Ambiguity, Risk, and Dividend Payout Policy

Transcription

1 Ambiguity, Risk, and Dividend Payout Policy Jay Dahya Richard Herron Yehuda Izhakian July 18, 2017 Abstract We study the effect of ambiguity Knightian uncertainty on dividend payout policy. We find that firm-level risk decreases and delays dividends, while firm-level ambiguity increases and accelerates dividends. These findings can be explained by the attractiveness of investment opportunities, which potentially increases in risk and leaves less capital for dividend payout. In contrast, since ambiguity leads investors to overweight the likelihoods of bad outcomes and underweight the likelihoods of good outcomes, the attractiveness of investment opportunities decreases in ambiguity. Consistent with this positive effect of ambiguity on dividends, we find that dividend initiation announcement returns increase in ambiguity. Keywords: Ambiguity, Knightian Uncertainty, Dividends. JEL Classification Numbers: D81, D83, G35. We appreciate helpful comments and discussions by Yakov Amihud, Ryan Davies, Michael Goldstein, Shingo Goto, Jasmina Hasanhodzic, Laurie Krigman, Andrew Lo, Gordon Phillips, Jérôme Taillard, and Jaime Zender. We thank seminar and conference participants at Babson College, the University of Rhode Island, the 7 th International Conference of the Financial Engineering and Banking Society, and the 2017 Financial Management Association European Conference. Baruch College, City University of New York, One Bernard Baruch Way, New York, NY 10010, United States. Office Fax Jay.Dahya@baruch.cuny.edu. Babson College, 326 Tomasso Hall, Babson Park, MA Office Fax rherron1@babson.edu. Stern School of Business, New York University; and Baruch College, City University of New York, One Bernard Baruch Way, New York, NY 10010, United States. Office Fax yud@stern.nyu.edu.

2 I Introduction Dividend payout policy decisions are among the most important in the life of the firm and depend heavily on the firm s future prospects. These prospects are largely driven by investment opportunities, which are subject to two dimensions of uncertainty: risk and ambiguity. Risk is the uncertainty of outcomes, while ambiguity Knightian uncertainty is the uncertainty of probabilities. 1 Risk and ambiguity bear different implications for evaluating investment opportunities and for dividend payout policy. Consider a manager who must choose between retaining earnings to fund an investment opportunity or distributing earnings as dividends (or share repurchases). Suppose that the probabilities associated with the outcomes of an investment opportunity are well understood, perhaps based on experience or previous investments. When the expected return compensates appropriately for risk, the decision to retain earnings for investment is straightforward and delays dividend distribution. In contrast, suppose that the probabilities associated with the outcomes of the investment opportunity are uncertain. Such uncertainty makes retention to invest less attractive, and thus makes the manager less likely to delay dividend distribution. Previous studies focus mainly on the effect of firm-level risk on dividend payout and find a negative effect (e.g., Chay and Suh, 2009; Hoberg and Prabhala, 2008; Hoberg et al., 2014). To best of our knowledge, we are the first to focus on the implication of firm-level ambiguity for dividend payout. Firms may also distribute earnings as share repurchases. The relation between repurchases and uncertainty can be explained similarly. Firms with profitable, appropriately compensating, risky investment opportunities delay and decrease repurchases, while firms with ambiguous investment opportunities hasten and increase repurchases. We focus on 1 Risk is a condition where outcomes are a priori unknown, but the odds of all possible outcomes are perfectly known. Ambiguity is a condition where not only are outcomes a priori unknown, but also the odds of outcomes are unknown or not uniquely assigned. Knight (1921) defines the concept of (Knightian) uncertainty as distinct from risk and as conditions under which the set of events that may occur is a priori unknown, and the odds of these events are either not unique or unknown. 1

3 dividend payouts rather than repurchases for the following reasons. First, as opposed to repurchases, regular dividends are not driven by extra cash, temporary earnings, or (perceived) equity mispricing. Second, dividends are less confounded by capital structure decisions, either in isolation or in response to employee stock options. Third, dividend level and timing are clearly observable, so market responses can be attributed exclusively to dividend initiations. Regardless, our empirical findings are qualitatively similar with either dividends or repurchases. We derive our hypotheses from a two-period stylized model of the optimal decision between investment and dividend payout in the presence of risk and ambiguity. The intuition of our model is that higher risk is accompanied by higher expected returns, which may appropriately compensate for that risk. In turn, this encourages retention and investment, and delays the return of capital. In contrast, since higher ambiguity leads firms and investors to overweight the likelihoods of bad outcomes and underweight the likelihoods of good outcomes (e.g., Izhakian and Yermack, 2017), higher ambiguity reduces the perceived attractiveness of investment opportunities (i.e., a lower perceived expected return). This behavior accelerates the return of capital via dividends. Notably, risk and ambiguity act through different channels in our model. Risk affects investor expected utility through the utility of each outcome. Ambiguity affects expected utility through the perceived probability of each outcome (i.e., through the way individuals interpret uncertain probabilities). In related work, Shefrin and Statman (1984) examine the effect of managers perceived probabilities on dividend payout policy through the lens of prospect theory (Kahneman and Tversky, 1979). They explain dividend payout policy by self-control and probability weighting derived by mental accounting. However, they do not explore the effect of ambiguity. 2 We test two main hypotheses, derived from the two-period stylized model of a firm 2 Later, Tversky and Kahneman (1992) introduce ambiguity into prospect theory through non-additive probabilities. 2

4 that chooses between dividend distribution and investment. The first hypothesis is that the propensity to pay dividends decreases in firm-level risk. The second hypothesis is that the propensity to pay dividends increases in firm-level ambiguity. We find robust empirical support for both hypotheses. In particular, we find that firm-level risk negatively affects dividend payout timing and level, and firm-level ambiguity positively affects dividend payout timing and level. These effects of risk and ambiguity are distinct from one another in both the cross section and time series. We test two additional hypotheses about the effect of ambiguity and risk on dividend payout policy. First, that dividend initiation announcement cumulative abnormal returns (CARs) decrease in firm-level risk. Second, that dividend initiation announcement CARs increase in firm-level ambiguity. The intuition of these two hypotheses is that investors condition their response to dividend initiation announcements by how appropriate they consider the initiation. Firms with profitable, appropriately compensating, risky investment opportunities should retain and invest, so dividend initiation announcement CARs decrease in firm-level risk. Conversely, firms with ambiguous investment opportunities should payout dividends, so dividend initiation announcement CARs increase in firm-level ambiguity. We find robust statistical support for the positive relation between ambiguity and dividend initiation announcement returns, although the risk relation point estimates are negative. To estimate equity risk and ambiguity, we follow Izhakian and Yermack (2017). Namely, we estimate risk as the volatility of daily returns and ambiguity as the volatility of daily return probability distributions, estimated from intraday data. This ambiguity measurement is based on Izhakian s (2017) model of decision making under ambiguity. This model separates ambiguity from risk, separates tastes from beliefs, and delivers a risk-independent measure of the extent of ambiguity. 3 In particular, it provides a theoretical framework for 3 Other decision-making frameworks do not allow for the extent of ambiguity to be measured in isolation of tastes for ambiguity or risk. For example, in Gilboa and Schmeidler (1989) the set of priors captures both ambiguity and aversion to ambiguity. In Schmeidler (1989) capacities also capture ambiguity and aversion to it. In contrast, Izhakian s (2017) model separates ambiguity and aversion to it. 3

5 measuring ambiguity by the volatility of probabilities, analogous to measuring risk by the volatility of returns. Extensive tests by Brenner and Izhakian (2016) address concerns that our ambiguity measure captures other well-known dimensions of uncertainty. Nevertheless, our own robustness tests show that the same is true in the context of dividend payout policy. We find that ambiguity and volatility measure distinctly separate aspects of financial uncertainty. The effect of our ambiguity measure is also robust to the inclusion of alternative measures of uncertainty (i.e., volatility of mean returns, volatility of volatility returns, and dispersion of analyst price forecasts) and various market microstructure measures (i.e., effective bid-ask spreads and illiquidity). These alternative measures do not reduce the economic or statistical significance of the positive relation between ambiguity and dividend payout policy. Our approach of measuring firm-level risk by the volatility of daily equity returns is similar to Chay and Suh (2009) measurement of firm-level risk by the volatility of monthly stock returns. Hoberg and Prabhala (2008) decompose risk into systematic and idiosyncratic components and Hoberg et al. (2014) measure firm-level risk by fluidity, which they propose as a measure of product-market competition. Our risk findings are consistent with all three sets of authors. As well, our results are robust to Hoberg et al. s (2014) fluidity measure. Our empirical tests use quarterly firm-level data over 1993 to 2016 and provide robust support for our model s predictions. The cross-sectional logit and Tobit tests show that firms with higher ambiguity have a higher propensity to pay dividends and among firms that already pay dividends those with higher ambiguity tend to pay higher dividends as a fraction of either earnings or total assets. Controlling for the propensity to pay dividends, our event studies show that dividend initiation announcement CARs increase in firm-level ambiguity. With respect to dividend payout level, we find that in the cross-section larger shocks to ambiguity are associated with larger shocks to dividend payout level. Finally, our survival regression tests demonstrate that non-dividend paying firms with higher ambiguity are quicker to initiate dividends and that dividend paying firms with lower ambiguity are 4

6 quicker to omit dividends. Consistent with our stylized model, the empirical results show that risk has the opposite effect of ambiguity. In particular, the cross-sectional regression tests show that firms with higher risk have a lower propensity to pay dividends and among firms that already pay dividends those with higher risk tend to pay lower dividends as a fraction of either earnings or total assets. The survival regression tests demonstrate that non-dividend paying firms with higher risk are slower to initiate dividends and that dividend paying firms with higher risk are quicker to omit dividends. Controlling for the propensity to pay dividends, our regression tests show that dividend initiation announcement CARs decrease in firm-level risk, but these results are not statistically significant. Unlike previous studies, we show that dividend payout policy is driven by both firm-level ambiguity and risk, which are first-order determinants of the attractiveness of investment opportunities. We show that our empirical findings cannot be attributed to other known determinants of dividend payout policy. Throughout, we control for the standard dividend payout predictors from Fama and French (2001) and DeAngelo et al. (2006), and find that our results are robust. In addition, we demonstrate robustness to a host of alternative explanations, including free cash flows, agency conflicts, clienteles, illiquidity, and product market fluidity (Hoberg et al., 2014). Our results are also consistent with the negative relation between dividends and investment opportunities that Fama and French (2001) identify with U.S. data, Brav et al. (2005) support with surveys, and Denis and Osobov (2008), and Von Eije and Megginson (2008) confirm around the world. 4 We proceed as follows. Section II establishes a stylized model and develops the hypotheses. Section III describes the sample selection and variable definitions. Section IV tests the hypotheses about the effect of ambiguity and risk on dividend payout policy. Section V expands this analysis and Section VI concludes. 4 DeAngelo et al. (2008) provide an exhaustive survey of the dividend literature. 5

7 II II.A Model The decision theoretic model of ambiguity We distinguish the concepts of risk and ambiguity (Knightian uncertainty) by using the theoretical framework of expected utility with uncertain probabilities (EUUP) established in Izhakian (2017). 5 EUUP considers two tiers of uncertainty, one with respect to outcomes and the other with respect to the probabilities of these outcomes. It assumes two differentiated phases of the decision-making process, one for each of these tiers. In the first phase, the investor forms her perceived probabilities for all events that are relevant to her decision. In the second phase, she assesses the expected value (utility) of each alternative using her perceived probabilities and chooses accordingly. Ambiguity the uncertainty about probabilities dominates the first phase, while risk the uncertainty about consequences dominates the second phase. 5 The concept of Knightian uncertainty can be viewed as underpinning two branches of literature. The first is the unawareness literature, which assumes that decision-makers may not be aware of a subset of events (e.g., Karni and Vierø, 2013). The second is the ambiguity literature, which assumes that the set of events is perfectly known but their probabilities are either not unique or are unknown (e.g., Schmeidler, 1989; Gilboa and Schmeidler, 1989). These two literatures can be viewed as overlapping when dealing with monetary outcomes (real numbers). In this case, the uncertain risky and ambiguous variable is defined by a measurable function from states into the real numbers such that there is no real monetary outcome that the decision-maker is not aware of. The decision-maker may not be aware of some events (the so-called black swans), which affects the uncertainty about the probabilities of some outcomes. This uncertainty, however, is already accounted for by ambiguity the uncertainty about the probabilities of outcomes. Parameter uncertainty assumes the set of events is known and the nature of the probability distribution is known, but the parameters governing the distribution are unknown and the decision-maker maximizes utility using posterior parameters that generate a set of priors, which can be viewed as reflecting both information (beliefs) and tastes for ambiguity (e.g., Coles and Loewenstein, 1988; Coles et al., 1995). Thus, parameter uncertainty may be viewed as a special case of ambiguity, in which the nature of the probability distributions is known. In this view, model uncertainty is also a special case of ambiguity. This class of models assumes an uncertainty about the true probability law governing the realization of states, and a decision-maker, with her concerns about misclassification, looks for a robust decision-making process (e.g., Hansen et al., 1999; Hansen and Sargent, 2001). Other studies take an empirical view of model uncertainty (or model risk). In this perspective, while estimating an empirical model, there is uncertainty about the true set of predictive variables. To account for such a model misspecification, a Bayesian (predictive distribution) approach may be taken by assigning each set of variables (or model) a posterior probability (e.g., Pástor and Stambaugh, 2000; Avramov, 2002; Cremers, 2002). 6

8 To formally define the uncertain payoff X, let (S, E, P) be a probability space, where S is a state space, E is a σ-algebra of subsets of the state space (i.e., a set of events), P P is a probability measure, and the set of probability measures P is convex. An algebra Π of measurable subsets of P is equipped with a probability measure, denoted ξ. The uncertain outcome is then given by the uncertain variable, X : S R. Denote by ϕ (x) the (uncertain) marginal probability (density function or probability mass function) associated with the (uncertain) cumulative probability P P of outcome x. The expected marginal and cumulative probability of x, taken using the second-order probability measure ξ, are then respectively defined by E [ϕ (x)] P ϕ (x) dξ and E [P (x)] P P (x) dξ, (1) and the variance of the marginal probability is defined by Var [ϕ (x)] P ( ϕ (x) E [ϕ (x)] ) 2dξ. (2) With these definitions in place, the expected outcome and the variance of outcomes are computed using the expected probabilities. That is, E [X] E [ϕ (x)] xdx and Var [X] E [ϕ (x)] ( x E [x] ) 2 dx. (3) Notice that double-struck capital font designates expectation or variance of outcomes with respect to expected probabilities, while regular straight font designates expectation or variance of probabilities with respect to second-order probabilities. Investors have distinct preferences concerning risk and ambiguity. As usual, preferences concerning risk are modeled by a bounded, strictly-increasing and twice-differentiable utility function U : R + R. Risk aversion takes the form of a concave U ( ), risk loving takes the form of a convex U ( ), and risk neutrality takes the form of a linear U ( ). We normalize U 7

9 to U (k) = 0, where k is the investors reference point. Like Tversky and Kahneman s (1992) cumulative prospect theory, EUUP assumes that investors have a reference point, relative to which returns are classified as either unfavorable (loss) or favorable (gain). As investors are sensitive to ambiguity, they do not compound the set of priors P and the prior ξ over P in a linear way (compounded lotteries), but instead they aggregate these probabilities in a non-linear way, reflecting their aversion to ambiguity. Preferences concerning ambiguity are defined by preferences over mean-preserving spreads in probabilities and modeled by a strictly-increasing and twice-differentiable function over probabilities, Υ : R + R, called the outlook function. Similar to risk, ambiguity aversion takes the form of a concave Υ ( ), ambiguity loving takes the form of a convex Υ ( ), and ambiguity neutrality takes the form of a linear Υ ( ). In EUUP, ambiguity aversion is exhibited when an investor prefers the expectation of an uncertain probability of each payoff over the uncertain probability itself. 6 Suppose that the decision to save one unit of wealth is made at the beginning of the period, and the outcome, which is the only source of wealth, occurs at end of the period. In EUUP, the expected utility of this investment opportunity can be approximated by 7 W (X) x k x k ( ) U (x) E [ϕ (x)] 1 Υ (1 E [P (x)]) Var [ϕ (x)] dx + (4) Υ (1 E [P (x)]) }{{} Perceived Probability of Unfavorable Outcome ( ) U (x) E [ϕ (x)] 1 + Υ (1 E [P (x)]) Var [ϕ (x)] dx. Υ (1 E [P (x)]) }{{} Perceived Probability of Favorable Outcome 6 Recall that risk aversion is exhibited when an investor prefers the expected outcome of the uncertain outcome over the uncertain outcome itself. 7 This functional representation is obtained by taking the Taylor expansion of the dual representation of EUUP, proposed by Izhakian (2017). The reminder of this approximation is of order o ( [ E ϕ (x) E [ϕ (x)] 3] xdx ) as ϕ (x) E [ϕ (x)] dx 0, meaning that the accuracy of the approximation is equivalent to the accuracy of the cubic approximation, o E x E [x] 3]), in which the fourth ( [ and higher absolute central moments of outcomes are of strictly smaller order than the third absolute central moment as x E [x] 0, and are therefore negligible. 8

10 Notice that when investors are ambiguity neutral (Υ ( ) is linear), investors compound probabilities linearly and Equation (4) collapses to the conventional expected utility. In contrast, when the investors are ambiguity averse (Υ ( ) is concave), they do not aggregate probabilities linearly and the perceived probabilities are affected by the intensity of aversion to ambiguity. In this case, investors overweight the probabilities of the unfavorable outcomes and underweight the probabilities of favorable outcomes. The advantage of EUUP is that ambiguity preferences are applied exclusively to probabilities such that ambiguity aversion is defined as aversion to mean-preserving spreads in probabilities. Conceptually, the perceived probability of a given outcome can be viewed as the unique certain probability values that the investor is willing to accept in exchange for its uncertain probability (i.e., a certainty equivalent probability). The notion of mean-preserving spreads in probabilities in Equation (4) can be used to derive a measure of ambiguity (Izhakian, 2017, Theorem 6). This measure, defined by the expected volatility of probabilities, is formally given by 2 [X] E [ϕ (x)] Var [ϕ (x)] dx. (5) The measure 2 (mho 2 ) can be used either in a continuous state space with infinitely many outcomes or in a discrete state space with finitely many outcomes. Unlike other measures of ambiguity, which are outcome-dependent (and thus risk-dependent) and consider only the variance of a single moment of the distribution (e.g., the variance of the variance or the variance of the mean), our measure is outcome-independent (and thus risk-independent) and accounts for the variance of all the moments of the outcome distribution. 8 Furthermore, our 8 Sometimes the literature takes the volatility of volatility or the volatility of the mean as measures of ambiguity. The measure of ambiguity 2 is broader than either of these measures in that it accounts for both, as well as for the volatility of all higher moments of the probability distribution (e.g., skewness and kurtosis) through the variance of probabilities. As opposed to the volatility of the volatility and the volatility of the mean, the measure 2 is outcome- and risk-independent, as it does not depend upon the magnitudes of outcomes but only upon their probabilities. Furthermore, 2 solves some major issues that arise from the use of only the volatility of the volatility or only the volatility of the mean as measures of ambiguity. For 9

11 measure of ambiguity can be employed in empirical studies using stock data (e.g., Brenner and Izhakian, 2016; Izhakian and Yermack, 2017). To observe the distinct impact of ambiguity and ambiguity aversion on the value of an investment opportunity, consider a binomial asset with low payoff (L) and high payoff (H). Suppose that the reference point k satisfies L k E [X] < H. 9 By Equation (4), the value of this asset in terms of expected utility is ( W (X) U (L) E [ϕ (L)] ( U (H) E [ϕ (H)] 1 Υ (1 E [P (H)]) Υ (1 E [P (H)]) ) Var [ϕ (L)] ) 1 + Υ (E [P (H)]) Var [ϕ (H)] Υ (E [P (H)]). + (6) Expected utility in this functional representation is assessed using the investor s perceived probabilities. Ambiguity and ambiguity aversion are modeled in Equation (6) through the investor s marginal perceived probabilities. Consider the high payoff, H. The expression ( ) Q(H) E [ϕ (H)] 1 + Υ (E [P (H)]) Var [ϕ (H)] Υ (E [P (H)]) (7) is the marginal perceived probability of this outcome occurring. 10 This marginal perceived probability is a function of the degree of ambiguity, measured by Var [ϕ (H)], and the investor s attitude toward ambiguity, captured by Υ ( ). For an ambiguity-averse investor Υ ( ) with Υ ( ) Υ ( ) > 0, a higher aversion to ambiguity or a higher degree of ambiguity results in lower marginal perceived probabilities of good states and higher marginal perceived probabilities of bad states. This in turn implies a lower expected utility. example, two equities could have constant volatility but different degrees of ambiguity, or two equities could have constant means but different degrees of ambiguity. 9 We assume that the expected outcome is greater than the reference point; otherwise, a rational decision maker would not consider the investment opportunity. 10 Note that, since every P P is additive, 1 E [P (L)] = E [P (H)]. In this case, the variance of the probabilities of L is equal to the variance of the probabilities of its complementary event H, so that Var [ϕ (L)] = Var [ϕ (H)]. 10

12 II.B Dividend decisions To study the effect of ambiguity and risk on dividend payout, we employ the EUUP framework to develop a stylized static model, as in Miller and Modigliani (1961) and Baker and Wurgler (2004). We consider a one-period decision by a manager who is free of agency conflicts and maximizes the expected utility of investors, who are risk and ambiguity averse. As such, this manager can be viewed as a representative investor. We assume a standard structure, where the only variation is the specification of probabilities. As in Baker and Wurgler (2004), we model investment and payout decisions directly through the investor s utility function, rather than through the cost of capital. Note that the cost of capital is determined by risk and ambiguity preferences, which are formed by the investor s utility function. Suppose that at date 0 the firm has a free cash available in the amount C. At date 0, the manager decides between a liquidating dividend D 0 = C and a risky and ambiguous investment opportunity (a project). Suppose that the project s net return can be either +g in the high state or g in the low state, where g > 0. If the manager accepts the project, then at date 1 the firm pays out a liquidating dividend D H = C (1 + g) or D L = C (1 g) in high or low states of the investment, respectively. The manager s decision is solely about the free cash and does not involve new funds, which may effect the optimal capital structure of the firm (Izhakian et al., 2017). The expected utility incorporates both risk and ambiguity preferences; for simplicity, we assume neutral time preferences. 11

13 By Equation (6), the objective function of the utility-maximizing investors is max s.t. { } U (D 0 ), [1 Q(H)] U (D L ) + Q(H)U (D H ) D H = D L = 0, if D 0 = C; D H = C(1 + g), if D 0 = 0; D L = C(1 g), if D 0 = 0; g > 0, (8) where Q(H) is defined in Equation (7). This objective function simplifies to an inequality, implying that the firm pays a date 0 dividend when the following condition is met U (C) > (1 Q(H)) U (C(1 g)) + Q(H)U (C(1 + g)). (9) Suppose that the project become riskier (g increases). The concavity of U (risk aversion) implies that, when Q(H) is sufficiently high or when risk aversion is sufficiently low such that Q(H) > U (C(1 g)) U (C(1 g)) + U (C(1 + g)) (10) the right hand side (RHS) of Equation (9) becomes greater as g increases. 11 the following. This implies Hypothesis 1 The propensity to pay dividends decreases in firm-level risk. The intuition of this hypothesis is as follows. When the perceived probability of the high payoff is relatively high, an increase in risk is accompanied by an increase in (perceived) expected payoff. For moderately risk-averse investors, this increase in (perceived) expected 11 This condition is obtain by differentiating the RHS with respect g. 12

14 payoff provides adequate compensation for the higher risk. The investors in this case would prefer the risky investment over the dividend payout. Hypothesis 1 of a negative effect of risk on dividend payout is consistent with Chay and Suh (2009), Hoberg and Prabhala (2008), and Hoberg et al. (2014). It is important to note that we do not assume that risk is the variance of either payoffs or returns, since we do not assume that either utility is quadratic or returns are normally distributed. We expect that the propensity to pay dividends is also subject to investors risk aversion. However, since we are not aware of a verified methodology to elicit risk aversion from stock data, we focus on the effect of risk. Suppose now that risk is constant and ambiguity increases (the volatility of probabilities increases). By Equation (7), since Υ ( ) is concave (ambiguity aversion, Υ ( ) Υ ( ) > 0), this results in a lower perceived probability Q(H) of state H, implying that the RHS of Equation (9) becomes smaller. This implies the following. Hypothesis 2 The propensity to pay dividends increases in firm-level ambiguity. The intuition of this hypothesis is as follows. When the ambiguity of the project increases, the perceived probability of the high payoff decreases and the perceived probability of the low payoff increases, such that the (perceived) expected payoff decreases. This makes the project less attractive and investors would prefer the dividend payout over the ambiguous investment. The effect of aversion to ambiguity is similar. Higher ambiguity aversion reduces the (perceived) expected payoff of the project, which makes it less attractive. As with risk aversion, since we are not aware of a verified methodology to elicit ambiguity aversion from stock data, we focus on the effect of ambiguity. Two additional observations about value changes around dividend initiations can be derived from Equation (9). The difference between the left hand side (LHS) and the RHS of Equation (9) is the date 0 expected utility the firm provides as a dividend payer versus the expected utility the same firm provides as a dividend nonpayer. When the LHS is larger, initiating a dividend increases investor expected utility and firm value. Conversely, when the 13

15 RHS is larger, initiating a dividend decreases both investor expected utility and firm value. The CAR around dividend initiation announcement may capture this change in expected utility. Hypothesis 3 Dividend initiation announcement CAR decreases in firm-level risk. Hypothesis 4 Dividend initiation announcement CAR increases in firm-level ambiguity. III Data The primary data sources for our analysis are Compustat for historical information on dividend payout and firm fundamentals, Intraday Trade and Quote (TAQ) data for estimation of firm-specific degree of ambiguity, and Center for Research in Security Prices (CRSP) data for estimation of firm-specific risk. For a given firm, we require Compustat data and stock price information in TAQ and CRSP, which leaves us with a sample of 8109 firms with 208,837 quarterly observations from 1993 to 2016 for which we can extract joint information on ambiguity, risk, and dividend payout policy. 12 Our empirical investigation looks at dividend payout at quarterly resolution, as most dividend payout decisions are made on a quarterly basis, including initiation and omission decisions. Our results throughout are qualitatively similar using annual data. III.A Dividends Our dividend measures are based on common cash dividends, which the quarterly Compustat database reports as cumulative millions of U.S. Dollars paid fiscal year-to-date. To recover quarterly dividends, we use dividends as reported in the first fiscal quarter, or as the quarterly 12 We omit the first two quarters of 1993 because we require two-quarter lags of both ambiguity and risk. We omit the fourth quarter of 2016 because the Compustat fundamental data are not yet available for all firms. 14

16 change in fiscal year-to-date dividends otherwise. We consider a firm a dividend payer in a given quarter if dividends are strictly positive and a dividend nonpayer otherwise. We consider a firm a dividend initiator in a given quarter if it is a dividend payer, but was not a dividend payer in any of the previous eight quarters. Conversely, we consider a firm a dividend omitter in a given quarter if it is a dividend nonpayer, but was a dividend payer in all of the previous eight quarters. 13 To further test the propensity to pay dividends, we also look at dividend payout levels using the dividend payout ratio, computed as the ratio of common cash dividends to quarterly net income. We follow Fama and French (2001) and Skinner (2008) to determine net share repurchases. For firms that use the treasury stock method, we measure net share repurchases as the positive quarterly change in treasury stock. Otherwise, we use the positive portion of repurchases of common and preferred stock net of new issues of common and preferred stock. We consider a firm a repurchaser if net share repurchases are strictly positive in a quarter or in any of the preceding eight quarters. 14 III.B Estimating ambiguity and risk We estimate ambiguity of a firm s equity to proxy for firm-level ambiguity. 15 The intuition is that equity ambiguity represents the uncertainty in future outcome probabilities of a firm s projects. projects. Similarly, equity risk represents the uncertainty in future outcomes of a firm s We employ Izhakian and Yermack s (2017) empirical method to estimate the degree of ambiguity using intraday stock trading data from the TAQ database. We compute the degree of ambiguity, given in Equation (5), for each stock each month and use the trailing 13 Our results are qualitatively similar if we instead use a four-quarter threshold for dividend initiation and omission. 14 Allowing a two-year window to identify repurchasers is consistent with Skinner (2008). 15 Because they are based on stock returns data, both risk and ambiguity measure uncertainty about the firm s equity. Consistent with Hoberg and Prabhala (2008), for simplicity, we report results with equitybased uncertainty measures. Our results are qualitatively similar when using unlevered stock returns data to generate risk and ambiguity. 15

17 three-month moving average. We handle risk the same way and use the trailing three-month moving average. 16 We compute monthly firm-level ambiguity using the following procedure. 17 We suppose the existence of a representative agent with a set of priors over intraday returns. The observed intraday returns on the underlying asset are assumed to be a realization of one specific prior. That is, every day is characterized by a different distribution of returns, and the set of these distributions over a month represents the agent s set of priors. Assuming that stock returns are normally distributed, the degree of ambiguity of return r j on equity j can be measured by 2 [r j ] = E [φ (r j ; µ j, σ j )] Var [φ (r j ; µ j, σ j )] dr j, (11) where φ (r j ; µ j, σ j ) stands for the normal probability density function of r j conditional upon the mean µ j and the variance σ 2 j. To estimate the set of possible probability distributions of returns using TAQ data, we sample the price of the stock every five minutes from 9:30 until 16:00. The decision to use five-minute time intervals is motivated in part by Andersen et al. (2001), who show that this time interval is sufficient to eliminate microstructure effects. In cases where there is no trade at a specific time interval, we take the volume-weighted average of the closest trading prices. Using these prices, we compute five-minute returns for a maximum of 78 intraday returns on any given day. We ignore returns between closing and next-day opening prices, thereby eliminating the impact of overnight price changes and dividend distributions. For each stock, we drop all trading days with fewer than 15 different five-minute time intervals, 16 The results are qualitatively similar if we instead use the last ambiguity and risk observation in each fiscal quarter. 17 We emphasize that our empirical tests use a measure of the degree of ambiguity, defined by Equation (5), which is distinct from aversion to ambiguity. The former, which is a matter of beliefs (or information), is estimated from the data, while the latter, which is a matter of tastes, is endogenously determined by the empirical estimations. 16

18 and we drop all trading months with fewer than 15 intraday return distributions. In addition, we winsorize extreme five-minute returns (i.e., plus or minus 10 % log returns), as many of these are mistaken orders that the stock exchange later cancels. Each day for each stock we compute the time-normalized mean µ j and variance σ 2 j five-minute returns. 18 We follow French et al. (1987) and adjust the variance of returns for non-synchronous trading as Scholes and Williams (1977) propose. 19 of We assume that intraday returns are normally distributed, and for each stock j we construct the set of priors P j, where each prior P j within the set P j is defined by a pair of µ j and σ j. The set P j of (normal) probability distributions of each stock j for a given month consists of 15 to 22 different probability distributions. To compute the monthly degree of ambiguity of a given asset, specified in Equation (11), we represent each daily return distribution by a histogram. We divide the range of daily returns into 160 intervals (bins) from 40 % to 40 %, each of width 0.5 %. For each day, we compute the probability of the return being in each bin, as well as the probability of the return being lower than 40 % and the probability of the return being higher than 40 %. Using these probabilities, we separately compute the mean and the variance of probabilities for each of the 162 bins, assigning equal weights to each probability distribution in the set P j (i.e., all histograms are equally likely). This is equivalent to assuming that the daily ratios µ j σ j are student s-t distributed. 20 Then we 18 This normalization is applied since for less liquid stocks the return is obtained over time intervals longer than 5 minutes. 19 The Scholes and Williams (1977) adjustment for non-synchronous trading suggests that the volatility of returns takes the form σt 2 = 1 N t (r t,i E [r t,i ]) 2 1 N t + 2 (r t,i E [r t,i ]) (r t,i 1 E [r t,i 1 ]). We also N t N i=1 t 1 i=2 test our model without the Scholes and Williams correction for non-synchronous trading. The results are essentially the same. 20 When µ σ is Student s t-distributed, cumulative probabilities are uniformly distributed. See, for example, Proposition 1.27 of Kendall and Stuart (2010). This is consistent with the idea that the representative investor does not have any information indicating which of the possible probability distributions is more likely, and thus she acts as if she assigns an equal weight to each possibility. 17

19 estimate the degree of ambiguity of each stock j for each month by the discrete form 2 [r j ] = 1 π ( 0.01 w ) 1+ 1 π 2 E [ Φ (r j,0 ; µ j, σ j ) ] Var [ Φ (r j,0 ; µ j, σ j ) ] E [ Φ (r j,i ; µ j, σ j ) Φ (r j,i 1 ; µ j, σ j ) ] i=1 Var [ Φ (r j,i ; µ j, σ j ) Φ (r j,i 1 ; µ j, σ j ) ] + E [ 1 Φ (r j,160 ; µ j, σ j ) ] Var [ 1 Φ (r j,160 ; µ j, σ j ) ], (12) where Φ ( ) stands for the cumulative normal probability distribution, r 0 = 0.40, w = r i r i 1 = 0.005, r 160 = 0.40, and 1 π probabilities to the bins size. 21 ( 0.01 w ) 1+ 1 π 2 scales the weighted-average volatilities of This scaling, which is analogous to Sheppard s correction, has been tested to verify that it minimizes the effect of the selected bin size on the values of 2. Brenner and Izhakian (2016) empirically rule out the concern that 2 may capture other well-known uncertainty factors including skewness, kurtosis, variance of variance, variance of mean, downside risk, mixed data sampling measure of volatility forecasts (MIDAS), investors sentiment, among several others. Their tests also rule out the concern that observed returns are generated by a single (additive) probability distribution. In unreported results, we confirm this with a weak correlation of 0.10 between monthly ambiguity and risk. As expected, when aggregating risk and ambiguity over quarters, their correlation rises to 0.43 in Table II. Our robustness tests further rule out concerns that 2 may capture other well-known uncertainty factors, as well as market-microstructure factors. Along with ambiguity, risk serves as the most important explanatory variable in our analysis. We compute risk with standard methods, using daily returns adjusted for dividends obtained from the CRSP database. Since probabilities are uncertain, volatilities can be viewed as computed using the expected probabilities of outcomes (see Izhakian, 2017). For each individual stock j in a given month t, we calculate the standard deviation, Std j,t, of 21 1 We find that this scale improves Izhakian and Yermack s (2017) scale of w ln 1 w the sensitivity of the estimated 2 to the selection of the bin s size. 18 in the sense that it reduces

20 the stock s daily returns over that month, again applying the Scholes and Williams (1977) correction for non-synchronous trading and a correction for heteroscedasticity (see French et al., 1987). III.C Other explanatory variables In addition to ambiguity and risk, our empirical models include the control variables of Fama and French (2001) and DeAngelo et al. (2006). In particular, we proxy growth opportunities with quarterly asset growth rates and market-to-book asset ratios. The quarterly asset growth rate is the quarterly change in the book value of total assets relative to the book value of total assets. The market-to-book asset ratio (Market/Book) is the market value of total assets at the end of each quarter divided by the corresponding book value of total assets. We proxy profitability with Return on Assets, which is operating income before depreciation divided by the book value of total assets. We proxy size with the natural log of the market value of equity. We follow DeAngelo et al. (2006) and proxy firm life cycle as the ratio of earned to contributed equity, which is retained earnings divided by the book value of common equity (Retained Earnings/Book Equity). We also include the ratios of research and development (R&D) and capital expenditures to the book value of total assets. These allow us to explore whether firms with high ambiguity invest less in either research and development or capital expenditures. Quarterly Compustat reports both R&D and capital expenditures as fiscal year-to-date. To recover R&D, we take R&D as reported in the first fiscal quarter, or as the change in R&D relative to the previous quarter otherwise. We follow the same approach to generate quarterly capital expenditures. As well, we follow Hovakimian et al. (2001) and replace missing R&D values with zeros. We winsorize all ratios, ambiguity, and risk by 5 % in each tail. 19

21 III.D Summary statistics Table I presents summary statistics for the full sample from 1993 to 2016, as well as separately for dividend payer and dividend nonpayer firms. The first row provides the first support for Hypothesis 2 of a positive relation between ambiguity and dividend payout. The average degree of ambiguity is higher for payers at and lower for nonpayers at With a sample of 208,837 firm-quarter observations and a standard deviation of ambiguity of 0.019, the difference in ambiguity between the two samples is statistically significant at the 0.1 % level. Tables I and II report one-quarter lags of ambiguity and risk because we use onequarter and two-quarter lags of ambiguity and risk throughout to reduce reverse causality concerns. The second row provides the first support for Hypothesis 1 of a negative relation between risk and dividend payout. The average risk of dividend nonpayers is statistically higher than that of dividend payers at and 0.013, respectively. Risk over the entire sample is on average, consistent with the extant literature (e.g., Chay and Suh, 2009, Table 1). Notice that the averages of both ambiguity and risk are higher than the medians because by definition both are left-censored at zero. Nevertheless, as with the averages, median ambiguity is higher and median risk is lower for dividend payers relative to nonpayers. The remaining summary statistics in Table I are consistent with the dividend literature (Fama and French, 2001; DeAngelo et al., 2006). The fraction of payers is in line with the literature at Computing the ambiguity variable requires stocks with sufficient trade data, which could slightly bias the sample towards larger firms, which are more likely to pay a dividend. Consistent with the literature, the Market/Book ratio is larger for nonpayers than for payers (i.e., vs ). Conversely, Return on Assets, log(market Equity), and Retained Earnings/Book Equity are all larger for dividend payers than for nonpayers (i.e., vs , vs , and vs , respectively). [Table I] 20

22 Table II presents the correlations of the key variables. 22 Ambiguity is negatively correlated with risk at Again this correlation rises from 0.10 to 0.43, when moving from monthly observations to quarterly averages of monthly observations. The positive correlation of 0.41 between ambiguity and dividend payers indicator variable is consistent with Hypothesis 2. The other notable positive correlations with ambiguity are Return on Assets at 0.33 and log(market Equity) at Two notable negative correlations are with Capital Expenditures at 0.02 and R&D at 0.24, which support our intuition that firms with high ambiguity make less investment through either Capital Expenditures or R&D. [Table II] IV Empirical findings We start by investigating the effect of ambiguity and risk on the selected payout method. We use a multinomial logit test of the choice of no payout, repurchases only, or dividends. The first two columns in Table III describe the findings of Model 1, which includes only one-quarter lags of ambiguity and risk, as well as year fixed effects. The last two columns describe Model 2, which adds the standard predictors suggested by Fama and French (2001), DeAngelo et al. (2006), and Skinner (2008). In both models the base category is firms that are neither dividend payers nor share repurchasers. Both models cluster standard errors by two-digit industry. Both models show a significantly positive effect of ambiguity on dividends with point estimates that are at least three times as large as the positive effect of ambiguity on repurchases only. All standard predictors enter with the expected signs. We focus on dividends rather than repurchases since dividend decisions are less confounded by extra cash, temporary earnings, (perceived) mispricing, and capital structure decisions, and are clearly observable. Furthermore, Fama and French (2001) show that 22 For robustness, we also compute correlations among the different variables for each firm and examine the average correlations and p-values across firms. The findings are qualitatively similar. 21

23 many repurchases are made by firms that also pay dividends, so the bulk of repurchase decisions are associated with dividend decisions. Regardless, our results are qualitatively similar if we replace dividends with repurchases. [Table III] IV.A Dividend payout To test Hypotheses 1 and 2, we first look at the fraction of payers by dependent sorts on ambiguity and risk. Panel A of Figure 1 first sorts into risk quintiles each year, then sorts into ambiguity quintiles within each risk-year quintile. Panel A demonstrates that the fraction of payers monotonically increases in ambiguity quintiles within each risk quintile. Panel B repeats this analysis, but first sorts into ambiguity quintiles each year, then sorts into risk quintiles within each ambiguity-year quintile. As before, the fraction of dividend payers is negatively related to risk and positively related to ambiguity. In both panels, for all quintiles of risk and ambiguity the differences between high and low quintiles of the dependent sorts are statistically significant. The findings in Figure 1 support Hypotheses 1 and 2 and show that dividend payment is negatively related to risk, positively related to ambiguity, and that the two reactions are distinct. [Figure 1] To verify these findings, we conduct cross-sectional regression tests using Fama and Mac- Beth (1973) methodology with quarterly first-stage logit regressions. 23 Table IV reports the time-series means of these quarterly cross-sectional logit regression coefficients using Newey and West (1987) standard errors to correct for serial correlation to eight quarterly lags. Recall that ambiguity is determined using intraday returns and is independent of overnight 23 Although not reported in tables, the findings hold in panel logit and linear probability models, with either firm or two-digit industry fixed effects. 22

24 returns. Thus, there is no mechanical relation between ambiguity and dividends. However, it could still be the case that dividend payout affects risk and ambiguity contemporaneously. To address this causality concern, we lag both ambiguity and risk in our tests throughout. Column 1 includes only the one-quarter lag of ambiguity to confirm the positive effect of firm-level ambiguity on dividend payout in Tables I and II and Figure 1. To identify the economic significance of ambiguity, we use an odds-ratio interpretation. With respect to ambiguity, the interquartile range of the one-quarter lag of ambiguity is (not reported in tables). Accordingly, the odds ratio of an interquartile rise is exp( ) = 7.28, implying an economically sizable effect of a 628 % increase in the odds of paying a dividend. Column 2 in Table IV replaces the one-quarter lag of ambiguity with the one-quarter lag of risk, again to verify the negative effect of firm-level risk on dividend payout that appears in Tables I and II and Figure 1. The effect of risk on the propensity to pay dividends is of the same order of magnitude as the effect of ambiguity, but in the opposite direction. The coefficient of the one-quarter lag of risk is similar in magnitude at The interquartile range of the one-quarter lag of risk is (not reported in tables) and suggests an odds-ratio 0.105, which is an economically sizable effect of a 89.5 % decrease in the odds of paying a dividend. Column 3 includes the one-quarter lags of both ambiguity and risk. Both coefficient point estimates remain economically meaningful and statistically significant, providing a unique perspective on the dividend decision. Column 4 adds the standard predictors from Fama and French (2001) and DeAngelo et al. (2006), and shows that both ambiguity and risk point estimates remain economically meaningful and statistically significant. The standard predictors all enter with the expected signs. For ambiguity, the odds ratio of an interquartile rise is 2.33 and for risk it is For a frame of reference, the other strongest dividend determinant in Column 4 is log(market Equity), which has an odds ratio of 2.16 for an interquartile rise. Columns 5 to 8 in Table IV repeat the analyses of Columns 1 to 4 with two-quarter lags of ambiguity and risk. The point estimates and statistical significance are qualitatively 23