long-run effect since we want to be able to explain appearance of trends in idiosyncratic risk of securities, not per-period changes in idiosyncratic risk. Therefore our tests do not contradict. evidence in Brandt, Brav, and Graham (2005), just address a different research question. So far we have seen that. the trend in the price is related to the trend in id- iosyncratic risk, but the nature or causality of this relationship is not quite clear. Speculative trading in cheap stocks is not a likely reason since the effect of lowering the price on risk should be transmitted via an increased frequency of trading. which is not observed in our sample. Security prices, like firm’s size, can measure effects of various economic factors. Given our evidence we cannot yet definitely conclude which one is at play. Altogether the evidence shows that well performing companies, which are increas— ing in the total market value, have growing earnings and decreasing earnings’ volatility and decreasing leverage, are more likely to have a decreasing idiosyncratic risk. The opposite holds for the firms which are. not doing as well (decreasing in size and re- turns, have increasing leverage). Ii’istitutional owners tend to increase their share in the first type of companies and decrease in the second. Not surprisingly, the stock 49 price. of the first type. is likely to increase, while of the second - to decrease. It. is not at all clear therefore whether the idiosyncratic risk is increasing due to a decreasing price or the other way around. A third plausible possibility is that risk and price are related to some other variables which cause appearance of a statistical relationship between the two. As we discussed in the previous section, some market wide factors could as well be driving the changes in the it’liosyncratic risks of securities, either via fundamentals or in addition to their influence. While institutional ownership and speculative trading seem less likely to be the major factors. 2.3.2 Robustness checks We would like to conduct several robustness checks of our conclusions. For this purpose we divide our sample into several sub-samples (Table B5). Specifically, we perform our multinomial logit regressions on samples of high—priced and low-priced securities, on CLMX and Post-CLMX period, securities with long and short life, and securities that were listed before 1997 and afterwords. 1. The first split of the sample is necessary as some authors showed (for example Brandt, Brav, and Graham (2005)) that influence of institutional ownership on idiosyncratic risk is different. for high-priced and low-priced stocks. The coefficients on other characteristics may be sensitive as well to the price level of security. \V'c define. security to be a l(_)w-pr'ice if in 70 00 of the observations its (inflation-adjusted) price is above 5 dollar level (also adjusted by current. inflation level). and low-price otherwise. The results are the first. two columns in Table. B5. As the estimates indicate, the effect of trends in institutional ownership share on probabilities of trends in idiosyncratic risk does not. depend on whether the stock is high-price or low- price. Coefficient magnitudes and significance levels do not change much if we split the sample according to price. Book-to—inarket, leverage and volatility of earnings change significance levels in some cases, while size and cash ratio change significance and sign. we also want to make sure that our results are unaffected by the fact that we combine CLMX and post-CLMX periods. we split our sample into the two sub- samples and compare the resulted estimates to the original regression (models three and four in Table 8.5). Several coefficients have changed the significance in the resulting sub-samples. Earnings. earnings volatility and size coefficients seem to be non-robust to this split. For instance. in the I')(_)St-CLi\lX period increasing size corresponds to a. lower probability of observing negative trend in risk, while in the total and CLle samples the relationship is the opposite. Similarly increasing volatility of earnings corresponds to a lower probability of observing a positive trend in idiosyncratic risk during CL.\IX period, while the opposite is true for the total and post-CLMX samples. This analysis suggests that such measures of firm fundamentals as earning per share. earnings volatility, and size may not have a stable (in time) relatimiship with firm-specific risk. Additionally we need to address the problem of unbalanced panel in our sample. Different companies in our cross-section are first. listed at different times: some in early fills, others in the recent. years. Such firms could be quite different. Therefore we divide our sample into two groups: securities first. listed in or before 1998 and those originally listed afterwords. Also various companies have different life spans: some existed for one-two years, others for ten years or more. To accmint for this (.lifference we divide the total sample into two groups according to life span: those, which existed for less than ten years and those that existed longer. The results are presented in the last two models in Table B5. 3. When the sample is split according to the security listing date no major dif- ferences can be detected in the regression estimates. Several variables changed the significance levels in some places: cash ratio, book-to-market, earnings, size, leverage, turnover, price, and return. Dummy for positive trend in institutional ownership changed the sign in the equation for the probability of trend in id- iosyncratic risk. 4. Even fewer differences compared to the original estimates are observed when the sample is split according to the life spans of securities. Cash ratio, institutional ownership, leverage, size, return. and earnings volatility change significance of the coefficients in some places. Dummy for positive trend in earnings changes the sign (to negative) in the equation for the probalinlity of positive trend in idiosyncratic risk. 2.3.3 Explaining magnitudes of trend coefficients Motivation and tests description So far we have focused our investigation on the question of how appearance of trends in ii rm char-acteristics affects the probability of observing a trend in the firm~specific risk. In other words, our research question was: is there a long-term relationship across firms between risk and firm cl“1ara(':teristics and what is its direction. Now let us ask a question whether the strength of this effect is similar across securities. If so, the effect of the companys characteristics will also show up in the magnitudes of the estimated trend cmsfficients. For example. a stronger trend in earnings may imply a stronger trend in idiosyncratic risk in addition to the fact. that an ezrfz'stiny trend in earnings implies existence of an opposite trend in volatility. In this example cross-sectional association between trend magnitudes means that not only decreasing earnings of a firm imply increasing volatility. but also that the strength of this relationship is similar across firms. If on the other hand no relationship between trend coefficient magnitudes can be found, idiosyncratic risk and earnings are oppositely related, but the relationship coefficient. can be different in magnitude across firms. To address this question we regress the trend coefficient on risk on the. coefficients on trends in firm characteristics. Results are summarized in Table 8.6. \Ve consider three cases: least squares regression of the trend coefficients (regardless of their signs or significance levels in the first. stage, model 1); Tobit regression of the sample of positive significant. (at least at. 5 (76 level) trend coefficients of idiosyncratic risk as a dependent variable (model 2); and Tobit regression of negative significant trend coefficients of idiosyncratic risk (model 3). Estimation results Only two fundamental variables appear as robustly significant explanatory factors for the magnitudes of trends in idiosyncratic risk: size and earnings’ volatility. Trend coefficient on size has a significant. diminishing effect on the trend coefficient on idiosyncratic risk. i.e. more quickly growing companies have a slower decreasing risk. If the firm has faster diminishing total market value (possibly in distress) its idiosyncratic risk also increases at a faster rate. Coefficient on trend in volatility of earnings affects coefficient on trend in risk only in the case of the negatively trending (risk) securities. According to the estima- tion results, a higher rate of decrease of earnings” \=-'ola.tilit.y corresponds to a faster decreasing firm-specific risk. These results further confirm our ”quality” hypotlnrsis; i.e.. decreasing idiosyn- cratic risk firms are increasing in quality and vise versa. The strength of this relation- Cf] DO ship is quite random across firms, with the exception of size and earnings’ volatility, for which we can reasonably well predict what firm should have a stronger relation- ship. Based on our overall evidence in this section we conclude that o The firms with increasing idiosyncratic risk are more likely to be distressed or otherwise not performing well on the market, while the the firms with decreasing idiosyncratic risk are characterized by improving performance. 0 Trends in the stock price should reflect this fact and therefore it is not clear whether speculative trading plays a role in the relationship between price and firm-specific risk. 0 The fundamentals like earnings and their volatility are good indicators of the firms’ condition and therefore are good predictors of the trends in risk. 0 Institutional owners may prefer well performing companies and thus their rela- tionship with the idiosym-ratic risk may be via the relationship with the firms’ fundzn'nentals and not directly related to idiosyncratic risk. 2.4 Conclusions and discussion This paper im'estigates appearance of trends in idiosyncratic risk at the security level. Current research in the area concentrated on the explanations of the trend in the economy average idiosyncratic risk. Lumping all firms together though may leave out some important properties of the trend. We investigate these properties in the firm-by-firm trend estimation and the effects on the average idirmyucratic risk as well as 1;>(;)rtfolio implications for investors. Our results indicate that 0 New lists cannot fully account for "the observable patterns in the average id- iosyncratic risk on US market. The trend behavior of idiosyncratic risk differs from security to security. About. 30% of the existing stocks have positive trends and about 20% have negative trends. 0 Changing (in time) proportions of the two groups result in stronger influence of one group on the market average idiosyncratic risk. This induces fluctuations of the average risk around its trend line. 0 Trends in firms fundamentals affect the appearance of trends in idiosyncratic risk. In agreement with the current literature negative trend in earnings and positive trend in earnings" volatility correspond to a positive trend in risk. 0 Contrary to suggestions in the literature increasing institutional ownership cor- responds to a deereasing idiosyncratic risk. According to our evidence the differ- ence in results stems from a model misspecification problem, which we. attempt. to correct. o In agreement with the literature an increasing (real) stock price implies a neg- ative trend in it'liosyncratic risk. Our analysis of turnover though indicates it has a negative long—run relationship with risk. This result does not support the proposed in the literature hypothesis that increases in idiosyncratic volatility are due to bursts of speculation in the low—priced stocks. The results of this paper suggest that idiosyncratic risk of individual security has a non-trivial relationship with its fimdamental variables. This of course is not counter intuitive and in fact should be anticipated. What seems strange is why should this effect persist in time? In other words, if firms with increasing risk are deteriorating in perforinance, why are they not being delisted or at least forced by the capital market. to inmrove perfmmance'? \V'c }_>ropose (but do not investigate) a few possibilities in this regard: 1. The literature suggests that financial markets are becoming less restrictive in standards for the listed securities (see for example Fama(04)). It is being argued that newly listed companies are allowed to be less profitable and to have more volatile cash flows. On the other hand, the same market conditions should allow existing firms to lower their perfm'mance standards (and use less managerial effort), which would lead to the upward trends in their risk. This argument though brings up a different question: why does the market lower its standards? Is there increasingly more available capital to invest so it is hard to find best use for all of it? Or is there something about. investors7 psychology? These or other possibilities can make an interesting topic for future research. As the data suggests the munber of securities has increased dramatically since early 60s. If the munber of investors have. not significantly changed. less investor attention can be devoted to each security. This could mean worse capital market supervision and worse performance. The investors can be compensated for such losses via increasml diversification benefits. The observed relationships could also be the result of measurement or modeling issues. The market model is a static relationship. If the relationship is in fact dynamic, faster speed of market adjustments can lead to our inability to spot the static equilibriiun. CHAPTER 3 On causality of the relationship between institutional ownership and idiosyncratic risk 3. 1 Introduction Idiosyncratic volatility has experienced growing interest in the finance literature since a study by Campbell, Lettau, Malkiel, and Xu (2001), which showed presence of a significant. trend in the market average firm-specific risk. Subsequent research in- vestigated the causes as well as the consequences of these changes in idiosyncratic volatility. Among numerous suggested drivers behind idiosyncratic risk is institu- tional ownership, initially advocated by Malkiel and Xu (2003). The authors rely on the observed positive trend in institutional ownership, similar to the one found in average idiosyncratic risk. They propose the following reasoning for the existence of such a relationship (p. 636): "’...b1.1ying and selling is more likely to be coordinated across institutions. and market prices may be more volatile and more quickly re- sponsive to new information or to changes in risk perceptions". Their cross-sectional regression analysis confirms this intuition in that institutional ownership is positively associated with idiosyncratic risk. Several studies that followed investigated further this relationship. Thus, Dennis 57 and Strickland (2005) show Malkiel and X11 (2003)‘s results to be robust to inclusion of leverage and firm focus as other potential explanatory variables. Chang and Dong (2005) investigate how institutional herding (measured as changes in institutional ownership) affect idiosyncratic volatility and find a similar significant relationship. Brandt. Brav, and Graham (2005) on the other hand show that the relationship, although it retains its significance. has a reversed sign in the sub-sample of high- priced securities. Vozlioublennaia (2006) shows that the sign of the relationship in the pooled regression is sensitive to the inclusion of some firm characteristics. Even though the sign of the relationship may be somewhat illusive. its significance seems to be established in empirical literature. The question remains though whether it is institutional ownership that is causing changes in idiosyncratic risk and not the other way around. A number of studies (theoretical and empirical) suggest this other possibility. A model of incmnplete information by Merton (1987), for example, implies that. firm managers tend to expand the investor base if idiosyncratic risk is increasing. This happens because investors are forced to hold part. of idiosyncratic volatility in their portfolios due to incomplete infermation. As a result, firms may want to increase the number of informed (about their securities) investors, thereby reducing the incomplete information effect and avoiding paying a higher premium for larger idiosyncratic volatility. Since institutionz-rl investors may be better able to collect and process information about. stocks. this implies increasing institutional ownership share. Alternatively. if managers choose to pay higher premiums for larger idi(,)syncratic risk. institutional owners being at advantage in collecting information and diversification will rationally buy stocks with high it'liosyncratic risk and extract profits. In either scenario. changes in idiosyncratic volatility cause changes in in- stitutional owni-‘rship. In fact, some studies (e.g., Boehme, Danielsen, Kumar, and Sorescu (2005) and Kelly (2005)) use institutional (m’nership as a. proxy for investor attention received by a firm, in line with Merton (10897) and our int uition. Further- more, Falkcnstcin (1006) empirically confirms that institutional owners tend to hold securities with larger idiosyncratic risk. Chang and Doug (2005) examine the possibility of reversed causality and its ef- fect on their results, and find (in a pooled regression setting) it to be negligible. we address this issue in a time-series set-up, i.e., a Vector Error Correction Model (VECM). This allows us not only to test directly for causality, but also to account for non-stationarity of the variables of interest. Our results show that there is indeed a cointegrating relationship between (detrended) market average institutional owner- ship and idiosyncratic risk, and changes in idiosyncratic risk can sometimes induce changes in institutional ownership, i.e. endogeniety is present in the relationship. Furtherinm‘e, we show that the effect of institutional ownership on idiosyncratic risk, though statistically significant, can be considered negligible for all practical purposes. Our estimates predict that it would take over hundred years to incorporate this effect. Additionally, we detect a structural shift in the long-run relationship of institutional ownership and risk around second quarter of 2000. We suggest it was caused by the Technological Bubble burst. in March 2000. Our testing method allows us to address directly the causality question in time- series set-up. This approach determines why a variable such as, for example, id- iosyncratic risk changes from period to period. not why it differs from security to security (as in cross-sectional set-up). The pooled regression analysis would make it impossible to scpa—trate the two effects. The dynamics of idiosyncratic risk is an importemt research topic as some previ- ous studies suggest that it may be priced (Aug, Hodrick, Xing, and Zhang (2006), Goya] and Santa-Clara (2001), among others). These papers show that past values of it'liosyncratic risk may help predict future returns. Many of these studies though use pooled estimation set-up and therefore do not distinguish between cross-sectional and time-series drivers of the relationship. In addition, the fact that idiosyncratic risk 50 may be non-stationary makes the results of such analysis even more questionable. 3.2 Data, test construction, and main result In this section we establish the main result for the relationship between average institutional ownership and idiosyncratic risk. First, we would like to confirm that a significant. relationship exists in time series set-up. after which we proceed with causality analysis. Our data. come. from CRSP (security returns) and 13(F) filings (institutional own- ership) databases. We consider period from January 1980 till December 2004. Since firm characteristics are measured quarterly, we use the same frequency for other vari— ables. Our measure of idiosyncratic risk is constructed as the end of the quarter average monthly variance of the Fama and French three factor model residual. The model is estimated for each month on the daily return data: (fit — 'I'ft) : o,- + V_t.ll’1'(‘/'",t — 1ft) + (tins/111)) +lri22121nlg+eih (3.1) 1 t MFR, = i 2‘; 6,5, (3.2) s: where IRF F is our measure of idiosyncratic risk, ”‘it is return of stock i in period t, Tmt is the market return, rft is the risk—free rate, smbt and hmlt are the Fama and French two factor portfolios (obtained from K. French’s web page). We require for statistical accuracy at least. ten daily return observations for each firm in a given month. We then find simple market average for both idiosyncratic risk and institutional owner- ship share. Next, we detrend both of these variables and use the residuals from the following equations: [RFFH = (1'1'1 +s3glt+€,‘fl. (33) 60 INS” = (1,2 +3312t+ 6N2: (3.4) where INS is average institutional ownership. Since stationarity issues play a signifi- cant role in time series analysis. we first check our variables for the presence of the unit root. Table C.1 reports the results of the Augmented Dicker-Fuller tests and confirms non-statiorrarity of both institutional ownership and idiosyncratic risk. Therefore, the two variables must. be cointegrated if they are related. The Johansen Cointegration Test confirms this conjecture. We apply the Johansen method (Johansen (1991) and Johansen (1995)). The specification we use allows the series to have linear trends. The likelihood ratio trace statistic is computed as follows: 1 Q0 2 —TZlog(l — )t.,), (3.5) i=0 where A,- is the i—th largest. eigenvalue. It is the test of H(0), no cointegrating equa- tions, against H(l), one cointegrating equation. The critical values for the test are taken from ()sterwald—Lenuni (1992). We first run a rolling estimation of the relationship (Table C2) to check for the possibility of structural changes. This step is dictated by the trajectory of idiosyn- cratic risk. which was gradually increasing until 2000 and fell abruptly afterward. We suspect the Technological Bubble burst of March 2000 may be responsible for shifts in the behavior of idiosyncratic risk as well as its relatitniship with institutional ownership The results of the rolling estimates show the relationship looses significance in the recent years. Following our intuition regarding the Bubble we add a dunn'ny variable to the relationship, which takes the value one for all the observations starting from the second quarter of 2000. Thus we allow the intercept (but not the coefficient) of the relatitmship to change after the Technological Bubble. As it turns out including this dunnny renders the relationship significant in the whole sample (including recent 61 years). The likelihood ratio statistic for the two variables is 34.67, while 5%(l%) critical values are 2968(3565). Therefore, we reject at 5% the hypothesis of no cointegration between average institutional ownership and idiosyncratic risk. We will keep the dunnny variable in the equation for the remaning tests of the long-run relationship. Our next. step is to check for short-run causality between ownership and risk. We will use Granger Causality tests for this purpose. We employ the following two-lag model: fl-‘t = (It) + flirt—1 + 0217—2 + (3191—1 + ,32yt—2 (3-6) to test whether y Granger-causes x. It is the Wold test for the joint hypothesis {:31 = 32 = 0, i.e. y does not cause x. The p—value for null hypothesis ”institutional ownership does not. Granger Cause idiosyncratic risk” is 0.61. We therefore unable to reject it at any conventional level. The p-value for the opposite hypothesis, i.e. ”id— iosyncratic risk does not Granger Cause institutional ownership”, is 0.18. Therefore, we can state that. the variables are unrelated in the short run. we will now proceed to investigation of the causality in the long-run using VECM. \Ve. estimate the following model: AIRFFt = 9901+ enECTt—r +9912AIRFF1_1+ ¢13A1RFFt_2 + 9:14AINS}_1+ 991,5A1N3t_2, (3.7) and AIMS} = €02 + $2.1EC‘Tt—1 +,:22AIRFF_1 + e2;5a1RF1~‘t_2 + ,52.1A1w's,_1 + o25AI./VS,_2, (3.8) where E ( 7T1 : (10+ INS) — (11 I RF F1 — (.12 D001, 000 is the dummy for observations starting with the seccmd quarter of 2000. We are interested in the significance of the coefficients on the error (‘OI‘I‘OCHOII term (ECT) in each equation: p11 and p21. If 62 both of them are significant the causality runs in two directions. If one is significant and the other one is not. we can clearly determine which variable is endogenous (the one with significant coefficient) and which one is exogenous (the one with insignificant coefficient) The estin’iation results for the above model are summarized in Table G3. ECT is estimated as ECT, = 006+ INSt—1~<-ll.95*IRFFt—0.31*D00; (the residual from the regression of ownership on risk and the dummy). The coefficients on error correction term confirm our intuition: p21 is significant, indicating that idiosyncratic risk affects institutional ownership. Since 9:11 is significant. as well the evidence suggests that causality runs in both directions. But before we reach a final conclusion regarding the causality in this rela-itionship let us examine economic significance of these coefficients. First, we note that coefficient on ECT in the dynamics of idiosyncratic risk is much smaller then that of institutional ownership. The two variables though have. very different variances. which makes these coefficients not directly comparable. This concern can be addressed by computing half-life for both using the following formula: In(1/2)/ln(1 —- ,9”). The half-life will tell us how many quarters it. takes for a shock in ECT to be reduced in its effect. on ownership or risk by half. In case of institutional ownership it is 43 quarters or almost 11 years. For idiosyncratic risk the estimate is 693 quarters or 173 years. \Ve would like to point out that such slow effect can hardly be considered economically significant in a world of quickly adjusting stock prices and risk. The combined effect of short. and long-run adjustments of institutional ownership and idiosyncratic risk to a. single shock can be observed in figures 1 and 2. As these trajectcn‘ies suggest it takes about 10 years for the system to reach the equililn'itnn. \Ve conclude that chamgcs in average idiosyncratic risk can potentially explain the raise in average institutional ownership while changes in ownership are unlikely to have an economically significant effect on idiosyncratic risk. 63 3.3 Future work As a. rolmstness check of these results we propose to repeat. the above tests with alter- native measures of idiosyncratic volatility. For instance. volatility can be measured as the residual of one-factor Market Model or the Market Model with other risk factors. such as momentum. \Ve ran the. model estimation month—by-month for each security, different specifi- cations (say. 5 years interval) can be considered as well. which may increase statistical accuracy of risk estimates (possibly in expense of betas’ flexibility). Malkiel and Xu (2003) used GARCH model as an alternative estimation technique, which can be incorporated in this analysis as well. Although GARCH imposes certain structure on the Variance, it has been proved very successful in modeling variances of financial series. Campbell, Lettau. Malkiel, and X11 (2001) proposed a technique, which allows to derive average market idiosyncratic risk without estimation of betas. This method assumes though no cross-correlation of betas. which their paper shows to be a minor issue. Another test of robustness would be an addition of several control variables used in related literature: average firm’s earnings per share, volatility of earnings, turnover, size, leverage and book—to-n‘iarket. Earnings per share and their \r’olatility were pro- posed hy \Vei and Zhang (2006) and Irvine and Pontiff (2005) as potential funda- mental explanatory variables for idiosyncratic risk. Size was included as a control factor along with institutional ownership by Malkiel and Xu (2003). Brandt, Brav, and Graham (2005) consider turncwer as an important variable in explanation of the behavior of idiosyncratic volatility. which they claim is a proxy for speculative trad— ing. Leverage, measured as the ratio of the book value of debt to total assets. was included by Dennis and Strickland (200:3). Book values though are slow to adjust following rapid changes of the market. therefore. we propose as well an alterm-rtive 6 4 measure of leverage based on the market values. This variable may serve as a better explanatory factor for risk. To test if a given control is responsible for the appearance of the relationship between institutional ownership and risk we propose first. to run cointegration test for the system of four variables: ownership. risk, dummy for the observations after the first quarter of 2000, and a control. If cointegration is established we can further test robustness of our results in the following VECM: A/RFFt 1' 9910 + sellECTit—i + ¢12ECTZt—l +‘W13A1RFFt—l+9914AIRFFt—2 +§315A1N81_1+¢JGAINSt_2+¢17AC701\*"TR()L1_1+3018ACONTROLt_2, (3.9) and AINSt = 9320 + 9921 ECTBt—l + #922ECT4I'—1 +5323AIRFFt—l + 5:24A1RFFt—2 +<,:25Al.\t’St_1 + ¢25A1N81_2 + ggyAC‘()NTR0L,_1 + oggACONTROL-t_2, (3.10) where RUTH = (1110 + liVSt — (‘i.11]]fFF{ — (112/2001. ECTZt .310 + COJVTROLIt —i311[RFFt — 33120001. ECTgt = 020 + IRFFt - (.121 INS} — 052213001, HUT,” : 5320 + C(LVTRO Lt — 321 INKS} — ,if‘,f22l)00t. The idea behind this set up is the following. We want to be able to determine pair—wise relationships among the three variables: ownership. risk and control. The question we ask here is whether institutional ownership adjusts to risk in equilibrium even after its equilibrium relationship with control has been accounted for (E CTQ). Same. holds for idiosyncratic risk. We still expect to find that. 9921 is significant even after deviations from equilibrium with control (terms ECTQ and [C(71) have been added to the system. One may consider as well a fii'iii-lm'el analysis of the specified relationship in a 65 sample of, say. 30 Dow Jones Industrial Average Index securities to test how the conclusions stand outside the market. averages. Same can be done for the portfolios of securities sorted by size or book-to-rnarket and weighted by market capitalization. Such a. procedure is shown to reduce considerably the noise. Finally. investigating the relationship for the possibility of non-linearity is another possible avenue for future research of this topic. 66 APPENDIX A Tables and Figures for Essay 1 Table A1 Descriptive statistics This table reports major statistical indicators for the variables of interest. All series are in logarithms. LIRCV is the CLMX idiosyncratic risk measure constructed using the value-weighted market index, LIRCE is the CLMX idiosyncratic risk measure constructed using the equally-weighted market. index, LIR is idiosyncratic risk constructed using the simple Market Model, LIR5Y is idiosyncratic risk constructed using the simple Market Model regressions by 5 year intervals, LIRF F is idiosyncratic risk constructed using the Market Model with Fama—French factors, LIS is idiosyncratic volatility of sales, LICF is idiosyncratic volatility of cash flows. and LIE is idiosyncratic volatility of earnings. ’7} is the log of Quasi—Herfindalrl Index. LNS is the total number of securities in the market. Sample size for all the variables is 498. Variables LIRCV LIRCE LIR LIR5Y LIRFF LIS LICF LIE 7t LNS mean -6.5429 -6.5561 -6.5-l95 -6.5567 —6.5644 2.7010 -0.6635 4.1464 -5.0134 8.5476 median -6.6429 -6.6634 -6.6545 -6.6564 —6.6682 2.2817 -l.0040 4.1570 -5.1245 8.7496 maximum —4.9816 -4.9984 -5.0060 —5.0215 ~5.0339 7.0935 5.5298 12.5329 -3.6089 9.1284 minimum —7.6146 -7.6292 -7.6115 -7.6348 -7.6406 1.3585 —3.1832 0.8304 -5.8782 7.6377 st .dev. 0.5999 0.5991 0.5964 0.5969 0.5969 1.2340 1.9674 1.8507 0.5864 0.4785 skewness 0.3622 0.3696 0.3593 0.3588 0.3618 1.8374 0.9901 1.0380 0.2934 -0.8611 Table A2. Correlation matrix This table reports correlrjition coefficients for major variables. Variables LIRCV LIRCE LIR LIR5Y LIRFF LIS LICF LIE "ft LNS LIRCV 1.0000 0.9998 0.9999 0.9997 0.9993 0.3544 0.5702 0.6243 —0.6808 0.7631 LIRCE 1.0000 0.9999 0.9998 0.9998 0.3554 0.5698 0.6257 -0.6847 0.7628 LIR. 1.0000 0.9999 0.9996 0.3541 0.5709 0.6256 -0.6842 0.7651 LIR5Y 1.0000 0.9997 0.3519 0.5700 0.6251 -0.6852 0.7662 LIRFF 1.0000 0.3532 0.5698 0.6260 —0.6891 0.7657 LIS 1.0000 0.7176 0.7532 -0.2698 0.4310 LIC'F 1.0000 0.7568 -0.3760 0.7134 11 [R 1.0000 -0.5680 0.7178 "ff 1.0000 -0.6798 LNS 1.0000 68 Table A.3. Augmented Dickey—filler unit root tests This table reports results of Augmented Dichey—Fuller tests for major variables. All tests include four lags. other specifications provide similar results and are available upon request. MacKinnon critical values are equal -3.4459 for the. 1% level and —2.8677 for the 5% level. The null hypothesis is the unit root in the data. ADF statistic —2.3771 -2.3461 -2.3706 -2.3826 -2.3284 —2.7401 -3.0162 -1.8641 -1 .3962 -1.8538 Table A4 Johansen cointegration tests This table reports the results of Johansen cointegration tests for the five measures of firm-specific. risk. In these tests each measure of idiosyncratic risk is paired with 71‘. . Specifications allows for a linear detern'iinistic trend in the data. Critical values are obtained from Osterwald-Lenum (1992) and are equal to 20.04 (1%) and 15.41 (5%). * indicates rejection of the null of no cointegrating equations at the 5% level. Idiosyncratic risk measures LIRCV LIRCE LIR LIR5Y LIRFF Likelihood ratio statistic 1741* 1726* 1721* 1723* 17.14* Table A5. Estimated cointegrating coefficients This table reports estimated coefficients in cointegrating equation for each of the measures of firm- specific risk. The normalization variable is idiosyncratic volatility, which coefficient is set equal to 1. Idiosyncratic risk measures Constant "if LIRCV 10.2915 0.7481 LIRCE 10.3257 0.7523 LIR 10.2940 0.7473 1.1R5Y 10.3038 0.7478 LIRFF 10.3445 0.7544 70 :29: 9:9: :29: E9: :89: 3.9: :39: :99: 3.5.: :29: e.:...::,_-_m €993 3.89: 2293 $29.: 8393 829: 3293 399:: 3593 829: . 9.2.? 22.: $2.? $2.: $2.? 32.: 22.? B2: 22.? 3.2.: as: 4 3343 £92.: 3:33 $39: 8:23 3:5 _: 32.3 359: £4.33 :29: . :29? :92: :29? :3: 299? “2.2.: 229:- :3: $2.? 2.2.: 3.1 e 4 3:33 :39 3 6393 8.99 3 £23-: 992...: 3:93 $5.91 3293 A t 2.. _ -: 2:9? 2:9? :89? 329? ::9..:. S....:.:. 3:9? :99? :::9:- :9...:.:- as; E: 4 3:93 $3.93 239:: 8393 3:23 9:243 €993 3:25-: 329:: 32.93 - :29: 2.3? :29: 2:3,? 29: $2.? .29: 22.? ::9: 22.? as E: 4 9.293 3:3 6.893 39:3 @593 32.4.: 92.3 333-: 2.393 34:99-: 2:9? 299? 2:9? :39? 3:9? 39? :39? $9? 899? $9? How 3::93 $2.3 3:993 33:: $9.93 $2.3 SE93 9.9.2:: $9.93 83:: :29? 2:9: :89? 2:9: :89? 2:9: :29? 2:9: :89? 2:9: 232:6 2.... 4 PE: 4 H2,. 4 is: 4 2c 4 m: 4 F 4 mom: 4 9. 4 .52: 4 .5 Km: >3: 25 moms Rom: ...:_.,.....§ 2 £33253; E Feim v.94. 952:3? w .47.: ociiimczx We 3:52: 32.53.53: .2: i arm—d 035.23 53:72.5? 2: m; >Q .55: 95.38.23,: 5:0 2: E PUB .572 ossoskxozt we 7.9:? 2:: £52.25.) .5. 29m? 1.2.5510 1:323 :33 7.2:- xmt 0598932? no measmwoa 35245 Bu 3on Dm> ..o.< $35. Table A.T. Cointegration tests with fundamentals This table reports estimates of Johansen cointegration tests with fundamentals. In these tests each measure of idiosyncratic fundamental volatility is combined with pairwise measures of idiosyncratic risk and ",t . LR is the likelihood ratio statistic. **(*) indicates rejection of the null of no cointe- grating equations at 1% (5%). 1% critical value is 20.04, 5% critical value is 15.41. and 10‘} critical value is 13.33. ldios. fundamental volatility measures LICF LIS LIE LNS LR for LIRCV 20.4999M 20.0327* 14.2305 19.8410* LR for LIRCE 20.1612" 19.8750* 14.0748 19.3278* LR for LIR 20.3141M 198612“ 256331” 196528“ LR for LIRSY 20.2935” 19.8707’“ 14.2560 19.4028* LR for LIRFF 198322“ 19.6132* 13.9562 190814“ LR for ”711 13.3258 10.8058 9.1718 6.8854 Table A8. ADF unit root and Cointegration tests by industry This table reports estimates of ADF unit root and Johansen cointegration tests by industry. LIR- CVi is industry is CLMX measure of idiosyncratic risk. All variables are in logarithms. LR is cointegration test statistics with own ’j’t and with market-Wide "lit. Critical values for the ADF test are 43.4459 (1%). and for the Cointegration test are 20.04 (1%). 15.11 (5%), and 13.33 (10%). * indicates failure to reject the unit root at. 1‘70, rejection of no Cointegration at 5%; ** indicates rejection of no cointegration at 1%. Industry 111103111511 ADF stat. q; ADF stat. LR (71?) LR (71 ) Agriculture LIRCVI -3.2511* 7.} —1.9599* 19.7413* 25.0021“ Food Products LIRCV‘Z —2.7.125* 1,2 —11.9151* 20.8746” 23.1777** Candy and Soda LIRCV3 ~5.l213 713 -1.8455* Alcoholic Beverages LlRCV-1 -3.2816* 7,4 —0.—1669* 14.1080 22.5550” Tobacco Products LIRCVS 6.1645 ’3'? —3.0989* Recreational Products LIRCVG -3.75-11 ”6 -2.959-1* Elitertainment LIRCV7 -2.761.4* 7.7 -2.l8‘21* 18.5267* 23.4248“ Printing and Publishing LIRCV8 —2.7961* “1’8 -2.-1-115* 22.5773M 19.2926* Consumer Goods LlRCVf) —3.100-1* ”,9 -l 6378* 12.6056 22.0305“ Apparel LIRCVIO uses-1* 7,10 —1 6281* 15.2811 22.9108” 1111111111 care LIRCVII —2.71.18* 1.,“ 4.11331 Medical Equipment LIRCVI‘Z -2. 1015* 7112 —2.0532* 15.5659“ 18.5034“ Pharmaceuticals LIRCV13 -1.961'2* 7,13 -2. 1031* 10.5335 12.0181 Chemicals LIRCVH —2.9772* 1.,“ 3,0271% 11'1.32ss* 23.0888“ Rubber and Plastic Liiicvia 43.7735 7,15 —‘2.:')625* 71 Table A.8. Continued Ni Industry IlliosRisk ADF stat. A ADF stat. LR (7i) LR. (7t ) Textiles LIRCV16 3.2971* 7,16 0.7193* 17.9547* 19.4017* Construction Materials LIRCV17 3.8534 1727 -1.4342* Construction L1RCVi8 3.8391 7,18 -2.1234* Steel works LIRCV19 3.6200 “1'39 -1.9498* Fabricated Products LIRCV20 3.3675* 730 ~1.9850* 19.2054* 25.3202** Machinery LIRCV21 -2.5696* 1.31 —2.9l67* 15.2304 19.9582* Electrical Equiplllellt LIRCV22 -‘2.6918* 1.22 -2.8660* 16.2018* 19.4589* h‘Iiscellaneous LIRCV23 3.8519 733 —2.5994* Automobiles and Trucks LIRCVQ4 -3.6‘288 “”24 -1.6831* Aircraft LIRCV25 3.2822* 735 —1.1743* 17.0173* 21 .22.97** Shipbuilding. Railroad Eq. LIRCV‘26 3.1210* 736 -0.8816* 13.2633 17.1311* Defense LIRCV27 3.6388 1.37 -0.7999* Precious Metals LIRCV28 —2.2823* ~38 —1.9758* 15.2195 11.2179 Nomnetallic Milling L1RCV29 —2.6887* 739 -2.7595* 16.4187* 18.0334* Coal LIRCV30 -3.4'231* 1530 -0.7669* 12.7933 19.9761* Petroleum and Natural Gas LIRCV31 —2.5463* ”H31 -1.2994* 13.6373 17.7780* Utilities Ll‘RCV32 -2.0038* 7132 -0.5984* 7.3575 15.0182 TelecomlllllllicatiOlis LIRCV33 —2.4935* #3 -0.9934* 20.9314** 15.7011* Personal Services LIRCV34 3.6696 7}” —2.2181* Business Services LIRCV35 —2.5169* 7135 -2.0530* 15.7882* 20.1710** Computers LIRCV36 -2.5181* 75,35 -0.9010* 17.3588* 18.1756* Electronic Equiplllellt LIRCV37 3.0445* 7637 —1.9206* 15.0323 25.0333** Measuring and Control Eq. LIRCV38 -2.4899* 728 -2.5675* 25.0613” 19.0872* Business Supplies LIRCV39 4.2395 ”,"?g —1.3407* Shipping Containers LIRCV40 3.9577 7;“) -1.7268* Transportation LIRCV41 ~2.9195* 7,;11 -‘2.7954* 16.3337* 22.8950M Wholesale LIRCV42 -2.9721* 17,42 -2.6398* 20.4188” 25.8683** Retail LIRCV43 -2.4071* 1.243 ~1.6‘299* 14.8658 19.2374* llestnrir-ains. Hotel. More] LIRCVM 3.951 1* 7;” -2.0320* 17.6985* 21 .2958** Banking LlRCVl5 -2.6500* 7.315 -17366* 11.4328 13.9035 IIISIII'HIICG LIRCV46 -3.’2()9T* 7216 -2.04()9* 2031611M 19.89()‘2* Real Estate LIRCV47 3.0345* 7,17 -0.9277* 11.0977 15.1180 Trailing LIRCV48 —2.7504* 7.318 —1.6783* 15.8643* 110495 The rest LIRCV49 3.31 10* 6,49 -2.2784* 17.9879* 17.8371* 72 Table A9. VECIVI and cointegrating equation coefficients by industry This table reports eslimales ol‘ \’E‘(.‘l\1 and cointegrating equation coefficients for each industry. LIRCVi is industry is CLMX measure of idiosyncratic risk. All variables are in logarithms. CE coef. is the estimated coefficient on market concentration in the cointegrating equation where idiosyncratic risk coefficient is normalized to -1. t stat.(1) is the t statistics on the error correction term in the equation for the changes in idiosyncratic risk as the dependent variable. t stat.(2) is the t statistics on the error correction term in the equation for changes ill the market concentration as the dependent variable. *(**) indicates significance at least. at the 5(1)% level. A, 1 Industry _ "1 7t CE coef. t stattl) t stat. (2) CE coef. t stat.(1) t stat. (2) Agriculture -0.888 -5.78** —0.65 0.510 -4.20** 199* Food Products -0.802 —-'1.90** -0.57 1.798 —4.51** 237* Alcoholic Beverages -0.612 -5.28** 0.99 Entertainment -0.859 -5.32** 0.02 1.446 -3.95** 239* Printing and Publishing —0.588 -4-.66** 0.38 -0.639 -4.13** 1.56 Consumer Goods -0.:329 —4.58** 0.46 Apparel 0659 -4.91** 0.61 Medical Equipment -l.036 -4.26** —0.64 -2.306 -3.22** —1.37 Chelllicals —0.7‘2-“1 -5.47** —0.02 2.192 -3.47** 215* Textiles -0.3159 -4.70** 0.25 -0.016 —4.10** 244* Fabricated Products -0.882 -5.23** -2.12* 0.348 —4.2-1** 1.01 Machinery -0.829 -4.95** -0.90 Electrical Equipment -0.774 —4.50** -0.10 3.567 -3.34** 0.24 Aircraft -0.4~11 -5.08** 1.19 0.926 -5.07** 0.30 Shipbuilding, Railroad Eq. -0.815 -5.45** -1.91 Nonmetallic Mining -0.986 -4._7()** -1.42 -1.754 -3.68** -0.78 Coal -0.723 —5.23** -1.15 Petroleum and Natural Gas -0.811 -4.13** -1.93 Teleconnnunications - l .042 -4.03** -1.46 -0.693 -5.10** ~ 1 .06 Business Services -0.793 -4.49** 0.05 0.413 —3.29** 228* Computers ~0.917 -4.36** —0.14 -0.913 —4.20** -1.93 Electronic Equipment -0.665 —5.14** -0.29 Measuring and Control Eq. -1.039 -4.32** —0.92 -l.572 -2.53* -3.61** Transportation -0.682 -5.36** -1.15 —0.689 —3.94** -0.39 \NhOiESflie —0.708 —4.73** 0.12 —0.784 —4.09** —0.40 Retail —0.816 -4.47** 0.10 Restaurants, Hotel. Motel -0.657 -5.14** —0.63 1.241 —4.47** -0.02 Insurance -0.502 -4.78** -0.10 -0.212 —4.48** 0.94 Trading 0.321 -4.45** 1.93 The rest 41507 -4.80** ~0.75 —0.672 -4.05** 4-85 Table A.10. VECM for selected average idiosyncratic risk This table reports VECM estimates for selected average idiosyncratic risk. The numbers ill brackets are standard errors (first. line) and bootstrapped standard errors (second line). Dependent variables A Lle .3 Alt Constant 5.12 * 10 "0 -0.001 (0.009) (0-001) (0.009) (0.004) ECT 0.302 0.002 (0.027“) (0.012) (0.048**) (0009) Lag] A LIRS -0.463 0.0004 (0.040“) (0.018) (0.063**) (0.015) Lag2 A Lle -0.218 -0.003 (0.040”) (0.018) (0.073”) (0012) Lag] A ’7‘) 0.011 -0.282 (0.982) (0.045”) (0.092) (0.164) 1.2192 A 7t 0.063 -0.131 (0.983) (0.045") (0.083) (0.076) Table A.11. The Market IVIodel with GARCH(1,1) errors This table reports variance equation estilllates for the Market Model with GARCH (1.1) errors. p-values are given in parentheses. Company all M 9‘2 133 Alcoa INC. 2.82 =1: 10-5 0.156 0.604 —8.36 :1: 10-6 (00372) (<0.0001) (<0.0001) (0.0058) Amer. Illtl. Group 8.69 * 10“) 0.159 0.788 1.34 =1: 10’-5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Amer. Express INC. 4.62 * 10-5 0.203 0.653 —1.87 =1 10' 6 (<0.0001) (0.0003) (<0.0001) (0.4209) Boeing co. 1.65 it 10-4 0.168 0.616 1.98 i: 10—5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Citigrollp INC. 399 =1 10—5 0.158 0.602 —1.2 $10—-5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Caterpillar INC. 335 * 10-0 0.152 0.601 —6.63 =1 10*6 (<0.0001) _ (<0.0001) (<0.0001) (0.0659) DuPont —3.83 =1: 10—0 0.163 0.607 —1.69 =1 10-5 (0.0039) (<0.0001) (<0.0001) (<0.0001) Walt Disney co. 1.11:1:10’"1 0.156 0.604 1.21 110*“5 (<0.0001) (<0.0001) (<0.0001) (0.00.11) Table A.11. Continued Company 501 19"} 172 (1’3 Gen. Electric co. 2.13 :1: 10-5 0.154 0.602 —3.36 :1: 10*6 (<0.0025) _ (<0.0001) (<0.0001) (0.0132) Gen. Motors —7.02 =1: 10-7 0.185 0.622 —2.3 :1: 10'—5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Home Depot INC. —6.02 4:10—5 0.181 0.693 —1.6 410—5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Honeywell INTL. CO. 2.14 =1: 10-6 0.201 0.704 —6.82 it 10—6 (0.8255) (<0.0001) (<0.0001) (0.0016) Hewlett Packard co. —2.09 e 10*4 0.162 0.600 —6.12 4 10-5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Intl. Business l\1ach. —3.04 >1: 10—5 0.171 0.612 —1.16 :1: 10’5 (0.0052) (<0.0001) (<0.0001) (<0.0001) Intel CP. -—3.58 it 10—5 0.170 0.615 -3.06 * 10-5 (0.1601) (<0.0001) (<0.0001) (<0.0001) Johnson and Johns. DC. —6.61=1<10‘6 0.203 0.636 —8.97 410—6 (04713) (<0.0001) (<0.0001) (<0.0001) JPMorgan Chase CO. 1.45 :1: 10*"1 0.191 0.634 1.94 =1: 10—5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Coca Cola co. 1.96 e 10—5 0.165 0.608 —5.65 * 10-6 (0.0357) (<0.0001) (<0.0001) (0.0024) McDonalds CP. 2.05 =1: 10* 4 0.180 0.624 2.64 * 10—5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) 3M Co. —-9.43 :1: 10*6 0.193 0.629 —9.27 =1: 10—6 (0.3316) (<0.0001) (<0.0001) (<0.0001) Altria Group INC. 6.69 >1: 10-5 0.153 , 0.601 1.24 * 10-8 (0.0013) (<0.0001) (<0.0001) (0.9975) Merck CO. INC. 2.27 *10—5 0.168 0.611 —5.17 =1: 10—6 (00683) (<0.0001) (<0.0001) (0.0322) Microsoft. CP. —4.49 it 10—5 0.153 0.602 —1.36 it 10-5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Pfizer INC. 1.76 410-5 0.132 0.797 —8.95 1110—7 (00124) (<0.0001) (<0.0001) (0.5132) Procter and Gamble CO. —1.69 >1: 10—4 0.150 0.601 —4.7 * 10—5 (<0.0001) (0.0004) (<0.0001) (<0.0001) ATT INC. —7.7 :1: 10-5 0.165 0.608 —2.38 1: 10-5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) United Tet-Ii. 1.02 * 10—4 0.157 0.605 8.65 it 10-6 (<0.0001) (<0.0001) (<0.0001) (0.0033) Verizon Colnnlllll. —8.31 * 1075 0.156 0.603 —2.22 =1: 10-5 (0.5286) (0.3034) (0.1750) (0.5150) wtililnrt Stores 1.3 =1: 10" 4 0.192 0.636 1.26 e 10—5 (<0.0001) (<0.0001) (<0.0001) (<0.0001) Exxon Mobil C‘P. — 1.75 it 10-6 0.189 0.625 ——9.71 =1: 10—6 (00061) (<0.0001) (<0.0001) (<0.0001) ‘1 {:1 Figure A.1. : Idiosyncratic volatility This figure plots average idiosyncratic volatility (ill logarithms) on U S market. from 1063 till 2004. —45 ~50- -55.. -504 -8.5-( 1111 ~7.54 -80 .11f3.,..,r,,,TVTYY.,rrVVYT.....r'ev,.y.v 85 7D 75 BO 85 ..D 95 Figure A2 : Quasi-Herfindahl Index This figure plots average Qllasi—llerfilldahl Index (ill logarithms) for U.S. market from 1963 till 2004. air] ‘60 v'rfivw‘r Irvvrf‘rrv YtVV'YVTV vvvxrrrr " ‘ f V I Y I V 65 7D .75 80 8‘5 90 96 DD E19951] 76 Figure A.3. : Idiosyncratic fundamental volatility This figure plots three measures of average idiosyncratic fundamental volatility (in logarithms) on U.S. market for period 1963 - 2004. LICF, LIE. and LIS are the fundamental volatilities measured using cash flow, earnings. and sales, respectively. 16 12— '1 i t: i 'I It. 8— I 6 , L 1‘! 1| .1 1 1'” Fl:- r q " IL'M'H' JJ|IIL~1II"L"JI|‘:L‘ I! J ._1 limp” Figure A.4. : Total number of securities This figure plots the total number of securities (in logarithms) 011 U.S. market from 1963 till 2004. 92 8.8 - ‘/\~v/J \ a 4 2 a o _ //_‘”/‘ 7 B I l l l l V l 135 713 75 80 85 no 95 oo 77 APPENDIX B Tables and Figures for Essay 2 78 Table B.1. Trends in idiosyncratic volatility of individual securities This table reports appearance of trends ill securities idiosyncratic volatility. The numbers represent the total number of securities ill each category. Shares (in percentages) are. given in parenthesis. The securities included in the samples are those with at. least 2 years of monthly data. The columns refer to the. sample of securities with significant. (at. least. at. 5% level) positive, significant. negative, insignificant estin’lated trend coefficient. and the total sample. Idiosyncratic risk is measured as an average squared residual in monthly regressions of the Emma FTenCh three factor model. Time period Positive significant Negative significant Insignificant Total Jul 63 — Dec 05 6759 5548 9553 21860 Total period (30.92%) (25.38%) (43.70%) (100%) Jul 63 - Dec 97 54-10 3719 8220 17379 CLMX period (31.30%) (21.40%) (47.30%) (100%) Jan 98 - Dec 05 1193 4521 4055 9769 Post CLMX period (12.21%) (46.28%) (41.51%) (100%) Jul 63 — Dec 75 2258 363 3126 5747 (39.29%) (6.32%) (54.39%) (100%) ..Ian 76 - Dec 85 1677 1554 4596 7827 (21.43%) (19.85%) (58.72%) (100%) Jan 86 ~ Dec 95 33-11 _ 1988 5433 10762 (31.04%) (18.47%) (50.49%) (100%) Jan 96 - Dec 05 238-1 3861 5455 11700 (21).:18(7(-) (33.00%) (46.62%) (100%) Table 8.2. Descriptive statistics of firm characteristics This table reports major statistical indicators for firm characteristics. All characteristics except turnover and size are in millions of dollars. Size is the logaritlml of the market value of total equity, book-to~111arket is the ratio of book value to market value of equity, cash ratio is the ratio of cash to total assets, earnings per share is the ratio of earnings to the number of shares outstanding, leverage book value of long term debt to market value of assets. turnover is the share of the company’s listed securities traded on the market. per year. RnD expenditures is the ratio of RnD expenditures to market value of equity. N is the total number of non missing observations. Characteristics mean standard deviation minimum maximum skewness size 1.29 2.21 -9.73 13.34 0.14 book-to-market 0.90 1.43 0 99.77 21.15 cash ratio 0.30 0.68 0 4.98 4.98 earnings per share —l.29 1.37 —2.4--1 2.62 0.51 leverage 0.23 0.24 0 1 0.98 turnover 0.07 0.19 0.003 1.61 ‘ .75 RnD expenditures 0.02 0.0-1 0 0.28 3.7-1 m2: Ems SE E: z 33 3.3 83 2.5: :8 Assess exams: essays §a§a @848 Assess Assad; gangs cameo Sesame goes: $533 was... as; :3 Sam was was 3S $3 8% one 2% 83 3.? game: sage £35 Assam: $.35 Asses: Aswfi: $5.3 £35 £33 gent $13: was as as” 3.2 as .8: 3% as $2 tom. 82 2% 8V $.33 E3: $58.5 253.3 $.55 Q33 Essa: Agave exam-e game $.53 GEE: we... 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The dependent variable takes the value 1 if the securitv had a significant (at least. at. 5 70) positive trend, 2 - if significant 111g11tiv',1 and 3- if 11151g111f11 ant t11nd in idiosy111iati1 1isk. Th1 has1 1.11s1 is insig11ifi1ant trend. with probability Pr(0). Pr(+ ) and Pr(-) are the probabilities ol having a. significant positive and a significant negative trend in idiosyncratic volatility, respectively. Regressors are dummy variables for trends in each of the firm characteristics. Positive sign indicate that the dummy takes the value 1 in case of the positive significant. trend and 0 otherwise, negative sign indicates that the dummy takes the value 1 in case of the negative significant trend and 0 otherwise. Standard errors are given in parenthesis. Bold fase characters indicate significance at least at l % level. Pr +‘ ) Refill-95501.5 lOg( 137(0)) lOg( PT——(;(0)) intercept. -l.186 -l.188 —l.184 -1.197 -0.741 -0.861 -0.861 43.855 -0.615 -0.912 eps+ eps‘ Ueps+ Ueps‘ bnfi bnz‘ cashr+ (vislir“ ins+ i118" lev+ lev— 31:6 size' furn+ furnfi ret+ ref— 11+ P— rnd+ rnd‘ (0.075) (0.075) (0.074) (0.073) (0.050) —0.295 -O.298 -0.263 -0.308 -O.369 (0.055) (0.055) (0.054) (0.048) (0.054) 0.362 0.362 0.359 0.358 0.433 (0.062) (0.062) (0.062) (0.055) (0.061) 0.409 0.413 0.411 0.405 0.349 (0.051) (0.050) (0.050) (0.050) (0.049) -0007 -0007 -0.017 -0.002 -0.004 (0.051) (0.051) (0.050) (0.050) (0.050) 41.048 -0059 -0073 -0.056 -0.027 (0.063) (0.062) (0.062) (0.062) (0.062) 0.139 0.140 0.134 0.136 0.191 (0.073) (0.073) (0.072) (0.072) (0.072) 0.201 0.188 0.188 0.186 0.210 (0.063) (0.062) (0.062) (0.062) (0.062) 0.196 0.197 0.190 0.199 0.217 (0. 067) (0. 067) (0. 066) (0. 067) (0. 066) -0. 216 -0.223 -0. 238 -0. 159 (0. 057) (0. 057) (0. 055) (0. 056) 0.449 0.444 0.439 0.514 (0.082) (0.082) (0.082) (0.082) 0.229 0.229 0.224 0.227 0.253 (0.056) (0.056) (0.056) (0.056) (0.056) 0.090 0.090 0.089 0.089 0.112 (0.070) (0.070) (0.069) (0.070) (0.069) 0.033 0.038 —0.025 0.024 -0129 (0.062) (0.062) (0.059) (0.061) (0.061) 0.805 0.797 0.863 0.792 0.961 (0. 061) (0. 061) (0. 060) (0. 061) (0. 061) -0. 040 -0. 043 -0.084 0.008 (0.052) (0.052) (0.051) -0020 -0.018 -0.017 (0.069) (0.069) (0.069) (0.068) -0.357 -0.354 -0.344 -0.355 -0.394 (0.048) (0.048) (0.048) (0.048) (0.047) 0.487 0.485 0.486 0.486 0.512 (0. 048) (0. 048) (0. 048) (0. 048) (0. 048) -0. 578 -0. 575 -0. 574 -0.574 (0. 084) (0.084) (0.084) (0.084) .720 0.722 0.720 0.721 (0.062) (0.062) (0.062) (0.062) —0 217 (0.051) -0050 (0.102) 0.012 (0.120) 83 (0.069) (0.069) (0.068) (0.065) (0.052) 0.210 0.197 0.184 0.567 0.296 (0.055) (0.055) (0.055) (0.048) (0.054) -0.451 -0445 -0.456 -0.622 -0514 (0.077) (0.077) (0.077) (0.071) (0.076) -0.683 -0.675 -0.712 -0593 -0.614 (0.055) (0.054) (0.054) (0.054) (0.053) 0.000 -0.008 0.000 -0052 -0020 (0.049) (0.049) (0.049) (0.049) (0.049) -0221 -0243 -0199 -0.242 -0.289 (0.069) (0.068) (0.067) (0.068) (0.068) -0.019 -0042 —0.017 0.012 -0.065 (0.068) (0.068) (0.066) (0.067) (0.066) -0.192 -0.220 -0.172 -O.188 -0239 (0.069) (0.069) (0.068) (0.068) (0.068) -0.148 -0.146 -0091 -0157 -0155 (0.064) (0.064) (0.062) (0.063) (0.062) 0.556 0.536 0.635 0.499 (0.054) (0.054) (0.054) (0.053) -0.114 -0.130 -0.131 -0209 (0.114) (0.114) (0.112) (0.112) -0.376 -0.369 -0.348 -0345 -0.396 (0.060) (0.060) (0.059) (0.059) (0.059) -0.162 -0.175 -0143 -0.161 -0.187 (0.067) (0.066) (0.065) (0.066) (0.065) 0.410 0.404 0.609 0.483 0.532 (0.059) (0.059) (0.055) (0.059) (0.057) -0. 258 -0. 269 -0. 264 -0. 253 -0. 420 (0. 085) (0.085) (0. 086) (0.086) (0. 083) 0.794 0.787 0.865 0.971 (0. 060) (0. 060) (0. 060) -0. 067 -0. 065 0054 (0.088) (0.088) (0.087) (0.087) -0.070 0064 -0.086 —O.()63 -0.012 (0.046) (0.046) (0.046) (0.046) (0.046) 0.044 0.041 0.041 0.016 0.018 (0.053) (0.053) (0.052) (0.052) (0.052) 0.439 0.441 0.439 0.413 (0.061) (0.061) (0.061) (0.061) -0. 286 -0. 284 -0. 268 -0. 258 (0. 057) (0. 057) (0. 056) (0. 056) 0.337 (0. 059) -0. 024 (0.120) -0. 435 (0.111) Table 8.5. Sub-sample multinomial logit regressions This table describes results of multinomial logit regressions for firm characteristics for sub-samples. The original sample is split by price (low-high). time period (CLMX and post-CLMX), security life (long-short). and date security was listed (early-late). The dependent variable takes the value 1 if the security had a significant (at least at 5 %) positive trend, ‘2 - if significant negative, and 3 - if insignificant trend in idiosyncratic risk. The base case is insignificant trend. with probability Pr(0). Pr(+) and Pr(-) are the probabilities of having a significant positive and a significant negative trend in idiosyncratic volatility, respectively. Regressors are dummy variables for trends in each of the firm characteristics. Positive. sign indicate that the dummy takes the value 1 in case of the positive significant trend and 0 otherwise. negative sign indicates that the durmny takes the value 1 in case of the negative significant. trend and 0 otherwise. Standard errors are given in parenthesis. Bold fase characters indicate significance at least at l ‘70 level. Pr + Pr __ Regressors l()g( 75272)) 10g( 73-2—0?) ph’g" plow CLMX post-CLMX ph‘gh plow CLMX post-CLMX intercept -1401 -0.962 -1.095 -1.385 -0595 -l.639 -1353 0.252 (0.095) (0.129) (0.061) (0.138) (0.077) (0.159) (0.063) (0.080) 6113+ -0.195 -0514 0.117 —0.015 0.185 0.771 -0.407 0.337 (0.069) (0.095) (0.073) (0.258) (0.061) (0.142) (0.084) (0.115) eps- 0.346 0.488 0.159 0.580 -0.439 «0.798 -0.638 0.542 (0.077) (0.110) (0.085) (0.119) (0.083) (0.221) (0.110) (0.075) apt-Jr 0.492 0.309 -0.314 0.092 -0.718 -0503 -0.440 0.183 (0.064) (0.084) (0.061) (0.108) (0.061) (0.128) (0.067) (0.069) reps" -0048 0.025 0.029 -0.528 -0053 0.257 0.032 -0.421 (0.066) (0.078) (0.063) (0.114) (0.057) (0.103) (0.070) (0.074) mm -0192 0.106 -0.076 -0.251 -0.246 —0.103 -0153 -0.261 (0.081) (0.098) (0.055) (0.096) (0.079) (0.147) (0.067) (0.066) 6m- 0.044 0.351 0.012 0.087 -0.036 —0.094 0.197 -0.040 (0.086) (0.137) (0.060) (0.132) (0.074) (0.165) (0.058) (0.071) (6,919+ 0.258 0.085 0.069 -0242 -0.146 -0322 -0040 -0.317 (0.080) (0.102) (0.058) (0.100) (0.079) (0.152) (0.071) (0.066) cashr" 0.239 0.100 -0045 -0049 —0.111 -0.118 -0012 0.045 (0.082) (0.115) (0056) (0130) (0.071) (0.145) (0.058) (0.071) 613+ 01 17 -0.369 -0.160 -1.800 0.422 0.502 0.302 -0.988 (0.066) (0.123) (0.050) (0.099) (0.060) (0.137) (0.053) (0.060) ins“ 0.535 0.354 0.087 0.301 —0.003 -0351 0.093 0.053 (0.117) (0.116) (0.062) (0.101) (0.140) (0.219) (0.082) (0.081) 16-qu 0.184 0.313 0.167 -0052 -0377 -0.453 -0.050 -0005 (0.071) (0.093) (0.054) (0.094) (0.067) (0.135) (0.061) (0.064) lee“ 0.115 0.038 0.067 -0533 —0.122 —0.394 0.016 -0105 (0.087) (0.117) (0.062) (0.116) (0.075) (0.151) (0.062) (0.067) 5171+ 0.064 0.157 -0.241 -1.183 0.378 0.125 0.695 -0.871 (0.073) (0.129) (0.061) (0.138) (0.066) (0.140) (0.071) (0.071) 14:6- 0.942 0.698 0.375 0.803 0.011 -0502 -0.473 0.551 (0.085) (0.094) (0.059) (0.097) (0.106) (0.151) (0.097) (0.075) tum+ -0.006 0.013 0.213 —0.412 0.683 0.646 0.578 0.208 (0.066) (0.091) (0.059) (0.164) (0.066) (0.145) (0.081) (0.074) mm- 0.118 -O.‘256 -0023 0.697 -0064 0.221 0.299 0.448 (0.092) (0.111) (0.104) (0.088) (0 099) (0.210) (0.142) (0.059) 121+ -0335 -0.338 -0275 0064 —0.192 0.306 0.009 0.472 (0.062) (0.077) (0.097) (0.277) (0.053) (0.100) (0.089) (0.138) m- 0.462 0.511 1.308 2.229 0.041 -0073 -().018 0.277 (0.064) (0.076) (0.100) (0.212) (0.060) (0.123) (0.172) (0.218) p+ -0.617 -0.460 -0353 —0.955 0.390 0.724 0.448 -0.067 (0.101) (0.161) (0.074) (0.193) (0.067) (0.147) (0.064) (0.073) ,r 0.782 0.626 0.827 0.664 -0203 -0.394 0.059 -0.036 (0.077) (0.112) (0.059) (0.119) (0.064) (0.126) (0.062) (0.070) Table B5. Continued Regressors ‘ Ice intercept eps+ eps— veps+ veps— bnr+ bm ‘ cushr+ (:11. s In" Iins+ 1115" + lev‘ 8136+ size‘ turn+ turn— ret+ ref" 11* P" . Pr(+) PI-(—) [0g( P710) ) 109(W) 1717;8’10" 11/610719 1751671601151 115167110“? 1.: feS’Wt 11 felony 1151671611114 121.417.4111“ -1.262 -0.891 -1.110 -1.400 -1.349 -0.225 -1.253 -0.160 (0.100) (0.120) (0.087) (0.156) (0.100) (0.112) (0.093) (0.115) -0.369 -0.312 -0.247 -0.344 0.700 -0.190 -0.090 0.308 (0.086) (0.074) (0.071) (0.093) (0.089) (0.072) (0.079) (0.083) 0.346 0.324 0.442 0.255 -0.942 -0.436 -0.580 -0.366 (0.100) (0.085) (0.086) (0.097) (0.144) (0.095) (0.112) (0.110) 0.372 0.557 0.469 0.287 -1.167 -0.373 -0.738 -0.673 (0.075) (0.071) (0.064) (0.085) (0.090) (0.074) (0.079) (0.081) -0.058 0.054 —0.039 0.039 0.340 -0.263 -0.101 0.118 (0.077) (0.069) (0.062) (0.090) (0.080) (0.066) (0.068) (0.077) —0.132 -0.023 -0.028 -0.052 -0.079 -0.255 -0.198 0.013 (0.118) (0.074) (0.073) (0.127) (0.150) (0.077) (0.084) (0.127) 0.223 0.090 0.260 -0.052 0.037 -0.019 -0.390 0.196 (0.198) (0.079) (0.102) (0.108) (0.186) (0.071) (0.097) (0.100) 0.2412 0.154 0.050 0.487 0.148 -0.272 -0.303 0.201 (0.122) (0.074) (0.076) (0.114) (0.149) (0.077) (0.088) (0.118) —0.210 0.256 0.150 0.201 -0.372 -0.061 -0.102 -0.l25 (0.152) (0.075) (0.086) (0.104) (0.150) (0.069) (0.083) (0.101) -0.219 -0.259 -0.509 0.288 0.939 0.481 0.793 0.485 (0.141) (0.064) (0.072) (0.095) (0.120) (0.062) (0.071) (0.090) 0.554 0.355 0.261 0.932 —0.164 —0.152 0.079 0.109 (0.153) (0.098) (0.094) (0.176) (0.230) (0.130) (0.139) (0.216) 0.143 0.238 0.263 0.202 -0.517 -0.325 -0.232 -0.438 (0.111) (0.067) (0.071) (0.095) (0.128) (0.068) (0.077) (0.099) 0.038 0.069 0.131 0.045 -0.530 -0.060 -0.144 -0.208 (0.157) (0.079) (0.094) (0.109) (0.155) (0.072) (0.090) (0.101) 0.039 -0.079 -0.004 0.111 0.282 0.478 0.720 0.018 (0.149) (0.074) (0.078) (0.106) (0.122) (0.075) (0.080) (0.096) 0.800 0.785 0.874 0.728 -0.539 -0.306 0.073 -0.575 (0.108) (0.081) (0.075) (0.109) (0.142) (0.113) (0.112) (0.136) -0.114 -0.037 -0.092 0.043 1.211 0.244 0.650 0.679 (0.080) (0.074) (0.068) (0.084) (0.093) (0.082) (0.084) (0.090) 0.022 41.013 -0.122 0.166 -0.117 0.063 -0.109 0.404 (0.100) (0.106) (0.087) (0.143) (0.136) (0.125) (0.112) (0.153) -0.490 -0.272 -0.271 -0.433 0.142 -0.287 -0.180 -0.039 (0.072) (0.066) (0.061) (0.080) (0.073) (0.063) (0.066) (0.071) 0.629 0.330 0.572 0.252 0.027 0.064 0.159 -0.143 (0.068) (0.069) (0.058) (0.089) (0.083) (0.072) (0.069) (0.086) -0.629 -0.532 -0.577 -0.550 0.585 0.400 0.691 0.110 (0.118) (0.123) (0.096) (0.183) (0.089) (0.091) (0.082) (0.102) 0.785 0.554 0.658 0.865 -0.400 -0.256 -0.284 -0.555 (0.085) (0.093) (0.073) (0.135) (0.083) (0.083) (0.079) (0.092) 85 This table reports results of the regressions on estimated trend coefficients. The dependent variable is estimated value of the. trend coefficient. from first. stage time-series regressions. All numbers are. Table B.6. Regressions on trend coefficients scaled by 104. Model (1) includes the total sample and uses least squares regression. Model (2)((3)) includes only firms with positive (negative) significant (at 5 %) estimates of trend coefficient and uses T obit regression. Standard errors are given in parenthesis. Bold fase characters indicate significance at. 1 % level. Regressors intercept. 0.181 0.177 (0.033) (0.013) eps —0.847 -1.677 (0.922) (0.541) veps 3.131 2.143 (0.600) (0.478) 11111 0.448 0.775 (0.391) (0.328) eashr -1.559 -0.380 (2.689) (1.068) ins -7.082 -3.685 (1.287) (1.015) lev 3.582 4.572 (2.995) (1.978) size -2.858 -3.944 (0.726) (0.376) turn —1 . 108 -1.692 (2.197) (1.715) wt 89.901 3.796 (119.067) (74.649) p 23.032 0.187 (10.887) (0.097) Rn 1) 62.146 (32.121) (2) 0.417 0.398 -0.115 -0.093 (0.079) (0.034) (0.019) (0.011) 6.067 -1924 0.694 -0.648 (5.866) (1.923) (0.480) (0.240) 0.287 41.540 1.383 1.132 (4.057) (2.395) (0.414) (0.294) 0.063 0.047 0.441 0.414 (0.938) (0.496) (0.655) (0.331) —5.968 -2.408 3.214 0.618 (5.577) (2.251) (1.637) (1.267) 9890 -6.609 -2.571 -1.008 (5.883) (3.431) (1.105) (0.697) 4.887 6.658 2.083 -0.065 (8.825) (4.005) (1.742) (0.952) -6.330 -7.602 1.659 0.922 (1.725) (0.921) (0.331) (0.244) -26.082 -10.720 -5.064 -5.323 (22.849) (8.639) (1.287) (1.244) 235.431 64.751 10.205 29.374 (222.294) (107.976) (31.032) (49.320) 26.593 52.929 3.145 —7.457 (14.102) (14.228) (9.082) (5.650) 62.102 33.141 (16.157) (22.693) Figure B.1. : Market composition effect This figure plots market composition effect on average idiosyncratic risk. Irff is market average idiosyncratic risk computed using Fama and Hench monthly regressions, Irstr is market average idiosyncratic risk where risk of securities with a trend (positive or negative) is set equal to its starting value. 196.3 1965 1970 1975 1980 1985 1990 1995 2000 2005 Ir'ff — — - - Irs‘rr 87 Figure 8.2. : Market average risk with positive trends removed. This figure plots market composition effect when positive firm-level trend is removed. Irff is market average idiosyncratic risk computed using Fama and French monthly regressions, Irnop is market average idiosyncratic risk where risk of securities with a positive trend is set equal to its starting value. -5" i . , ? will) " l 1 : ' 1111 ' 1 ’ -6 I I ., 1 ‘ 1 101411. ‘-‘ 1 ,1» 1.11M 3 1 l {11 I ”1 1': i 51.1 -7 l '1’ .1 l 1‘ l ‘ I _ 1.57 ’ -81 1963 1965 19701975 1980 1985 1990 1995 2000 2005 irff ---- Irnop 88 Figure B3. : Market average risk with negative trends removed. This figure plots market composition effect when negative firm-level trend is removed. Irfl' is market average idiosyncratic risk computed using Fama and French monthly regressions, Irnon is market average idiosyncratic risk where risk of securities with a negative trend is set equal to its starting value. -5‘ -6. 1 ‘l 1 ‘ i -7. ’ ' 11 11‘ ‘ ll' [ Ii' '7 M“ \ 1 ‘ ' 71 I 1 i -8- 1963 1965 1970 1975 1980 1985 1990 1995 2000 2005 nr‘ff ————— mnon 89 Figure 34. : Idiosyncratic volatility of the NASDAQ firms This figure plots idiosyncratic volatility of the NASDAQ sample of sequrities. ..5‘ M ’I l 1 :1 . 1 11,111 "11'. 1% '1 1 1| 1‘1 [IUU‘ lg‘ ‘ —e 1' 1 11 1 .3 . 1 ‘ 1 .1? c ' 1 h) 1 1 1 w“ | . i All 15' l; A!) I 1 ‘l l _7— fi( 1') NRA ‘ 6i i 1. Ln,“ kl “I '1 |/\, 11 1“ 11; 1‘ l 1963 1965 1970 1975 1980 1985 1990 1995 2000 2005 Irff ---- irsfr‘ Figure B.5. : Idiosyncratic volatility of the non-NASDAQ firms This figure plots idiosyncratic volatility of the non—NASDAQ sample of sequrities. -51 -6* . , 1.1 1 ll 11) 'I 1 ’1‘1 111 - 1 I 11 1 1| 1. 1| 5 l l Ill ll 1* 5 ll “1 ‘1‘1 51 (1 ll _7« ,1 l 1 ll] 5 l l1 . ‘11 l) I l I :1“ ll 11 I 1“ 1 i! i 1 l 1. 1‘ . I "it, 1” ll\\’/v " I ‘ ' I 1‘ | , 1 ‘1‘1 8 11 (.f 1963 1965 1970 1975 1980 1985 1990 1995 2000 2005 mff ~--— "”511" ..1__. 90 Figure B.6. : Idiosyncratic volatility of the new firms This figure plots idiosyncratic volatility of the new firms in each month. 1963 1965 1970 1975 1980 1985 1990 1995 2000 2005 Figure 8.7. : Idiosyncratic volatility excluding new firms This figure plots idiosyncratic volatility excluding new firms in each month. -5— . . 1, (I I; I 1 lleill)1 full.“ I —e 1 1 1 1 1 1 1 1 1 11...»..11111 l 1 ’1‘ L l 111 . 1)?th '1 -7. ,1 (ll )4“ 1'1"." 111 11 L”? J (t 11,) . '.,~v.1"111‘.11=1‘*' 111111“ 1 1 V” —8 ‘1 1963 1965 1970 1975 1980 1985 1990 1995 2000 2005 91 Figure B.8. : This figure plots idiosyncratic volatility of thc firms first listed in January 1980. Idiosyncratic volatility of the 1980 firms -5- -6 . All; ‘5 l El Ill/[kl ”I l «l _ l * l|1| '1 I“ In. -7'- l ll'llnuni A l lililfi' “ll Ill 1 ' ’1 {4. lg? 3J1 AHA}! Al” 9" {V “I a“. ll ‘ l , l {W li'Wl [Vi/1 Mil/$1 '! l‘ I ‘xj'W 1963 1963 19701975 1980 1985 1990 1995 2000 2005 Figure B.9. : Institutional ownership This figurc plots average institutional owncrsliip sharc. /\ // i / ""V V o 20- \ f , > / \._// 015 1980 1985 1990 1995 2000 2005 92 APPENDIX C Tables and Figures for Essay 3 93 Tahle C21. Augmented Dickey-Fuller unit root tests This table reports results of Augmented Dickey-Fuller tests for main variables. All tests include four lags. other specifications provide similar results and are. available upon request. ('V are MacKinnon critical values are equal -3.50 for the 1% level and -2.89 for the 5% level. The null hypothesis is the unit root in the data. The data range. is 198021 - 20014. Variables AD F statistic INS -l.58 IRFF -2.28 Table C2. Rolling cointegration and VEC model estimates This table reports estimated coefficients on error correction term (EC‘T) in VECM for the relationship between institutional ownership (INS) and idiosyncratic risk (IRFF) rolled by one year. The last column contains Likelihood Ratio statistics for Johansen cointegration tests, for which critical values are 20.04 (1%) and 15.41 (5%) (except for the last line, for which the values are 35.65 and 29.68, respectively). t statistics are given in parentheses. ECT A INS A IRFF LR 1980:] — 19994 0.142 0.009 19.19** (-257) (2.47) 198121 - 20004 0.189 0.010 1731* (-225) (-157) 19821 - 2001:4 0.007 0.001 1555* (-140) (3.20) 1983:] - 20024 0.004 0.001 1649* (-1.16) (3.33) 198421 — 2003:.1 0.012 0.002 13.92 (1.07) (-279) 198.3:1 — 20011 0.080 0.009 12.27 (-150) (-235) 1 . 91 Table C3. VEC model for idiosyncratic risk and institutional ownership This table reports estimated VECM for the relationship between institutional ownership (INS) and idiosyncratic risk (IRFF) with a dummy variable included for observations 2000:2 - 2004z4. ECT is the error correction term. DV is the dependent variable. t statistics are given in parentheses. The data range is 19801 - 20044. DV A INS A IRFF Constant 0.000 -0.000 (0.30) (-0.34) ECT -0.016 0.001 (-2.52) (2.43) A INS* lagl -0.430 -0.000 (4.07) (0.04) A INS“ lag2 -0.065 -0.003 (-O.Gl) (-0.40) AIRFF lagl -2.491 -0.368 (-1.56) (—3.58) AIRFF lag2 0 562 -0.365 (0.36) (—3.66) R—squared 0.21 0.29 Figure C.1. : Idiosyncratic risk adjustments to shock in VECM This figure. plots changes of idiosyncratic volatility due to a single shock in the VECM of two variables (institutional ownership and idiosyncratic risk). 00008 00006 - 00004 — .00002 - 900000 Y'UIVVVUIVVYVIVVI' I'VI'IY'I'I"YYI'V‘UIY'YTI'YYIIII'Itfl'rl'vIII'V'I'l'V'V' 1 0 20 30 40 50 50 70 Figure C2. : Institutional ownership adjustments to shock in VECM This figure plots changes of institutional ownership due to a single shock in the VECM of two variables (institutional ownership and idiosyncratic risk). 0 0000 00002 .7 0 0004 s 0 0006 '1 0 0008 _ 0 0010 7" VII IIII 17" YI'I 77" ‘VYV "" 'r" 17" VVII II‘I "" I'I' 'YY' l' I I I I I I I l l I l 1 0 2'0 30 4'0 so 60 96 Figure C3. : Idiosyncratic volatility This figure. plots average idiosyncratic volatility (detrended) on U.S. market from 1963 till 2005. 0.004 0003 — 0.002 « 0 001 -1 0.000 W -0 001 u -0 .002 l 80""0'23""éli""éé"' 'é'e'i' "0'0 '"§'2'""éli""éé""éé"' 0'0" "0'2""011" Figure 04. : Institutional ownership This figure plots average institutional ownership share (detrended) on U.S. market. from 1963 till 2005. 0.08 004 ~ 002 ~ 0 00 . 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