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PAGE 1 Two Essays on Market Efficiency Tests of Idiosyncratic Risk: Informed Trading versus Noise and Arbitrage Risk, and Agen cy Costs and the Underlying Causes of Mispricing: Information Asymmetr y versus Conflict of Interests by Jung Chul Park A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Finance College of Business Administration University of South Florida Major Professor: Christos Pantzalis, Ph.D. J. Barry Lin, Ph.D. Ninon Sutton, Ph.D. Jianping Qi, Ph.D. Date of Approval: March 9, 2007 Keywords: Idiosyncratic volatility, Market efficiency, Noise trading, Arbitrage risk, Equity mispricing, Agency costs Copyright 2007, Jung Chul Park PAGE 2 Table of Contents List of Tables iii List of Figures iv Abstract v Essay 1 Tests of Idiosyncratic Risk: Informed Trading versus Noise and Arbitrage Risk 1 Introduction 1 Literature Review 4 Data and Measures 7 Measures of Idiosyncratic Volatility 7 Measures of Mispricing 14 Idiosyncratic Volatility and Equity Mispricing 19 Univariate Analyses 19 Multivariate Analyses 22 Robustness Tests 27 Interpretations and the Nonlinear Relationship 34 Measures of Firms Uncertainty 34 Measures of Shortselling Constraints 37 Analysis of Nonlinear Relation 40 Summary and Conclusions 45 Essay 2 Agency Costs and the Underlying Causes of Mispricing: Information Asymmetry versus Conflict of Interests 48 Introduction 48 Hypotheses Development 52 Data and Measures 59 Measures of Equity Mispricing 60 Measures of Agency Costs 71 Agency Costs and Equity Mispricing 77 Univariate Analyses 77 Multivariate Analyses 79 Robustness Tests 81 Interpretation of the Positive Relation between Agency Cost and Equity Mispricing 82 Summary and Conclusions 90 i PAGE 3 References 92 About the Author End Page ii PAGE 4 List of Tables Table 1 Variable Definitions 10 Table 2 Descriptive Statistics 13 Table 3 Correlations Coefficients between Mispricing Measures 19 Table 4 Univariate Tests 21 Table 5 Idiosyncratic Volatility and Equity Mispricing 25 Table 6 Robustness Checks of Regression of Equity Mispricing on Idiosyncratic Volatility 29 Table 7 Idiosyncratic Volatility and Informationbased Trading 33 Table 8 Firms with Very High Idiosyncratic Volatility 41 Table 9 Coefficient of Idiosyncratic Volatility and Inflation Point for Subsamples 43 Table 10 Variable Definitions 65 Table 11 Descriptive Statistics 68 Table 12 Correlations Coefficients between Index and Individual Measures 69 Table 13 Univariate Tests 78 Table 14 Agency Cost and Equity Mispricing 80 Table 15 Robustness Checks of Regression of Equity Mispricing on Agency Cost 83 Table 16 Different Effects of Agency Cost on Equity Mispricing 88 iii PAGE 5 List of Figures Figure 1 Empirical Design of Time Line for Idiosyncratic Volatility and Equity Mispricing Measurements 8 Figure 2 Timeseries of Idiosyncratic Volatility and Rsquare 14 Figure 3 Equity Mispricing by Idiosyncratic Volatility 22 Figure 4 Tests of Three Hypotheses and Evidence 44 Figure 5 Agency Costs, Fundamental Value, and Equity Mispricing 53 Figure 6 Comparisons of Equity Mispricing Levels 84 iv PAGE 6 Two Essays on Market Efficiency Tests of Idiosyncratic Risk: Informed Trading versus Noise and Arbitrage Risk, and Agency Costs and the Underlying Causes of Mispricing: Information Asymmetry versus Conflict of Interests Jung Chul Park ABSTRACT I examine the informational efficiency of stock markets by testing the relation between idiosyncratic volatility and equity mispricing. I find that the level of mispricing declines with idiosyncratic volatility consistent with the notion that greater levels of firmspecific risk reflect greater participation of informed traders in the market for the stock. However, I also find that mispricing increases with idiosyncratic volatility for highly volatile stocks, and this is attributed to both noise trading and arbitrage risk. In addition, I investigate the link between agency costs and equity mispricing, and whether it exists due to information asymmetry or the degree of conflict of interests between managers and shareholders. I provide evidence that the level of agency costs is positively related with mispricing. In contrast to previous studies claim that the information asymmetry level is a key determinant in the equity mispricing, I find that the conflict of interests is more important than information asymmetry in explaining equity mispricing. Furthermore, the evidence suggests that stock option grants, originally intended to resolve conflicts of interests, actually exaggerate this problem. v PAGE 7 Essay 1 Tests of Idiosyncratic Risk: Informed Trading versus Noise and Arbitrage Risk I. Introduction What does idiosyncratic volatility mean? In the context of asset pricing, idiosyncratic volatility measures the part of the variation in returns that cannot be explained by the particular asset pricing model used. Other than the stale econometric definition of idiosyncratic volatility, there is little consensus regarding the meaning of idiosyncratic risk in the context of market efficiency. The finance literature has argued that idiosyncratic volatility can reflect the capitalization of private information into prices, noise trading and/or costly arbitrage.1 This paper contributes to the finance literature by reconciling the different views on idiosyncratic risk. The goal of this study is to clearly distinguish if and when each of the three aforementioned views of idiosyncratic volatility is more appropriate. In order to achieve my goal, I investigate the relationship between equity mispricing and idiosyncratic risk and develop three hypotheses, one predicting a negative relationship between idiosyncratic volatility and mispricing, and the other two predicting a positive one. On one hand, the informed trading hypothesis regards idiosyncratic risk as a sign of active trading by informed arbitrageurs who trace firms fundamental value, and thus predicts that equity mispricing should be lower for high idiosyncratic risk firms. On the other hand, the noise trading hypothesis regards idiosyncratic risk as a sign of 1 For a description of the different views on idiosyncratic risk, see Roll (1988), Morck, Yeung and Yu (2000), Wurgler and Zhuravskaya (2002), Durnev, Morck and Zarowin (2003), Kelly (2005) and Pontiff (2005), among many others. 1 PAGE 8 uninformed traders noise trading which causes the stocks price to deviate from fundamental value, and thus predicts a positive relation between idiosyncratic risk and mispricing. The arbitrage risk hypothesis proposes that idiosyncratic risk reflects costs of arbitrage, and also predicts a positive relation. I test these hypotheses in an empirical framework that utilizes equity mispricing proxies based on several relative valuation measures, which are constructed as absolute deviations of a firms equity value from its fundamental value. When I estimate a linear regression model of the relation between mispricing and idiosyncratic volatility, I find that the level of mispricing declines in idiosyncratic risk, consistent with the informed trading hypothesis. However, both univariate tests as well as multivariate tests of models that include a secondorder idiosyncratic risk term provide strong evidence of a nonlinear, Ushaped relationship. Specifically, I find that the level of equity mispricing first decreases until a firmspecific risk (1 2 R ) approaches levels in excess of 90%, but then increases thereafter. The number of observations after the inflection point accounts for 10% of total firmyear observations. These findings suggest that in most cases (about 90% of total), idiosyncratic risk implies that informed trading leads to low equity mispricing. Moreover, the results also suggest that at extremely high idiosyncratic risk levels, noise trading and/or arbitrage risk are causing prices to deviate from fundamentals. To establish if only one of the two or both factors (i.e., noise trading and/or arbitrage risk) are reflected in the right arm of the Ushaped curve that empirically describes the relationship between mispricing and idiosyncratic volatility, I reexamine the relationship for subsamples constructed by classifying firms on firmlevel 2 PAGE 9 uncertainty and shortselling constraints measures. Assuming that the proportion of noise traders increases with the firms informational uncertainty (see Black (1986)), I employ a composite measure of uncertainty to sort firms into subsamples that are (are not) dominated by noise traders. Furthermore, assuming that, in the absence of constraints to shortsales, informed investors have more and better opportunities to engage in arbitrage, I sort on measures of shortselling constraints to construct subsamples of firms that are (are not) affected by arbitrage risk. The test results reveal that the nonlinear, Ushaped relationship between mispricing and IV remains significant for subsamples of firms that display low levels of either noise trading or arbitrage risk. The nonlinear relationship collapses to a linear one for the subsample containing firms that are classified as having both a less uncertain information environment and low shortselling constraints. In this subsample, equity mispricing is monotonically decreasing in idiosyncratic volatility. This evidence is consistent with the notion that the increase in mispricing associated with high idiosyncratic risk levels (i.e., highly volatile stocks) reflects both noise trading and arbitrage risk. Therefore, based on my findings, I conclude that idiosyncratic volatility in stock returns may primarily reflect informational market efficiency, but extremely high levels of idiosyncratic risk are associated with noise traders frenzy and limits to arbitrage (i.e., arbitrage risk). The rest of the paper is organized as follows. In the next section, I review related literature and prior findings and present the testable hypotheses. Section III describes the data selection process and the measures of idiosyncratic volatility and equity mispricing. 3 PAGE 10 Section IV explains the empirical methodologies, and reports univariate and multivariate test results. Section V contains additional tests and provides a more detailed investigation of the nature of the nonlinear relation between idiosyncratic volatility and mispricing. The last section includes a summary and concluding remarks. II. Literature Review Roll (1988) points out that U.S. firms display low Rsquares for common asset pricing models; the average Rsquare is about 20% for daily returns models and about 35% when monthly returns are used. In the conclusion (p. 564) of his article, Roll proposes that this evidence seems to imply the existence of either private information or else occasional frenzy unrelated to concrete information. Using crosscountry data, Morck, Yeung, and Yu (2000) find that stocks in countries with stronger property rights have higher idiosyncratic volatility. They argue that strong property rights promote informed arbitrage, leading to more firmspecific information and thus high idiosyncratic volatility. Durnev, Yeung and Zarowin (2003) find that firms and industries with greater idiosyncratic volatility display greater stock price informativeness. They define informativeness as the amount of information stock prices contain about future earnings, which they estimate from a regression of current stock returns against future earnings changes. They argue that if idiosyncratic volatility reflects the capitalization of private information into prices, high idiosyncratic volatility is a sign of active trading by informed arbitrageurs and implies that the stock price is tracking its fundamental value closely. In addition, Jin and Myers (2006) in a study involving stock returns from 40 4 PAGE 11 countries over the 19902001 period test whether limited information (lack of transparency) can affect the division of risk bearing between inside managers and outside investors. They provide evidence consistent with the notion that if a firm is less transparent, insiders will be able to capture more firmspecific risk. Greater opaqueness leads to lower amounts of firmspecific risk absorbed by outside investors and therefore to lower levels of idiosyncratic volatility, i.e. high levels of Rsquare. In this context, outside investors have limited ability to evaluate changes in cash flows, and consequently their evaluation on equity value will be less accurate. Based on the above, the informed trading hypothesis predicts that idiosyncratic volatility and mispricing are negatively related because high idiosyncratic risk levels are associated with greater trading by informed arbitrageurs who trace firms fundamental value. On the other hand, in line with Rolls alternative interpretation of idiosyncratic volatility as occasional frenzy, idiosyncratic volatility can reflect noise trading. For example, Bhagat, Marr, and Thompson (1985) show that firms with higher equity issuing costs have higher firmspecific daily stock return volatility, which is a proxy for asymmetric information between firm insiders and outsiders. Krishnaswami and Subramaniam (1999) use idiosyncratic volatility as one of measures of information asymmetry and find that firms engage in spinoffs to reduce information asymmetry. Kelly (2005) provides evidence that a low market model Rsquare (high idiosyncratic volatility) is indicative of a poor information environment with greater impediments to informed trade. If idiosyncratic volatility reflects greater impediments to informed trades 5 PAGE 12 and/or informational asymmetry, then it should be associated with noise trading. In this view, named the noise trading hypothesis, it is predicted that the relationship of idiosyncratic volatility and mispricing is positive because in the presence of noise trading stock prices will deviate from fundamental value. In addition to the informed trading and noise trading interpretations of idiosyncratic risk, many authors share the view that idiosyncratic risk reflects risk related to costly arbitrage.2 For example, Pontiff (2005) points out that arbitrageurs are averse to trading when firms are idiosyncratic. This limit of arbitrage opportunity is also addressed by Shleifer and Vishny (1997), Gromb and Vayanos (2002) and Chen, Hong, and Stein (2002), who provide a possible explanation for persistent mispricing. In particular, Shleifer and Vishny (1997) argue that any systematic mispricing could not be quickly and completely traded away if arbitrage costs exceed arbitrage benefits. Systematic mispricing may epitomize arbitrageurs limit of opportunity to perfectly hedge fundamental risk in their portfolios. Therefore, the prediction of the arbitrage risk hypothesis is that the mispricing of high arbitrage risk stocks should be higher than the mispricing of low arbitrage risk stocks. In sum, the informed trading hypothesis predicts a negative relation between idiosyncratic volatility and equity mispricing, while the other two hypotheses (the noise trading hypothesis and the arbitrage risk hypothesis) predict a positive relation. 2 See, for example, (e.g., Wurgler and Zhuravskaya (2002), Ali, Hwang and Trombley (2003), Pontiff and Schill (2003), Mendenhall (2004), and Mashruwala, Rajgopal, and Shelvin (2005)). 6 PAGE 13 III. Data and Measures I extract return data from the Center for Research in Securities Prices (CRSP) where NYSE, AMEX, and Nasdaq stocks are listed. The initial sample includes all firms in CRSP from 1980 to 2004, omitting financial (SIC 60006999) and utility (SIC 49004999) firms. I also exclude firms if their industry affiliation is not clear (i.e., SIC codes are missing). For the measure of idiosyncratic volatility, I use weekly stock returns. The choice of a weekly data is a compromise solution to the twin problems associated with a) the relatively low number of monthly observations, and b) the missing observations from nontrading occurrences in daily data (see Conrad and Kaul (1988)). Following Durnev et al. (2003 and 2004), I drop firms if they do not have complete return data over 52 weeks in a year to avoid problems associated with firms that experience IPOs, delisting, or trading halts. Accounting and financial data are drawn from COMPUSTAT. Firms with market value of equity less than $20 million are excluded in order to avoid cases of firms with distorted valuation multiples used in the construction of the mispricing measures. These requirements result in a final sample that includes 6,956 firms with 44,639 firmyear observations covering the 25 year period from 1980 to 2004. A. Measures of Idiosyncratic Volatility I estimate Rsquare and idiosyncratic volatility variables for each stock for each calendar year using weekly data to regress stock returns on the returns of the market 7 PAGE 14 index.3 Figure 1 illustrates how idiosyncratic volatility variables are measured using a time line. Figure 1 Empirical Design of Time Line for Idiosyncratic Volatility and Equity Mispricing Measurements The above time line illustrates the methods used to compute idiosyncratic volatility measures and equity mispricing measures. Idiosyncratic volatility measures are computed using 52 weekly returns over each year t. Equity mispricing measures are computed at the mid time of each year (i.e., at the end of June in each year t). Mispricing variables (EXVRI, EXVBO, EXVRK, EXVMB, and MI) are measured at the end of June in year t Jan Feb Ma r A pr Ma y Jun Jul Aug Se p Oc t N ov Dec Year t Idiosyncratic volatility variables ( 2 R 2e 22e and ) are measured using 52 weekly returns over year t The regression model estimated for each stock i in year t is as follows: ri,w,t = i,t + i,t rm,w,t + ei,w,t, (1) where ri,w,t is the excess return for stock i on week w in year t, and rm,w,t is the valueweighted excess market index return on the week w in year t. From this regression equation, the idiosyncratic variance is defined as 2222,,,,()ietitimtmt where 2,it = 3 In the robustness tests (Table 6), I also use idiosyncratic volatilities obtained from regressions of stock returns on returns of the market index and industry indices, or alternatively, on the three Fama and French factors. 8 PAGE 15 92,mt Var(ri,w,t), = Var(rm,w,t), and im,t = Cov(ri,w,t, rm,w,t). I compute each stocks relative idiosyncratic volatility (i.e., the ratio of idiosyncratic volatility to total volatility), 22,,ietit 2,itR or equivalently 1 for each year t. The relative idiosyncratic volatility is transformed to a logistic version as follows. 22,,,222,,,1lnlnitietitititietRR (2) Logistic relative idiosyncratic volatility (i,t) measures the ratio of unexplained variance to explained variance.4 Table 1 describes the Rsquare and idiosyncratic volatility variables, and Table 2 presents descriptive statistics for theses measures over the sample period, 1980 to 2004. I estimate volatility within each sample year t, yielding 44,639 firmyear observations. The average Rsquare is about 0.152 which is very similar to that shown in other studies (e.g., 0.152 in Kelly (2005)) but lower than the average Rsquares of 0.20 and 0.35 computed from daily and monthly returns, respectively, reported in Roll (1988). This relatively low average Rsquare for my sample is consistent with the increase in idiosyncratic volatility observed over the recent years and reported in Campbell, Lettau, Malkiel, and Xu (2001). In my sample, idiosyncratic volatility on average represents about 85% of total individual stock volatility, in line with Ferreira and Laux (2007) who also report an 85% average relative idiosyncratic volatility. 4 In addition to logistic relative idiosyncratic volatility ( ,it or 2,22,,ietitiet2,iet ln), I use idiosyncratic volatility ( ) and relative idiosyncratic volatility ( 22,,ietit ). All results in univariate and multivariate tests show consistent patterns. PAGE 16 Table 1 Variable Definitions Variables Descriptions Idiosyncratic volatility measures 2 R Rsquare measured using a regression of stock returns on the returns of the market index, ri,w,t = i,t + i,t rm,w,t + ei,w,t, where ri,w,t is the excess return for stock i on week w in year t, and rm,w,t is the valueweighted excess market index return on the week w in year t. 2e Idiosyncratic volatility. From the regression, ri,w,t = i,t + i,t rm,w,t + ei,w,t, idiosyncratic variance is defined as 2222,,, ,, where ()ietitimtmt 2,it = Var(ri,w,t), 2,mt = Var(rm,w,t), and im,t = Cov(ri,w,t, rm,w,t). 22e Relative idiosyncratic volatility which is the ratio of idiosyncratic volatility to total volatility, 2 2, ,ietit or equivalently 1 2,it R Logistic relative idiosyncratic volatility. 22,,,222,,,1lnlnitietitititietRR Mispricing measures EXVRI Absolute value of excess value based on Ohlsons (1995) residual income value approach. EXVRIit ln()ititPRICEIV ,where PRICEit is the stock price at the end of June of each year from CRSP, and I(V)it is intrinsic value using the residual income model (Ohlson (1995)) and median values of analysts forecasts issued in June, as in Frankel and Lee (1998). [/(ititCPTLICPTL EXVBO Absolute value of excess value based on Berger and Ofek (1995) approach. EXVBOi,t ,)], where CPTLi,t is total capital, which is market value of equity plus book value of debt, I(CPTLi,t) is the imputed value derived as the product of firm sales and the median capital to size ratio in the firms industry. The industry classification here is based on the FamaFrench 48 sectors. This measure of mispricing is constructed in a similar fashion as the first one (EXVRIi,t), but uses firms total capital instead of price and computes imputed value based on FamaFrench 48 industry classification. Thus the intrinsic value here is a size and industry benchmark. EXVRK Absolute value of the excess value based on RhodesKropf et al. (2005). Fundamental value, V is estimated by decomposing the markettobook into two components: a measure of price to fundamentals (ln(M/V)), and a measure of fundamentals to book value (ln(V/B)). The first component captures the part of booktomarket associated with mispricing. This component is further decomposed into firmspecific and industryspecific misprising. I use the firmspecific mispricing component based on Model III of RhodesKropf et al. (2005) that also accounts for net income and leverage effects. ln(Mi,t)= 0j,t + 1j,t ln(Bi,t)+ 2j,t ln(NI)+i,t + 3j,t I(<0)ln(NI)+i,t + 4j,t ln(LEVi,t)+ i,t, where M is firm value, B is book value, NI+ is absolute value of net income, I(<0)ln(NI)+ is an indicator function for negative net income observations, and LEV is the leverage ratio. EXVMB Absolute value of the industryadjusted markettobook ratio. MBIAi,t , ln[()]MBMedMB itjt where, MBi,t is the market to book ratio for firm i at time t, and Med(MBj,t) is the jth industry median of MBt. MI Mispricing index which is constructed each year for each observation i = 1,,N as: where Rankk(EXVi,k) is the rank function which assigns a rank for each observation from least misvalued (rank of one) to most misvalued (rank of N). EXVi,k is the kth measure of mispricing for firm i in my sample, and K represents the dimensions of mispricing measures. The denominator, K, averages the ranks by the number of mispricing values available for each firm in the sample in a particular year. Finally, dividing by N, I scale the MI from 0 (least mispriced) to 1 (most mispriced). ,(1/)(1/)()KikikkMINKRANKEXV 10 PAGE 17 Table 1 (Continued) Variables Descriptions Informativeness measure PIN Annual probability of informationbased trading of Easley et al. (1996a, 1996b, 1997a, 1997b, 2002, 2005). /() s bPIN where is the probability and information event occurs, is the arrival rate of informed trades, and s and b are the arrival rates of uninformed sells and buys respectively. is the expected arrive rate of informed trades and s b is the arrival rate for all orders. Uncertainty measures EQ1 The first measure of earnings quality. Absolute value of firmspecific residuals from a FamaFrench 48 annual industry regression of total accruals on the reciprocal of total assets, sales growth, and fixed assets. ,,123 ,1TACCRPPESALES ,,,,ititiitit1it1it1it1kkkTATATATA where TACCRi,t ,)= firm is total accruals in year t, = change in current assets between year t1 and year t, = change in current liabilities between year t1 and year t, (itititititCACLCASHSTDEBTDEPN ,,,, ,itCA ,itCL ,itCASH = change in cash between year t1 and year t, ,itSTDEBT = change in debt in current liabilities between year t1 and t, = depreciation and amortization expense in year t, ,itDEPN iSALES = change in sales between year t1 and t, = property, plant, and equipment in year t, and = total assets in year t1. ,itPPE ,it1TA EQ2 The second measure of earnings quality. Absolute value of firmspecific residuals from a FamaFrench 48 annual industry regression of total accruals on lagged, contemporaneous, and leading cash flow from operations. ,,,,0123 ,TACCRCFOCFOCFO itit1itit+1itiiiikkkkTATATATA where CFOi,t is firm is cash flow from operations in year t and computed as net income before extraordinary items minus total accruals. All variables are scaled by average total assets (TAi). AFE Analyst earnings forecast error. , ,, ()/()ititi,t+1itMedAFEPSMedAF AFE where forecast error, Med(AF)i,t EPSi,t+1, is the absolute value of the difference between the median forecast (Med(AF)i,t) and the actual earnings per share (EPSi,t+1). AFD Analyst earnings forecast dispersion. , ,, ../ititit ()()AFDStdDevAFMedAF where Std.Dev.(AF)i,t is standard deviation of one year ahead forecasts. UI Firm uncertainty index. UI is computed each year for each observation i = 1,,N as: where Rankk(UNCERi,k) is the rank function which assigns a rank for each observation from least uncertain (rank of one) to most uncertain (rank of N). UNCERi,k is the kth measure of uncertainty for firm i in my sample, and K represents the dimensions of uncertainty measures (EQ1, EQ2, AFE, and AFD). The denominator, K, averages the ranks by the number of uncertainty values available for each firm in the sample in a particular year. Finally, dividing by N, I scale the TI from 0 (least uncertain) to 1 (most uncertain). ,(1/)(1/)()KikikkUINKRANKUNCER 11 PAGE 18 12 Table 1 (Continued) Variables Descriptions Shortselling constraint measures SIZE Log of total assets. INSTP Institutional ownership. Percentage of shares held by institutions. SI Shortselling constraint index. SI is constructed each year for each observation i = 1,,N as: where Rankk(SHORTi,k) is the rank function which assigns a rank for each observation from the lowest shortsale constraint (rank of one) to the highest shortsale constraint (rank of N). SHORTi,k is the inverse value of kth measure of shortsale constraint for firm i in my sample, and K represents the dimensions of shortsale constraint measures (SIZE and INSTP). The denominator, K, averages the ranks by the number of shortsale constraint values available for each firm in the sample in a particular year. Finally, dividing by N, I scale the SI from 0 (lowest shortsale constraint) to 1 (highest shortsale constraint). ,(1/)(1/)()KikikkSINKRANKSHORT Firm characteristics LEV Leverage. The ratio of longterm debt to total assets. ROA Return on assets. The ratio of net income to total assets. AGE Firm age. AGE = ln(1+ age), where age is the number of years since the stock inclusion in the CRSP database. DIVER Diversification dummy that equals one if a firm operates in multisegments and zero otherwise. DD Dividendpayer dummy that equals one if a firm pays dividends and zero otherwise. PAGE 19 Table 2 Descriptive Statistics Reported are descriptive statistics for my sample firms. The sample contains 44,639 firmyear observations (6,956 firms) over the period 1980 2004. All variables are as defined in Table 1. Variables N Mean Std.Dev. 5% Median 95% Idiosyncratic volatility measures Rsquare ( 2 R ) 44,639 0.152 0.139 0.002 0.113 0.434 Idiosyncratic volatility ( 2 e ) 44,639 0.004 0.013 0.001 0.003 0.013 Relative idiosyncratic volatility ( 22 e ) 44,639 0.848 0.139 0.566 0.887 0.998 Logistic relative idiosyncratic volatility ( ) 44,639 2.476 1.933 0.266 2.059 6.159 Mispricing measures Ohlson (1995) approach (EXVRI) 41,163 0.762 0.863 0.068 0.638 1.853 Berger and Ofek (1995) approach (EXVBO) 44,433 0.627 0.595 0.035 0.476 1.705 RhodesKropf et al. (2005) approach (EXVRK) 44,637 0.369 0.345 0.024 0.275 1.047 Industryadjusted markettobook ratio (EXVMB) 44,639 0.390 0.370 0.017 0.288 1.125 Mispricing index (MI) 44,639 0.502 0.189 0.216 0.485 0.847 Informativeness measure Probability of informationbased trading (PIN) 16,670 0.182 0.059 0.097 0.178 0.286 Uncertainty measures Francis et al. (2005) (EQ1) 33,314 0.332 0.593 0.014 0.166 1.082 Dechow and Dichev (2002) (EQ2) 28,879 0.170 0.565 0.012 0.111 0.469 Analyst earnings forecast error (AFE) 39,345 0.837 6.120 0.006 0.133 2.637 Analyst earnings forecast dispersion (AFD) 38,235 0.228 1.399 0 0.050 0.714 Uncertainty index (UI) 43,747 0.503 0.207 0.173 0.494 0.865 Shortselling constraint measures Firm size (SIZE) 44,639 19.74 1.658 17.36 19.54 22.77 Institutional ownership (INSTP) 30,399 0.503 0.244 0.093 0.512 0.892 Shortselling constraint index (SI) 44,639 0.507 0.260 0.107 0.496 0.929 Firm characteristics Leverage (LEV) 44,497 0.169 0.180 0 0.113 0.549 Return on assets (ROA) 44,639 0.035 0.115 0.162 0.052 0.160 Firm age (AGE) 44,639 2.362 0.815 1.099 2.398 3.526 Diversification dummy (DIVER) 35,729 0.345 0.475 0 0 1 Dividendpayer dummy (DD) 42,942 0.432 0.495 0 0 1 Next, to verify what Campbell et al. (2001) document as a secular decline in Rsquares in the U.S. market from 1960 to 1997, I compute annual average Rsquare and (logistic transformed) idiosyncratic volatility ( t ) and analyze the time trend by plotting them by year. Figure 2 shows clearly that annual average idiosyncratic volatility increases and equivalently annual average Rsquare declines. To verify this trend statistically, I run the simple regression of annual average t on year, and find that the 13 PAGE 20 coefficient of YEAR is 0.037 with tstatistic of 1.70. Abnormally high average Rsquare observed for 1987 can be attributed to the market crash in October 1987. Figure 2 Timeseries of Idiosyncratic Volatility and Rsquare This figure presents averages of annualized logistic relative idiosyncratic volatility ( t ) and Rsquare for the period from 1980 to 2004. The timeseries relation is computed as the regression of t on calendar year. The coefficient of YEAR is 0.037 with tstatistic of 1.70. 0123451980198119821983198419851986198719881989199019911992199319941995199619971998199920002001200220032004YearVolatility00.10.20.30.4Rsqure Logistic relative idiosyncratic volatility Rsquare t = 72.059 + 0.037 YEAR + t B. Measures of Mispricing Firm mispricing is measured as the deviation of a firms equity value from its intrinsic or fundamental value. I employ five alternative mispricing measures. The first four measures employ alternative techniques in estimating intrinsic value benchmarks, 14 PAGE 21 while the last one is an index that combines all individual measures. The mispricing measures are: 1) EXVRIi,t, the absolute value of the natural logarithm of the ratio between the stock price and its intrinsic value obtained from Ohlsons (1995) residual income valuation model. EXVRI is computed at the end of June of each year. EXVRIi,t ,,ln()ititPRICEIV (3) where PRICEi,t is the CRSP stock price at the end of June of each year, and I(V)i,t is the intrinsic value using the residual income model (Ohlson (1995)) with median values of analysts forecasts issued in June, as was done in Frankel and Lee (1998). There is strong empirical evidence in support of the residual income valuation ratio, V/P, as an indicator of mispricing.5 2) EXVBOi,t, the absolute excess value computed at the end of June of each year as the natural logarithm of the ratio between a firms capital and its imputed value, based on the Berger and Ofek (1995) approach. EXVBOi,t ,,ln()ititCPTLICPTL (4) where CPTLi,t is total capital, which is market value of equity plus book value of debt, I(CPTLi,t) is the imputed value derived as the product of firm sales and the 5 Lee, Myers and Swaminathan (1999) report that V/P predicts onemonthahead returns on the Dow 30 stocks better than aggregate booktomarket. Frankel and Lee (1998) also show that the residual income value is a better predictor than book value of the crosssection of contemporaneous stock prices, and that V/P is a predictor of the oneyearahead crosssection of returns. In addition, Ali et al. (2003) show that after controlling for several possible risk factors, V/P continues to significantly predict future returns. DMello and Shroff (2000) apply V/P to measure mispricing of equity repurchases, and Dong, Hirshleifer, Richardson, and Teoh (2006) to takeovers. 15 PAGE 22 median capital to sales ratio in the firms primary industry. The industry classification here is based on the FamaFrench 48 sectors. This measure of mispricing is constructed in a similar fashion as the first one (EXVRIi,t), but uses firms total capital instead of price and computes imputed value based on FamaFrench 48 industry classification. 3) EXVRKi,t, the absolute value of the firmspecific component of the difference between market value and fundamental value, based on the procedure outlined in RhodesKropf, Robinson, and Viswanathan (2005). This procedure differs from the residual income valuation approach in the sense that it does not rely on analysts earnings forecasts. According to RhodesKropf et al. (2005), fundamental value, V is estimated by decomposing the markettobook into two components: a measure of price to fundamentals (ln(M/V)), and a measure of fundamentals to book value (ln(V/B)). The first component captures the part of booktomarket associated with mispricing. In extreme cases where markets perfectly price stocks, this component would be equal to zero, otherwise positive (overvaluation) or negative (undervaluation). This component is further decomposed into firmspecific and industryspecific misprising. In my tests, I use the firmspecific mispricing component based on Model III of RhodesKropf et al. (2005) that also accounts for net income and leverage effects. ln(Mi,t) = 0j,t + 1j,t ln(Bi,t) + 2j,t ln(NI)+i,t + 3j,t I(<0)ln(NI)+i,t + 4j,t ln(LEVi,t) + i,t (5) 16 PAGE 23 where M is firm value, B is book value, NI+ is absolute value of net income, I(<0)ln(NI)+ is an indicator function for negative net income observations, and LEV is the leverage ratio. 4) MBIAi,t, the absolute value of the industryadjusted markettobook ratio. MBIAi,t ,,ln()itjtMBMedMB (6) where, MBi,t is the market to book ratio for firm i at time t, and Med(MBj,t) is the jth industry median of MBt. Several empirical studies have utilized MB as a mispricing measure (see, among others, Walkling and Edmister (1985), Rau and Vermaelen (1998) and Ikenberry, Lakonishok and Vermaelen (1995)). However, as RhodesKropf et al. (2005) point out, the market to book ratio can be viewed as not only a proxy for misvaluation but also as a measure of future growth opportunities and managerial ability. 5) MIi,t, a mispricing index (MI) that combines all four mispricing measures described above.6 The mispricing index (MI) is constructed each year for each observation i = 1,,N as: ,11()KikkMIRANKEXVNK ik (7) where Rankk(EXVi,k) is the rank function which assigns a rank for each observation from least misvalued (rank of one) to most misvalued (rank of N). EXVi,k is the kth measure of mispricing for firm i in the sample, and K represents the dimensions of 6 In constructing MI, I employ the methodology outlined in Butler, Grullon, and Weston (2005). In their paper, they create a liquidity index that aggregates the rankings of six different liquidity measures. 17 PAGE 24 mispricing measures. The denominator, K, averages the ranks by the number of mispricing values available for each firm in the sample in a particular year. For example, the sum of the Rankk(EXVi,k) values of a firm that has only three mispricing measures is divided by K=3. Finally, dividing by N, I scale the MI from zero (least mispriced) to one (most mispriced). I argue that, since it is computed as the average of all available ranks from four different mispricing measures, MI provides a more complete picture of mispricing. Variable definitions and summary statistics for all measures are reported in Table 1 and Table 2, respectively. Table 3 shows the coefficients of correlations between the different mispricing measures. As expected, all measures are positively correlated. The correlations are significant at the one percent level or better, despite the fact that these valuation measures are based on widely different theoretical concepts, measurement constructions and accounting/financial variables. I also find that generally individual mispricing measures are more significantly correlated with the mispricing index (MI) than with the other individual measures. This suggests that MI balances out the effects and shortcomings of the individual mispricing measures, while aggregating their informativeness. Therefore, MI is an appropriate aggregate measure of mispricing for use in the tests. For the most part, in this paper I present results based on MI for the sake of brevity. However, results obtained using the individual mispricing measures are qualitatively similar to those using MI. 18 PAGE 25 Table 3 Correlations Coefficients between Mispricing Measures This table shows the correlations coefficients between the mispricing measures, EXVRI, EXVBO, EXVRK, MBIA, and MI. The corresponding pvalues are reported in brackets. All variables are as defined in Table 1. *** indicates significance at the 1%level. Mispricing index (MI) Ohlson (1995) approach (EXVRI) Berger and Ofek (1995) approach (EXVBO) RhodesKropf et al. (2005) approach (EXVRK) Ohlson (1995) approach (EXVRI) 0.319*** [0.000] Berger and Ofek (1995) approach (EXVBO) 0.523*** [0.000] 0.083*** [0.000] RhodesKropf et al. (2005) approach (EXVRK) 0.713*** [0.000] 0.174*** [0.000] 0.252*** [0.000] Industryadjusted markettobook ratio (EXVMB) 0.736*** [0.000] 0.141*** [0.000] 0.300*** [0.000] 0.746*** [0.000] IV. Idiosyncratic Volatility and Equity Mispricing This section contains univariate analyses, a description of how I designed the empirical methodology, and regression evidence on the relation between idiosyncratic volatility and equity mispricing. A. Univariate Analyses Table 4 illustrates how high idiosyncratic risk firms differ from low idiosyncratic risk firms in terms of firm characteristics. It reports mean values of all variables used in the study for the quartile groups classified on the level of idiosyncratic volatility (). Also reported are the mean differences between the two extreme groups (highest versus lowest quartiles) and the corresponding tstatistics for the mean difference tests. The 19 PAGE 26 20 pattern of mean MI values across quartiles is not consistent with a monotonic relation between MI and Average MI decreases in the first three subsamples, Q1 through Q3, but finally increases in the qua rtile consisting of the highest idiosyncratic risk firms, Q4. This nonlinear, Ushape relation is also shown in Figure 3. The evidence from the remaining variables is consistent with prior studies examining the relationship of firm char acteristics and idiosyncratic risk. High idiosyncratic volatility firms are associated with high probability of informationbased trading and greater uncerta inty. In addition, high firms have greater leverage and lower ROA, are younger, less diversified and le ss likely to pay di vidends than low firms. Moreover, idiosyncratic volatility is higher wh en shortselling constraints become more binding, consistent with the no tion that idiosyncratic volati lity captures arbitrage risk. PAGE 27 21 Table 4 Univariate Tests Reported are mean values of variables for the quartile subsamples sorted on the logistic relative idiosyncratic volatility ( ). Also reported are the differences in mean values between highand lowfirms and the corresponding tstatistics. All variables are as defined in Table 1. *** indicates significance at the 1%level. Sorted on the logistic relative idiosyncratic volatility ( ) Low Q1 Q2 Q3 High Q4 Mean diff.: High Low tstat: Diff.=0 Mispricing measures Ohlson (1995) approach (EXVRI) 0.785 0.749 0.744 0.770 0.015 1.16 Berger and Ofek (1995) approach (EXVBO) 0.636 0.621 0.619 0.631 0.004 0.55 RhodesKropf et al. (2005) approach (EXVRK) 0.403 0.369 0.352 0.352 0.051*** 10.72 Industryadjusted markettobook ratio (EXVMB) 0.416 0.391 0.376 0.376 0.040*** 7.85 Mispricing index (MI) 0.513 0.499 0.495 0.499 0.014*** 5.55 Informativeness measure Probability of informationbased trading (PIN) 0.163 0.183 0.192 0.204 0.041*** 32.98 Uncertainty measures Francis et al. (2005) (EQ1) 0.323 0.340 0.344 0.323 0.0002 0.02 Dechow and Dichev (2002) (EQ2) 0.175 0.175 0.165 0.165 0.010 0.83 Analyst earnings forecast error (AFE) 0.500 0.683 0.862 1.322 0.822*** 7.57 Analyst earnings forecast dispersion (AFD) 0.147 0.208 0.258 0.319 0.172*** 8.15 Uncertainty index (UI) 0.464 0.499 0.515 0.535 0.071*** 25.64 Shortselling constraint measures Firm size (SIZE) 20.67 19.82 19.40 19.06 1.608*** 76.39 Institutional ownership (INSTP) 0.579 0.527 0.473 0.422 0.156*** 41.66 Shortselling constraint index (SI) 0.368 0.482 0.556 0.624 0.256*** 80.50 Firm characteristics Leverage (LEV) 0.146 0.161 0.176 0.192 0.046*** 19.19 Return on assets (ROA) 0.054 0.039 0.028 0.020 0.035*** 23.82 Firm age (AGE) 2.602 2.381 2.268 2.196 0.406*** 38.12 Diversification dummy (DIVER) 0.416 0.343 0.321 0.301 0.114*** 16.00 Dividendpayer dummy (DD) 0.556 0.442 0.389 0.338 0.218*** 32.92 PAGE 28 Figure 3 Equity Mispricing by Idiosyncratic Volatility This figure presents averages of mispricing index (MI) for the quintile subsamples sorted on the logistic relative idiosyncratic volatility ( ). 0.5140.5040.4950.4980.4980.480.490.500.510.52LowQ2Q3Q4HighLogistic relative idiosyncratic volatility B. Multivariate Analyses Univariate tests can only provide limited, preliminary evidence on whether equity mispricing has truly a nonlinear relationship with idiosyncratic volatility because a pattern could disappear after controlling for other factors that affect idiosyncratic volatility. Therefore, more tests in a multivariate setting are necessary to uncover the true relationship between mispricing and idiosyncratic volatility. I use the timeseries average 22 PAGE 29 of crosssectional annual regressions as outlined in Fama and MacBeth (1973) and estimate the following model:7 MIit = 0 + 1 it + 2 SIZEit + 3 LEVit + 4 ROAit + 5 AGEit + 6 DIVERit + 7 DDit + it, (8) where i indexes firms, t is a yearly time index, and it is a logistic transformation of relative idiosyncratic volatility. The control variables are market capitalization (SIZE), leverage (LEV), profitability (ROA), firm age (AGE), a diversification dummy (DIVER), and a dividendpayer dummy (DD). Descriptions of all variables can be found in Table 1 and descriptive statistics in Table 2. To examine whether there is a nonlinear relation between idiosyncratic risk and mispricing, I include the secondorder idiosyncratic volatility ( 2it ) in the model, resulting in the following equation. MIit = 0 + 1 it + 2 2it + 3 SIZEit + 4 LEVit + 5 ROAit + 6 AGEit + 7 DIVERit + 8 DDit + it. (9) If the pattern observed in the univariate tests persists, the regression will show the significantly negative sign for the coefficient of firstorder idiosyncratic volatility, 1, and positive sign for the coefficient of secondorder, 2. If I find that 1 is significant and negative but 2 is insignificant, then my tests would lend support to the informed trading hypothesis only. 7 Following Fama and MacBeth (1973), I estimate separate annual regressions and calculate tstatistics as follows. ()()1jjjtsn where j is the mean coefficient over the sample years, () j s is the standard deviation of the yearly estimates, and n is the number of years. 23 PAGE 30 The results of the multivariate tests appear in Table 5. In Panel A, I report results of regressions using the mispricing index (MI, columns [1] and [2]) and the logistictransformed mispricing index (columns [3] and[4]) as dependent variables.8 In Panel B, I show regression results using the four individual mispricing measures as dependent variables. The results in Panel A show a significant negative relation between idiosyncratic risk and mispricing, suggesting that higher idiosyncratic volatility is strongly associated with lower level of equity mispricing. In column [1], for example, the estimated coefficient of idiosyncratic volatility is 0.004 with tstatistic of 3.36. However, more importantly, the coefficients of secondorder idiosyncratic volatility in columns [2] and [4] are significantly positive (e.g., 0.002 with tstatistic of 6.01 in column [2]) without reducing the significance in the firstorder coefficient. The evidence in Panel B based on the individual mispricing measures is qualitatively similar to that using the mispricing index. The and 2 coefficients are always negative and positive, respectively, and significant in almost all cases. This evidence provides room for two important interpretations. First, consistent with the informed trading hypothesis, the significant and negative sign for the firstorder relation supports the notion that higher levels of idiosyncratic volatility signal more informationladen stock prices. Second, the significant positive sign for the secondorder coefficient combined with the significant negative sign for the firstorder coefficient implies that the informed trading hypothesis view of idiosyncratic volatility does not hold 8 This transformation is to guard against a possibility that mispricing index (MI) which takes value from 0 to 1 can lead to erroneous interpretation of results. I find that the results are, as shown, very similar to ones obtained from the original regressions. 24 PAGE 31 25 for firms with very high levels of idiosyncratic risk. The positive relation between mispricing and idiosyncratic volatility beyond a certain point could be driven by the predominance of uninformed noise traders and/or by the inability of arbitrageurs to find close substitutes for high idiosyncratic volatility firms when they want to hedge fundamental risk. Both of these two effects are consistent with increases in mispricing for high levels of idiosyncratic volatility. Table 5 Idiosyncratic Volatility and Equity Mispricing This table shows timeseries average of crosssectional regressions of mispricing on idiosyncratic volatility and other firm characteristics. Panel A reports results of regressions using mispricing index (MI) or logistic mispricing index as dependent variable, while Panel B reports results of regressions using individual mispricing measure as dependent variable. All variables are as defined in Table 1. *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. Panel A: Dependent variable is mispricing index (MI) or logistic mispricing index. Dep. var. = MI Dep. var. = ln(1+MI) [1] Linear [2] Nonlinear [3] Linear [4] Nonlinear Intercept 0.652* ** (19.74) 0.704*** (21.58) 0.497*** (22.69) 0.530*** (24.15) Logistic relative idiosyncratic volatility ( ) 0.004*** (3.36) 0.017*** (7.45) 0.003*** (2.95) 0.011*** (6.86) 2 0.002* ** (6.01) 0.001*** (5.72) Log of total assets (SIZE) 0.002 (0.91) 0.003* (2.04) 0.001 (0.93) 0.002* (1.99) Leverage (LEV) 0.211** (11.10) 0.205*** (10.93) 0.136*** (10.75) 0.133*** (10.56) Return on assets (ROA) 0.111* (1.80) 0.105* (1.74) 0.069 (1.68) 0.063 (1.59) Log of firm age (AGE) 0.025** (9.89) 0.025*** (9.89) 0.016*** (9.63) 0.016*** (9.65) Diversification dummy (DIVER) 0.030** (11.22) 0.030*** (11.17) 0.019*** (10.55) 0.019*** (10.49) Dividendpayer dummy (DD) 0.038** (10.13) 0.205*** (10.93) 0.025*** (10.19) 0.024*** (10.29) N 34,471 34,471 34,471 34,471 Average R2 11.96% 12.27% 11.50% 11.79% PAGE 32 26 Table 5 (Continued) Panel B: Dependent variable is individual mispricing measure. Dep. var. = EXVRI Dep. var. = EXVBO Dep. var. = EXVRK Dep. var. = EXVMB [1] Linear [2] Nonlinear [3] Linear [4] Nonlinear [5] Linear [6] Nonlinear [7] Linear [8] Nonlinear Intercept 0.689*** (4.60) 0.756*** (4.28) 0.595*** (14.01) 0.650*** (12.86) 0.586*** (14.37) 0.682*** (14.89) 0.851*** (19.46) 0.959*** (20.30) 0.003 (0.45) 0.025 (1.62) 2 0.006* (1.78) 0.020** (2.33) 0.008*** (4.94) 0.031*** (6.66) 0.012*** (5.89) 0.037*** (7.43) 0.003** (2.18) 0.002 (1.30) 0.003*** (4.64) 0.003*** (5.77) 0.015** 0.013*** 0.011*** 0.005** 0.013*** SIZE (2.40) 0.013* (1.92) (6.05) (4.86) 0.001 (0.66) (2.48) (6.10) 0.017*** (7.95) 0.389*** 0.378*** 0.246*** 0.392*** 0.382*** LEV (5.15) (5.15) 0.252*** (4.82) (4.77) (10.49) (10.55) 0.317*** (9.72) 0.305*** (9.71) 1.550*** 1.556*** 0.306*** 0.295*** ROA (5.97) (6.00) 0.013 (0.09) 0.021 (0.14) (4.32) (4.18) 0.815*** (6.45) 0.804*** (6.38) 0.068*** 0.037*** 0.037*** AGE 0.028 (1.38) 0.027 (1.37) 0.068*** (10.93) (10.91) (13.92) (13.50) 0.053*** (13.12) 0.054*** (13.00) 0.030*** 0.029*** 0.037*** 0.037*** DIVER (3.26) (3.21) 0.045*** (5.61) 0.045*** (5.76) (9.25) (9.43) 0.052*** (17.91) 0.052*** (17.58) 0.078*** 0.075*** 0.061*** 0.076*** 0.074*** DD (5.46) (5.39) 0.063*** (8.42) (8.37) (12.41) (12.74) 0.060*** (8.43) 0.058*** (8.47) N 31,420 31,420 33,707 33,707 33,751 33,751 33,751 33,751 Average R2 7.01% 7.27% 5.18% 5.37% 12.02% 12.37% 15.05% 15.37% PAGE 33 In order to better identify the size and composition of the group of firms belonging to the righthand of the Ushape curve, I compute the inflection point using the coefficients of firstand secondorder terms of volatility obtained from estimating the nonlinear regression models. I find that the inflection point is far to the right of the distribution, indicating that mispricing declines with for most of firms. For example, the relation between MI and is inflected at a of 4.930 (equivalently, idiosyncratic volatility (1 2 R ) of 99.28%) in regression model [2]. Even though idiosyncratic risk of that magnitude is extremely high, the number of observations with values greater than the inflection point is not negligible. The total number of firms residing on the righthand side of the Ushape curve accounts for about 10% of the total firmyear observations (i.e., 3,388 out of 34,471). Overall the evidence from Table 5 suggests that in most cases (about 90%), higher idiosyncratic risk implies that the activity of informed traders leads to lower equity mispricing, but that in the presence of extremely high idiosyncratic risk levels the effects of noise and/or arbitrage risk cause higher mispricing. C. Robustness Tests In this subsection I conduct several robustness checks, which aim at determining whether or not the findings in Table 5 are due to the particular model of returns used to estimate idiosyncratic volatility or to the estimation methodology used. I start my robustness tests by using alternative idiosyncratic volatility measures. First, I reestimate idiosyncratic volatility by adding each firms industry returns into the 27 PAGE 34 28 market model (equation (1)) as was s uggested by other authors (e.g., Durnev et al (2003 and 2004) and Kelly (2005)). The FamaFrenc h 48 industry SIC classification code is used to define the industry. Second, I use idiosyncratic volatility estimates from the FamaFrench threefactor model of returns. Fama and French (1992, 1993, 1995, and 1996) suggest that a threefact or model explains the timeseries of stock returns. The three FamaFrench factors are the excess return on the valueweighted market portfolio, Rm, the return on a zero investment portfolio measured as the difference between the return on a large firm portfolio and the return on a small firm portfolio, SMB and the return on a zero investment portfolio estimat ed as the return on a portfolio of high booktomarket minus the return on a portfolio of low booktomarket stocks, HML Third, in order to solve the problem that arises with crosssectional time series models when differences between firms are regarded as pa rametric shifts of th e regression function, I use a fixedeffects model to control for po ssible differences across firms. Fourth, I compute differenceindifferences estimates by including year fixedeffects as well as firm fixedeffects. Fifth, I compute statistical significances using Whites (1980) standard errors which are robust to heteroskedasticity. Finally, I estimate a model using only the firstyear observation of each firm. This check wi th the test that uses firstyear data only allows me to see whether previous results are not driven by multiple observations on the same firms. PAGE 35 29 Table 6 Robustness Checks of Regression of Equity Mispricing on Idiosyncratic Volatility This table reports robustness checks of regressions of mispricing on idiosyncratic volatility and other firm characteristics. Reported are the coefficients and tstatistics of regression models [3] and [4] in Table V which use logtransformed mispricing index, ln(1+MI), as a dependent variable. Columns [1] and [2] report results using idiosyncratic volatility estimates from a model controlling market returns and industry returns according to the FamaFrench 48 industry SIC classification. Columns [3] and [4] report results using idiosyncratic volatility estimates from FamaFrench threefactor model of returns. Columns [5] and [6] report results using panel regressions. Columns [7] and [8] report results of regressions computing differenceindifference estimates (i.e., including firm fixedeffects and year fixedeffects). Columns [9] and [10] report results using Whites (1980) heteroskedasticity correction model. Columns [11] and [12] report results only using the firstyear data of each firm. All variables are as defined in Table 1. *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. Industrymodel FamaFrenchmodel Panel regression model Differenceindifferences White (1980) model Firstyear regression [1] Linear [2] Nonlinear [3] Linear [4] Nonlinear [5] Linear [6] Nonlinear [7] Linear [8] Nonlinear [9] Linear [10] Nonlinear [11] Linear [12] Nonlinear Intercept 0.539*** (22.81) 0.591*** (24.60) 0.508*** (23.51) 0.530*** (24.30) 0.770*** (34.79) 0.780*** (35.11) 0.823*** (31.77) 0.838*** (32.14) 0.530*** (28.90) 0.549*** (29.67) 0.525*** (18.61) 0.557*** (19.19) 2 0.006*** 0.019*** (6.27) (9.89) 0.006*** (4.61) 0.019*** (6.07) 0.001*** (3.03) 0.004*** (5.70) 0.001*** (2.65) 0.005*** (5.59) 0.004*** (9.75) 0.010*** (9.35) 0.007*** (8.12) 0.016*** (7.56) 0.003*** (7.99) 0.004*** (4.36) 0.0004*** (4.86) 0.0004*** (4.93) 0.001*** (6.20) 0.001*** (4.55) 0.003** 0.005*** 0.002* 0.017*** 0.019*** 0.003*** 0.003** SIZE (2.55) (4.26) 0.001 (1.34) (1.99) (12.81) 0.017*** (13.04) (12.77) 0.019*** (13.14) 0.002** (2.39) (3.00) 0.002 (1.39) (2.02) LEV 0.132*** (10.46) 0.126*** (9.99) 0.135*** (10.56) 0.133*** (10.35) 0.055*** (8.90) 0.054*** (8.73) 0.057*** (8.92) 0.055*** (8.58) 0.162*** (24.47) 0.160*** (24.17) 0.187*** (18.20) 0.183*** (17.68) ROA 0.062 (1.58) 0.059 (1.51) 0.065 (1.63) 0.064 (1.60) 0.009 (1.25) 0.010 (1.39) 0.012 (1.63) 0.014* (1.81) 0.047*** (5.42) 0.048*** (5.47) 0.071*** (5.70) 0.072*** (5.75) 0.016*** 0.016*** 0.016*** 0.016*** AGE (9.98) (10.26) (9.73) (9.61) 0.013*** (6.25) 0.013*** (6.11) 0.018*** (6.62) 0.018*** (6.58) 0.014*** (8.94) 0.014*** (9.01) 0.005* (1.80) 0.006** (2.20) DIVER 0.019*** (10.31) 0.019*** (10.11) 0.019*** (10.50) 0.019*** (10.42) 0.001 (0.27) 0.00004 (0.02) 0.003 (1.29) 0.003 (1.40) 0.017*** (6.60) 0.018*** (6.74) 0.022*** (5.04) 0.023*** (5.21) DD 0.024*** (9.67) 0.024*** (9.50) 0.025*** (9.99) 0.024*** (9.92) 0.003 (0.99) 0.003 (1.07) 0.002 (0.80) 0.003 (0.85) 0.018*** (6.19) 0.018*** (6.26) 0.011** (2.43) 0.012*** (2.57) N 34,468 34,468 34,471 34,471 34,471 34,471 34,471 34,471 34,471 34,471 5,284 5,284 R2 11.63% 12.12% 11.54% 11.80% 5.74% 5.90% 5.81% 5.93% 10.08% 10.23% 11.40% 11.75% PAGE 36 The results of these robustness checks are reported in Table 6. To save space, Table 6 only reports the results of regression models [3] and [4] in Table 5, which use logtransformed msipricing index, ln(1+MI), as a dependent variable.9 I find that all regressions show a consistent pattern of coefficients on the estimates of idiosyncratic volatility. The firstand secondorder coefficients remain significantly negative and positive, respectively. Therefore, the previous results are confirmed by these various robustness checks. The univariate and multivariate tests on the relation between idiosyncratic volatility and equity mispricing have provided evidence that idiosyncratic volatility can imply informed trading as well as noise trading and/or arbitrageurs risk. This evidence can be confirmed by focusing on information flow and examining whether the probability of informationbased trading (PIN) is strongly related to idiosyncratic volatility. Recent research has utilized the probability of informationbased trading (PIN) to proxy private information flow. According to Easley et al. (1996a, 1996b, 1997a, 1997b, 2002, and 2005), the PIN is estimated as the ratio of expected informed order flow to total order flow: s bPIN (10) where is the probability that an information event occurs, is the arrival rate of informed trades, and s and b are the arrival rates of uninformed sells and buys respectively. is the expected arrive rate of informed trades and s b is the 9 I obtain similar results to the ones presented here when I repeat the tests using the individual mispricing measures. These results are available upon request. 30 PAGE 37 arrival rate for all orders. Consequently, the ratio is the fraction of orders that arise from informed traders or the probability that the opening trade is information based.10 PIN is expected to be related to idiosyncratic volatility according to three hypotheses established for the relation between idiosyncratic volatility and equity mispricing. The informed trading hypothesis regards idiosyncratic risk as a sign of active trading by informed traders, and thus predicts that probability of informationbased trading (PIN) should be higher for high idiosyncratic volatility firm (i.e., positive relation between PIN and idiosyncratic volatility). The noise trading hypothesis regards idiosyncratic volatility as a sign of uninformed traders noise trading, and thus predicts the negative relation between PIN and idiosyncratic volatility. The arbitrage risk hypothesis regards idiosyncratic volatility as a sign of limited opportunities for informed traders to arbitrage, and thus predicts the negative relation between PIN and idiosyncratic volatility. If the evidence of Ushape relation between mispricing and idiosyncratic volatility from Table 5 is true and supported by the analysis using PIN, the relation between PIN and idiosyncratic volatility is expected to be nonlinear, i.e., have a concave shape. To test the above predictions, I estimate the following regression equation using the private information flow proxy (PIN) as dependent variable: PINit = 0 + 1 it + 2 SIZEit + 3 LEVit + 4 ROAit + 5 AGEit + 6 DIVERit + 7 DDit + it, (11) PINit = 0 + 1 it + 2 2it + 3 SIZEit + 4 LEVit + 5 ROAit + 6 AGEit 10 The yearly PIN estimates are available on Soeren Hvidkjaers web site: http://www.smith.umd.edu/faculty/hvidkjaer/data.htm 31 PAGE 38 + 7 DIVERit + 8 DDit + it. (12) I report these regression results in Table 7. Columns [1] and [2] display the results of models using the raw PIN as dependent variable, while columns [3] and [4] show results when a logtransformed version, ln(1+PIN), is used. PIN is found to be positively related to the idiosyncratic volatility, which supports the informed trading hypothesis that high idiosyncratic risk is caused by informed arbitrageurs who trade in stocks using private information to trace fundamental firm value. The conjecture is that high idiosyncratic volatility stocks are associated with high private informationbased trading. This evidence is in line with the findings of other authors. For example, Kelly (2005) finds that PIN is higher for low Rsquare (i.e., high idiosyncratic risk) firms. Ferreira and Laux (2007) show that PIN is negatively correlated with the governance index which, in turn, is negatively correlated with idiosyncratic volatility. Their findings also imply a positive relation between PIN and idiosyncratic volatility. Regression results for models that include the secondorder idiosyncratic volatility also reveal a nonlinear relation between PIN and volatility. Thus, while the coefficient of is positive, the coefficient of 2 is negative. Moreover, both coefficients are significant. This finding is in line with the evidence that mispricing increases beyond a certain high level of idiosyncratic volatility. Accordingly, the nonlinear relation is inflected at the idiosyncratic volatility (1 2 R ) of 99.75%, and the number of observations after the inflection point accounts for 568 firms (about 5%) of firmyear observations used in the regression (11,741 firms). The inflection point is similar to the one on the relation between idiosyncratic volatility and mispricing in Table 5. The U32 PAGE 39 shape was inflected at the idiosyncratic volatility (1 2 R ) of 99.28% and about 10% of observations were included in the right side of Ushape curve. Table 7 Idiosyncratic Volatility and Informationbased Trading This table shows timeseries average of crosssectional regressions of probability of informationbased trading on idiosyncratic volatility and other firm characteristics. All variables are as defined in Table 1. *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. Dep. var. = PIN Dep. var. = ln(1+PIN) [1] Linear [2] Nonlinear [3] Linear [4] Nonlinear Intercept 0.219*** (52.28) 0.210*** (53.52) 0.198*** (57.16) 0.190*** (59.24) Logistic relative idiosyncratic volatility ( ) 0.007*** (8.30) 0.012*** (11.76) 0.006*** (8.53) 0.010*** (11.97) 2 0.001** (2.67) 0.001*** (3.08) Log of total assets (SIZE) 0.023*** (27.43) 0.027*** (27.90) 0.019*** (27.19) 0.019*** (27.54) Leverage (LEV) 0.012*** (3.91) 0.011*** (3.66) 0.010*** (3.89) 0.009*** (3.64) Return on assets (ROA) 0.045*** (5.31) 0.041*** (5.01) 0.038*** (5.38) 0.035*** (5.07) Log of firm age (AGE) 0.013*** (10.53) 0.012*** (10.27) 0.011*** (10.37) 0.010*** (10.13) Diversification dummy (DIVER) 0.010*** (8.42) 0.010*** (7.89) 0.009*** (8.51) 0.008*** (7.97) Dividendpayer dummy (DD) 0.004 (1.62) 0.003 (1.51) 0.003* (1.71) 0.003 (1.60) N 11,741 11,471 11,741 11,741 Average R2 38.67% 39.30% 39.48% 40.14% However, the results from Table 7 do not provide us with a clear answer to the question of why the level of equity mispricing increases for very high volatility firms. It could be because uninformed noise traders dominate trading for highly volatile firms, or because high firms are associated with arbitrage risk. Consequently, in order to further investigate the above question I will repeat the multivariate tests using different sub33 PAGE 40 samples where noise trading and/or arbitrage risk are more (or less) likely. This analysis is conducted in the coming section. V. Interpretations on the Nonlinear Relationship To answer to the question of why mispricing rises with idiosyncratic volatility for high volatility stocks, I create subsamples consisting of stocks classified based on whether they are more or less likely to have noise trading as well as whether they are more or less likely to display arbitrage risk. First, I use uncertainty11 as a measure of probability of low/high noise trading, by assuming that if a firms information environment is less uncertain, the market participants for these stocks are better informed and thus there are relatively fewer noise traders compared to other stocks. Second, I use shortsale constraints as a measure of the extent of arbitrage risk. The use of the shortselling constraints as a proxy for the likelihood of arbitrage risk relies on the assumption that informed traders have a better opportunity to engage into arbitrage when shortselling constraints are less binding. In the following subsections, I describe how I computed aggregate measures of firm uncertainty and shortselling constraints from a number of proxies. A. Measures of Firms Uncertainty To measure uncertainty, I focus on the measures of earnings quality, captured by the absolute size of abnormal accruals, and on measures of the quality of security 11 Black (1986) argues that noise caused by uncertainty makes it difficult for either practitioners or academic researchers to understand how financial or economic markets work. 34 PAGE 41 analysts forecasts. Abnormal accruals (i.e., accruals larger or smaller than expected) reflect poor earnings quality, which is likely to occur in the presence of uncertainty. I use two measures based on Francis, LaFond, Olsson, and Schipper (2005) and Dechow and Dichev (2002). The first measure of earnings quality (EQ1) is defined as the absolute value of firmspecific residuals from an industry regression of total accruals on the reciprocal of total assets, sales growth, and fixed assets. ,123,,,,1ititiitit1it1it1it1TACCRPPESALESkkkTATATATA ,, (13) where TACCRi,t = firm is total accruals in year t, = change in current assets between year t1 and year t, ,,,,()itititititCACLCASHSTDEBTDEPN ,itCA ,itCL = change in current liabilities between year t1 and year t, ,itCASH = change in cash between year t1 and year t, ,itSTDEBT = change in debt in current liabilities between year t1 and t, = depreciation and amortization expense in year t, = change in sales between year t1 and t, = property, plant, and equipment in year t, and = total assets in year t1. ,itDEPN iSALES ,itPPE ,it1TA Following Dechow and Dichev (2002) I also create an alternative earnings quality (EQ2) measure, which is the absolute value of firmspecific residuals from the regression of total accruals on lagged, contemporaneous, and leading cash flow from operations. ,,,,0123itit1itit+1itiiiiTACCRCFOCFOCFOkkkkTATATATA , (14) 35 PAGE 42 where CFOi,t is firm is cash flow from operations in year t and computed as net income before extraordinary items minus total accruals. All variables are scaled by average total assets (TAi). I also use two variables constructed from nonstale security analyst one fiscal yearahead forecasts, issued every June and extracted from I/B/E/S Detail History Database. These are the absolute value of the analyst forecast error (AFE) and the dispersion of analyst forecasts (AFD). The forecast error captures forecasting ability of security analysts covering the firm. The absolute value of the forecast error has been also used by several studies as a proxy of information asymmetry (e.g., see Atiase and Bamber (1994), and Christie (1987)). If there is less uncertainty, a considerable amount of information about future earnings is available to market participants, and so analysts should be in better position to make accurate earnings forecasts. Barron, Kim, Lim and Stevens (1998) show that analyst forecast dispersion reflects both diversity of analyst beliefs and the uncertainty (lack of precision) in analyst forecasts. Prior studies have used the dispersion of analyst forecasts as an information uncertainty proxy (e.g., see Zhang (2005)), as well as an information asymmetry proxy (e.g., see Krisnhnaswami and Subramaniam (1999)). Therefore, I expect analyst forecast error and dispersion will increase with uncertainty. AFE and AFD are computed as follows: ,,,,()()itit+1ititMedAFEPSAFE=MedAF (15) ,,,..()()itititStdDevAFAFD=MedAF (16) 36 PAGE 43 where forecast error, Med(AF)i,t EPSi,t+1, is the absolute value of the difference between the median analyst forecast (Med(AF)i,t) and the actual earnings per share (EPSi,t+1), while Std.Dev.(AF)i,t is standard deviation of one year ahead analyst forecasts. All four aforementioned variables (EQ1, EQ2, AFE, and AFD) are positively related to uncertainty. Thus, I construct an uncertainty index (UI) for each firm by combining the inverse ranks of the four variables. The methodology used to construct UI is the same as the one used for the mispricing index (MI). UI is computed each year for each observation i = 1,,N as: ,11(KikkUIRANKUNCERNK )ik (17) where Rankk(UNCERi,k) is the rank function which assigns a rank for each observation from least uncertain (rank of one) to most uncertain (rank of N). UNCERi,k is the kth measure of uncertainty for firm i in my sample, and K represents the dimensions of uncertainty measures (EQ1, EQ2, AFE, and AFD). The denominator, K, averages the ranks by the number of uncertainty values available for each firm in the sample in a particular year. Finally, dividing by N, I scale the UI from 0 (least uncertain) to 1 (most uncertain). Table 1 provides detail descriptions of uncertainty measures and Table 2 documents descriptive statistics. B. Measures of Shortselling Constraints I control for the effects of shortsale constraints using two alternative proxies: size (SIZE), and institutional ownership (IO). I also construct an aggregate measure, a short37 PAGE 44 sale costs index (SI). Previous research suggests firm size as a shortselling characteristic (see Chen et al. (2002), and Diether, Malloy, and Scherbina (2002) among others). The supply of shortable shares for small firms is generally low because small capitalization stocks tend to be held primarily by individual investors who rarely lend their shares. Furthermore, outstanding shares of small firms are not necessarily floated since insiders may hold a considerable portion of the shares outstanding. Large capitalization firms, however, are held more widely, and so finding a lender of shares should be less difficult. Shares of small firms are also less likely to be on special than those of large firms (Reed (2003)). Finally, search and bargaining costs involved in shortselling are more likely to be higher in small firms than in large ones. Therefore, based on the above arguments, the cost of borrowing and shorting small capitalization stocks is expected to be higher than in large capitalization stocks. As a second proxy for shortselling constraints, I use institutional ownership (INSTP). DAvolio (2002) shows that institutional ownership is the major determinant of the quantity of shares supplied to the market. Therefore, the cost of shortselling should be less (more) expensive for stocks with high (low) institutional ownership. Gompers and Metrick (2001) report a strong relationship between institutional ownership and liquidity. This suggests that the cost of trading large quantities of shares for stocks with high institutional ownership should be low. The search and bargaining cost for stocks with high institutional ownership is also expected to be low. Indeed, if several institutional investors are lending many shares, it should be less costly to locate them and competition should lower the cost of direct borrowing. Finally, derivative instruments, and in 38 PAGE 45 particular put options, an alternative method of creating short positions, are likely to be more often available for stocks with high levels of institutional shareholdings.12 Therefore, stocks with low institutional ownership are subject to a higher shortselling cost. Finally, a shortselling constraints index (SI) is constructed using the inverse of both firm size and institutional ownership (see also Doukas, Kim, and Pantzalis (2006)). SI is computed each year for each observation i = 1,,N as: ,11(KikkSIRANKSHORTNK )ik (18) where Rankk(SHORTi,k) is the rank function which assigns a rank for each observation from the lowest shortsale constraint (rank of one) to the highest shortsale constraint (rank of N). SHORTi,k is the inverse value of kth measure of shortsale constraint for firm i in my sample, and K represents the dimensions of shortsale constraint measures (SIZE and INSTP). The denominator, K, averages the ranks by the number of shortsale constraint values available for each firm in the sample in a particular year. Finally, dividing by N, I scale the SI from 0 (lowest shortsale constraint) to 1 (highest shortsale constraint). Details of all shortselling variables are provided in Table 1 and summary statistics are documented in Table 2. 12 Ofek, Richardson and Whitelaw (2004) show that the violation of the putcall parity is strongly related to lending fees. Lending fees, however, are related to institutional ownership. 39 PAGE 46 I begin my analysis of the nonlinear relationship by comparing the mean values of uncertainty and shortselling constraint measures across firms that belong to the lefthand side and the righthand side of the Ushape relationship between MI and The comparison is presented in Table 8. In the left half of the table I present evidence based on the sample used in the main multivariate test presented in Table 5, which had 34,471 observations. The results for model [2] showed a nonlinear (Ushape) relation between MI and A firm that lies on the right side of the Ushape curve (i.e., one with very high idiosyncratic volatility) is a firm whose idiosyncratic volatility () is greater than the inflection point (which was at = 4.930). 3,388 firms (about 10% of the total sample) are included in the highvolatility group. Alternatively, in the right half of Table 8, I use all sample observations (N=44,639) and sort firm into highvolatility group if its volatility is ranked within top 10%. The results reported in Table 8 show that firms with high volatility display greater levels of uncertainty and are subject to higher shortsale constraints than firms with low idiosyncratic volatility. The mean differences are significant in most cases. Since uncertainty is more likely to be associated with noise trading and more binding shortsale constraints with more arbitrage risk, this evidence is also consistent with the notion that firms with high idiosyncratic volatility will be characterized by both more noise trades and higher arbitrage risk, compared to firms with normal levels of idiosyncratic volatility. C. Analysis of Nonlinear Relation 40 PAGE 47 41 Table 8 Firms with Very High Idiosyncratic Volatility This table reports mean values of firm uncertainty measures and shortselling constraint measures for firms with very high idiosyncratic volatility () and for the other firms. Columns [1] and [2] test 34,471 observations used in the regression [2] of Table 5. The relation is inflected at the point where is at 4.930. Firms with very high idiosyncratic volatility are included in column [1] if is greater than 4.930. Columns [3] and [4] test all sample observations. Firms with very high idiosyncratic volatility are included in column [3] if is ranked within top 10%. All variables are as defined in Table 1. and *** indicate significance at the 10%and 1%levels, respectively. Observations used in the regression [2] of Table 5 (N = 34,471) All sample observations (N = 44,639) [1] [2] Firms with very high (N=3,388) The other firms (N=31,083) Mean diff.: [1] [2] tstatistics: difference =0 Firms with very high (N=4,475) [3] [4] The other firms (N=40,164) Mean diff.: [3] [4] tstatistics: difference =0 Uncertainty measures Francis et al. (2005) (EQ1) 0.302 0.339 0.037*** 3.15 0.317 0.334 0.017 1.55 Dechow and Dichev (2002) (EQ2) 0.158 0.173 0.015 1.27 0.161 0.171 0.010 0.91 Analyst earnings forecast error (AFE) 1.191 0.727 0.465*** 4.03 1.415 0.775 0.640*** 6.14 Analyst earnings forecast dispersion (AFD) 0.232 0.192 0.040* 1.71 0.317 0.220 0.096*** 3.72 Uncertainty index (UI) 0.519 0.496 0.023*** 6.32 0.541 0.499 0.042*** 12.75 Shortselling constraint measures Firm size (SIZE) 18.94 19.69 0.751*** 27.03 18.93 19.83 0.898*** 34.85 Institutional ownership (INSTP) 0.406 0.516 0.110*** 21.19 0.400 0.513 0.114*** 23.69 Shortselling constraint index (SI) 0.634 0.512 0.122*** 27.12 0.649 0.492 0.158*** 39.27 PAGE 48 Next, I classify firms into different subsamples after independently sorting on both on the uncertainty and shortselling constraint measures and retest the regressions for all subsamples in order to establish which of the two effects (i.e., noise trades and/or arbitrage risk) is reflected in the right side of the Ushaped curve. Table 9 documents the coefficients of the firstand secondorder terms of idiosyncratic volatility and the inflection point obtained from estimating the regression. If any one of the two effects that can cause the positive relation between mispricing and firmspecific risk for high idiosyncratic volatility stocks dominates, the nonlinearity should disappear only in the subsample where the possibility of that effect is restricted. For instance, I construct a group which contains only firms with low uncertainty, i.e., a subsample of firms with few noise traders. If the Ushaped relationship is not significant for this subsample, it is possible that the increase of mispricing for high volatility firms is attributed to noise traders. Similarly, if the nonlinearity becomes insignificant only for firms with low shortselling constraints, the positive relation between MI and for high volatility firms could be associated with arbitrage risk. 42 PAGE 49 43 Table 9 Coefficient of Idiosyncratic Volatility and Inflection Point for Subsamples This table shows the coefficient of idiosyncratic volatility and inflection point in the timeseries average of crosssectional regressions of Table V. Subsamples are classified on firm uncertainty and shortselling constraint. All variables are as defined in Table 1. *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. Dep. var. = MI Dep. var. = ln(1+MI) Subsamples [1] Linear [2] Nonlinear at infl. point 1R2 at infl. point % of obs. after infl. point [3] Linear [4] Nonlinear at infl. point 1R2 at infl. point % of obs. after infl. point 0.006*** (2.82) 0.021*** (3.42) 0.004** (2.60) 0.013*** (3.30) [1] Less uncertain (low UI) firms (= few noise traders) 2 0.002** 4.850 (2.43) 99.22% 8.85% 0.001** (2.36) 4.861 99.23% 8.82% 0.005** (2.23) 0.027*** (4.45) 0.003* (1.87) 0.017*** (4.19) [2] Low shortselling cost (low SI) firms (= low arbitrage risk) 2 0.005*** 2.800 0.016** (2.49) 0.029* (2.00) 0.011** (2.38) 0.019* (2.02) [3] Low UI & low SI firms (= few noise traders & low arbitrage risk) 2 (3.56) 94.27% 18.11% 0.003*** (3.39) 2.752 94.00% 18.79% 0.007 (1.21) N/A N/A N/A 0.004 (1.27) N/A N/A N/A 0.005** (2.68) 0.018*** (3.04) 0.003** (2.47) 0.011*** (2.89) [4] Low UI & nonlow SI firms (= few noise traders & arbitrage risk) 2 0.002** 4.465 (2.16) 98.86% 13.44% 0.001** (2.08) 4.414 98.80% 13.92% 0.005 (1.63) 0.026*** (2.96) 0.003 (1.37) 0.017*** (2.75) [5] Nonlow UI & low SI firms (= noise traders & low arbitrage risk) 2 0.004** 3.163 (2.46) 95.94% 13.36% 0.003** (2.24) 3.132 95.82% 13.79% 0.005** (2.27) 0.016*** (6.46) 0.003** (2.08) 0.010*** (5.90) [6] Nonlow UI & nonlow SI firms (= noise traders & arbitrage risk) 2 0.001*** 5.511 (5.68) 99.60% 8.38% 0.001*** (5.71) 5.410 99.55% 8.86% Not available due to the insignificance of nonlinear relation. PAGE 50 Figure 4 Tests of Three Hypotheses and Evidence This figure describes the empirical evidence of nonlinear relationships among idiosyncratic volatility, equity mispricing, and private informationbased trading. Based on the findings, tested are three hypotheses; 1) the noise trading hypothesis, 2) the informed trading hypothesis, and 3) the arbitrage risk hypothesis. Private informationbased trading Idiosyncratic volatility Idiosyncratic volatility The informed trading hypothesis is supported. The noise trading hypothesis is rejected. The arbitrage risk hypothesis is rejected. 5 10% of sam p le 90 95% of sam p le The informed trading hypothesis is rejected. The noise trading hypothesis is supported. The arbitrage risk hypothesis is supported. Equity Mispricing 44 PAGE 51 In Table 9, results show that the nonlinear relation remains significant both for low uncertainty firms (subsample [1]) and for firms with low shortselling constraints (subsample [2]). The nonlinear relationship collapses to a linear one only for the subsample containing firms that have both low uncertainty and low shortselling constraints (subsample [3]). In this subsample, while the negative linear relationship remains strong, the nonlinear relation becomes insignificant. These results indicate that the increase in mispricing for highly volatile stocks cannot be attributed to only one effect. The results indicate that both noise trading and arbitrage risk contribute to an increase in MI when is very high. Consistent with the previous evidence in Table 5, firmspecific risk (1 2 R ) at the inflection point is very high, ranging from 90% to 99%. The percentage of total observations in the range to the right of the inflection point is somewhere between 8% and 19%. In summary, all test results in this paper provide evidence that idiosyncratic volatility in stock returns primarily reflects informational market efficiency. Moreover, extremely high volatility implies the possibility of both noise traders frenzy and limits of informed arbitrage. To clarify the relation between idiosyncratic volatility and equity mispricing based on three hypotheses, I sketch the main results in Figure 4. VI. Summary and Conclusions In this paper, I revisit three alternative interpretations of idiosyncratic volatility found in past studies and attempt to provide an answer as to if and when each view is suited for describing idiosyncratic risk. Past studies have argued that idiosyncratic 45 PAGE 52 volatility may reflect informed arbitrageurs trading, uninformed noise traders frenzy without concrete information about a firm, and/or limits to arbitrage opportunities. I test three hypotheses of the relation between idiosyncratic volatility and equity mispricing corresponding to each of the aforementioned views. The informed trading hypothesis proposes that idiosyncratic volatility is a sign of active trading by informed arbitrageurs who trace the firms fundamental value, and thus predicts that equity mispricing should be lower for high idiosyncratic volatility firm. On the contrary, the noise trading hypothesis regards idiosyncratic volatility as a sign of uninformed investors noise trading which causes deviation from the stocks fundamental value, and thus predicts that equity mispricing should be higher for high idiosyncratic volatility firm. The arbitrage risk hypothesis predicts that arbitrage activity is impeded when idiosyncratic risk is high because arbitrageurs cannot hedge their positions successfully. Systematic mispricing may epitomize arbitrageurs limit of opportunity to perfectly hedge fundamental risk in their portfolios. Therefore, the prediction of the arbitrage risk hypothesis is that the equity mispricing of high arbitrage risk stocks should be higher than one of low arbitrage risk stocks. I test the three hypotheses by employing several mispricing measures as well as an aggregated measure, the mispricing index (MI). I find that the level of mispricing declines in volatility, consistent with the informed trading hypothesis. However, I also find a strong nonlinear, Ushape relation; the level of equity mispricing decreases first with idiosyncratic risk but then increases for high levels of idiosyncratic risk. Regressions for subsamples created after sorting on uncertainty and shortselling constraints indicate 46 PAGE 53 that high volatility reflects both noise trades and arbitrage risk, thereby inducing a positive relation with equity mispricing. Recently, the finance literature has emphasized the importance of idiosyncratic volatility but provided different ways to interpret it. The contribution of this paper is to reconcile the different views of several areas of finance research, and, specifically, to produce evidence on the link between idiosyncratic volatility and stock mispricing, which allows a clearer understanding of idiosyncratic volatility. In summary, the findings in this paper are consistent with the Rolls (1988) former view that idiosyncratic volatility is associated with informationladen stock prices and efficient markets. For extremely high volatility, however, we should not ignore the possibility of noise traders frenzy as well as limits of informed arbitrages. 47 PAGE 54 Essay 2 Agency Costs and the Underlying Causes of Mispricing: Information Asymmetry versus Conflict of Interests I. Introduction Both theory and empirical evidence support the notion that equity mispricing has an impact on managers investment and financing decisions. For example, misvaluation can drive firms takeover behavior.13 Furthermore, there is evidence that the levels of firms investment are affected by inefficient market valuations14 and that firms try to time equity issues to take advantage of misevaluation.15 There are several possible reasons why equity mispricing exists. These are related to market imperfections such as information asymmetry, transactions costs, unsophisticated market participants or unequal access to prices. According to the proponents of the efficient markets hypothesis and rational asset pricing, stock mispricing, i.e., the deviation from intrinsic (fundamental) value can be either a shortterm temporary phenomenon quickly exploitable by arbitrageurs (Friedman (1953)), or a rational compensation for risks that are not accounted for in asset pricing models (see, for example, Fama and French (1993 and 1996)). On the other hand, advocates of behavioral finance regard persistent mispricing as the result of the existence of an irrational (behavioral) component to asset prices. In this study, unlike previous studies that link 13 Shleifer and Vishny (2003), Dong, Hirshleifer, Richardson, and Teoh (2006), RhodesKropf and Viswanathan (2004), and RhodesKropf, Robinson, and Viswanathan (2005). 14 Polk and Sapienza (2003) and Baker, and Stein and Wurgler (2003). 15 Ritter (1991), Loughran and Ritter (1995), Rajan and Servaes (1997), and Baker and Wurgler (2002). 48 PAGE 55 market inefficiency to equity mispricing, my focus is on providing evidence on whether agency theory can reliably explain equity mispricing. Agency theory defines agency costs as the costs associated with divergent objectives between agents (management) and owners (shareholders). These conflicts of interest cause problems that are exacerbated in the presence of information asymmetry where agents discriminately have better/more information than owners. I hypothesize that a sizeable component of stock mispricing is due to the lack of transparency at the corporate level.16 The term lack of transparency in this context refers to the opacity caused by information asymmetry and conflict of interests between managers and shareholders. However, while most prior studies have focused on the linkage between information asymmetry and stock misvaluation,17 there is little direct evidence in the literature on the potentially important effect of conflict of interests between managers and outside shareholders on equity mispricing. Suppose, for instance, that there are large differences in the quality and availability of information between managers and outside investors of a particular firm. Then, one may expect that the firms stock is likely to be mispriced because ambiguity about future cash flows leads to stock mispricing (see, for example, Kumar (2005) and Zhang (2006)). The question that I want to examine is what happens to the size of mispricing if the firm attempts to reduce managerial disincentives, e.g., if the board of directors provides an incentiveladen compensation package to managers. In this case, 16 Alternatively, mispricing can exist due to 1) high transactions costs (Ali, Hwang, and Trombley (2003)), 2) lack of investor sophistication, 3) noise trading (Roll (1988)) etc. 17 See, among others, Nanda and Narayanan (1999), and Healey and Palepu (2001). 49 PAGE 56 even if investors have difficulty obtaining true, reliable information about the firms future cash flows, they may credibly rely on inference from observing managers decisions, and thereby the ambiguity that causes misvaluation could be mitigated. Thus, if my conjecture is correct, the level of mispricing should be related to components of managerial compensation packages which are intended to resolve the conflict of interests (or, incentive conflicts). Using ten agency conflict proxy variables, I identify the firms which are most likely to have agency problems. However, it is unclear whether these variables measure the level of information asymmetry or incentive conflicts. In fact, they could represent one or the other, or even both. This is because information asymmetry and incentive conflicts are highly correlated. In order to identify which component of agency conflict (i.e., information asymmetry or conflict of interests) drives mispricing, I employ managerial compensation data and investigate whether and how mispricing is affected by equitybased compensation, which is known as the tool that can align managerial interests with those of shareholders but not necessarily as a tool suited for resolving information asymmetry. Previous studies suggesting stockbased compensation is an efficient agency problem resolution mechanism typically do not differentiate among different stockbased incentives and relate them to both lowered agency costs and enhanced firm stock value.18 In light of the recent public skepticism about the effectiveness of equitybased compensation fueled from financial scandals (i.e., Enron 18 For a detailed discussion about equitybased compensation, see Bhagat, Brickley, and Lease (1985), Jensen and Murphy (1990a and 1990b), DeFusco, Johnson, and Zorn (1990), Mehran (1995), Core and Guay (2001), Datta, IskandarDatta, and Raman (2001), Loughran and Vijh (1997), Frye (2004), Core and Larcker (2002), and Nam, Tang, Thornton, and Wynne (2006). 50 PAGE 57 and WorldCom) and academic evidence (e.g., Bergstresser and Philippon (2006)), in my analysis I consider separately both major equitybased compensation components, i.e. stock options and restricted stock grants. While options have been shown to induce managerial myopia (i.e., shorterterm orientation), restricted stock grants have been shown to induce managers to become less myopic (i.e., longerterm orientated).19 My results show a significant positive relation between agency problems and equity mispricing. Furthermore, using CEO compensation data, I find that, contrary to previous studies argument that information asymmetry is a key determinant in equity mispricing, information asymmetry is not a powerful explanatory variable of mispricing. When I interact agency costs proxies with variables that capture managerial compensation components intended to resolve the interests conflict between CEO and owners, the models explain a significant proportion of mispricing. My findings obtained from several univariate and multivariate tests support the notion that the positive relation of agency costs with mispricing is mainly driven by stock options awards to the CEO. The empirical evidence also suggests that the use of restricted stock grants that are known to not be associated with managerial myopia is a better choice in terms of reducing interest conflicts. The rest of the paper is organized as follows. In the next section, I develop the main hypotheses to prove the relation between incentive conflicts and mispricing. Section III describes the data sources and measures of main variables. Section IV introduces empirical methodology and reports test results. Section V conducts additional tests 19 See Aboody and Kaznik (2000), Watts and Zimmerman (1986), Gao and Shrieves (2002), and Bergstresser and Philippon (2006). 51 PAGE 58 52 utilizing managerial compensation data and pr ovides a more detailed explanation of the relation between agency costs and mispri cing. Section VI includes a summary and concluding remarks. II. Hypotheses Development I assume that a sizeable component of st ock mispricing is due to the lack of transparency (i.e., opacity) at the corporate level, which stems from two sources. First, outside investors ambiguity about firms future cash flows increases when they have limited access to information or when investors information is of poor quality relative to that of firm insiders. Therefore, the more opaque the information available to investors about a firms true but unobs ervable distribution of future cash flows, the greater the degree of deviation of market value from intrinsic value.20 Second, the lack of transparency can be also caused by the severity of the conflict of interests that may exist between managers and investors. If this is true, the mispriced firms should have greater agency costs than other firms. This rela tion is graphically de picted in Figure 5 Hypothesis # 1: Firms with high agency costs are more likely to display high levels of equity mispricing. 20 Since Myers and Majluf (1984) showed that firms subject to higher information asymmetry are more likely to refuse valuable investment opportunities a nd to suffer from unfavorable misvaluation, many authors have documented the impact of asymmetry information on misevaluation. Nanda and Narayanan (1999) formally develop an information related argument in the context of divestitures through a model of asymmetric information about firm value between th e managers and the market. They assume that the market can observe the aggregate cash flows of the firm but not the individual divisional cash flows, which results in misvaluation of the firms securities. Heal ey and Palepu (2001) argue that misvaluation arises when there is information asymmetry between managers and investors that is not fully resolved. PAGE 59 Firm with high agency costs Firm with low agency costs Undervaluation Overvaluation Second best optimal stock price with low agency costs Second best optimal stock price with high agency costs First best optimal stock price without any agency costs Mispricing of firm with low agency costs Mispricing of firm with high agency costs Figure 5 Agency Costs, Fundamental Value, and Equity Mispricing 53 This figure graphically describes the relation between agency costs and equity mispricing. PAGE 60 Agency costs, by definition, are the costs incurred by a firm that are associated with problems such as divergent objectives between management and shareholders and/or information asymmetry where insiders discriminately have access to better/more information than outside shareholders. If mispricing is due to the information asymmetry, equitybased compensation should not be significantly related to the level of mispricing. In contrast, if mispricing is due to the degree of the conflict of interests between managers and shareholders, it should be related to components of managerial incentive compensation. Hypothesis # 2: The positive impact of agency costs on equity mispricing is mainly attributed to the conflict of interests rather than to information asymmetry. The finance literature has adopted two different views on the linkage between agency problems and executive compensation. First, many authors21 regard managerial compensation as a potential agency conflict resolution mechanism. Under this view, corporate boards design compensation packages to provide managers with the correct incentives to maximize shareholder value. Several studies found that firms stock performance is positively related to the fraction of equitybased compensation suggesting that equitybased compensation resolves agency problems.22 21 They are Bhagat et al. (1985), Jensen and Murphy (1990a and 1990b), DeFusco et al. (1990), Mehran (1995), Core and Guay (2001), Datta et al. (2001), and Core and Larcker (2002). 22 For example, Bhagat et al. (1985) find that the adoption of employee stock purchase plans result in an increase in shareholder wealth, and that equitybased compensation schemes motivate top managers more than lowerlevel employees. Jensen and Murphy (1990a and 1990b) suggest that equitybased, rather than cashbased, compensation is more efficient in aligning the interests of managers and shareholders. DeFusco et al. (1990) find that implicit share price variance and stock return variance increase after the firm approves an executive stock option plan. Moreover, their event study analysis results indicate that the announcement of approval of stock option plans leads to an increase in stock price along with a significant negative reaction in the bond market, suggesting that executive stock options may transfer wealth from bondholders to stockholders. Mehran (1995) shows that firm performance is positively related to the 54 PAGE 61 The alternative view of executive compensation found in the literature is that of executive compensation being part of the agency problem itself. Recent corporate scandals involving excessive managerial pay coupled with abysmal performance and wealth expropriation of outside shareholders, such as those at Enron and WorldCom, have cast doubts over prior beliefs about the effectiveness of equitybased compensation. Moreover, researchers suggesting stockbased compensation as an efficient mechanism used to solve agency problems typically treated all stockbased incentives equally and related them to lowered agency costs as well as enhanced firm stock value. The skepticism about the effectiveness of equitybased compensation motivated my decision to analyze equitybased compensation by separately considering its stock optionsand restricted stock grants components. It is intuitively appealing to think that incentive stock options should have a positive impact on firm performance. But options may also impose a penalty on the firm because they tend to make managers more myopic. In particular, because managers gains from stock option grants are exponentially greater than stock appreciation returns, managers ownership and the amount of shares provided by their compensation packages. He also shows that firms with higher percentage of shares held by outside blockholders use less equitybased compensation. Based on theses findings, he suggests that the monitoring by outside blockholders can be a substitute for incentive equity compensation for executives. Core and Guay (2001) show that firms use options to attract and retain certain types of employees as well as to create incentives to increase firm value. Datta et al. (2001) document a positive relation between equitybased compensation received by acquiring managers equitybased compensation and acquirer firms stock price response around and following corporate acquisition announcements. They also find that acquiring firms with high equitybased compensation do not show underperformance documented by Loughran and Vijh (1997) and others. Frye (2004) provides evidence that firms with high percentage of equitybased compensation show better performance measured by Tobins q. Core and Larcker (2002) show that mandatory increases in the level of managerial equity ownership result in improvements in accounting returns and stock returns. Nam et al. (2006) examine the effectiveness of equitybased compensation in mitigating the agency costs in singleand multisegment firms, and find that the effect for multisegment firms, where agency costs are expected to be higher, is much greater than for singlesegment firms. 55 PAGE 62 managers have an incentive to maximize shortterm stock price appreciation to increase their options exercise value. It is conceivable then that an increase in stock value could lead to a substantial enough increase in the value of the stock option grants to provide the managers with an incentive to cash out and leave the company. Such a scenario would be especially true if projects and investments chosen by the managers have a shortterm focus at the expense of longterm wealth creation. The finance and accounting literatures broadly document that executives have the ability to manage the timing of stock option grants and/or the information flow around option grants. 23 In a recently published study Lie (2005) proposes an alternative way in explaining the abnormal return pattern around options grants (i.e., return which is abnormally negative before executive option grants and abnormally positive afterward). Unlike previous studies (e.g., Yermak (1997)) that argue conventional grant timing, Lie (2005) argues that, to enrich their senior executives, firms may simply backdate the stock option grant date to a time period where the market price was particularly low.24, 25 23 Yermack (1997) investigates corporate managers influence over the terms of their own compensation by analyzing the timing of CEO stock option awards. He finds that CEO option awards are followed by significantly positive abnormal returns. Aboody and Kasznik (2000) suggest that CEOs make opportunistic voluntary disclosure decisions to maximize their stock option compensation. Chauvin and Shenoy (2001) show that stock price significantly decreases in the 10 days prior to stock option grants. Carpenter and Remmers (2001) find that abnormal stock returns after exercises by top managers at small firms are significantly negative. Huddart and Lang (2003) examine the stock option exercise decisions of over 50,000 employees at seven corporations and present evidence that stock exercise is high before the stock price decreases and low before stock price increases. They suggest that the timing when both senior and junior employees exercise their stock options can be used to predict future stock returns. 24 Heron and Lie (2007) look at a 2002 change in regulatory law that requires companies to report option grants within 48 hours. They document that the return pattern (i.e., returns which are abnormally negative before executive option grants and abnormally positive afterward) weakens after the SEC requirement. They find that when companies reported options the same day they were granted, there was no pattern of share prices quickly rising. But the pattern continued when companies delayed reporting option grants. These findings support the Lies backdating theory. 25 The theory has been also supported by the recent anecdotal evidence from the SECs investigation of many cases (e.g., Mercury Interactive). SEC investigators previously had posited that companies were 56 PAGE 63 Another negative aspect of option grants is that options appear to lead executives to take risks that might not be in the best interest of shareholders. This can occur because stock option grants offer substantial upside potential, but impose little downside risk on managers (see Sanders (2001)). They serve as motivational carrots but lack the complementary disciplinary stick. Thus, executives may view the potential option payouts as a form of compensation lottery.26 Watts and Zimmerman (1986) argue that managers of firms with earnings based compensation incentives maximized their awards by choosing income increasing accounting methodologies.27 Based on the above evidence I expect that options grants effectively make CEOs more myopic. In other words, as the proportion of options in a CEOs compensation package increases, so does the incentive to make shortterm wealth maximization decisions that might not be in the best interest of longterm stakeholders. Restricted stock grants endow managers with a number of shares of firms equity, but also restrict managers from reselling or transferring shares and contain provisions that invalidate the award if managers quit or are fired before the restricted period. While options have been shown to induce managerial myopia, restricted stock grants have been shown to reduce managerial myopia.28 Another important difference between restricted timing grants to benefit from positive corporate news that would drive up stock prices, such as strong earnings. But increasingly they are focusing on backdating (11/11/2005, Wall Street Journal). 26 Warren Buffett shares this opinion as he conceded that we dont give options because it would be a lottery ticket. 27 Gao and Shrieves (2002) find that option grants and exercisable inthemoney options are positively correlated with earnings management intensity. Bergstresser and Philippon (2006) provide evidence that during years of high discretionary accruals CEOs exercise unusually large numbers of options and sell large quantities of shares. 28 For example, Narayanan (1996) theoretically investigated the relationship between two types of compensation, cash and noncash, and the managers decision horizon. He did not investigate the effect of options as a form of noncash compensation but rather focused on restricted stock grants. He found that all57 PAGE 64 stock and options is that restricted stock grants have more of a linear payoff relative to stock option grants.29 It is also reasonable to argue that restricted stock grants provide less incentive for earnings management because the reversion of earnings management accruals will likely manifest before managers can realize large personal gains (see Gao and Shrieves (2002)). Therefore, it is expected that restricted stock grants are effective in resolving agency problems and thereby improving firm performance. Because, as discussed above, options have been shown to induce managerial myopia, while restricted stock grants have been shown to induce managers to become less myopic, I focus on the two incentive compensation plans separately. On one hand, mispricing can be reduced when incentive conflicts are resolved by a compensation package, which contains a high proportion of restricted stocks. On the other hand, mispricing can be exaggerated when firms provide CEOs with compensation packages which have many stock options. cash contracts induce managers to underinvest in the long term while restricted stock grants induce managers to overinvest in the long term. He concluded that a combination of both cash and restricted stock produces efficient investment. Kole (1997) finds that stock options and restricted stocks are common in R&D intensive industries, but the difference in corporate use of restricted stocks between highand lowR&D intensive industries is economically and statistically more significant than the difference of corporate use of stock options. However, Ryan and Wiggins (2002) report that R&D investment is positively related to stock options but negatively related to restricted stocks. This finding is, they interpret, because the linear payoff of restricted stock encourages managers to avoid risky investment and the nonlinear payoff of options motivates risktaking behavior. 29 Bryan, Hwang and Lilien (2000), and Ryan and Wiggins (2002) contend that restricted stock grants, due to their linear payoffs, are relatively inefficient in inducing riskaverse CEOs to accept risky, valueincreasing investment projects. On the other hand, it is plausible that the linear payoff of restricted stock grants does not adversely affect CEO decisions because it precludes the potential of earning a windfall in the shortterm and discourages CEOs from making decisions that could be harmful to stakeholders longterm interests. 58 PAGE 65 Hypothesis # 3a: All other things equal, equity mispricing caused by agency conflicts between managers and outside investors should be mitigated by the use of restricted stock grants in CEO compensation packages. Hypothesis # 3b: All other things equal, equity mispricing caused by agency conflicts between managers and outside investors should be exaggerated by the use of stock option grants in CEO compensation packages. III. Data and Measures I extract return data from the Center for Research in Securities Prices (CRSP) where NYSE, AMEX, and Nasdaq stocks are listed. The initial sample includes all firms in CRSP from 1985 to 2004, omitting financial (SIC 60006999) and utility (SIC 49004999) firms. Accounting and financial data are drawn from COMPUSTAT. Firms with market value of equity less than $20 million are excluded in order to avoid cases of firms with distorted valuation multiples in the mispricing measures. I collect CEO compensation data from the sample of firms in Standard and Poors (S&P) ExecuComp database. The S&Ps ExecuComp database covers the period from year 1992 to 2003, and includes executive compensation data for firms in the S&P 1500 index, which comprises the S&P 500, the S&P 400 mid cap, and the S&P 600 small cap indices. ExecuComp also contains information on firms that are not currently in the S&P500, the S&P400, and the S&P 600 indices, but were previously included in one of the aforementioned indices. According to ExecuComp, CEOs total compensation is comprised of seven items: 1) salary, 2) bonus, 3) stock options granted, 4) restricted stock grants, 5) longterm 59 PAGE 66 incentive plan, 6) other annual compensation, and 7) all other compensation. Details of all compensation variables are provided in Table 10 and summary statistics are documented in Table 11. The final sample includes 38,781 firmyear observations with 6,446 firms during the sample period. For the tests that utilize CEO compensation data the sample is reduced to 8.657 firmyear observations. A. Measures of Equity Mispricing Firm mispricing is measured as the deviation of a firms equity value from its intrinsic or fundamental value. I develop six alternative mispricing measures. The first four measures employ alternative techniques in estimating intrinsic value benchmarks, the fifth measure is based on a standard asset pricing model, and the last one is an index that combines all measures. The mispricing measures are as follows. 1) EXVRIi,t, the absolute value of the natural logarithm of the ratio between the stock price and its intrinsic value from Ohlsons (1995) residual income value approach. EXVI is computed at the end of June of each year. EXVRIi,t ,,ln()ititPRICEIV (1) where PRICEi,t is the stock price at the end of June of each year from CRSP, and I(V)i,t is intrinsic value using the residual income model (Ohlson (1995)) and median values of analysts forecasts issued in June, as in Frankel and Lee (1998). There is 60 PAGE 67 strong empirical evidence in support of the residual income valuation, V/P, as an indicator of mispricing.30 2) EXVBOi,t, the absolute value of excess value computed at the end of June of each year as the natural logarithm of the ratio between a firms capital and its imputed value, based on Berger and Ofek (1995) approach. EXVBOi,t ,,ln()ititCPTLICPTL (2) where CPTLi,t is total capital, which is market value of equity plus book value of debt, I(CPTLi,t) is the imputed value derived as the product of firm sales and the median capital to sales ratio in the firms industry. The industry classification here is based on the FamaFrench 48 sectors. This measure of mispricing is constructed in a similar fashion as the first one (EXVRIi,t), but uses firms total capital instead of price and computes imputed value based on FamaFrench 48 industry classification. 3) EXVRKi,t, the absolute value of the firmspecific component of the difference between market value and fundamental value, based on Model III of RhodesKropf et al. (2005). This procedure differs from the residual income valuation approach in the sense that it does not rely on analysts earnings forecasts. According to RhodesKropf et al. (2005), fundamental value, V is estimated by decomposing the markettobook into two components: a measure of price to fundamentals (ln(M/V)), and a measure of 30 Lee, Myers and Swaminathan (1999) report that V/P predicts onemonthahead returns on the Dow 30 stocks better than aggregate booktomarket. Frankel and Lee (1998) also show that the residual income value is a better predictor than book value of the crosssection of contemporaneous stock prices, and that V/P is a predictor of the oneyearahead crosssection of returns. In addition, Ali et al. (2003) show that after controlling for several possible risk factors, V/P continues to significantly predict future returns. DMello and Shroff (2000) apply V/P to measure mispricing of equity repurchases, and Dong et al. (2006) to takeovers. 61 PAGE 68 fundamentals to book value (ln(V/B)). The first component captures the part of booktomarket associated with mispricing. In extreme cases where markets perfectly anticipate, this component would be equal to zero, otherwise positive (overvaluation) or negative (undervaluation). This component is further decomposed into firmspecific and industryspecific misprising. In my tests, I use the firmspecific mispricing component based on Model III of RhodesKropf et al. (2005) that also accounts for net income and leverage effects. ln(Mi,t) = 0j,t + 1j,t ln(Bi,t) + 2j,t ln(NI)+i,t + 3j,t I(<0)ln(NI)+i,t + 4j,t ln(LEVi,t) + i,t (3) where M is firm value, B is book value, NI+ is absolute value of net income, I(<0)ln(NI)+ is an indicator function for negative net income observations, and LEV is the leverage ratio. 4) MBIAi,t, the absolute value of the industryadjusted markettobook ratio. MBIAi,t ,,ln()itjtMBMedMB (4) where, MBi,t is the market to book ratio for firm i at time t, and Med(MBj,t) is the jth industry median of MBt. Several empirical studies have utilized MB as a mispricing measure (see, among others, Walkling and Edmister (1985), Rau and Vermaelen (1998) and Ikenberry, Lakonishok and Vermaelen (1995)). 5) ARET, the absolute value of a firms average monthly abnormal return for each year. The expected return of month t is computed using the factor coefficients obtained from the Fama/French threefactor model estimated over the fiveyear period 62 PAGE 69 immediately preceding month t. For example, the 60month period from January 1987 to December 1991 is used to estimate the parameters used to compute the expected return for January 1992. The estimation of the parameters is based on the following model: E(Ri,t) Rf,t = 0 + M (Rm,t Rf,t) + SMB SMBt + HML HMLt + it (5) where E(Rit) is the rate of return on the ith companys common stock in month t, Rf,t is riskfree rate, Rm,t is the valueweighted market portfolio return, and SMBt and HMLt are the size and booktomarket factors as in Fama and French (1993, 1996). Abnormal returns, ARETi,t, are computed as differences of actual returns, Ri,t, from the expected returns derived from the parameters of model (5). The mispricing from standard asset pricing model is: ARETi,t= Ri,t E(Ri,t) (6) 6) MIi,t, a mispricing index that combines all five mispricing measures described above.31 The mispricing index is constructed each year for each observation i = 1,,N as: ,11()KikkMIRANKEXVNK ik (7) where Rankk(EXVi,k) is the rank function which assigns a rank for each observation from least misvalued (rank of one) to most misvalued (rank of N). EXVi,k is the kth measure of mispricing for firm i in the sample, and K represents the dimensions of mispricing measures. The denominator, K, averages the ranks by the number of 31 In constructing MI, I employ the methodology outlined in Butler, Grullon, and Weston (2005). In their paper, they create a liquidity index that comprises the effects of ranking on 6 different liquidity measures. 63 PAGE 70 64 mispricing values available for each firm in the sample in a particular year. For example, the sum of the Rankk( EXVi,k) values of a firm that has only 3 mispricing measures is divided by K =3. Finally, dividing by N I scale the MI from 0 (least mispriced) to 1 (most mispriced). By com puting average of all ranks from five different mispricing measures, MI has the advantage that it balances out the effects and shortcomings of all other mispricing measures while aggregating their informativeness, and thereby provides a more complete picture of mispricing. Detailed descriptions for all variables used to construct MI and their summary statistics can be found in Tables 10 and 11, respectively. Panel A of Table 12 shows the coefficients of correlations between the diffe rent mispricing measures. As expected, all mispricing measures are significantly positivel y correlated at the one percent level, or better, even though these valuation measures are based on widely di fferent theoretical concepts and their measurements rely on a variety of accounting and/or financial variables. All individual mispricing meas ures are more significantly and positively correlated with the mispricing index ( MI) than with the other individual measures, suggesting that MI is an appropriate aggregate measure of mispricing for use in the tests. PAGE 71 Table 10 Variable Definitions Variables Descriptions Mispricing measures EXVRI Absolute value of excess value based on Ohlsons (1995) residual income value approach. EXVRIit ln()ititPRICEIV ,where PRICEit is the stock price at the end of June of each year from CRSP, and I(V)it is intrinsic value using the residual income model (Ohlson (1995)) and median values of analysts forecasts issued in June, as in Frankel and Lee (1998). [/(ititCPTLICPTL EXVBO Absolute value of excess value based on Berger and Ofek (1995) approach. EXVBOi,t ,)], where CPTLi,t is total capital, which is market value of equity plus book value of debt, I(CPTLi,t) is the imputed value derived as the product of firm sales and the median capital to size ratio in the firms industry. The industry classification here is based on the FamaFrench 48 sectors. This measure of mispricing is constructed in a similar fashion as the first one (EXVRIi,t), but uses firms total capital instead of price and computes imputed value based on FamaFrench 48 industry classification. Thus the intrinsic value here is a size and industry benchmark. EXVRK Absolute value of the excess value based on RhodesKropf et al. (2005). Fundamental value, V is estimated by decomposing the markettobook into two components: a measure of price to fundamentals (ln(M/V)), and a measure of fundamentals to book value (ln(V/B)). The first component captures the part of booktomarket associated with mispricing. This component is further decomposed into firmspecific and industryspecific misprising. I use the firmspecific mispricing component based on Model III of RhodesKropf et al. (2005) that also accounts for net income and leverage effects. ln(Mi,t)= 0j,t + 1j,t ln(Bi,t)+ 2j,t ln(NI)+i,t + 3j,t I(<0)ln(NI)+i,t + 4j,t ln(LEVi,t)+ i,t, where M is firm value, B is book value, NI+ is absolute value of net income, I(<0)ln(NI)+ is an indicator function for negative net income observations, and LEV is the leverage ratio. EXVMB Absolute value of the industryadjusted markettobook ratio. MBIAi,t , ln[()]MBMedMB itjt where, MBi,t is the market to book ratio for firm i at time t, and Med(MBj,t) is the jth industry median of MBt. ARET Absolute value of a firms average monthly abnormal return for each year. The expected return of month t is computed using benchmarks from the Fama/French threefactor model estimated over the fiveyear period immediately preceding month t. The estimation of the parameters is based on the model, E(Ri,t) Rf,t = 0 + M (Rm,t Rf,t) + SMB SMBt + HML HMLt + it where E(Rit) is the rate of return on the ith companys common stock in month t, Rf,t is riskfree rate, Rm,t is the valueweighted market portfolio return, and SMBt and HMLt are the size and booktomarket factors as in Fama and French (1993, 1996). Abnormal returns, ARETi,t, are computed as differences of actual returns, Ri,t, from the expected returns derived from the parameters of model, and ARETi,t= Ri,t E(Ri,t) MI Mispricing index.kik, where Rankk(EXVi,k) is the rank function which assigns a rank for each observation from least misvalued (rank of one) to most misvalued (rank of N). EXVi,k is the kth measure of mispricing for firm i in my sample, and K represents the dimensions of mispricing measures. The denominator, K, averages the ranks by the number of mispricing values available for each firm in the sample in a particular year. N is number of observations. MI is scaled from 0 (least mispriced) to 1 (most mispriced). ,(1/)(1/)()Ki kMINKRANKEXV 65 PAGE 72 Table 10 (Continued) Variables Descriptions Agency cost measures FCF Free cash flows computed as the interaction of the growth with free cash flows. ,,,, ititititFCFFreecashflowsTotalassetsGowthdummy where Free cash flow = operating income before depreciation (taxes + interest expense + dividends paid). Growth dummy = 1 if the firms Tobins q is less than 1 and 0 otherwise. Tobins q = [market value of common equity + preferred stock liquidating value + longterm debt (shortterm assets shortterm liabilities)] / (total assets). EXPR Expense ratio which measures the inefficiency in the management control of operating costs. ,,,ititit E XPROperating expenseSales AUR Asset utilization ratio which measures the effectiveness of firms management in deploying assets. ,,,ititit A URSalesTotal assets INDB Proportion of independent directors on corporate board. IO Institutional ownership which is the percentage of shares that are owned by institutional investors. GI Corporate governance index constructed by Gompers et al. (2003) to proxy for the level of shareholder rights. The Governance Index is constructed by counting 28 provisions listed in 5 categories: Delay, Protection, Voting, Other, and State. Among 28 provisions, 24 are unique and equally weight in index. A firm with high governance index (i.e., many antitakeover provisions) is expected to have high level of agency problem. CMPT Product market competition which is computed as the inverse value of Herfindahl concentration index. CMPTi = 221j j, where Salesj is the annual sales of jth firm belonging to the industry in which firm i is included. A higher CMPT (i.e., lower Herfindahl index) thus indicates that a product market is more competitive. jjSalesSales ACOV Analyst coverage is computed as residual from the regression of analyst coverage on firm size. Forecast variable is extracted from security analyst one fiscal yearahead forecasts collected every June from I/B/E/S Detail History Database. AFE Analyst earnings forecast error. ,,, , ()()ititit+1itAFEMedAFEPSMedAF where Med(AF)i,t is the median forecast and the actual earnings per share EPSi,t+1 is the actual earnings per share. Variables are extracted from security analyst one fiscal yearahead forecasts collected every June from I/B/E/S Detail History Database. AFD Analyst earnings forecast dispersion. ,, , ..()()itititStdDevAFMedAF AFD where Std.Dev.(AF)i,t is standard deviation of one year ahead forecasts. Variables are extracted from security analyst one fiscal yearahead forecasts collected every June from I/B/E/S Detail History Database. ACI Agency cost index. ACI is constructed by using the same methodology for mispricing index (MI) and by combining all ranks of five variables (FCF, EXPR, GI, AFE, and AFD) and inverse ranks of five variables (AUR, INDB, IO, CMPT, and ACOV). ACI is scaled from 0 (least agency costs) to 1 (greatest agency costs). 66 PAGE 73 67 Table 10 (Continued) Variables Descriptions Compensation variables TCOMP Total compensation (in thousand $) which comprises 7 items: 1) salary, 2) bonus, 3) exercised options, 4) restricted stock grant, 5) longterm incentive plan, 6) other annual compensation, and 7) all other compensation. SALARY Salary which is the dollar value (in thousand $) of the base salary (cash and noncash). BONUS Bonus which is the dollar value (in thousand $) of a bonus (cash and noncash). RSTOCK Restricted stock grant which is the value (in thousand $) of restricted stock granted which is determined as of the date of the grant. OPTION Stock option grant is the aggregated dollar value (in thousand $) of stock options granted to the CEO during the year as valued using S&Ps BlackScholes methodology. LTIP Longterm incentive plan is the dollar value (in thousand $) paid out to the CEO under the company's longterm incentive plan. forgiveness, 3) imputed Interest, 4) payouts for cancellation of stock options, 5) payment for unused vacation, 6) tax reimbursements, 7) signing bonuses, 8) 401K contributions, and 9) life insurance premiums. OTHERC Other annual compensation which is the dollar value (in thousand $) of other annual compensation not properly categorized as salary or bonus. This includes items such as: 1) perquisites and other personal benefits, 2) above market earnings on restricted stock, options/SARs or deferred compensation paid during the year but deferred by the officer, 3) earnings on longterm incentive plan compensation paid during the year but deferred at the election of the officer, 4) tax reimbursements, and 5) the dollar value of difference between the price paid by the officer for company stock and the actual market price of the stock under a stock purchase plan that is not generally available to shareholders or employees of the company (Note: This does not include value realized from exercising stock options). ALLOC All other compensation which is the dollar value (in thousand $) listed under "All Other Compensation" in the Summary Compensation Table. This is compensation that does not belong to other categories, which includes items such as: 1) severance payments, 2) debt forgiveness, 3) imputed Interest, 4) payouts for cancellation of stock options, 5) payment for unused vacation, 6) tax reimbursements, 7) signing bonuses, 8) 401K contributions, and 9) life insurance premiums. %RSTOCK Restricted stock grant / total compensation. %OPTION Stock option grant / total compensation. Firm characteristic SIZE Log of total assets. LEV Leverage. The ratio of longterm debt to total assets. ROA Return on assets. The ratio of net income to total assets. AGE Firm age. AGE = ln(1+ age), where age is the number of years since the stock inclusion in the CRSP database. DIVER Diversification dummy that equals one if a firm operates in multisegments and zero otherwise. DD Dividendpayer dummy that equals one if a firm pays dividends and zero otherwise. PAGE 74 68 Table 11 Descriptive Statistics Reported are descriptive statistics for my sample firms. The sample contains 38,781 firmyear observations (6,446 firms) over the period 1985 2004. All va riables are as defined in Table 10. Variables N Mean Std.Dev. 5% Median 95% Mispricing measures Ohlson (1995) approach ( EXVRI ) 36,115 0.794 0.841 0.077 0.677 1.889 Berger and Ofek (1995) approach ( EXVBO ) 38,582 0.641 0.608 0.036 0.489 1.739 RhodesKropf et al. (2005) approach ( EXVRK) 38,779 0.385 0.355 0.025 0.288 1.081 Markettobook ratio approach ( EXVMB ) 38,781 0.404 0.379 0.018 0.302 1.155 Abnormal return approach ( ARET ) 38,775 0.102 0.056 0.039 0.089 0.207 Mispricing index ( MI) 38,781 0.502 0.172 0.240 0.489 0.805 Agency cost measures Free cash flow ( FCF ) 27,129 0.013 0.035 0 0 0.084 Expense ratio ( EXPR ) 27,815 0.375 4.196 0.047 0.228 0.692 Asset utilization ratio ( AUR) 38,781 1.208 0.807 0.243 1.071 2.648 Independent board of directors (INDB ) 9,373 0.626 0.193 0.273 0.667 0.889 Institutional ownership ( IO ) 30,483 0.503 0.243 0.093 0.513 0.892 Governance index ( GI ) 15,613 9.073 2.748 5 9 14 Product market competition ( CMPT) 38,781 0.876 0.105 0.669 0.914 0.971 Analyst coverage ( ACOV ) 36,827 2 109 5.517 7.623 0.574 10.39 Analyst earnings forecast error ( AFE) 34,022 0.823 6.306 0.005 0.130 2.587 Analyst earnings forecast dispersion ( AFD ) 33,097 0.220 1.272 0.009 0.048 0.706 Agency cost index ( ACI ) 38,781 0.505 0.130 0.295 0.503 0.724 Compensation variables Total compensation (TCOMP) 10,812 3,768 13,820 322.9 1,366 12,919 Salary ( SALARY ) 10,812 592.0 338.7 206.1 530.0 1102 Bonus ( BONUS ) 10,812 580.5 1061 0 311.8 2000 Restricted stock grant ( RSTOCK ) 10,812 425.0 9053 0 0 1307 Stock options ( OPTION ) 10,812 1851 9684 0 0 8460 Longterm incentive plan ( LTIP ) 10,812 139.4 793.4 0 0 714.0 Other annual compensation ( OTHERC) 10,812 43.20 225.9 0 0 182.1 All other compensation ( ALLOC ) 10,812 136.8 794.4 0 16.64 400.3 % of restricted stock grant ( %RSTOCK ) 10,812 0.052 0.142 0 0 0.393 % of stock options ( %OPTION ) 10,812 0.182 0.296 0 0 0.858 Firm characteristics Firm size ( SIZE ) 38,781 19.76 1.677 17.36 19.56 22.86 Leverage ( LEV ) 38,647 0.163 0.179 0 0.103 0.536 Return on assets ( ROA) 38,781 0.031 0.121 0.182 0.049 0.161 Firm age ( AGE ) 38,781 2.334 0.843 1.099 2.398 3.555 Diversification dummy ( DIVER ) 31,798 0.328 0.469 0 0 1 Dividendpayer dummy ( DD ) 37,350 0.381 0.486 0 0 1 PAGE 75 Table 12 Correlations Coefficients between Index and Individual Measures This table shows the correlations coefficients between index and individual measures and corresponding pvalues in brackets. All variables are as defined in Table 10. *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. Panel A: Correlations between mispricing index (MI) and individual measures Constructed sign of correlation with MI MI EXVRI EXVBO EXVRK EXVMB Ohlson (1995) approach (EXVRI) + 0.323*** [0.000] Berger and Ofek (1995) approach (EXVBO) + 0.514*** [0.000] 0.084*** [0.000] RhodesKropf et al. (2005) approach (EXVRK) + 0.688*** [0.000] 0.175*** [0.000] 0.252*** [0.000] Markettobook ratio approach (EXVMB) + 0.705*** [0.000] 0.142*** [0.000] 0.300*** [0.000] 0.749*** [0.000] Abnormal return approach (ARET) + 0.435*** [0.000] 0.117*** [0.000] 0.206*** [0.000] 0.200*** [0.000] 0.191*** [0.000] 69 PAGE 76 70 Table 12 (Continued) Constructedsign of correlation with ACI ACI FCF EXPR AUR INDB IO GI CMPT ACOV AFE Free cash flow (FCF) + 0.160*** [0.000] Expense ratio (EXPR) + 0.049*** [0.000] 0.012* [0.051] Asset utilization ratio (AUR) 0.438*** [0.000] 0.139*** [0.000] 0.044*** [0.000] Independent board of directors (INDB) 0.163*** [0.000] 0.008 [0.453] 0.026** [0.020] 0.017 [0.109] Institutional ownership (IO) 0.415*** [0.000] 0.027*** [0.000] 0.013* [0.041] 0.038*** [0.000] 0.244*** [0.000] Governance index (GI) + 0.074*** [0.000] 0.024*** [0.007] 0.027*** [0.002] 0.034*** [0.000] 0.263*** [0.000] 0.103*** [0.000] Product market competition (CMPT) 0.346*** [0.000] 0.003 [0.659] 0.006 [0.328] 0.115*** [0.000] 0.037*** [0.000] 0.057*** [0.000] 0.032*** [0.000] Analyst coverage (ACOV) 0.364*** [0.000] 0.147*** [0.000] 0.001 [0.923] 0.017*** [0.001] 0.012 [0.253] 0.043*** [0.000] 0.018** [0.023] 0.015*** [0.005] Analyst earnings forecast error (AFE) + 0.150*** [0.000] 0.002 [0.817] 0.001 [0.831] 0.026*** [0.000] 0.019* [0.090] 0.044*** [0.000] 0.005 [0.570] 0.008 [0.165] 0.031*** [0.000] Analyst earnings forecast dispersion (AFD) + 0.184*** [0.000] 0.005 [0.460] 0.011 [0.103] 0.050*** [0.000] 0.013 [0.210] 0.040*** [0.000] 0.001 [0.862] 0.015*** [0.006] 0.020*** [0.000] 0.684*** [0.000] PAGE 77 B. Measures of Agency Costs Financial economists have attempted to measure firms propensity for agency conflicts by using measures of internal and external agency problem resolution mechanisms. Agrawal and Knoeber (1996) address the empirical implications of the interdependence among such mechanisms. They examine seven mechanisms that potentially can control agency problems and present evidence of interdependence, suggesting that results obtained from crosssectional OLS regressions of firm performance on several single mechanisms may be misleading. Therefore, to avoid this problem, I utilize ten measures used in past studies, and combine them into an agency costs index for each firm. These measures are described below. 1) FCF, free cash flow. Agency conflicts involving free cash flows are likely to be prevalent in low growth firms because they generally have substantial free cash flow, which managers could decide to overinvest. In contrast, high growth firms are not as likely to suffer from the free cash flow problem because they are usually short of cash after using internal funds for funding new projects and often need to rely on external financing to cover their financing needs. Therefore, following Doukas, Kim, and Pantzalis (2000) I proxy agency costs of free cash flow using the interaction of a poor growth opportunities indicator with free cash flows standardized by total assets. ,,,, ititititFreecashflows F CFGowthdummyTotalassets (8) where Free cash flow is measured as operating income before depreciation minus the sum of taxes, interest expense, and dividends paid (see Lehn and Poulsen (1989)). 71 PAGE 78 Growth dummy takes the value of 1 if the firms Tobins q is less than 1 (indicating a poorly managed firm) and the value of 0 otherwise, where Tobins q is computed as [market value of common equity + preferred stock liquidating value + longterm debt (shortterm assets shortterm liabilities)] / (total assets), as in Chung and Pruitt (1994). 2) EXPR, the expense ratio which measures managers inefficiency in terms of controlling operating costs. High EXPR represents high agency costs. ,,, itititOperatingexpenseEXPRSales (9) 3) AUR, the asset utilization ratio which measures the effectiveness of firms management in deploying assets. The idea behind the asset utilization ratio as a measure of agency costs is that when a firm has low salestoasset ratio, it is likely that managers act inefficient ways by making poor investment decisions, consuming executive perquisites, etc. Therefore, AUR should be inversely related to agency costs. ,,, itititSalesAURTotalassets (10) Both EXPR and AUR have been used in Ang, Cole, and Lin (2000). 4) INDB, the proportion of independent directors on corporate board. A smaller INDB is an indicator of higher potential for agency conflicts. Cotter, Shivdasani, and Zenner (1997) show that target shareholder gains from tender offers are higher when the targets board is more independent, suggesting that independent directors are more 72 PAGE 79 likely to use resistance strategies to enhance shareholder wealth. This notion is also supported by the findings of Uzun, Szewczyk, and Varma (2004). They show that the likelihood of corporate fraud declines as the fraction of independent directors increases. 5) IO, the institutional ownership which is the percentage of shares that are owned by institutional investors. Given institutional investors monitoring role, IO should be inversely related to agency costs. Brickley, Lease, and Smith (1988) show that institutional investors and other blockholders vote more actively on antitakeover amendments than nonblockholders, and that institutional opposition is greater when the proposal seems to harm stockholders. McConnell and Servaes (1990) find a significant and positive relation between Tobins q and the fraction of shares owned by institutional investors. Jiambalvo, Rajgopal, and Venkatachalam (2002) find that the extent to which stock prices lead earnings is positively associated with the level of institutional ownership. Hartzell and Starks (2003) find that institutional ownership concentration is positively related to the payforperformance sensitivity of managerial compensation and negatively related to the level of compensation. They suggest that the institutional investors serve a monitoring role in mitigating the agency problems between shareholders and managers. Therefore, the higher the percentage ownership by institutions, the lower should be the agency costs. 6) GI, the corporate governance index constructed by Gompers, Ishii, and Metrick (2003) to proxy for the level of shareholder rights. The Governance Index is constructed by counting 28 provisions related to shareholder protection and listed in 5 73 PAGE 80 categories: Delay, Protection, Voting, Other, and State. Among the 28 provisions, 24 are unique and enter the index with equal weight. Gompers et al. (2003) construct the governance index without requiring any judgment about the efficacy or wealth effects of any of these provisions but consider their impact on the balance of power between managers and outside shareholders. Based on Jensens (1986) argument that threat of takeover is a strong form of managerial discipline, a firm with high governance index (i.e., many antitakeover provisions) is expected to have high level of agency problem. 7) CMPT, product market competition. The competition in the product markets drives prices towards minimum average cost in an activity, thereby motivating managers to increase firm efficiency. Hart (1983), in a theoretical model shows that the competition in the product market reduces the amount of managerial slack. Some studies have empirically tested the relation between product market competition and corporate agency costs. For example, Jagannathan and Srinivasan (1999) show that competition in the product market reduces agency costs. My proxy for the competition in the product market is computed as the inverse value of Herfindahl concentration index. CMPTi = 1 Herfindahl concentration index 221jjjSalesSales j (11) where Salesj is the annual sales of jth firm belonging to the industry in which firm i is included. If the total amount of sales in the industry is dominated by few firms, then the Herfindahl index will show a high value near one. Higher values of CMPT (i.e., 74 PAGE 81 lower Herfindahl index) thus indicate that the product market is more competitive, and therefore CMPT should be negatively related to agency costs. 8) ACOV, analyst coverage. Security analysis can act as a monitoring mechanism in reducing agency costs (Doukas et al. (2000)), and therefore ACOV is expected to be negatively related to agency costs. Hong, Lim, and Stein (2000) point out that there is a strong firmsize effect on analyst coverage. Therefore, the analyst coverage measure is based on the residuals from the regression of analyst coverage on firm size. 9) AFE, analyst earnings forecast error. The forecast error captures forecasting ability of security analysts covering the firm. The absolute forecast error has been also used by several studies as a proxy of information asymmetry (e.g., see Atiase and Bamber (1994), and Christie (1987)). If a firm is transparent, the considerable amount of information about future earnings is available to market participants, and so analysts make accurate earnings forecasts. Therefore, AFE should be positively related to agency costs. ,,,,()()itit+1ititMedAFEPSAFE=MedAF (12) where Med(AF)i,t is the median forecast and the actual earnings per share EPSi,t+1 is the actual earnings per share. 10) AFD, analyst earnings forecast dispersion. Barron, Kim, Lim and Stevens (1998) show that analyst forecast dispersion reflects both diversity of analyst beliefs and the lack of precision in analyst forecasts. Prior studies have also used the dispersion of analyst forecasts as an information asymmetry proxy (e.g., see Krisnhnaswami and 75 PAGE 82 Subramaniam (1999)). AFD is therefore supposed to be positively related to agency costs. ,,,..()()itititStdDevAFAFD=MedAF (13) where Std.Dev.(AF)i,t is standard deviation of one year ahead forecasts. Analyst coverage, ACOV, and the two analyst forecastbased variables (AFE and AFD) are constructed from security analysts one fiscal yearahead forecasts collected every June from the I/B/E/S Detail History Database. 11) ACI, an agency cost index that combines all ten agency cost measures described above. Five variables (FCF, EXPR, GI, AFE, and AFD) are positively related to agency costs, while the other five variables (AUR, INDB, IO, CMPT, and ACOV) are inversely related. Thus, I construct an index (ACI) for firms agency costs by combining ranks of former five measures and inverse ranks of later five variables. The methodology used in the construction of ACI is the same as the one used for the mispricing index (MI). Table 10 provides detailed descriptions of all variables used to construct ACI and Table 11 documents descriptive statistics. Correlation coefficients are reported in Panel B of Table 12. By construction, free cash flows, expense ratio, governance index, forecast error, and forecast dispersion are positively associated with the agency cost index. In contrast, asset utilization ratio, proportion of independent directors, institutional ownership, product market competitiveness, and analyst coverage are negatively related to agency cost index. 76 PAGE 83 77 IV. Agency Costs and Equity Mispricing In this section, I present analysis base d on univariate tests, the design of my multivariate tests empirical methodology, and regression evidence on the relation between agency costs and equity mispricing. A. Univariate Analyses Table 13 illustrates how high agency cost firms differ from low agency cost firms in terms of firm characteristics. It reports m ean values of all variables used in the study for the quintile groups classified based on the level of the agency cost index (ACI ). Also reported are the mean differences across the two extreme groups (highest versus lowest ACI quintiles) and the corresponding tstatistics for the mean difference tests. In line with hypothesis #1, the mispricing index ( MI) shows a positive relation with the level of agency costs. The mean difference of MI between the highest and lowest ACI quintile groups is 0.038 with tstatistic of 13.92. The dollar amount of the different CEO compensation components, in most cases, is on average lower for firms in the highest ACI quintile compared to firms in the lowest ACI quintile. The evidence from the remaining firmspecific variables is consistent with prior studies examining the relationship of agency costs and firm characte ristics. Firms with high levels of agency costs are generally younger, sma ller, more levered and less pr ofitable than firms with low levels of agency costs. They are also more likely to be diversified across many industries, and less likely to pay dividends. PAGE 84 78 Table 13 Univariate Tests Reported are mean values of variables for the quartile subsamples sorted on agency cost index (ACI). Also reported are the differences in mean values between highand lowACI firms and the corresponding tstatistics. All variables are as defined in Table 10. and *** indicate significance at the 10%and 1%levels, respectively. Sorted on agency cost index (ACI) Low Q1 Q2 Q3 Q4 High Q5 Mean diff.: High Low tstat: Diff.=0 Mispricing measure Mispricing index (MI) 0.504 0.479 0.482 0.502 0.541 0.038*** 13.92 Compensation variables Total compensation (TCOMP) 4899 3926 3202 3388 2367 2531*** 4.30 Salary (SALARY) 613.4 611.9 577.3 573.8 553.1 60.34*** 5.28 Bonus (BONUS) 660.9 651.8 534.2 526.2 403.5 257.4*** 7.97 Restricted stock grant (RSTOCK) 829.5 266.8 327.3 255.5 244.0 585.4 1.18 Stock options (OPTION) 2518 2061 1393 1712 874.1 1644*** 5.78 Longterm incentive plan (LTIP) 109.7 190.8 152.3 121.9 101.8 7.949 0.32 Other annual compensation (OTHERC) 45.19 40.88 40.57 43.25 48.27 3.079 0.38 All other compensation (ALLOC) 122.3 102.7 177.3 155.0 142.4 20.12 0.93 % of restricted stock grant (%RSTOCK) 0.054 0.047 0.057 0.048 0.055 0.001 0.28 % of stock options (%OPTION ) 0.238 0.203 0.162 0.146 0.094 0.144*** 14.08 Firm characteristics Firm size (SIZE) 20.04 19.98 19.78 19.58 19.42 0.614*** 23.57 Leverage (LEV) 0.104 0.139 0.165 0.188 0.217 0.114*** 38.96 Return on assets (ROA) 0.084 0.059 0.037 0.006 0.031 0.114*** 61.95 Firm age (AGE) 2.399 2.440 2.383 2.301 2.150 0.250*** 18.96 Diversification dummy (DIVER) 0.299 0.339 0.346 0.340 0.314 0.015* 1.80 Dividendpayer dummy (DD) 0.471 0.472 0.418 0.332 0.202 0.269*** 36.15 PAGE 85 B. Multivariate Analyses Univariate tests can only provide limited insight into whether the positive impact of agency costs on equity mispricing is driven by other firm variables. This potential limit of univariate testing can be overcome in a multivariate test setting. I perform the multivariate analysis of the relation between agency costs and mispricing by using timeseries average of crosssectional regressions (as in Fama and MacBeth (1973)).32 I estimate the following regression equation: MIi,t = 0 + 1 ACIi,t + 2 SIZEi,t + 3 LEVi,t + 4 ROAi,t + 5 AGEi,t + 6 DIVERi,t + 7 DDi,t + i,t, (14) where i indexes firms, t is a yearly time index, and ACI is the agency cost index. Based on the literature on equity mispricing, I use a number of different control variables. They are market capitalization (SIZE), leverage (LEV), profitability (ROA), firm age (AGE), a diversification dummy (DIVER), and a dividendpayer dummy (DD). Descriptions of all variables are in Table 10 with descriptive statistics provided in Table 11. 32 Following Fama and MacBeth (1973), I estimate separate annual regressions and calculate tstatistics as follows. ()()1jjjtsn where j is the mean coefficient over the sample years, () j s is the standard deviation of the yearly estimates, and n is the number of years. 79 PAGE 86 Table 14 Agency Cost and Equity Mispricing This table shows timeseries average of crosssectional regressions of mispricing on idiosyncratic volatility and other firm characteristics. All variables are as defined in Table 10. ** and *** indicate significance at the 5%and 1%levels, respectively. Dep. var. = MI Dep. var. = Log of MI [1] [2] [3] [4] Intercept 0.448*** (70.37) 0.771*** (24.94) 0.360*** (72.46) 0.584*** (27.35) Agency cost index (ACI) 0.106*** (8.39) 0.031*** (2.87) Log of ACI 0.100*** 0.024** (8.04) (2.25) Log of total assets (SIZE) 0.008*** (4.48) 0.005*** (4.62) Leverage (LEV) 0.198*** (10.81) 0.126*** (10.18) Return on assets (ROA) 0.069** (2.47) 0.047** (2.61) Log of firm age (AGE) 0.029*** (21.04) 0.019*** (20.00) Diversification dummy (DIVER) 0.030*** (10.06) 0.020*** (9.64) Dividendpayer dummy (DD) 0.065*** (16.59) 0.044*** (16.40) N 38,781 30,716 38,781 30,176 Average R2 0.91% 21.61% 0.83% 21.57% The regression results appear in Table 14.33 Columns [1] and [2] display the models where the mispricing index (MI) is the dependent variable, while columns [3] and [4] show results for models where the logtransformed mispricing index is used as dependent variable.34 The results show a significant positive relation between agency costs and mispricing, suggesting that higher agency costs are strongly associated with higher levels of equity mispricing. In regressions [1] and [2], the estimated coefficient of 33 It should be noted that the results I obtained using the individual mispricing measures compiled in MI are qualitatively similar to the ones reported here. They are left out of the paper for the sake of brevity, but are available upon request. 34 This transformation is to guard against a possibility that mispricing index (MI) which takes value from 0 to 1 can lead to erroneous interpretation of results. I find that the results are, as shown, very similar to ones obtained from the original regressions. 80 PAGE 87 the agency cost index is 0.106 with a tstatistic of 8.39 and 0.100 with a tstatistic of 8.04, respectively. Controlling for other firm characteristics does not qualitatively change the result, even though the coefficients of the agency cost variable and the corresponding tstatistics are reduced. The coefficients of the control variables suggest that equity mispricing is especially high for firms that are small, less leveraged, less profitable, young, and less likely to pay dividends. Contrary to previous studies, e.g. Berger and Ofek (1995), industrial diversification is found to be negatively related to equity mispricing. Overall, the results from Table 14 indicate that the level of agency costs is a strong determinant of equity mispricing in support of hypothesis #1. C. Robustness Tests In this subsection I present several robustness checks aimed at ensuring that the findings in Table V are not due to the particular estimation methodology used. First, since my study relies on crosssectional/timeseries data, I use a fixedeffects model which regards differences between firms as parametric shifts of the regression function and controls for possible differences across firms. Second, I compute differenceindifferences estimates by including year fixedeffects as well as firm fixedeffects. Third, I compute statistical significances using Whites (1980) standard errors which are robust to heteroskedasticity. Finally, I estimate a model using only the firstyear observation of each firm. This robustness check with the firstyear data allows me to assess whether or not previous results are driven by the existence of multiple observations on the same firms. The results of these robustness checks are reported in Table 15. To save space, 81 PAGE 88 82 Table 15 only reports the results of regressi on models that include all firmspecific control variables. I find that all regressions s how a consistent pattern of coefficients on the agency costs index ( ACI ). They all remain positive and statistically significant. Therefore, the previous results shown in Table 14 are confirmed by these alternative regression models. V. Interpretation of the Positive Rela tion between Agency Costs and Equity Mispricing So far, I have found that the level of ag ency costs is significantly and positively related with equity mispricing. As discussed ea rlier, agency theory defines agency costs as the costs incurred by an organization that are associated with problems such as interest conflicts between management and sharehol ders and/or information asymmetry where managers discriminately have better and/or more information than shareholders. In my previous results, I cannot convey whethe r mispricing is caused by informational asymmetry or incentive conflicts To directly test this, I control for equitybased compensation which can potentially resolve ag ency problems, but not necessarily reduce information asymmetry. PAGE 89 Table 15 Robustness Checks of Regression of Equity Mispricing on Agency Cost This table reports robustness checks of regressions of mispricing on agency cost and other firm characteristics. Reported are the coefficients and tstatistics of regression models [2] and [4] in Table V. Columns [1] and [2] report results using panel regressions. Columns [3] and [4] report results of regressions computing differenceindifference estimates (i.e., including firm fixedeffects and year fixedeffects). Columns [5] and [6] report results using Whites (1980) heteroskedasticity correction model. Columns [7] and [8] report results only using the firstyear data of each firm. All variables are as defined in Table 10. *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. Panel regression model Differenceindifferences Whites (1980) heteroskedasticity correction model Firstyear regression [1] Dep. var = MI [2] Dep. var = Log of MI [3] Dep. var = MI [4] Dep. var = Log of MI [5] Dep. var = MI [6] Dep. var = Log of MI [7] Dep. var = MI [8] Dep. var = Log of MI Intercept 0.961*** (54.42) 0.700*** (59.44) 0.957*** (50.17) 0.694*** (54.70) 0.789*** (31.44) 0.596*** (34.72) 0.749*** (20.77) 0.567*** (24.15) Agency cost index (ACI) 0.035*** (4.19) 0.035*** (4.17) 0.031** (2.52) 0.051*** (2.95) 0.030*** 0.031*** 0.024* 0.043** Log of ACI (3.65) (3.71) (1.94) (2.55) 0.018*** 0.012*** 0.017*** 0.011*** 0.008*** 0.006*** 0.007*** 0.005*** Log of total assets (SIZE) (19.01) (18.90) (16.86) (16.43) (6.23) (6.50) (3.60) (3.98) Leverage (LEV) 0.139*** 0.090*** (21.79) (21.28) 0.145*** (22.12) 0.094*** (21.75) 0.227*** (25.54) 0.146*** (24.42) 0.270*** (19.47) 0.169*** (18.98) Return on assets (ROA) 0.104*** 0.070*** (13.29) (13.36) 0.108*** (13.44) 0.072*** (13.58) 0.140*** (11.72) 0.091*** (12.03) 0.153*** (9.25) 0.097*** (9.14) Log of firm age (AGE) 0.033*** 0.022*** (20.21) (19.96) 0.033*** (18.97) 0.021*** (18.63) 0.029*** (13.58) 0.019*** (13.20) 0.017*** (5.50) 0.011*** (5.42) Diversification dummy (DIVER) 0.010*** 0.007*** (4.40) (4.72) 0.014*** (5.89) 0.010*** (6.01) 0.026*** (7.46) 0.018*** (7.46) 0.035*** (6.11) 0.023*** (6.23) Dividendpayer dummy (DD) 0.041*** 0.029*** (14.29) (15.05) 0.042*** (13.97) 0.030*** (15.01) 0.061*** (14.73) 0.042*** (14.90) 0.063*** (10.05) 0.042*** (10.37) No. of observations 30,716 30,716 30,716 30,716 30,716 30,716 4,883 4,883 Average R2 19.56% 19.57% 20.05% 20.10% 20.86% 20.74% 19.39% 19.37% 83 PAGE 90 84 Figure 6 Comparisons of Equity Mispricing Levels This figure presents averages of mispricing measures for users and nonusers of restricted stock grant (in Panel A) or stock options (in Panel B). *** indicates significance at the 1%level. Panel A: Comparisons of mispricing levels between users and nonusers of restricted stock grants. Panel B: Comparisons of mispricing levels between users and nonusers of stock options. EXVRI EXVBO EXVRK EXVMB ARET EXVRI EXVBO EXVRK EXVMB ARET 0.800.830.860.89NonusersUsers 0.500.550.600.65NonusersUsers 0.300.350.400.45NonusersUsers 0.300.350.400.45NonusersUsers 0.070.080.090.10NonusersUsers 0.800.830.860.89NonusersUsers 0.500.550.600.65NonusersUsers 0.300.350.400.45NonusersUsers 0.300.350.400.45NonusersUsers 0.070.080.090.10NonusersUsers Difference: 0.004*** Difference: 0.060*** Difference: 0.068*** Difference: 0.048*** Difference: 0.018 Difference: 0.017*** Difference: 0.099*** Difference: 0.090*** Difference: 0.085*** Difference: 0.040*** PAGE 91 My tests focus on equitybased compensation, i.e., restricted stock and stock option grants. I create two dummy variables which take the value of one if a firm uses restricted stock grant (alternatively, stock options) for CEO compensation, and take the value of zero otherwise. The relationship between equity based compensation components and the different mispricing measures is graphically reported in Figure 6. Panel A shows how the five individual mispricing measures differ for firms that use versus firms that do not use restricted stock grants, while Panel B shows the corresponding comparison between firms that use versus firms that do not use stock options. Figure 6 clearly shows that firms providing restricted stock grants to their CEOs are substantially less mispriced than firms which do not. All differences are economically and statistically significant. As shown in Panel B, however, the use of stock option grants for CEOs is positively associated with mispricing. This evidence provides support for the notion that CEOs may want to induce stock mispricing when their compensation relies heavily on stock options. The univariate tests results that correspond to Figure 6 are in line with the second hypothesis, which suggests that the impact of agency costs on mispricing gets stronger (weaker) when the proportion of the CEOs compensation that comes from options (restricted stocks) increase. This implies that the coefficient of the agency cost index (ACI), 1 in equation (14), can be expressed as: 1 = 0 + 1 (%RSTOCKi,t) + 2 (%OPTIONi,t) (15) 1 and 2 capture the effect of restricted stock grants (%RSTOCKi,t) and option grants (%OPTIONi,t) as percentages of total compensation respectively, on agency costs. These 85 PAGE 92 two coefficients represent the effect on mispricing from the firms choice of equitybased compensation, which determine the degree of interest conflicts in an agency problem. Here 0 represents the leftover effect of agency costs (i.e., that related to information asymmetry) on mispricing. Subsequently, I plug equation (15) into the expression of equation (14) and rewrite the model as: MIi,t = 0 + 1 ACIi,t + 2 (ACIi,t %RSTOCKi,t) + 3 (ACIi,t %OPTIONi,t) + 4 SIZEi,t + 5 LEVi,t + 6 ROAi,t + 7 AGEi,t + 8 DIVERi,t + 9 DDi,t + i,t. (16) If my tests provide support for the second hypothesis, the first coefficient (1, capturing the effect of information asymmetry on mispricing) should no longer be significant. If the third hypothesis is supported, the coefficient of the interaction term between agency cost and restricted stock grant (2) will be negative and the coefficient of the interaction term between agency cost and stock options (3) will be positive. Table 16 documents the coefficients of the above regression model. I estimate the timeseries average of crosssectional regressions, as in Table 14 and the three other robustness regressions as in Table 15. My results show that, in contrast to the findings of studies claiming that information asymmetry is a key determinant in equity mispricing, the leftover agency cost (i.e., information asymmetry) is not a powerful explanatory variable in most cases after controlling for the interaction terms of ACI with compensation variables that are directly related to the degree of the conflict of interests between CEO and owners. As predicted in hypothesis #3, the interaction between restricted stock grants and agency costs generally shows a negative impact on mispricing. 86 PAGE 93 87 However, this effect is not statistically signi ficant. Moreover, I find that the coefficient of the interaction term between option grants and agency costs is significant and positive in all models. This result is consistent with the notion that mispricing increases as the use of stock options exaggerates the agency probl em between managers and shareholders. In sum, my findings provide two important insights. First, in addition to the level of information asymmetry, the conflict of in terests between management and investors is an important explanatory variable of equity mispricing. Second, the use of stock options does not resolve the interest conflicts, but it exaggerates the problem. The findings suggest that the use of restricted stock grants, which are less likely related to managerial myopia, is a better choice to reduce intere st conflicts in that it does not exacerbate mispricing. PAGE 94 Table 16 Different Effects of Agency Cost on Equity Mispricing Reported are the coefficients and corresponding tstatistics of regression models which control interacted terms of equity compensation variables. Columns [1] and [2] report results using timeseries average of crosssectional regressions. Columns [3] and [4] report results using panel regressions. Columns [5] and [6] report results of regressions computing differenceindifference estimates (i.e., including firm fixedeffects and year fixedeffects). Columns [7] and [8] report results using Whites (1980) heteroskedasticity correction model. Columns [9] and [10] report results only using the firstyear data of each firm. All variables are as defined in Table 10. *, **, and *** indicate significance at the 10%, 5%, and 1%levels, respectively. 88 PAGE 95 Timeseries average of crosssectional regression Panel regression model Differenceindifferences Whites (1980) heteroskedasticity correction model Firstyear regression 89 Table 16 (Continued) [1] Dep. var = MI [2] Dep. var = Log of MI [3] Dep. var = MI [4] Dep. var = Log of MI [5] Dep. var = MI [6] Dep. var = Log of MI [7] Dep. var = MI [8] Dep. var = Log of MI [9] Dep. var = MI [10] Dep. var = Log of MI Intercept 0.824*** 0.613*** (12.37) (13.48) 1.058*** (26.34) 0.752*** (28.01) 1.040*** (24.25) 0.738*** (25.80) 0.758*** (14.04) 0.566*** (15.67) 0.982*** (13.07) 0.708*** (14.57) Agency cost index (ACI) 0.005 (0.30) 0.011 (0.65) 0.012 (0.67) 0.031 (1.20) 0.064* (1.76) 0.003 ACI (%RSTOCK ) 0.032 (1.05) (0.14) 0.002 (0.07) 0.001 (0.03) 0.008 (0.12) 0.112*** ACI (%OPTION) (5.89) 0.067*** (6.55) 0.069*** (6.63) 0.128*** (8.09) 0.156*** (5.63) 0.044* Log of ACI 0.002 (0.11) 0.012 (0.70) 0.013 (0.74) 0.029 (1.12) (1.90) 0.008 Log of ACI (%RSTOCK) 0.027 (1.04) 0.005 (0.28) 0.04 (0.21) 0.0005 (0.02) (0.14) Log of ACI (%OPTION) 0.089*** (5.85) 0.054*** (6.30) 0.055*** (6.41) 0.101*** (7.99) 0.121*** (5.40) 0.008** 0.020*** 0.012*** 0.011*** Log of total assets (SIZE) 0.005** (2.50) (2.47) (9.53) 0.012*** (9.06) 0.019*** (8.71) (8.18) 0.005* (1.83) 0.003** (1.83) 0.017*** (4.56) (4.55) Leverage (LEV) 0.252*** 0.160*** (9.75) (9.39) 0.137*** (9.66) 0.090*** (9.50) 0.139*** (9.74) 0.091*** (9.58) 0.273*** (14.29) 0.177*** (13.81) 0.252*** (8.04) 0.159*** (7.85) Return on assets (ROA) 0.058* 0.042* (1.85) (2.11) 0.112*** (6.54) 0.078*** (6.79) 0.113*** (6.44) 0.078*** (6.65) 0.106*** (4.14) 0.074*** (4.58) 0.070 (1.46) 0.046 (1.49) Log of firm age (AGE) 0.029*** 0.018*** (9.22) (9.34) 0.039*** (10.54) 0.025*** (10.26) 0.038*** (9.99) 0.024*** (9.69) 0.031*** (6.89) 0.020*** (6.67) 0.031*** (6.14) 0.020*** (5.99) Diversification dummy (DIVER) 0.029*** (5.86) 0.020*** (6.18) 0.012*** (3.12) 0.009*** (3.50) 0.012*** (2.73) 0.008*** (2.94) 0.035*** (5.79) 0.024*** (5.87) 0.018* (1.95) 0.013** (2.13) Dividendpayer dummy (DD) 0.078*** 0.052*** (17.38) (18.59) 0.054*** (9.85) 0.036*** (10.11) 0.056*** (9.80) 0.038*** (10.15) 0.075*** (10.29) 0.050*** (10.37) 0.082*** (8.44) 0.054*** (8.57) No. of observations 8,657 8,657 8,657 8,657 8,657 8,657 8,657 8,657 1,481 1,481 R2 24.68% 24.22% 21.21% 21.01% 21.41% 21.22% 24.14% 23.68% 27.22% 26.91% PAGE 96 VI. Summary and Conclusions Recently, the finance literature has emphasized the importance of equity mispricing. The contribution of this paper is that it reconciles different views of mispricing and its causes, and specifically develops evidence on a link between agency theory and stock mispricing. Finance theory defines agency costs of equity as the organizational costs associated with problems arising from conflicts of interest between managements and shareholders in the presence of information asymmetry, i.e. in cases where managers discriminately have better and/or more information than shareholders. Previous studies have found that there is a strong positive relation between information asymmetry and equity mispricing, but have generally neglected the effect of conflicts of interest on mispricing. In this paper, I utilize ten agency costs proxies and provide evidence that the level of agency costs is significantly and positively related with equity mispricing. Unlike the existing literature, I find that the conflict of interests is a more important variable than information asymmetry in explaining the equity mispricing. Previous studies suggesting that stockbased compensation is an efficient mechanism for resolving agency problems typically treat all stockbased incentives equally and relate them to both lowered agency costs and enhanced firm stock value. Given both academic evidence and the recent skepticism about the effectiveness of equitybased compensation fueled from financial scandals (i.e., Enron and WorldCom), I separately analyze two different components of equitybased compensation, i.e., stock options and restricted stock grants. I find that the use of stock options, originally intended to resolve interest conflicts, actually exaggerates 90 PAGE 97 the problem and results in more stock mispricing. 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He hol ds a M.B.A. (2003) from SUNYBinghamton University, and a Bachelors degree in Economics (2000) from Kyonggi University, South Korea. xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 001912532 003 fts 005 20071010105057.0 006 med 007 cr mnuuuuuu 008 071010s2007 flu sbm 000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0001944 035 (OCoLC)173973052 (FTS)USF ETD onl 040 FHM c FHM 049 FHMM 090 HF71 (ONLINE) 1 100 Park, Jung Chul. 0 245 Two essays on market efficiency : b tests of idiosyncratic risk: informed trading versus noise and arbitrage risk, and agency costs and the underlying causes of mispricing: information asymmetry versus conflict of interests h [electronic resource] / by Jung Chul Park. 260 [Tampa, Fla.] : University of South Florida, 2007. 502 Dissertation (Ph.D.)University of South Florida, 2007. 504 Includes bibliographical references. 516 Text (Electronic dissertation) in PDF format. 538 System requirements: World Wide Web browser and PDF reader. 530 Mode of access: World Wide Web. 500 Document formatted into pages; contains 100 pages. Title from PDF of title page. Includes vita. 3 520 ABSTRACT: I examine the informational efficiency of stock markets by testing the relation between idiosyncratic volatility and equity mispricing. I find that the level of mispricing declines with idiosyncratic volatility consistent with the notion that greater levels of firmspecific risk reflect greater participation of informed traders in the market for the stock. However, I also find that mispricing increases with idiosyncratic volatility for highly volatile stocks, and this is attributed to both noise trading and arbitrage risk. In addition, I investigate the link between agency costs and equity mispricing, and whether it exists due to information asymmetry or the degree of conflict of interests between managers and shareholders. I provide evidence that the level of agency costs is positively related with mispricing. In contrast to previous studies' claim that the information asymmetry level is a key determinant in the equity mispricing, I find that the conflict of interests is more important than information asymmetry in explaining equity mispricing. Furthermore, the evidence suggests that stock option grants, originally intended to resolve conflicts of interests, actually exaggerate this problem. 590 Adviser: Christos Pantzalis, Ph.D. 653 Idiosyncratic volatility. Market efficiency. Noise trading. Arbitrage risk. Equity mispricing. Agency costs. 690 Dissertations, Academic z USF x Business Administration Doctoral. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.1944 