Managerial Risk Incentives and a Firm s Financing Policy

Transcription

1 Managerial Risk Incentives and a Firm s Financing Policy Sigitas Karpavičius a and Fan Yu b a Accounting & Finance, Adelaide Business School, University of Adelaide. sigitas.karpavicius@adelaide.edu.au. b Department of Applied Finance and Actuarial Studies, Macquarie University. fan.yu@mq.edu.au. September 1, 2015 Abstract This paper provides a theoretical explanation for how risk preferences of a firm s manager impact a firm s optimal financing policy and shareholder value. The developed model implies that the increase in risk aversion of the firm s manager leads to higher (lower) debt level for firms with positive (negative) growth opportunities. Further, debt level increases when both growth opportunities and managerial risk aversion move in the same direction. The predicted impacts on shareholder value are just the opposite of those on leverage. The empirical analysis generally supports all the model s predictions except those related to firms with negative growth opportunities. Key words: Capital structure; Growth opportunities; Risk preferences. JEL classifications: D21; D22; D58; G32. The authors would like to thank Terry Walter and seminar participants at 2014 Annual Summer Meeting of Economists in Vilnius, Shanghai University of Finance and Economics, and University of South Australia for their helpful comments and suggestions. Corresponding author.

2 1 Introduction Managerial risk and time preferences are believed to impact corporate policies (see, for example, Graham et al., 2013). However, our knowledge both empirical and theoretical on how managerial risk preferences impact a firm s optimal financing policy is quite limited. Moreover, the empirical results on the relation between leverage and a manager s risk preferences are mixed. For example, Coles et al. (2006) and Chava and Purnanandam (2010) find that book leverage decreases with CEO vega after controlling for industry fixed effects. 1 Coles et al. (2006) find that vega does not have significant impact on leverage, if firm fixed effects are included in the model. Cain and McKeon (2014) find that book leverage decreases with CEO vega after controlling for CEO-pilot dummy and firm fixed effects. The most relevant theoretical studies for this paper are Berk et al. (2010) and Bhagat et al. (2011). The dynamic model with risk-averse employees and risk-neutral investors in Berk et al. (2010) implies that optimal leverage for firms with more risk-averse employees is lower. A dynamic principal-agent model in Bhagat et al. (2011) predicts that short-term debt (i.e., negative cash reserve), as well as total debt, should decrease with the managerial risk aversion but long-term debt should increase with managerial risk aversion. Neither Berk et al. (2010) nor Bhagat et al. (2011) test these hypotheses empirically. Graham et al. (2013) show that risk-tolerant CEOs are more likely to be hired at high-growth companies and receive riskier compensation packages, that is, they are more likely to be paid with proportionally more restricted stock, options, and bonuses and with proportionally smaller salary. This suggests that firms strategically employ CEOs with certain risk preferences based on their growth opportunities. Thus, it is likely that managerial risk incentives have different impacts on firm value and corporate policies for low- and high-growth firms. The models in Berk et al. (2010) and Bhagat et al. (2011) do not include firms growth opportunities. Thus, it is not clear whether their results are applicable for both high- and low-growth firms. In this paper, we fill this gap in the 1 Less risk averse managers have lower vega. 1

3 literature. Specifically, we analyze how risk preferences of a firm s manager impact a firm s optimal financing policy and shareholder value and whether the effects differ for high- and low-growth firms. To develop testable hypotheses, we expand the dynamic partial equilibrium model developed in Karpavičius (2014b) to include external growth opportunities. The model assumes that a firm s manager maximizes a certain objective function that positively depends on shareholder value. In each time period, the firm s manager makes several simultaneous decisions, specifically, how much capital to raise in the external equity and debt markets, how much to produce, and how much to invest in productive capital stock. A firm uses a mix of equity and debt to finance its activities; however, there are no agency costs of debt. A firm produces a single tradable final good that is sold in a competitive market. The relation among all endogenous variables and their dynamics are jointly determined in equilibrium. We assume that a firm evolves along a stable growth path that proxies the firm s external growth opportunities. The model predicts that managerial risk preferences impact firm value and financing policy for high- and low-growth firms asymmetrically. The equilibrium relations imply that share price should decrease with managerial risk aversion for firms with positive growth opportunities and vice versa, share price should increase with managerial risk aversion for firms with negative growth opportunities. Further, the model implies that not only managerial risk aversion but also an interaction between it and external growth opportunities impacts shareholder value. Stock price is adversely affected when both growth opportunities and managerial risk aversion move in the same direction. The transmission mechanism between managerial risk preferences and firm value is as follows. The model suggests that the effective discount rate decreases with managerial risk aversion for firms with positive growth opportunities, and vice versa. The discount rate reflects the riskiness of the dividend stream and includes both the likelihood of generating free cash flows and the volatility of each cash flow. Risk-averse managers of firms operating in high-growth industries are likely to undertake less risky projects and are reluctant to 2

4 invest in profitable however riskier projects. The underinvestment would adversely impact free cash flows implying that dividend stream becomes riskier. Thus, dividends would be discounted using a higher discount rate. Similarly, if a high-growth firm is run by risk-seeking manager, a firm would exploit substantially more projects (including risky ones), ensuring that a firm would have enough financial resources to pay out dividends. Therefore, effective discount rate of dividends would be smaller. This implies that firms with positive (negative) growth opportunities run by risk-seeking (risk-averse) managers are more valuable. Similarly, for firms operating in the declining industries risk-seeking managers would overinvest in risky and value destroying projects jeopardizing dividend stream. Thus, the effective discount rate would be higher for such firms. The model predicts that the impact of managerial risk preferences on leverage are, in general, just the opposite to their impact on stock price. We find that a firm s external growth opportunities and managerial risk preferences have a limited and non-monotonic impact on optimal firm size or assets. Leverage is computed as the difference between firm s assets and equity over assets. If we assume that assets are constant then the predicted impacts on leverage are just the opposite of those on equity value. Thus, the increase in risk aversion of the firm s manager leads to higher (lower) debt level for firms with positive (negative) growth opportunities. Debt level increases when both growth opportunities and managerial risk aversion move in the same direction. Thus, according to the model, firm value is directly impacted by managerial risk aversion. However, the latter affects the firm s leverage indirectly. The unstable relation between leverage and managerial risk aversion across the spectrum of growth opportunities can help explain why the empirical evidence on the relation between leverage and a manager s risk preferences is mixed. 2 A dynamic principal-agent model in Bhagat et al. (2011) predicts that short-term debt as well as total debt should decrease with the managerial risk aversion but long-term debt should increase with managerial risk aversion. Our predictions are not consistent with the theoretical results in 2 See the discussion in the first paragraph of Section 1 (Introduction). 3

5 Bhagat et al. (2011) if we assume that the majority of firms are subject to positive growth opportunities. Further, John and John (1993) use a two-period model and show that there is a negative relation between pay-performance sensitivity and leverage. However, the recent studies argue that CEO vega rather than pay-performance sensitivity (which is equivalent to CEO delta) reflects managerial risk preferences (see, for example, Low, 2009). We test the model s implications using the sample of US industrial firms during the period According to the model, growth opportunities impact the demand of the firm s products; therefore, we measure firms growth opportunities using industry 3- year sales growth. Managers with higher vega are expected to be less risk averse and vice versa (Low, 2009). The panel data regressions generally support all model s predictions except those related to firms with negative external growth opportunities. We find that share price and capital structure of these firms are generally impacted neither by external growth opportunities nor managerial risk preferences. The rest of the paper is structured as follows. Section 2 introduces a non-stationary dynamic stochastic partial equilibrium model. We develop and test our hypotheses in Section 3. Finally, Section 4 concludes. 2 The model We use the non-stationary dynamic stochastic partial equilibrium (DSPE) model developed in Karpavičius (2014b). 3 The model replicates the performance of a representative firm in a dynamic world with a changing environment. We consider a firm with an infinite life span in discrete time. The firm s manager acts completely in the best interests of shareholders and has rational expectations about the future. In each time period, the firm s manager observes the changes in the environment that are defined by stock price and productivity shocks, and makes several decisions accordingly; namely, to choose how much capital to 3 In this section, the description of the model is broadly similar to one in Karpavičius (2014b). 4

6 raise in the external equity and debt markets, how much to produce, and how much to invest in capital stock (i.e., fixed assets used in production). The firm s manager does not know the timing of future shocks but knows their distributional properties. Thus, the decisions of the manager are made knowing that the future value of innovations is random but will have zero mean. The model is non-stationary; that is, a firm is subject to exogenous growth opportunities. A firm produces a single tradable final good that is sold in a competitive market. 2.1 A firm The firm s manager has the following intertemporal objective function: ( ) E 0 β t U t, (1) t=0 where β is the subjective discount factor and reflects the time preferences of the firm s manager. We assume that the firm s manager acts in the best interests of current shareholders and maximizes a certain objective function that increases with shareholder value. 4 Thus, the instantaneous objective function, U t, is given by: U t = (P t m N t ) 1 σ, 1 σ where P m t is market value of equity per share at time t and N t is the number of shares outstanding. σ is the coefficient of constant relative risk aversion (the inverse of elasticity of substitution). The firm s manager maximizes the objective function subject to the balance sheet 4 For more details, see the discussion on page 292 of Karpavičius (2014b). 5

7 equation and asset composition of the firm: Pt b N t = Pt 1N b t 1 + Pt 1N m t Pt 1N m t 1 +RE t (2) }{{} New share issue K t = κ(d t + P b t N t ). (3) P b t is book value of equity per share at time t. The left hand side of Equation (2) is the book value of equity. Therefore, ( P m t 1 N t P m t 1 N t 1) is the proceeds from issuance of common stock. 5 The relation between market value and book value of equity is given by: P m t = P b t e qt, (4) where q t is shock to market-to-book ratio and follows the AR(1) process: q t = ρ q q t 1 + η q t, (5) where η q t N(0, σ2 q), 0 ρ q < 1, and σq 2 > 0. q t measures the deviation of market value of equity per share from the book value and proxies the information asymmetry between the firm s manager and investors. Positive q t means that stock is overvalued, and vice versa. RE t denotes retained earnings: RE t = π t d t N t 1, (6) where d t is dividends at time t. They are paid to those who owned shares at time (t 1). Thus, investors who purchase shares at time t are not entitled to receive dividends in this period. π t represents net income. 5 This term controls for market timing activities. For example, a high stock price might trigger an equity issue. Similarly, if the share price falls below its fair value, a firm might decide to repurchase some shares, as it would be in line with the interests of shareholders. If N t < N t 1 then (P m t 1N t P m t 1N t 1) is equal to the funds spent to repurchase shares. 6

8 K t is capital stock at time t. D t is new borrowing; thus, D t 1 is debt a firm pays back in period t. For simplicity, it is assumed that debt consists of one-period securities. Equation (3) implies that a firm can invest only the κ fraction of its financial assets into capital stock. This assumption is introduced in order to make the model more realistic. For example, a mean of fixed assets-to-total assets ratio is equal to for the population of Compustat firms during The rest of the financial capital, (1 κ) (D t + Pt b N t ), can be seen as working capital. Thus, κ is the outcome of firm s working capital management. Stock of physical capital, K t, evolves according to: K t = (1 δ)k t 1 + I t, (7) where δ is the capital depreciation rate. I t stands for investment. The firm s net income is given by: π t = (S t C t δk t 1 D t 1 r t 1 ) (1 τ), (8) where S t is sales revenue. C t is the amount of production input (for example, labor and raw materials). It is assumed that the unit cost of C t is one. τ is corporate income tax. r t is the interest rate for a debt obtained in time t, D t. The interest rate at which a firm can borrow funds evolves according to the following equation: ( ) r t = r D t 1 + Φ r D t + Pt bn, (9) t where r is a constant and equal to the hypothetical interest rate on corporate bonds for firms with zero leverage. The last term in Equation (9) is the risk premium related to a firm s financial leverage. Φ r > 0 is the parameter of risk premium. The definition of interest rate implies that it is an increasing function of a firm s financial leverage. In the model, debt has advantages (such as tax deductibility of interest expenses and lower costs) 7

9 and disadvantages (increased bankruptcy risk). Sales revenue, S t, is the product of output volume, Y t, and the price per output unit, p t : S t = Y t p t. (10) The price per output unit depends on demand for a firm s products and is given by the following equation: ) η (Ỹt p t = p t, (11) Y t where Ỹt and p t are respectively the stable-growth path values of demand for a firm s products and their market price at time t. 6 Parameter η is price elasticity of demand. To produce a single tradable good, a firm uses the following Cobb-Douglas technology: Y t = Ae At K α t 1C 1 α t, (12) where A is the total factor of productivity. A t is the productivity shock that follows the AR(1) process: A t = ρ a A t 1 + η a t, (13) where ηt a N(0, σa), 2 0 ρ a < 1, and σa 2 > 0. α is capital share. Equation (12) implies that production output is the increasing function of capital stock and other production inputs. We assume that it takes one period for a firm to install the newly acquired productive capital stock before it can be used in production. Dividends per share evolve according to the following equation: d t = ψ d t + (1 ψ) π t N t 1, (14) where d t is the stable-growth path value of dividends per share. ψ is subjective dividend smoothness parameter that reflects the manager s perception on the dividend policy. Equa- 6 Throughout this paper, variables with tildes denote stable-growth path values. 8

10 tion (14) shows that dividends per share, d t, consist of constant and variable parts. The constant part is equal to the stable-growth path dividends per share, d t, multiplied by ψ. 7 It is equivalent to a certain amount of cash per share distributed to shareholders at the end of each period. The variable part is proportional to the firm s net income per share. 2.2 The equilibrium In each period, the firm s manager observes the values of the shocks and parameters and chooses strategy {C t, K t, N t, D t } t= t=0 to maximize her expected lifetime utility subject to constraints (Equations (2) and (3)), initial values of debt, capital stock, share price, the number of shares outstanding and a no-ponzi scheme constraint of the form: lim j E t D t+j j i=1 (1 + r i) 0. (15) To simplify the firm s manager s optimization problem, we assume that the firm s manager does not consider an option of strategic default while running a firm. We admit that, in some cases, it could be optimal from the shareholder perspective to liquidate a firm in order to avoid further losses. However, in reality, we do not observe (at least, we are not familiar with) cases where a manager liquidated a firm with positive net assets; that is, when a firm s assets exceeded its liabilities. Usually, managers try to run a firm as long as possible; thus, creditors initiate bankruptcy procedure. However, this occurs when a firm s net assets are negative. The potential explanations for why managers do not file for bankruptcy when firms net assets are still positive include agency-related reasons (managers do not want to lose their jobs and thus salaries important source of their income), information asymmetry (managers are more likely to have better information regarding the firm s prospects than other stakeholders), and behavioral reasons (managers might be overconfident about their firm s prospects and their abilities). Thus, without loss 7 The stable-growth path value of dividends per share, d t, can be seen as the long-term historical average dividends per share or the target dividends per share. In good times, actual dividends per share exceed the stable-growth path value but in bad times, actual dividends per share are lower than it. However, the average actual dividends per share are equal to the stable-growth path value. 9

11 of generality, we assume that the firm s manager does not foresee the possibility that a firm might default. Maximization of objective function (Equation (1)), subject to the evolution of shareholder value and asset composition of a firm (Equations (2) and (3)), yields the following first-order conditions: C t : C t = (1 α)(1 η)s t, (16) ( ) σ [ ( ) : (e qt ) 1 σ Kt K t κ D Nt+1 t λ t + βe t {λ t e qt 1 N t [ +κψ (1 τ) α(1 η) S ( ) ]]} 2 t+1 δ + Φ r r Dt κ = 0, (17) K t K t [ e q t 1 ( )] [ Kt 1 : λ t N t N t 1 κ D t 1 = βe t {λ t+1 e N ( ) ]} qt t+1 Kt (N t ) 2 κ D t + ψ d t, (18) [ ] σ : (e qt ) 1 σ Kt D t κ D t λ t { [ ( Nt+1 βe t λ t e qt 1 N t ) + ψe ψ t+1 (1 τ) r [ 1 + 2Φ r κ D ]]} t K t = 0, (19) where λ t is a Lagrange multiplier. Equation (16) defines the optimal level of production input, C t, and Equations (17)-(19) are Euler conditions. The equilibrium of the model is defined by the evolution of shareholder value, asset composition constraint, first-order conditions, several variable definitions (in total 15 equations), and two shocks. 8 The number of endogenous variables is equal to the number of equations; thus, the model can be solved. To understand long-term equilibrium relations among the model s variables, we analyze the properties of the model assuming a nonstochastic environment. We solve for the non-stochastic steady state of the model by using 8 Specifically, the equilibrium of the model is defined by Equations (2)-(4), (6)-(12), (14), (16)-(19) and two exogenous processes: Equations (5) and (13). 10

12 the following procedure: we detrend non-stationarly variables, then all shocks are set to zero, the time subscripts are dropped, and the steady-state values of each endogenous variable are expressed in terms of parameters. 2.3 Stable growth path and steady state We assume that the majority of variables feature the following law of motion: X t = X 0 e gt, (20) e g = Γ t Γ t g, (21) where X t is any variable, g is a quarterly growth rate, and Γ t is growth factor. d t, p t, r t, P b t, and P m t are stationary variables. Euler conditions imply that a Lagrange multiplier, λ t, decreases at a σg rate (i.e., a Lagrange multiplier s growth factor is e σg ). 9 To obtain steady-state relations, we detrend non-stationary variables by dividing them by their growth factor. 10 When all shocks are set to zero and the time subscripts are dropped, the model reduces to 13 equations: Equation (11) cancels out and the steady-state expressions of Equations (2) and (14) are identical. To express the steady-state values of each endogenous variable in terms of parameters and constants, the number of endogenous variables must be equal to the number of equations. Thus, we assume that steady-state values of the number of shares outstanding, N, and dividends, d, are known. We re-arrange steady-state expressions of Equations (3) and (18) and ascertain that market value of equity per share in the steady state is as follows: 11 P m = βe σg ψ d 1 βe σg e g. (22) 9 λ t grows at the same rate as the marginal utility. 10 The term steady state refers to the deterministic steady state. Throughout this paper, variables with bars denote steady-state values. 11 See Appendix A for more details. 11

13 If we assume that βe σg is the effective discount factor, then the effective discount rate is as follows: R = 1 βe σg βe σg = eσg β 1. (23) If g is a smal number, growth factor, e g, can be expressed as (1 + g). Then Equation (22) can be rewritten as follows: P m = ψ d R g. (24) Equation (24) is similar to the Gordon dividend growth model, except that the latter considers whole dividends (i.e., constant and variable parts) and implies that firms with greater growth opportunities are more valuable (see Williams (1938, p. 88) and Gordon (1959)). Previous studies usually assume that share price is equal to the present value of future dividend stream. The fact that our model is consistent with Gordon dividend growth model helps validate our model. 2.4 Calibration There is no consensus in the literature on the calibration of the coefficient of relative risk aversion. Some studies report or use the value of the coefficient equal to or less than one. Huddart (1994) sets the coefficient of relative risk aversion to 0.5 and Oyer and Schaefer (2005) use a coefficient of relative risk aversion value of one. Bhagat et al. (2011) set the coefficient of risk aversion to Lambert and Larcker (1987) use the Box-Cox estimation for the sample of 370 US firms from 1970 to 1984 and find that the mean (median) coefficient of relative risk aversion is (0.400). Brown and Kim (2014) find that 95 out of 101 (or 94%) experiment participants have the coefficient of relative risk aversion smaller than 0.97 in Epstein and Zin s (1989) framework. However, the value of the coefficient of relative risk aversion of the representative agent used in macroeconomic literature is normally between one and two. For example, Khan and Tsoukalas (2012) 12 The manager s utility function in Bhagat et al. (2011) is defined as U(x) = x 1 2 γx2. 12

14 estimate that it is 1.08, Smets and Wouters (2007) report a value of The recent survey by Graham et al. (2013) finds that CEOs are very different from the rest of the population. Graham et al. (2013) report that only 8.4% of CEOs have the coefficient of relative risk aversion greater than 3.76, in contrast to 64.6% of the general population of a similar age (Barsky et al., 1997). This suggests that CEOs are significantly less risk averse than ordinary individuals and could prompt their coefficient of relative risk aversion to be smaller than one, as assumed by the previous studies (for example, Huddart (1994)). We assume that the coefficient of manager s risk aversion, σ, is set to 0.97; that is, the value that is less than but close to one. The quarterly growth rate, g, is assumed to be 0.02 which is slightly lower than the average industry sales and assets growth rate. The quarterly discount factor, β, is set to It corresponds to an 8% annual discount rate, consistent with Bhagat et al. (2011). The values of β and g imply that the coefficient of relative risk aversion, σ, should be somewhat smaller than one, as only then do the exogenous growth opportunities lead to higher shareholder value (see Equation (22)). 14 This provides a further reason to set σ to The rest of the model is calibrated similarly as in Karpavičius (2014b) (see Table 1). 15 We assume that the variables are measured quarterly. The steady-state values for the number of shares outstanding, N, and dividends, d, are normalized to one. Following macroeconomic literature, quarterly capital depreciation rate, δ, is set to and capital share in the production function, α, is set to Further, we assume that a firm can invest 28% of its financial resources in productive capital; that is, κ = 0.28). The value is similar to average net property, plant, and equipment scaled by total book value of assets for US public firms over the last two decades. The steady-state quarterly interest rate on corporate bonds, r, is set equal to It implies that the hypothetical annual interest rate for unlevered firms is 6%. It is approximately equal to Moody s Seasoned Aaa 13 In addition, many studies (for example, Justiniano et al., 2010) use a log-utility function that assumes that the coefficient of relative risk aversion is equal to one. Others, for example, Gertler et al. (2012) set the coefficient of relative risk aversion as equal to two. 14 The exact relation among share price, σ, and g is derived in Section In this paper, we do not run any simulations; therefore, we do not calibrate the parameters of the stochastic processes. 13

15 Table 1: Calibration of the parameters and steady-state values of some variables This table presents the calibrated parameter values and steady-state values of some variables. Coefficient Description Value N Shares outstanding in the steady state 1 d Dividends in the steady state 1 g Quarterly growth rate 0.02 κ Fixed assets-to-capital ratio 0.28 τ Corporate income tax rate 0.3 r Interest rate for unlevered firm α Capital share 0.33 η Price elasticity of demand 0.15 β Subjective discount factor 0.98 ψ Weight of the constant part of dividends 0.7 Φ r Parameter of risk premium 1 δ Capital depreciation rate σ Coefficient of constant relative risk aversion 0.97 Corporate Bond Yield during the period. 16 The corporate income tax rate, τ, is 0.3, which is approximately equal to an average value of corporate marginal tax rate simulated in Graham and Mills (2008). To achieve reasonable leverage ratios, we calibrate the rest of the parameters respectively. We assume that ψ is 0.7. It implies that the weight of the constant part of the dividends is 0.7. We assume that price elasticity of demand, η, is It implies that if the production supply increases by 10%, the sale price decreases by 1.5%, and vice versa. The parameter of risk premium, Φ r, is set equal to one. It implies that if a firm s leverage increases by one percentage point, the quarterly interest rate will increase by 1.5 basis points if r is The calibrated parameter values imply quite reasonable firm characteristics in the steady state. Book (market) leverage, L = D P b, is N+ D Quarterly dividend yield is and implying that shareholders earn 11.5% per year on their investment. 17 Thus, equity financing is more expensive than debt financing. Net profit margin (net income, π, over sales, S) is equal to Source: 17 Share price, P m t, is a stationary variable; therefore, capital gains are zero. 18 Table B.1 in Appendix B presents the steady-state values of all variables. 14

16 3 Results In this subsection, we analyze the implications of the model, develop and test hypotheses concerning external growth opportunities and a firm s financing policy. 3.1 Implications of the model The expression of share price in the steady state (see Equation (22)) implies that a firm s stock price is impacted by the manager s time and risk preferences, growth opportunities, and dividend policy. To investigate the relation between share price, P m, and either managerial risk aversion, σ, or patience, β, we compute partial derivatives of share price, P m, with respect to the parameters: de σg P m β = ψ [ ] 1 βe g(1 σ) 2 > 0, (25) P m σ P m σ = βψ dge σg [ 1 βe g(1 σ) ] 2, (26) < 0 if g > 0, = 0 if g = 0, > 0 if g < 0. Equation (25) shows that share price is higher for more patient managers. The result is consistent with theoretical and empirical findings in Karpavičius (2014a) who uses a stationary model in the analysis. Equation (26) suggests that greater managerial risk aversion leads to higher stock prices only for firms with negative growth opportunities. If the growth opportunities are positive, shareholder value is higher if managers are less risk averse. If a firm has no growth opportunities (i.e., g = 0) then managerial risk aversion does not impact share price per equity. The implications are driven by the effective discount rate, R, which 15

17 is used to discount dividend stream (see Equation (23)). The model suggests that the effective discount rate decreases with managerial risk aversion for firms with positive growth opportunities, and vice versa. The discount rate reflects the riskiness of the dividend stream and includes both the likelihood of generating free cash flows and the volatility of each cash flow. Risk-averse managers of firms operating in high-growth industries are likely to undertake less risky projects and are reluctant to invest in profitable however riskier projects. The underinvestment would adversely impact free cash flows implying that dividend stream becomes riskier. Thus, dividends would be discounted using a higher discount rate. Similarly, if a high-growth firm is run by risk-seeking manager, a firm would exploit substantially more projects (including risky ones), ensuring that a firm would have enough financial resources to pay out dividends. Therefore, effective discount rate of dividends would be smaller. This implies that firms with positive (negative) growth opportunities run by risk-seeking (risk-averse) managers are more valuable. Similarly, for firms operating in the declining industries risk-seeking managers would overinvest in risky and value destroying projects jeopardizing dividend stream. Thus, the effective discount rate would be higher for such firms. This leads to the following hypotheses: Hypothesis 1a: For firms with positive growth opportunities, the decrease in managerial risk aversion leads to higher share price. Hypothesis 1b: For firms with negative growth opportunities, the decrease in managerial risk aversion leads to lower share price. Equation (26) shows that not only managerial risk aversion but also an interaction between it and external growth opportunities impacts shareholder value. Thus, we compute mixed second order partial derivative of stock price, P m, with respect to g and σ: 2 P m σ g = βψ de σg { [ [ ] 1 βe g(1 σ) 3 (σg 1) 1 βe g(1 σ)] 2g(1 σ)βe g(1 σ)}. (27) The left-hand side of Equation (27) is equal to 1,859.12, assuming that the model is calibrated as in Table 1. This implies that share price, P m, decreases if both growth 16

18 opportunities, g, and managerial risk aversion, σ, increase. Due to the complexity of Equation (27), it is difficult to infer the impact of different values of growth opportunities, g, and managerial risk aversion, σ, on a value of analysis of 2 P m σ g with respect to σ and g. 2 P m σ g. Thus, we perform sensitivity We calculate the values of the mixed second order partial derivative of share price, P m, with respect to growth opportunities, g, and managerial risk aversion, σ, for different values of the two parameters. The results are presented in Table 2 where cells with negative values are shaded. We find that the partial derivative is negative mostly for small values of growth opportunities and/or when the coefficient of relative risk aversion is close to one. For example, the mixed second order partial derivative is negative if 0.02 g 0.02 and 0 σ 1.75 or if g and 0.5 σ 1.5. Lambert and Larcker (1987) use the Box-Cox estimation for the sample of 370 US firms from 1970 to 1984 and find that the mean (median) coefficient of relative risk aversion is (0.400) and that 25 th (75 th ) percentile is (1.800). Thus, it is likely that for the majority of firms, the mixed second order partial derivative of share price, P m, with respect to growth opportunities, g, and managerial risk aversion, σ, is negative. Thus, our next hypothesis is: Hypothesis 2: Share price decreases when both growth opportunities and managerial risk aversion increase (or decrease). Using Equations (22) and (A.3), one can derive the following expression for the firm s financial leverage (debt-to-assets ratio), L: L = 1 e σg κβψ d N K (1 βe σg e g, where (28) ) K = Λ 2 Λ 2 ± 2 4Λ 1 Λ 3, (29) 2Λ 1 2Λ 1 ] Λ 1 = η [δ + r κ (1 + φ r), (30) [ ] 1 Λ 2 = α(1 η) 1 τ + (1 + 2φ r)r βe σg ψ d N 1 βe (1 σ)g, (31) ( βe Λ 3 = r σg ) 2 ψ d N φ r κ[η + 2α(1 η)] 1 βe (1 σ)g. (32) 17

19 in Table 2: Sensitivity analysis of mixed second order partial derivative of market value of equity per share with respect to g and σ ( ) This table presents the sensitivity analysis of mixed second order partial derivative of market value of equity per share with respect to g and σ 2 m P σ g the steady state. The model is calibrated ( as ) in Table 1. Cells with negative values are shaded. The highlighted numbers show the calibrated values for g and σ as well as the implied value of 2 m P in the steady state. σ g g σ , , ,715 1, , E+09 5, , E+06,7750 1, , E+06 11,840 1, , ,901 19,687 2, , ,978 37,069 2, ,715 87,935 85,207 4,568 1, ,715 49, ,048 7,723 1, ,715 30,486 2,442,278 15, ,715 19, E+09 36,920 5,359 1, ,715 13, E ,131 11,753 3, , ,982 2,430,750 36,772 7,669 1, ,715 6,765 49, E ,520 26,194 3, ,715 4,981 19, , E ,264 11, ,715 3,733 9,324 30, , E , ,1071 1,715 2,839 4,941 9,256 19,381 48, E ,083 1,358 1,715 2,185 2,814 3,670 4,862 6,561 12, ,503 1,559 1,588 1,618 1,650 1,682 1,715 1,749 1,785 1,821 1,859 1,898 1, ,838 1,802 1,785 1,767 1,750 1,732 1,715 1,698 1,681 1,664 1,647 1,631 1, ,166 7,082 5,184 3,861 2,916 2,227 1,715 1,329 1, E E ,102 2, , , E ,041 31,279 9,600 3,797 1, , , E , ,061 1, ,505 27, , E , ,540 7,942 37, E ,999 9,530 1, ,483 12, ,968 1,351,225 13,586 1, ,884 5,505 37, E+09 20,040 1, ,003 1, , ,

20 Leverage L= g σ Figure 1: Sensitivity analysis of leverage with respect to growth opportunities, g, and the coefficient of relative risk aversion, σ. The arrow indicates the value of leverage implied by current calibration (see Table 1). Due to the complexity of the formula for leverage, we do not compute its partial derivatives. Instead, we perform sensitivity analysis of leverage with respect to σ and g. We calculate the leverage values for different values of the two parameters. 19 The sensitivity analysis suggests that the impacts of σ and g on leverage are, in general, just the opposite to their impacts on stock price, P m (see Figure 1). 20 Figure 1 suggests that for firms with positive (negative) growth opportunities, leverage increases (decreases) with managerial risk aversion. If the firm has no growth opportunities, the coefficient of constant relative risk aversion does not impact leverage. The unstable relation between leverage and managerial risk aversion across the spectrum of growth opportunities can help explain why the empirical evidence on the relation between leverage and a manager s risk preferences is mixed. Coles et al. (2006) and Chava and Purnanandam 19 The unreported sensitivity analysis shows that leverage decreases with the subjective discount factor, β. This is consistent with Karpavičius (2014a) who finds that firms with more patient managers (i.e., managers with a higher subjective discount factor) have proportionally less debt. 20 One can notice that the evolution of leverage is not always continuous in Figure 1. For example, if g = 0.01 and if σ increases from 3 to 1.25, leverage increases from to However, if σ = 1, leverage is And if σ increases to 3, leverage gradually reaches the value of The non-continuous behavior of leverage is likely to be caused by its non-linear nature with respect to g and σ. 19

21 (2010) find that book leverage increases with CEO vega after controlling for industry fixed effects. Coles et al. (2006) find that vega does not have significant impact on leverage if firm fixed effects are included in the model. Cain and McKeon (2014) find that book leverage decreases with CEO vega after controlling for CEO-pilot dummy and firm fixed effects (the authors do not estimate regressions without the CEO-pilot dummy). Mehran (1992) reports that firms which grant their CEOs more stock options have greater long-term debtto-assets ratio. The most relevant theoretical study for this paper is Bhagat et al. (2011). A dynamic principal-agent model in Bhagat et al. (2011) predicts that short-term debt as well as total debt should decrease with the managerial risk aversion but long-term debt should increase with managerial risk aversion. Our predictions are not consistent with the theoretical results in Bhagat et al. (2011) if we assume that the majority of firms are subject to positive growth opportunities. Further, John and John (1993) use a two-period model and show that there is a negative relation between pay-performance sensitivity and leverage. However, the recent studies argue that CEO vega rather than pay-performance sensitivity (which is equivalent to CEO delta) reflects managerial risk preferences (see, for example, Low, 2009). This leads to the following hypotheses: Hypothesis 3a: For firms with positive growth opportunities, the decrease in managerial risk aversion leads to lower debt-to-assets ratio. Hypothesis 3b: For firms with negative growth opportunities, the decrease in managerial risk aversion leads to higher debt-to-assets ratio. Lastly, Figure 1 suggests that leverage increases when both growth opportunities and managerial risk aversion move in the same direction. Our last hypothesis is as follows: Hypothesis 4: Leverage increases when both growth opportunities and managerial risk aversion increase (or decrease). Unreported sensitivity analysis indicates that σ and g have a limited and not monotonic impacts on optimal firm size. Thus, for simplicity, one can assume that assets are constant when these parameters change. Therefore, the impacts of σ and g on leverage are, in 20

22 general, just the opposite to their impacts on stock price, P m ; that is, if the change in parameter value leads to higher stock price then leverage would decrease. 3.2 Empirical results In this subsection, we present our empirical results. First of all, we describe our sample. Then we test our hypotheses by estimating the least-squares dummy variable models (the fixed effects models). We include firm and year fixed effects in the models to control for unobserved firm-level heterogeneity, time period-related factors, and the fact that financing policy is highly firm specific. The standard errors are corrected for clustering at the firm level to accommodate heteroscekedasticity and within-firm autocorrelation Data Our initial sample is drawn from Compustat and ExecuComp. It covers the period 1992 to We eliminate financial firms (with Standard Industrial Classification (SIC) codes ) since they have different capital structure and might be subject to the regulatory authority. We also exclude public utility firms (with SIC codes ) because they operate in regulated industries and their financing and capital structure decisions might be impacted by the changes in the regulatory environment. To be included in our sample, firms must have positive values in book value of assets (Compustat item AT) and sales (Compustat item SALE) and non-missing SIC code (either Compustat item SIC or SICH). Further, all the firms must be incorporated in the United States. The final data set is comprised of more than 29 thousand firm-year observations. We measure the firms growth opportunities using industry (defined by the two-digit SIC code) 3-year sales growth, adjusted for inflation using the GDP deflator ( ISAL). 22 Industry-based growth proxy is superior to those based on firm level data, as it does not include idiosyncratic disturbances and thus better reflects the firms growth opportunities. 21 Our sample starts in 1992 when ExecuComp coverage begins. 22 See Table B.2 in Appendix B for variable definitions. 21

23 Coles et al. (2006) and Low (2009) argue that CEO vega rather than delta reflects CEO s risk preferences. Managers with higher vega are expected to be less risk averse. We compute CEO vega following the methodology of Guay (1999). We find that CEO vega is highly skewed. Its mean (median) is (33.98) and standard deviation is Thus, we use either the natural logarithm of CEO vega (VEGA1) or CEO vega scaled by the book value of firm assets (VEGA2) in the analysis. Table 3 provides descriptive statistics for the sample. 3-year industry sales growth is on average, implying that annual sales of the whole industry increase by approximately 8.4% per year. Market value of equity per share ( P m ) is proxied by market-to-book ratio (Q). The mean (median) value of Q is (1.632). For robustness, we use two leverage measures: market leverage (or market debt ratio (MDEBT)) and book leverage (or book debt ratio (BDEBT)). The mean (median) value of MDEBT is (0.112). The respective statistics for BDEBT are approximately twice higher. The last four columns in Table 3 show coefficients of Pearson correlation when ISAL > 0 and ISAL < 0. There is a positive correlation between Q and CEO vega for firms with positive and negative growth opportunities (i.e., when ISAL > 0 and ISAL < 0), supporting Hypothesis 1a but not Hypothesis 1b. 23 Table 3 shows that there is a negative correlation between market leverage and CEO vega for firms with positive and negative growth opportunities. However, book leverage is positively correlated with VEGA1 and negatively correlated with VEGA2 for firms with positive growth opportunities. For firms with negative growth opportunities, the correlation coefficient between book leverage and CEO vega is negative; however, it is insignificant for VEGA1. The results support Hypothesis 3a and but not Hypothesis 3b The impact of managerial risk preferences on share price To test Hypotheses 1a and 1b, that for firms with positive (negative) growth opportunities, the decrease in managerial risk aversion leads to higher (lower) share price, we regress market-to-book ratio (Q) on vega controlling for certain firm characteristics and firm and 23 The full correlation matrix is available upon request. 22

24 Table 3: Descriptive statistics This table presents the descriptive statistics. ISAL is industry (defined by the two-digit SIC code) 3-year sales growth, adjusted for inflation using the GDP deflator. VEGA1 is the natural logarithm of CEO vega (the dollar change in the CEO s wealth for a 0.01 change in standard deviation of stock returns; see Guay (1999) for more details). VEGA2 is the CEO vega scaled by book value of assets (Compustat item AT). AGE is the number of year the company has data on COMPUSTAT. MDEBT is debt (the sum of long-term debt (Compustat item DLTT) and debt in current liabilities (Compustat item DLC)) over market value of assets (book value of assets common equity (Compustat item CEQ) + common shares outstanding (Compustat item CSHO) closing share price at the end of the fiscal year (Compustat item PRCC_F)). BDEBT is debt over book value of assets. ASSETS is the natural logarithm of book value of assets (in millions of U.S. dollars (converted into 2009 constant dollars using the GDP deflator)). Q is market value of assets divided by book value of assets. ROA is net income (Compustat item NI) divided by book value of assets. CASH is cash and short-term investments (Compustat item CHE) over book value of assets. PPE is net property, plant, and equipment (Compustat item PPENT) divided by book value of assets. CAPEX is capital expenditures (Compustat item CAPX) to book value of assets ratio. RD is research and development expense (Compustat item XRD) divided by book value of assets. RDD is equal to one when research and development expense is reported in Compustat and zero otherwise. *** and ** indicates significance at 1% and 5% levels, respectively. Correlation matrix ISAL > 0 ISAL < 0 Variable Obs. Mean Median 25 th perc. 75 th perc. St. dev. VEGA1 VEGA2 VEGA1 VEGA2 ISAL 29, *** *** VEGA1 29, *** 0.348*** VEGA2 29, *** 0.348*** MDEBT 29, *** 0.203*** 0.042** 0.256*** BDEBT 29, *** 0.128*** *** AGE 29, *** 0.148*** 0.195*** 0.182*** ASSETS 29, *** 0.250*** 0.392*** 0.297*** Q 29, *** 0.296*** 0.070*** 0.431*** ROA 29, *** 0.022*** 0.099*** 0.106*** CASH 29, *** 0.258*** 0.034* 0.364*** PPE 29, *** 0.125*** 0.079*** 0.213*** CAPEX 29, *** *** 0.052*** RD 29, *** 0.068*** 0.370*** RDD 29, *** 0.099*** 0.130*** 0.147*** 23

25 year fixed effects. Specifically, we estimate the following model separately for firms with positive and negative growth opportunities: Q it =β 0 + β 1 VEGA it + β 2 ISAL it + β 3 ASSETS it + β 4 ROA it + β 5 PPE it + β 6 CAPEX it +β 7 RD it + β 8 RDD it + λ t + µ i + ɛ it, (33) where the indices i and t correspond to firm and year, respectively, ASSETS is the natural logarithm of market value of assets (in millions of U.S. dollars (converted into 2009 constant dollars using the GDP deflator)), ROA is returns on assets, PPE is net property, plant, and equipment (NPPE) divided by book value of assets. RDD is equal to one when R&D expense is unreported in Compustat and zero otherwise, λ and µ are year and firm fixed effects, respectively. The standard errors are corrected for clustering at the firm level to accommodate heteroscekedasticity and within-firm autocorrelation. 24 For robustness, we estimate models using both proxies of CEO vega (VEGA1 and VEGA2). Greater either proxy of vega reflects lower risk aversion. Thus, we expect that coefficient estimates for vega are positive for the subsample of firms with positive growth opportunities and negative for the subsample of firms with negative growth opportunities. Models 1 and 2 in Table 4 show that market-to-book ratio increases with either proxy of vega for firms with positive growth opportunities. The results are significant at 0.01 level and support our Hypothesis 1a. However, they are in contrast to those in Habib and Ljungqvist (2005) who report the negative relation between Q and vega of options. 25 The results are consistent with those in Mehran (1995) who finds that ROA and Q increase with the percentage of equity held by managers and with the percentage of their compensation that is equity-based. We repeat the same analysis for firms with negative growth opportunities. Models 3-4 in Table 4 show the results. We find that vega positively impact market-to-book ratio 24 This applies to all regressions estimated in this paper. 25 The conflicting results could be due to different sample time periods, different set of control variables included in the regressions as well as different methodology (e.g., Habib and Ljungqvist (2005) do not include any fixed effects in their models). 24