Stock Market Returns and Corporate Governance in Capital Market Equilibrium Bruno Maria Parigi Loriana Pelizzon Ernst-Ludwig von Thadden January 2013. Preliminary draft. Why does capital market competition among firms not eliminate private benefits by inducing them to adopt more shareholder friendly governance provisions? What determines the heterogeneity of the governance provisions among companies? Why do corporate governance choices matter for stock returns if the stock market fully prices the insiders’ use of company resources to enjoy private benefits? To address these questions we propose a model that incorporates the determination of the amount of private benefits, a key dimension of corporate governance, in the CAPM framework. Corporate governance a§ects the disutility of managerial e§ort in that a weaker governance gives managers more scope for initiative which, in turn, increases firm cash flows. The quality of the corporate governance is chosen endogenously trading o§ the benefits of a stricter governance, which limits the cost of the extraction of private benefits, against the cost of lower managerial initiative. The model predicts that across firms the quality of the corporate governance correlates positively with the firm and the firm idiosyncratic volatility. We have tested these predictions on a sample of U.S. firms where the quality of corporate governance is measured by the index of Gompers, Ishii, and Metrick (2003) of antitakeover provisions. We found that the quality of the corporate governance is worse in firms with lower and with lower idiosyncratic volatility. Keywords: Corporate Governance, stock returns, CAPM JEL Classification: G32, G38, K22 We thank Mike Burkart, Paul Laux, Ulf von Lilienfeld-Toal, Andrew Metrick, Stew Myers, Matthew Rhodes-Kropf, Per Stromberg, and seminar participants at Yale University, Temple University, MIT, Boston College, and the Stockholm School of Economics for useful discussions and Ludovic Calès and Andrea Lax for excellent research assistance. The usual disclaimer applies. Corresponding author: Loriana Pelizzon, [email protected].
Transcript
Stock Market Returns and CorporateGovernance in Capital Market
Equilibrium
Bruno Maria Parigi Loriana Pelizzon Ernst-Ludwig von Thadden
January 2013. Preliminary draft.
Why does capital market competition among firms not eliminate private benefits by inducing them to adopt moreshareholder friendly governance provisions? What determines the heterogeneity of the governance provisionsamong companies? Why do corporate governance choices matter for stock returns if the stock market fullyprices the insiders’ use of company resources to enjoy private benefits? To address these questions we proposea model that incorporates the determination of the amount of private benefits, a key dimension of corporategovernance, in the CAPM framework. Corporate governance a§ects the disutility of managerial e§ort in thata weaker governance gives managers more scope for initiative which, in turn, increases firm cash flows. Thequality of the corporate governance is chosen endogenously trading o§ the benefits of a stricter governance,which limits the cost of the extraction of private benefits, against the cost of lower managerial initiative. Themodel predicts that across firms the quality of the corporate governance correlates positively with the firm
and the firm idiosyncratic volatility. We have tested these predictions on a sample of U.S. firms where thequality of corporate governance is measured by the index of Gompers, Ishii, and Metrick (2003) of antitakeoverprovisions. We found that the quality of the corporate governance is worse in firms with lower and with loweridiosyncratic volatility.
We thank Mike Burkart, Paul Laux, Ulf von Lilienfeld-Toal, Andrew Metrick, Stew Myers, Matthew Rhodes-Kropf, PerStromberg, and seminar participants at Yale University, Temple University, MIT, Boston College, and the Stockholm School ofEconomics for useful discussions and Ludovic Calès and Andrea Lax for excellent research assistance. The usual disclaimer applies.Corresponding author: Loriana Pelizzon, [email protected].
1 Introduction
Why should corporate governance matter for stock returns? After all, if a firm is run in a way such thatmanagers or large shareholders can use company resources at the expense of outside shareholders, the firm’sshare price should adjust to reflect such conflicts of interest and the firm’s stock returns should be una§ected.However, empirically, stock returns do seem to depend on corporate governance.1
The empirical literature that was initiated by Gompers, Ishii and Metrick (2003) has studied the problemby controlling returns for various factors and then relating excess returns to measures of corporate governancequality. We address the problem from a new perspective, both theoretically and empirical, by looking at thetwo components of stock returns volatility: systematic risk (measured by ) and idiosyncratic volatility of stockreturns. The advantage of this approach is twofold. First, it allows us to provide a theoretical explanation ofthe relationship between the quality of corporate governance on the one hand and stock return systematic andidiosyncratic risk on the other, that when subject to test delivers the positive relationship that we observe in thedata. Second, from an empirical stand point, measurement errors are large on the estimation of average stockreturns (and therefore on the estimation of abnormal returns) while the estimation of stock return volatilityis usually more accurate. Indeed the positive association between governance and abnormal returns identifiedby Gompers, Ishii and Metrick (2003), seem to disappear for the period 2000-2008 possibly because marketparticipants learn to appreciate the di§erence between firms’s corporate governance scores (Bebchuk, Cohenand Wang 2010). On the contrary our finding is empirically robust for the period 1990-2006.We start out with the firms’ cash flow fundamentals and embed the single-firm problem in a capital market in
which investors behave according to a simple one-factor CAPM. Hence, we rule out excess returns by assumption.When we then address the managerial e§ort problem that motivates the corporate governance restrictions inthe first place, we find that this agency problem influences the firm’s beta and the idiosyncratic return volatility.The key to a conceptual understanding of the impact of corporate governance is the agency model of
managerial behavior that underlies the corporate governance problem. There is a long literature with di§erentsuch models, going back to Jensen and Meckling (1976), and too vast to be reviewed here. We focus on tworelated but independent features of corporate governance. On the one hand, lax governance allows managersto use company resources to their own advantage, typically at a loss to outside shareholders. On the otherhand, strict corporate governance may be counterproductive because managerial discretion improves initiative,increases intrinsic motivation, and more generally, makes managers’ e§ort more worth their while2 . Hence, ifmanagerial discretion can create firm value, there is a tradeo§ between the gains from monitoring and thosefrom managerial initiative. We model this tradeo§ by means of a single parameter that represents the qualityof corporate governance: on the one hand strong corporate governance limits the extraction of private benefits,on the other it increases the cost of exerting managerial e§ort and hence reduces firms’ cash flows. This idea issimilar to the well established notion that in an agency context too much information, e.g. resulting from strictmonitoring, may be detrimental to value creation (see for example Crémer 1995, and Aghion and Tirole 1997).In our model the task of the owner-manager is to provide unobservable e§ort to increase firm cash flows. The
disutility of e§ort to the manager can be alleviated by making governance laxer. Since we embed the manager’sproblem in a capital market context, the manager can trade in her firm’s shares. This makes her ownershipstake endogenous, which therefore provides a second incentive mechanism for managerial e§ort. The marketprices the shares anticipating the e§ort that the owner-manager will exert given the governance choice and theinside equity she retains.
1 See our literature discussion below.2 See Shleifer and Vishny (1997), Gromp, Burkhart, Panunzi (1997) and Hellwig (2000) for excellent discussions of the costs and
benefits of corporate governance.
1
To preview our theoretical results we show, first, that the amount of private benefits extracted by theowner-manager is fully priced in the value of the stock. However, weak corporate governance may be optimalfor the owner-manager despite the ine¢ciency that the extraction of private benefits may entail, because of theincentives to e§ort that a weak governance provides. Or to put it di§erently the market would not tolerate aweak governance unless it had the e§ect of inducing cash flow-increasing e§ort.Second, to understand the heterogeneity of governance structures across firms we show that the higher is the
co-movement of a firm’s cash flows with the returns of the market portfolio, the lower is the amount of privatebenefits that the owner-manager chooses to consume, that is the weaker is the corporate governance that shechooses.Third, the heterogeneity of governance structures is also linked to the idiosyncratic risk of cash flows, in the
sense that the higher the stock return idiosyncratic volatility the weaker is the corporate governance.The latter two results provide our two main testable implications. First, stocks with a lower should have
weaker corporate governance. Second, an increase in firm-specific cash flow volatility is associated with a decreasein private benefits extraction, hence, empirically, the quality of corporate governance correlates positively withidiosyncratic return volatility in the CAPM-one- factor model regression. We test these predictions on a sampleof U.S. listed firms.Clearly, measuring the quality of corporate governance poses di¢culties. One widely used measure of the
(inverse of the) quality of corporate governance in the U.S. is the Gompers, Ishii, and Metrick (2003) Index ofanti takeover provisions (GIM Index; see the Appendix A for a description). In this study, we take the GIMindex as the measure of private benefits extraction.A test of the above implications must take into account that both in the model and in reality, the quality of
the governance, the stock , and the stock return idiosyncratic volatility are all endogenous. We thus resort to2SLS estimation where in the first stage the GIM Index is instrumented with the dividend yield. In the secondstage the and the stock normalized idiosyncratic volatility are regressed separately against the fitted GIMIndex along with controls. The results show negative and significant relations between the fitted GIM Index onone side and and the stock normalized idiosyncratic volatility on the other, as predicted by the theoreticalmodel.This paper is related to di§erent strands of the literature. First it is related to the studies that investigate the
relationship between corporate governance and asset pricing, most notably Gompers, Ishi, and Metrick, (2003),and other papers such as Cremers and Nair (2004), Ferreira and Laux (2007), Bebchuk, Cohen, and Ferrell,(2009), Cremers, Nair, and John (2009), Johnson, Moorman and Sorescu (2009), Sautner and Villalonga (2011),Acharya, Myers, and Rajan (2011), Acharya, Gottschalg, Hahn, and Kehoe (2011), and Bebchuk, Cremers, andPeyer (2011). All these studies start with the observation that corporate governance is heterogenous amongfirms and investigate its implications on share prices or abnormal equity returns. However, all these studies arelargely empirical, and do not address the puzzle that we have stated initially.Second, this paper is also related to the literature on opacity and governance, as bad governance is usually
associated with private information and low disclosure. In particular, our paper is related to Jin and Myers(2006) who show that lack of transparency drives R2 of stock returns higher in a cross-country study. In theirtheory, stocks are a§ected by one market factor observable to everyone and two idiosyncratic factors, only one ofwhich is observable also to outsiders. The fact that one factor is observable only to insiders (lack of transparency)allows them to extract benefits from the cash flows when they are high. This implies that less idiosyncratic riskis impounded into the stock price and thus that the R2 of stock returns is larger. Other important contributionsto this literature are Easley and O’Hara (2004) who show that uninformed traders require compensation to holdstocks with greater private information, and Lambert, Leuz and Verrecchia (2009) who show that the qualityof accounting information can influence the cost of capital in a CAPM framework. Our work is complementary
2
to this strand of literature as we investigate the relationship between corporate governance and systematic andidiosyncratic stock returns volatility without considering the hypothesis of opacity.The empirical paper closer to ours is Ferreira and Laux (2007) that generalizes Jin and Myers (2006) at the
U.S. company level and finds that worse governance quality is associated with a decrease in transparency, i.e. alower idiosyncratic volatility.3 Our results are qualitatively similar to those of Ferreira and Laux (2007): namely,a higher GIM Index is associated with higher opacity of stock returns, measured as idiosyncratic volatility overtotal volatility.The rest of this paper is organized as follows. In Section 2 we construct our theoretical model of asset pricing
that incorporates corporate governance choices in the CAPM. Section 3 derives our theoretical predictions.Section 4 describes the data. Section 5 tests the predictions with these data, and Section 6 concludes.
2 The Model: Description
In this section, we present a simple structural model that generates testable hypotheses about the relationshipbetween asset pricing and corporate governance. We do not take a stance on whether corporate governancedrives asset returns or vice versa, and rather work with a model in which both are endogenous and driven bythe same factors.Consider a competitive capital market with representative firm i, run by a manager who initially owns all
the shares. The model has three dates. At date 0, the owner-manager decides about the quality of corporategovernance of the firm. si describes the laxity of corporate governance: the larger si the less the owner-manageris monitored and the higher are managerial private benefits. Private benefits reduce the firm’s cash flows byhisi with hi > 0, because benefit-taking disrupts the firm’s operations or comes directly at the expense ofshareholders’ money. Managers and shareholders therefore have directly opposing interests over si. si is ameasure of corporate governance weakness and thus a theoretical counterpart to the GIM index.At date 1 the firm’s shares are traded publicly at the competitive price Pi1. The owner-managers can trade
shares at this price, provided that she discloses her final shareholding i.At date 2 the owner-manager exerts a privately observed e§ort ei to increase cash flows, and then final cash
flows Ci are realized. Managerial e§ort has a private cost, the monetary equivalent of which is
e2i2kisri
(1)
where r > 0, ki > 0. Hence, e§ort is less costly to the manager if she enjoys more discretion. In other words,all else being equal, strict corporate governance has a negative e§ect on managerial e§ort. This follows the“incentive approach" to corporate governance (Harris and Raviv, 2010) that emphasizes the potential costsof strict governance. Underlying these costs are the potentially discouraging e§ects of corporate governance,by restricting managerial initiative (Burkart, Gromb, Panunzi (1997)) or by crowding out intrinsic motivationby extrinsic motivation (Falk and Kosfeld, 2005).4 The alternative theory, that strict corporate governanceincreases managerial e§ort by decreasing e§ort costs, corresponds to the case r < 0 in (1). We shall later showthat, in our model, this assumption would lead to predictions inconsistent with the data.
3Other studies propose an informational interpretation of the idiosyncratic volatility: high levels of idiosyncratic volatility areassociated with more e¢cient capital allocation (Durnev, Morck, and Yeung 2004) and with stock prices being more informativeabout future earnings (Durnev et al. 2003). Furthermore low levels of idiosyncratic volatility are found in emerging marketscompared to developed markets (Morck, Yeung, and Yu 2000) and they are also associated with bad rule of law.
4 See Hellwig (1990), Shleifer and Vishny (1997), and Myers (2000) for careful discussions of the costs and benefits of corporategovernance.
3
There is a safe asset with interest rate Rf between between date 1 and date 2. For simplicity, we assumethat cash flows only accrue at the final date. The date-2 cash flow of firm i is assumed to be given by thestandard one-market factor model
Ci = Ai + iei +BiRM + "i (2)
where RM is the market return with mean RM and variance 2M , "i is random with mean 0 and variance 2"i,cov("i, RM ) = 0, Ai, Bi are constant, and i 0 is the marginal impact of managerial e§ort on cash flow.Stock market investors, who have mean-variance preferences over wealth at date 2, have homogenous ex-
pectations at date 1 and therefore invest according to two-fund separation and price the firm’s shares in linewith the classical CAPM. Investors take the firm’s corporate governance as given and correctly anticipate theowner-manager’s e§ort choice and public or net cash flow of Ci hisi at date 2. Thus corporate governancea§ects public cash flows at two stages: indirectly at the e§ort stage and directly at the stage of the extractionof managerial private benefits.Hence, the owner-manager’s final wealth consists of the net cash flow from her stake i in her own firm, the
monetary value of her private benefits, her holding of the market portfolio, and her cash from trading at date1. When selling the stake 1 i of her firm, the owner-manager realizes cash of (1 i)Pi1, out of which sheinvests mi 0 in the market portfolio, whose price we normalize to 1, and keeps the rest in the risk-free asset.Her final wealth therefore is
where ihisi with 0 i < 1 denotes the value of private benefits accruing from governance regime si. iis exogenous and depends on manager’s and firm characteristics such as its industry, as well as on aggregatefactors such as the legal framework or the overall governance standards in the market.Like all other investors, the owner-manager is risk-averse, with mean-variance utility
Ui = EWi i2var(Wi)
1
2kisrie2i (4)
where i denotes the risk aversion of the owner-manager, and, using (2),
var(Wi) = 2M (iBi +mi)
2+ 2i
2"i. (5)
Our results are driven by risk and managerial moral hazard. Risk is measured by i, Bi, 2M , and 2"i. The
importance of managerial moral hazard can be measured by 1/ki, the cost of providing e§ort, i, the e§ectof e§ort on cash flow, hi, the cash flow loss from private benefit taking, and i, the ease with which privatebenefits can be appropriated. Obviously not all of these parameters will have an independent influence, and wewill later normalize some of them.
3 The Model: Results and Predictions
We solve the model backwards, first determining the owner-manager’s e§ort at date 2, then the share price atdate 1 and the owner-manager’s trading and portfolio decision (i,mi), and then the corporate governance struc-ture si at date 0. Hence, the owner-manager determines si knowing that she can later adjust her shareholdings,but that the stock price will adjust in response to her trade.
4
3.1 E§ort choice
Since e§ort is additively separable in our model, inserting (2) into (4) yields the first-order condition for e§ortchoice as
ii 1
kisriei = 0,
ei = iikisri . (6)
Thus e§ort is increasing in i and in si. While the positive e§ect of inside equity on e§ort is standard andwell understood, the positive e§ect of si on e§ort (i.e. the negative e§ect of strict corporate governance one§ort) follows the incentive arguments discussed earlier, with the notion that close managerial monitoring stiflesmanagerial initiative and hence e§ort, as in Burkhart, Gromb, Panunzi (1997).Inserting (6) into (3) yields
This expression exhibits some of the e§ects of corporate governance on the owner-manager’s wealth quiteclearly. On the one hand, higher si decreases wealth through the dilution of net cash flow (the term ihisi),which depends on the owner-manager’s final ownership i. On the other hand, higher si increases her wealththrough, first, higher optimal e§ort (the term +i
2i kis
ri ) and second, through higher private benefits (the term
+ihisi). Of course, Wi is also indirectly a§ected through Pi1 and mi. It turns out that the second of thesedirect benefits is not necessary to derive our results. We therefore let i = 0 from now on to simplify theexpressions.5
3.2 Capital market equilibrium
Pricing at date 1 is a simple application of the CAPM. Recall that the value of the market portfolio at date 1is normalized to 1 and the return on the market as of date 1 is RM . By the CAPM, Pi1 adjusts such that
ERi = Rf + i(RM Rf ) (8)
where Ri = Pi2/Pi1 1 is the holding-period rate of return of firm i’s shares, and
i =cov(Ri, RM )
var(RM ). (9)
Substituting for Ri into the CAPM formula (8) yields
EPi2Pi1
1 = Rf +cov(Ri, RM )
var(RM )(RM Rf ). (10)
By (2),Pi2 = Ci hisi = Ai + iei +BiRM hisi + "i (11)
5All our results hold with i > 0.
5
which implies
cov(Ri, RM ) = cov(Pi2 Pi1Pi1
, RM ) =1
Pi1cov(Pi2, RM )
=1
Pi1cov((BiRM + "i), RM )
=BiPi12M . (12)
From (10), the expected rate of return of stock i therefore is
EPi2Pi1
1 = Rf +BiPi1(RM Rf ). (13)
Substituting for Pi2 in (13) from (11) yields Pi1, firm’s i date-1 market value:
Ai +BiRM + iei hisi = (1 +Rf )Pi1 +Bi(RM Rf )
) Pi1 =1
1 +Rf(Ai +RfBi + iei hisi) (14)
where we assume that hi is small enough that Pi1 > 0.Combining (14) with (11) yields
Ri =P2P1 1
= Rf +(1 +Rf )Bi
Fi + iei hisi(RM Rf ) +
1 +RfFi + iei hisi
"i, (15)
where Fi = Ai + BiRf . Equation (15) describes the classic linear regression of firm returns on the marketreturn. In this regression, the observed beta is given by
i =Bi (1 +Rf )
Fi + iei hisi. (16)
Writing the idiosyncratic return component in (15) as
i =1 +Rf
Fi + iei hisi"i. (17)
one can re-write (15) in the standard form
Ri = Rf + i (RM Rf ) + i (18)
which is the stochastic version of the expected-return CAPM equation (8), where the standard deviation ofidiosyncratic returns in (17) is
i =1 +Rf
Fi + iei hisi"i. (19)
Therefore, in a competitive market where stock prices are determined according to the CAPM, the amount of
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private benefits extracted by the insiders is fully priced in the value of the stock. Hence, corporate governancedoes a§ect returns even on average, and it does so via the risk component given by
3.3 Ownership and portfolio choice
When the owner-manager makes her ownership and portfolio choice, the market takes the corporate governancechoice si as given, correctly anticipates the induced value of e§ort, and sets the stock price consistent withmanagerial ownership. Hence, managerial ownership i, the owner-manager’s portfolio choice mi, and the stockprice Pi1 in (14) are determined simultaneously.Using the optimal e§ort (6), and inserting Pi1 from (14) into (4) yields the owner’s objective function at the
stage when she determines her final ownership position i and her market exposure mi at date 1:
max{mi,i}
Ui = Fi + i2i kis
ri
1
22i
2i kis
ri hisi + (iBi +mi)(RM Rf ) (20)
i2
2M (iBi +mi)
2 + 2i2"i
,
s.t.
i 1 (21)
mi (1 i)Pi1 =(1 i)1 +Rf
Ai +RfBi + i
2i kis
ri hisi
(22)
0 mi, (23)
where the budget constraint (22) means that the owner-manager cannot spend on the market portfolio morethan what she obtains by selling a fraction (1 i) of her firm or equivalently that she cannot short sell therisk-free asset, and constraint (23) means that she cannot short sell the market portfolio either.Di§erentiating (20) with respect to mi and i yields straightforward first-order conditions, which we sum-
marize in the following lemma.
Lemma 1 For any given governance choice si, the optimal ownership and portfolio choices are
i =tis
ri
Li + tisri(24)
mi =
RM Rfi2M
Bitis
ri
Li + tisri(25)
where ti = 2i ki and Li = i
2"i, to simplify notation.
It is straightforward to verify that the first-order conditions indeed yield an optimum. Interestingly, fromthe perspective of the owner in (20), her cash flow cost of lax governance does not depend on her ownershipstake i, although a priori she bears the dilution of cash flows only in proportion to her ownership stake (see(7)). This is because the market prices the dilution fully, which makes the owner bear the full cost of weakgovernance through the price Pi1 regardless of the ownership stake she decides to hold.Hence, the optimal ownership stake trades o§ e§ort incentives against risk sharing. The direct benefit and
cost of e§ort are given by the second and third term of (20), respectively, while terms 5 and 6 represent thetraditional risk-return tradeo§. Note that if the latter concern were absent, i.e. if Li = 0 (no risk or no riskaversion), then i = 1 and the owner would not sell out at all, just as in traditional theory (Leland and Pyle
7
(1977)), and by the constraints (22) and (23) mi = 0. Only if risk matters ownership matters, and this isinfluenced by the incentive e§ects of corporate governance.In fact, varying si as an exogenous parameter, Lemma 1 yields the following comparative statics.
Lemma 2 Optimal managerial ownership i and optimal managerial e§ort
ei =1
i
t2iLi + tisri
s2ri (26)
are increasing in si.
Hence, taking si as an exogenous parameter, the stricter is corporate governance, the less e§ort the managerprovides in equilibrium, and the lower is her ownership stake. In equilibrium, strict corporate governance andownership are substitutes, that is ownership might act as a moderator for the impact of managerial discretionon firm performance.The reason is that, by (6), governance weakness and ownership are strategic complements for e§ort provision,
with positive direct e§ects on managerial e§ort. Since the negative cash flow e§ect of weak corporate governanceis independent of ownership by rational expectations in stock market trading, increasing governance weaknesssi increases the marginal incentive e§ect of ownership. Hence, the direct e§ect of si on e§ort and the indirecte§ect via i both go in the same direction.Notice that the previous Lemma is considering corporate governance as an exogenous parameter. However,
since corporate governance is a decision variable as already stressed, it is worth to investigate what should bethe equilibrium choice of the corporate governance.
3.4 Governance choice
Inserting (24) and (25) in (20) yields
Ui = Fi +1
2
t2i s2ri
Li + tisri hisi +
RM Rf
2
2i2M. (27)
While the cost of weak governance does not a§ect ownership for a given governance level, as discussed above,it certainly does a§ect the decision about the optimal level of corporate governance. The following derivativesare straightforward to obtain and useful to note:
d
dsiUi =
rt2i2
s2r1i
(Li + tisri )2(2Li + tis
ri ) hi (28)
d2
ds2iUi =
rt2i s2r2i
2(Li + tisri )3
2(1 2r)L2i + 3(1 r)tiLis
ri + (1 r)t
2i s2ri
. (29)
An inspection of (28) and (29) shows that Ui has a unique, strictly positive maximum if r 1/2, i.e. if thepositive incentive e§ect of weak governance is not too strong. In order to get testable predictions we therefore
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impose this restriction from now on.6 With this assumption, (28) therefore implies:
Proposition 3 The optimal corporate governance decision is unique, satisfies si > 0, and is given by
rt2i (2Li + tisri ) = 2hi(Li + tis
ri )2s12ri . (30)
To understand the intuition behind Proposition (3) observe that the owner-manager chooses governance rulesto trade o§ the marginal cost and the marginal benefit of a more lax managerial monitoring. While the cost ofmore lax managerial monitoring is the well understood and documented consumption of private benefits, thebenefit of a more lax governance is more subtle. If managerial discretion improves initiative, increases intrinsicmotivation, lowers the cost of compliance, and more generally, makes managers’ e§ort more worth their while,a more lax managerial monitoring creates value for all shareholders. Hence the owner manager generally willnot adopt the most stringent governance rules (i.e. si = 0), precisely because the capital market fully pricesthe impact that governance has on e§ort, on inside equity and on public cash flows.Several conditions are needed for the above result to obtain. First, the agent who makes the governance
choices cannot be a pure portfolio owner who contributes nothing to cash flows. Otherwise she would choosethe strictest possible governance rules else she would pay the cost of a weak governance without any benefit interms of additional cash flows. Second, and related to the previous point, the very nature of the managerial jobin question must be such that the additional discretion, additional initiative, lower compliance costs, matter, sothat more lax governance rules can lead to a lower disutility of managerial e§ort. More formally we establish:
Corollary 4 If e§ort played no role, either because ki ! 0 or because i = 0, then ti = 0 and si = 0 by (27).
3.5 Testable propositions
In our model, neither does corporate governance have a causal e§ect on stock prices, nor is the opposite true.Instead, governance si and ownership i on the one hand, and returns Ri, idiosyncratic risk 2i and observed ion the other hand, are endogenous, driven by the same set of exogenous parameters. The uniqueness establishedin Proposition 3 shows that the equilibrium relation between the endogenous variables can be obtained byimplicitly di§erentiating the first-order condition (30) and using the equilibrium expressions for i and
2i.
Proposition 5 When the parameters Li, hi, and ti change, the equilibrium values of i and 2i move in the
same direction, and opposite to that of the governance variable si . The precise prediction is as follows:
si i 2iLi = i
2"i + +
hi + +
ti = 2i ki +
6 (28) and (29) show that the condition r 1/2 is clearly not necessary. Depending on the size of the other parameters, weakerconditions on r yield the same result. But the condition is simple and su¢ces to make the point. If weak governance has largepositive incentive e§ects that outweigh the costs considerably, then there may be no maximum and governance is as lax as possible.
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Given our simple one-factor model, it is clear that i and i comove positively, because from (16) and (19)we have
i =iBi"i.
The six other derivatives reported in Proposition 5 require more work that we sketch in the appendix.To understand the intuition of the results in Proposition (5) recall that we have established in Lemma (2)
that weaker governance increases e§ort. From equation (2) one can see that since the market portfolio factorloading Bi is constant, an increase in e§ort makes the firm’s cash flows larger for the same level of risk. Henceeach unit of cash flow is less risky and therefore its stock return less dependent on the return on the marketportfolio, which shows up in a lower of that firm. By the same argument from equation (2) one can see thatsince the idiosyncratic risk "i is constant, an increase in e§ort which increases return via higher cash flowsmakes the return less risky which shows up in a lower i. In sum as long as e§ort is not just a scale factor butis able to improve the trade o§ between the variability of cash flows and their average, the value of the firm islarger (P1 is higher) but the risk does not change. Thus as governance worsens the unit of risk (systematic andidiosyncratic) for each dollar invested is lower.The predictions of Proposition (5) are the subject of the empirical tests that we conduct in the following
section.
4 The data
4.1 Data description
As noted earlier, measuring corporate governance quality poses serious di¢culties. We choose to use a measurethat is already available and widely used in the literature, the GIM Index. As mentioned the GIM Index is theempirical counterpart of the private benefits si.The GIM Index includes 24 anti-takeover provisions: staggered board, poison pill, supermajority voting
requirement, limits to amend bylaws, limits to amend charters, golden parachute, etc. We have re-scaled the 19values of the GIM Index into 6 values on the ground that a less fine grid was more appropriate for the problemat hand. (A robustness check with the original 19 values is discussed later on). The mapping is as follows:values (1,2,3) of the GIM index become 0; (4,5,6)!1; (7,8,9)!2; (10,11,12)!3; (13,14,15)!4; (16,17,18,19)!5.0 is the best governance, 5 is the worse. The GIM Index is available for 4.016 U.S. firms covering more than93% of the total capitalization of the NYSE, AMEX and NASDAQ, and it is provided by RiskMetrix. Theavailable years are 1990, 1993, 1995, 1998, 2000, 2002, 2004 and 2006 for an average of 1750 firms per year. Welinearly interpolated the GIM Index for missing years. In Figure 1 we show the distribution of the observationsby GIM Index without interpolation for the missing years7.
INSERT Figure 1 HERE
Figure (1) presents a visual summary of frequency distribution of the GIM Index values. In line with theprediction of proposition 3, the governance choice is not zero in the large majority of cases, that is in the largemajority of the observations firms do not choose the strictest possible governance rules. Instead the maximum
7In Riskmetrix dataset the firms are identified through the ticker symbol. For the CRSP and S&P compustat weinstead preferred to use the "permno" code, the common code between the two datasets.
10
frequency of GIM Index values is at the centre of the distribution, suggesting that the governance choice is theresult of a trade-o§.Furthermore, Figure (1) shows that the governance choice is not unique among firms, and therefore it is
related to several potential firm characteristics.
4.2 Beta and Idiosyncratic Volatility
For each stock i and each year we regress the stock’s daily returns using the specification (15) with e§ort atits equilibrium level. Stocks returns data are from the Center for Research in Stock Prices (CRSP) while theothers statements variables that we use as controls are from S&P Compustat (see table 1 for the definitions andsources of variables). This regression yields Ri Rf , the yearly excess return of asset i, i, the yearly beta ofasset i, V Ri the yearly normalized idiosyncratic volatility of asset i, and 2M , the variance of the yearly returnsof the market portfolio. The latter is defined as the value weighted index of stocks in our dataset.
INSERT Table 1 HERE
Observe that the of the companies in our sample is rather stable over time: the average standard deviationof each company (computed over time) is 0.35 and the standard deviation of the cross section of the standarddeviation of each company’s is 0.19. Only 20 companies (out of the 2876 with more than a single observation)have a standard deviation of their higher than 1.Furthermore, we observe no major change in the GIM Index over time. Table 2 presents a transition matrix
showing the number of changes in the GIM Index for consecutive periods over the sample. Observe that whena change occurs it is most likely a worsening of the GIM Index.
INSERT Table 2 HERE
To determine if there is a relationship between the change in the GIM Index of a firm and the change in itsi in Table 3 we reported the change in i from time t to time t+1 following a change in the GIM Index fromtime t to time t+1 from the transition matrix 2. From Table 3 no pattern between the change of a firm i andthe change in its GIM Index can be identified, largely because for each firm the GIM Index is stable over time,as Table 2 shows.
INSERT Table 3 HERE
5 Results
5.1 Quality of governance, idiosyncratic volatility, and i
5.1.1 Univariate analysis
In Table 4 we present the i, idiosyncratic volatility and other firm’s characteristics according to the governanceindex. We winsorize extreme observations at the bottom and top 1% levels to avoid spurious inferences. We
11
observe that companies with better governance (GIM Index 0,1,2) have a higher i and higher idiosyncraticvolatility than companies with worse governance (GIM Index 3,4,5), and that the di§erences are statisticallysignificant. These results are in line with the testable proposition relating levels of i and idiosyncratic volatilityon one side, and corporate governance on the other. In the same table we present the descriptive statistics ofthe other explanatory variables.
INSERT Table 4 HERE
The binary correlations (Table 5) show that the relationship between the GIM Index and i is negativeand significant, that between the GIM Index and
pV Ri is negative and significant, and that between
pV Ri
and i is positive and significant which means that already the unconditional correlation analysis supports ourempirical predictions.
INSERT Table 5 HERE
5.1.2 Multivariate analysis
The previous univariate analysis have established the presence of a negative relationship between laxity incorporate governance, beta and idiosyncratic risk, on average. However, these results could be driven by otherfactors that are only incidentally correlated with governance. In the remainder of this section, we set out toestablish that corporate governance are at the core of the relationships. However, our theoretical model hashighlighted that the relationships we have identified are hard to investigate empirically because many factorscan lead to a choice of a certain si, and some of these variables could also a§ect directly idiosyncratic riskand beta (such as 2"i). Therefore, we cannot perform a simple panel regression analysis because of potentialendogeneity issues, i.e., that the relationship between corporate governance, idiosyncratic risk and beta arisebecause these variables are caused by the same set of variables (observable or not observable).We address the potential econometric problem in a number of ways. First, we make use of an extensive
number of control variables to reduce the possibility that corporate governance is related to idiosyncraticvolatility or beta just because of omitted variables, i.e. ignoring the presence of other factors that are onlyincidentally correlated with governance. Second, usually in panel regressions the residuals may be correlatedacross firms or across time, and OLS standard errors can be biased (see Petersen (2008)). Only clusteredstandard errors are unbiased as they account for the residual dependence created by the firm e§ect. Wetherefore estimate robust standard errors considering cluster e§ects. Third, we use instrumental variables. Theidentification of appropriate instruments is not trivial in our set up. The valid instruments should be exogenousand should not be influenced by the idiosyncratic risk and the beta of stock returns. It is desirable that theinstruments are strongly correlated with the corporate governance variable and it should influence the dependentvariable (in our case, idiosyncratic volatility and beta) only through its e§ect on the corporate governancevariable and not directly. Therefore, we need an instrument that is related to the corporate governance and notwith idiosyncratic risk and beta.In order to address this problem we employ the two-stage least squares method. More formally, we model
corporate governance in reduced form equation:
si,t = a+ ajDj + atDt + 1X1 + 2X2 + i,t (31)
12
where X1 and X2 are two sets of exogenous variables; i,t is the error terms, is the constant; Dj are industrydummies, Dt are time dummies, j , t are dummy coe¢cients; and 1 and 2 are vectors of coe¢cients.From the first-stage regression represented by Equation (31) we determine the fitted value bsi,t that we use
in the second-stage regression for the idiosyncratic risk and betas as:
i,t = b+ bjDj + btDt + 1bsi,t + 1X1 + i,t, (32)
i,t = c+ cjDj + ctDt + 1bsi,t + #1X1 + i,t, (33)
where i,t and i,t are the error terms, b and c are the constant; bj , cj , bt, ct, 1, and 1 are coe¢cients; and1 and #1 are vectors of coe¢cients. We use the exogenous variables X2 only in equation (31) where they serveas instruments for the corporate governance variable. The endogeneity in the model can arise from potentialcorrelations of the corporate governance variable and the error terms i,t, and i,t in equation (32). We performthe Kleibergen-Paap test in order to determine the goodness of the instrument used.We consider a number of controls: market value, price to book value, Return on Assets, leverage, firm age,
sectorial dummies and year dummies.The explanatory variable included in X2 as instrumental variable is the log of age (LNAGE). This variable
does not seem to be directly related to betas or idiosyncratic risk, but is statistically highly related to the levelof corporate governance as the Kleibergen-Paap test on endogeneity shows.Table 6 reports the first and second-stage panel estimation and it shows that the relation between betas
and idiosyncratic risk and corporate governance is in line with our theoretical predictions. Indeed, betas isnegatively related to the instrumented values of corporate governance. The coe¢cients is -0.21 and is statisticallysignificant at the 1% level. We obtain the same results for the idiosyncratic risk: 2i,t is negatively related tothe instrumented values of corporate governance. The coe¢cient is -0.56 and is statistically significant at the1% level.The tests for endogeneity does not allow us to reject the hypothesis that the instrument we used is exogenous:
the Kleibergen-Paap test for underidentification rejects the null hypothesis that the instruments are underiden-tified. Moreover, we also report the Kleibergen-Paap rk Wald F-statistic that rejects the null hypothesis thatthe instrument does not enter the first stage regression. Bound et. al (1995) mention that "F statistics closeto 1 should be cause of concern". We have a F statistics of 142.49, suggesting that our regression is unlikelyto be a§ected by a weak instrument. Moreover, since we are using only one instrument we have no problem ofoveridentification. Hence, the coe¢cient estimates are both consistent and e¢cient.
INSERT Table 6 HERE
In summary, we obtain two findings. First, the square root of the idiosyncratic volatilitypV Ri, has a
negative and significant relation on the GIM Index as our theoretical model predicts. Second, we find the novelresult that i is negatively related with the GIM Index as our theoretical model predicts.The above results suggest that two e§ects seem to be at work. First, we find the general e§ect that an
increase in private benefits is associated with a reduction of the idiosyncratic volatility.The second e§ect refers to the negative relationship between i and private benefits. This is a novel
and important result because it highlights a relevant and mostly disregarded issue: private benefits are notexogenous but are chosen by insiders. Our model is capable of providing an empirical prediction because it
13
accounts for the insiders’ choice of private benefits in a competitive framework. It shows that competition failsto eliminate private benefits altogether as there is trade o§ between a weaker governance and managerial e§ort.In equilibrium the controlling shareholder of an asset that presents a lower beta extracts more private benefits.But since private benefits are fully priced, outside investors are indi§erent. However, even if the amount ofprivate benefits extracted by the insiders is fully priced in the value of the stock, corporate governance doesa§ect average returns via the risk component given by .
5.2 Robustness and other analysis
We test the robustness of our results with respect to di§erent model specifications and di§erent regressionsmethodologies.First, two-stage regressions with the GIM Index scaled from 1 to 19 provide similar results (not reported
here for brevity, but available upon request).Second, we investigate whether the positive association between good governance and risk disappears in the
recent part of the sample as the positive relationship between governance and abnormal returns for the period2000-2008 as shown by Bebchuk, Cohen and Wang 2010. We performed eight cross-sectional regressions for thedi§erent years when the GIM index has been calculated (1990, 1993, 1995, 1998, 2000, 2002, 2004, and 2006)and find that the instrumented GIM index is always negatively related to the betas and the idiosyncratic riskand the coe¢cients are at least significant at 5% level (results are provided upon request). This means thatwhat we find is mainly a cross sectional e§ect rather than a time series e§ect as our model predicts and ourfinding is empirically robust for all the years 1990-2006.Third, we conduct a two-stage regression of beta and idiosyncratic risk variables with respect to the lagged
instrumented GIM Index to rule out possible reverse causality between the GIM Index and these factors, even ifwe do not take a stance on whether corporate governance drives asset returns or vice versa, and rather work witha model in which both are endogenous and driven by the same factors. We find that the lagged instrumentedGIM Index is significant and have the same sign as their non-lagged counterparts8 .We have also considered Insider ownership as control variable (in line with the work of Ferreira and Laux
(2007) and the work of Ellul, Giannetti and Cella (2012) that shows that institutional investor ownership mattersin amplifying shocks e§ect on stock returns). Our results, not reported here for brevity, are qualitatively similarto those in Table 6.We also investigate other instrumental variables. From a statistical point of view a good candidate is the
variable Dividend Yield (DY). The results are reported in Table 7 and are qualitatively similar to those reportedin Table 6 where Age is the instrumental variable. However, from the economic point of view we consider Ageless subject to managerial manipulation and therefore a more suitable instrument than DY.
INSERT Table 7 HERE
Our approach of modelling stock returns allows us to investigate other relationships besides that betweencorporate governance and stock return volatility which is the main focus of this paper. In particular we caninvestigate the comovements between corporate governance choice, beta, idiosyncratic risk on the one hand andinside ownership (i) and net cash flow (Ci hisi) on the other. The predicted comovements are as follows:
8Again, these results are available upon request.
14
i Ci hisiLi = i
2"i
hi ti =
2i ki + +
Thus using the results of Proposition (5) we can establish the following corollary
Corollary 6 When the parameters Li, hi, and ti change, the equilibrium values of the governance variable si ,
of ownership i, and of net cash flow Ci hisi move in the same direction, and the equilibrium values of the
beta i, and of the return idiosyncratic volatility 2i, move in the opposite direction of ownership i and net
cash flow Ci hisi.
An emprical test of the relationships involving the ownership variable is quite di¢cult because ownership dataused in various studies are often taken from specific databases, have several biases and hand-collecting ownershipdata from proxy statements is extremely cumbersome (see Anderson and Lee (1997) Dlugosz, Fahlenbrach,Gompers, and Metrick (2006) and von Lilienfeld-Toal and Ruenzi (2012)). For this reason we leave this issueto further research.Regarding the net cash flow, Cihisi, we could consider the Return on Assets (income divided by book total
assets) as a good proxy. Table 5 indicates that, in line with our predictions, ROA is positively and significantlyrelated to the GIM index and negatively and significantly correlated with beta and idiosyncratic risk. Moreover,in our two-stage regression analysis ROA is not anymore significantly related to the GIM index from the firststage (See 6)9. This could be due to the fact that other control variables, related to the ROA, reduce itsexplanatory power. However, ROA is still negatively and significantly related with beta and idiosyncratic riskin line with our theoretical predictions in the second stage. Again, to our knowledge this is the first paper thatattempts to provide a theoretical framework where both beta (i.e. systematic) and idiosyncratic stock returnsare related to the Returns on Assets.
6 Conclusion
To conclude, this paper is motivated by the attempt to investigate why corporate governance choices matterfor stock returns if the firm’s share price adjusts to reflect that managers or large shareholders use companyresources to enjoy private benefits. To address this question we have constructed a model that incorporates thedetermination of a key corporate governance provision, the amount of private benefits, in the CAPM framework.Corporate governance matters in that it a§ects the disutility of managerial e§ort. A weaker governance lowersthe monitoring of managerial activities and gives managers more scope for initiative which increases firm cashflows. The quality of the corporate governance is chosen endogenously by the owners-managers trading o§ thebenefits of a stricter governance, which limits the cost of the extraction of private benefits, against the cost oflower managerial initiative. Hence it is not in generally true that the owner-manager will chose the best possiblequality of governance precisely because the owners-managers anticipate that a competitive capital market willfully price the consumption of private benefits that a less strict governance entails.
9This result is in line with Gompers, Ishii and Metrick (2003). They find that the return on equity (income divided by bookequity) is not significantly related with the GIM-index, in some years with a positive coe¢cient and in some others with a negativecoe¢cient. We prefer to consider the Return on Assets rather then the Return on Equity because we would like to avoid that ourresults are a§ected by leverage.
15
Governance choices a§ect cash flows and through cash flows also a§ect the firm and the firm idiosyncraticvolatility. This allows us to establish a link between the heterogeneity of governance provisions across firms andboth their and their idiosyncratic volatility.The model delivers the testable predictions that across firms the quality of the corporate governance should
correlate positively both with the firm and with the firm idiosyncratic volatility, which we have tested on asample of U.S. firms where the quality of corporate governance is measured by the GIM Index of antitakeoverprovisions. The endogeneity of the quality of the governance, the stock , and the stock return idiosyncraticvolatility has been addressed through 2SLS estimation where in the first stage the GIM Index is instrumented,separately, with the age of the firm and with the dividend yield. In the second stage the and the stocknormalized idiosyncratic volatility are regressed against the fitted GIM Index from the first stage along withcontrols. We found that the quality of the corporate governance is worse in companies with lower and withlower idiosyncratic volatility.While the empirical result that an increase in private benefits is associated with a reduction of the idio-
syncratic volatility is not new (see for example Ferreira and Laux 2007), novel is both the identification of anegative relationship between and private benefits and the uncovering of the driving force behind these results.Namely private benefits are not exogenous but are chosen optimally to elicit e§ort. As long as e§ort is not justa scale factor but is able to improve the trade o§ between the variability of cash flows and their average, thevalue of the firm is larger but the risk does not change. Thus as governance worsens the unit of risk (systematicand idiosyncratic) for each dollar invested is lower.
16
Appendix A: The GIM Index
The "Governance Index" introduced by Gompers, Ishii, and Metrick (2003) is a proxy for the level of shareholderprotection in a company. It has been computed for about 1500 U.S. firms, covering more than 93% of the totalcapitalization of the NYSE, AMEX and NASDAQ, in 1990, 1993, 1995, 1998, 2000, 2002, 2004 and 2006. Thisindex is based on 24 corporate-governance provisions. It is computed as the number of provisions, among these24 provisions, which reduce shareholder’s rights. So, the index ranges from 0 to 24 and, the higher is the index,the weaker are the shareholder’s rights. 22 of these provisions are provided by the Investor ResponsibilityResearch Center (IRRC). 6 other provisions are instituted by state law, among which 4 are redundant with theIRRC provisions. However, not all the U.S. states have adopted these 6 provisions. So, in case of redundancyof two provisions, they count only for one. Thus, the index in made of 24 provisions. The list of the provisions,along with a short description, is provided below. The provisions are clustered in five functional groups: Delay:tactics for delaying hostile bidders; Voting: shareholder’s rights in elections or charter/bylaw amendments;Protection: protection for director/o¢cer against job-related liability, and compensations; Other: other anti-takeover provisions; and State: state laws.Some provisions may vary in amplitude: for instance, the supermajority threshold can vary from 51% to
100%; however, no distinction is made; only the presence of such provision is considered. Also notice that eventhough some provisions might have a positive e§ect for shareholders in certain circumstances, as long as theyincrease management’s power they are considered as weakening the shareholder’s protection. The Secret ballotand the Cumulative voting provisions are the only ones increasing the shareholder’s rights and their absenceincreases the index by one point each. Finally it is interesting to note that the index has no obvious industryconcentration.
List of provisions considered:
• Delay: tactics for delaying hostile bidders
— Blank check: the issuance of preferred stocks, which give additional rights to its owner, to friendlyinvestors is used as a "delay" strategy.
— Classified board: the directors are placed into di§erent classes and serve overlapping terms.
— Special meeting: it increases the level of shareholder support required to call special meetings
— Written consent: it limits actions beyond state law requirement
• Voting: shareholder’s rights in elections or charter/bylaw amendments
— Compensation plans: it enables participants in incentive bonus plans to cash out options or acceleratethe payout of bonuses in case of change in control.
— Contracts: contracts between the company and some directors/o¢cers indemnifying them from legalexpenses and judgments resulting from lawsuits. The contracts comes in addition to indemnification.
— Golden parachutes: severance agreements that provides a compensation to senior executives uponan event such as termination, resignation, etc.
— Indemnification: it uses bylaws and/or charters to indemnify directors/o¢cers from legal expensesand judgment. The contracts comes in addition.
— Liability: it is a limitation on director personal liability to the extent allowed by state law.
17
• Protection: protection for director/o¢cer against job-related liability, and compensations
— Bylaws: it limits the shareholder’s ability to amend the governing documents of a company throughbylaws.
— Charter: it limits the shareholder’s ability to amend the governing documents of a company throughcharter.
— Cumulative voting: it allows a shareholder to allocate his total votes in any manner desired.
— Secret ballot: an independent third party counts votes and the management agrees not to look atindividual votes
— Supermajority: it increases the level of the majority, with respect to the state law requirement,required to approve a merger
— Unequal voting: it limits the voting rights of some shareholders and expands those of others.
• Other: other anti-takeover provisions
— Anti-greenmail: it discourages agreements between a shareholder and a company whose aim is theaccumulation of large quantities of stocks.
— Director’s duties: it allows a director to consider constituencies other than shareholders, i.e. employ-ees, suppliers, etc., when considering a merger.
— Fair price: it limits the range of prices a bidder can pay in two-tier o§ers.
— Pension parachutes: it prevents an acquirer from using surplus cash in the pension fund of thecompany
— Poison pill: it provides special rights to their holders in case of specific events such as a hostiletakeover. Such rights are made to render the target unattractive.
— Silver parachutes: similar to golden parachutes except that it is extent to a large number of employees
• State: state laws
— Anti-greenmail law (7 U.S. states)
— Business combination law: imposes a moratorium on certain transactions between a large shareholderand a company (27 U.S. states)
— Cash-out law: enables shareholders to sell their stake to a controlling shareholder at a certain price(3 U.S. states)
— Directors’ duties law
— Fair price law
— Control share acquisition law: see supermajority
Appendix B: Proof of Proposition 5
Throughout the formulas, we drop the subscript i.
18
Comparative statics of si
Remember that si is given by the first-order condition (30):
rt2(2L+ tsr) = 2h(L+ tsr)2s12r
1. Letting c = 2h/rt2 and di§erentiating (30) with respect to Li yields
rtsr1ds
dL+ 2 = c(1 2r)(tsr + L)2s2r
ds
dL+ 2cs12r(tsr + L)
trsr1
ds
dL+ 1
.
After rearranging, multiplying by s1r(tsr + L), and using (30) on both sides, this is equivalent to
2Ls1r =3rtL+ rt2 + (1 2r)(2L+ tsr)(Lsr + t)
dsdL
Hence, dsdL < 0 under the maintained assumption that r < 1/2.2. Di§erentiating (30) and rearranging yields
Using (30) and re-arranging as in 1. above shows that the squared bracket is strictly positive, hence dsdh < 0.
3. Di§erentiating (30) with respect to t and rearranging along the lines sketched above yields dsdt > 0 as
claimed in the proposition.
6.1 Comparative statics of iRemember that i is given by (16), which in equilibrium (using (6) and (26)) reads
i =B (1 +Rf )
F + ei hs
=B (1 +Rf ) (L+ ts
r)
t2s2r + (F hs)(L+ tsr).
1. Hence, d/dL > 0 i§d
dL
t2s2r
tsr + L hs
< 0. (34)
19
Recall that dsdL < 0. Hence,
d
dL
t2s2r
tsr + L hs
= t2
"2rs2r1 dsdL (ts
r + L) s2rrtsr1 dsdL + 1
(tsr + L)2
# h
ds
dL
= t2
"dsdL
rts3r1 + 2rs2r1L
s2r
(tsr + L)2
# h
ds
dL
< 0
where the last inequality follows by solving out for h from (30) and rearranging.2. We have
d
dh
t2s2r
tsr + L hs
=
2rt2s2r1 dsdh
(tsr + L) t2s2rrtsr1 dsdh(tsr + L)
2 hds
dh s
Hence, a su¢cient condition for d/dh > 0 is
rt3s3r1 + 2rt2s2r1L h (tsr + L)2 > 0 (35)
which again follows by solving out for h from (30) and rearranging.
3. Similarly, d/dt < 0 i§d
dt
t2s2r
tsr + L hs
> 0.
We have
d
dt
t2s2r
tsr + L hs
=
2ts2r + 2rt2s2r1 dsdt
(tsr + L) s3rt2 t3rs3r1 dsdt(tsr + L)
2 hds
dt.
This has the same sign as
t2s3r + 2ts2rL+hrt3s3r1 + 2rt2s2r1L h (tsr + L)2
i dsdt.
Since dsdt > 0, the claim follows from (35).
20
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22
187
2478
5284
4535
1425
89
010
0020
0030
0040
0050
00Fr
eque
ncy
0 1 2 3 4 5GIM Index
Figure 1: Distribution of the GIM Index
This Figure shows the distribution of The GIM Index. The GIM Index is the empirical counterpart of the equilibrium control
benefit si . Higher GIM Index indicates worse governance.
23
Table 1: Variables description
VARIABLE DEFINITION SOURCEIdios. Vol. Annualized daily variance estimated Elab. on CRSP data
from market modelMarket vol. Annualized daily variance of the market portfolio Elab. on CRSP data
(value weighted index of stocks in our dataset)VR Normalized idiosyncrratic volatility given by Elab. on CRSP data
the ratio of Idiosyncratic volatility to Market volatilityBeta Yearly Beta of asset i Elab. on CRSP dataEPS Earnings Per Share (Basic) - Excluding Extraordinary Items S&P CompustatROA Return on Asset defined as the ratio Elab. on S&P
of Earnings to Total Assets Compustat dataLEV Leverage defined as the ratio of Elab. on S&P
long term debt to total assets Compustat dataMKTV Market Value defined as the Annual Fiscal Price Elab. on S&P
Close multiplied by Common Shares Outstanding Compustat dataPTBV Price to Book Value defined as the Annual Fiscal Price Elab. on S&P
Close multiplied by the Book Value per Share Compustat dataDY Dividend Yield defined by the ratio of Total Elab. on S&P
dividends to Market Value Compustat dataAGE Number of years between the year of observation Elab. on S&P
and the year of stock inclusion in the CRSP database Compustat data
This Table reports the description of the variables used in the analysis and the source of these variables.
Table 2: Transition matrix of the GIM Index
t \ t+1 0 1 2 3 4 50 70 48 9 0 0 01 13 1,244 381 23 5 02 0 89 2,912 463 16 03 1 5 178 2,764 175 04 0 3 8 110 926 175 0 0 0 0 9 57This table describes the number of firms thatreports a certain level of the GIM Index at timet (Rows) and the same or another GIM index attime t+1 (Columns). Higher GIM Index indicatesworse governance. The sample period is from1990 to 2006. Number of observations 13.004.
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Table 3: Change in beta after a change in GIM Index
- - - - (-0.19) (1.40)This table reports the change in beta from time t to t+1,of firms having a GIM Index at time t as in Rows and aGIM Index at time t+1 as in Columns. t-statistics in
parenthesis. Values without standard errors result from onlyone observation Higher GIM Index worse governance. Thesample period is from 1990 to 2006. N . of obs. 13004
Kleibergen-Paap test Chi-sq(1) p-value 0.000 0.000Kleibergen-Paap Wald F statistic [142.438 142.438
This table presents the estimation results of the two-stage least squares instrumental variable panel regression of the relationshipbetween the GIM Index (si,t) and respectively beta (i,t) and idiosyncratic risk (i,t ). 1st-stage column reports the first stage
where X1 and X2 are two sets of exogenous variables; i,t is the error terms, is the constant; Di are industry dummies, Dt aretime dummies, j , t are dummy coe¢cients; and 1 and 2 are vectors of coe¢cients. We also report the estimation results for
the second-stage regressions (32), and (33)
i,t = b+ bjDj + btDt + 1bsi,t + 1X1 + i,t,
i,t = c+ cjDj + ctDt + 1bsi,t + #1X1 + i,t,
where where bsi,t is the fitted values of si,t from the first-stage regression, i,t and i,t are the error terms, b and c are the
constant; bj , cj , bt, ct, 1, and 1 are coe¢cients; and 1 and #1 are vectors of coe¢cients. The dependent variables are the
return risk measures: factor loading to market portfolio i,t, ie. BETA (Yearly Beta of asset i) and idiosyncratic risk i,t , i.e.
sqrtVR (square root of the normalized idiosyncratic volatility given by the ratio of Idiosyncratic volatility to Market volatility).
Explanatory variables are as defined in table 1. The instrumental variable is LNAGE. Regressions are based on yearly data and
t-statistics are calculated using standard errors that are clustered at firm level. The sample period is 1990-2006. All variables are
winsorized at the bottom and top 1% levels. *** Coe¢cients significant at the 1% level, ** Coe¢cients significant at the 5% level,
Kleibergen-Paap test Chi-sq(1) p-value 0.009 0.009Kleibergen-Paap Wald F statistic 6.640 6.640
This table presents the estimation results of the two-stage least squares instrumental variable panel regression of the relationshipbetween the GIM Index (si,t) and respectively beta (i,t) and idiosyncratic risk (i,t ). 1st-stage column reports the first stage
where X1 and X2 are two sets of exogenous variables; i,t is the error terms, is the constant; Di are industry dummies, Dt aretime dummies, j , t are dummy coe¢cients; and 1 and 2 are vectors of coe¢cients. We also report the estimation results for
the second-stage regressions (32), and (33)
i,t = b+ bjDj + btDt + 1bsi,t + 1X1 + i,t,
i,t = c+ cjDj + ctDt + 1bsi,t + #1X1 + i,t,
where where bsi,t is the fitted values of si,t from the first-stage regression, i,t and i,t are the error terms, b and c are the
constant; bj , cj , bt, ct, 1, and 1 are coe¢cients; and 1 and #1 are vectors of coe¢cients. The dependent variables are the
return risk measures: factor loading to market portfolio i,t, ie. BETA (Yearly Beta of asset i) and idiosyncratic risk i,t , i.e.
sqrtVR (square root of the normalized idiosyncratic volatility given by the ratio of Idiosyncratic volatility to Market volatility).
Explanatory variables are as defined in table 1. The instrumental variable is DY (Dividend Yield). Regressions are based on yearly
data and t-statistics are calculated using standard errors that are clustered at firm level. The sample period is 1990-2006. All
variables are winsorized at the bottom and top 1% levels. *** Coe¢cients significant at the 1% level, ** Coe¢cients significant at
the 5% level, * Coe¢cients significant at the 10% level,
