Journal of Financial Economics 109 (2013) 40–62

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Journal of Financial Economics

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Market timing, , and risk management$

Patrick Bolton a,c,d, Hui Chen b,c, Neng Wang a,c,n a Columbia University, New York, NY 10027, USA b MIT Sloan School of Management, Cambridge, MA 02142, USA c National Bureau of Economic Research, USA d Center for Economic Policy Research, UK article info abstract

Article history: The 2008 financial crisis exemplifies significant uncertainties in corporate financing Received 16 February 2011 conditions. We develop a unified dynamic q-theoretic framework where firms have both Received in revised form a precautionary-savings motive and a market-timing motive for external financing and 17 February 2012 payout decisions, induced by stochastic financing conditions. The model predicts (1) cuts Accepted 2 April 2012 in investment and payouts in bad times and equity issues in good times even without Available online 13 February 2013 immediate financing needs; (2) a positive correlation between equity issuance and JEL classification: repurchase waves. We show quantitatively that real effects of financing shocks may be E22 substantially smoothed out as a result of firms’ adjustments in anticipation of future E44 financial crises. G30 & 2013 Elsevier B.V. All rights reserved.

Keywords: Risk management Liquidity Financial crisis Market timing Investment q theory

1. Introduction $ We are grateful to Viral Acharya, Michael Adler, Aydogan Alti, Nittai Bergman, Charles Calomiris, Doug Diamond, Andrea Eisfeldt, Xavier Gabaix, Zhiguo He, David Hirshleifer, Jennifer Huang, Nengjiu Ju, Dmitry The financial crisis of 2008 and the European debt crisis Livdan, Stewart Myers, Emi Nakamura, Paul Povel, Adriano Rampini, of 2011 are fresh reminders that corporations at times face Yuliy Sannikov, Antoinette Schoar, Bill Schwert (Editor), Alp Simsek, substantial uncertainties about their external financing Jeremy Stein, Neil Stoughton, Robert Townsend, Laura Vincent, and conditions. Recent studies show dramatic changes in firms’ seminar participants at 2012 American Economics Association Meetings, American Finance Association Meetings, Columbia, Duke, Fordham, financing and investment behaviors during these crises. For London Business School, London School of Economics, SUNY Buffalo, example, Ivashina and Scharfstein (2010) find aggressive Berkeley, UNC-Chapel Hill, Cheung Kong Graduate School of Business, credit line drawdowns by firms for precautionary reasons. University of California Los Angeles, Global Association of Risk Campello, Graham, and Harvey (2010) and Campello, Professionals, Theory Workshop on Corporate Finance and Financial Markets at New York University, and Minnesota Corporate Finance Conference for Giambona, Graham, and Harvey (2011) show that more their comments. Neng Wang acknowledges research support by Chazen financially constrained firms planned deeper cuts in invest- Institute of International Business at Columbia Business School. We are ment and spending, burned more cash, drew more credit particularly grateful to Jeffrey Wurgler (a referee) and an anonymous referee from banks, and engaged in more asset sales during the for their constructive and valuable comments. n crisis. Corresponding author at: Columbia Business School, New York, NY 10027, USA. Tel.: þ1 212 854 3869. Rational firms could plausibly adapt to fluctuations in E-mail address: [email protected] (N. Wang). financing conditions by hoarding cash, postponing or

0304-405X/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jfineco.2013.02.006 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 41 bringing forward , timing favorable market convexity also implies that it could be optimal for the conditions to raise more funds than they really need, or firm to engage in rather than hedging to hedging against unfavorable market conditions. Recently, increase the value of the market timing option. there has been much empirical work on the corporation’s Third, along with the timing of equity issues by firms cash holdings.1 Yet, very little theoretical research tries to with low cash holdings, our model predicts the timing of answer the following related questions. How should firms cash payouts and stock repurchases by firms with high change their financing, investment, and risk management cash holdings. Just as firms with low cash holdings seek to policies during a period of severe financial constraints? take advantage of low costs of external financing to raise How should firms behave when facing the threat of a more funds, firms with high cash holdings are inclined to future financial crisis? What are the overall real effects of disburse their cash through stock repurchases when changes in financing conditions when firms can prepare financing conditions improve. This result is consistent for future shocks through cash and risk management with the finding of Dittmar and Dittmar (2008) that policies? aggregate equity issuances and stock repurchases are We address these questions in a quantitative model of positively correlated. They point out that the finding that corporate investment, financing, and risk management for increases in stock repurchases tend to follow increases in firms facing stochastic financing conditions. Our model valuations contradicts the received wisdom builds on the recent dynamic frameworks by Decamps, that firms engage in stock repurchases because of the Mariotti, Rochet, and Villeneuve (2011) and Bolton, Chen, belief that their shares are undervalued. Our model and Wang (2011, henceforth BCW), mainly by adding provides a simple and plausible explanation for their stochastic financing opportunities. The five main building finding: improved financing conditions raises stock prices blocks of the model are (1) a constant returns-to-scale and lowers the precautionary demand for cash buffers, production function with independently and identically which in turn can result in more stock repurchases by distributed (i.i.d.) productivity shocks and convex capital cash-rich firms. adjustment costs as in Hayashi (1982), (2) stochastic Fourth, we show that a greater likelihood of deteriora- external financing costs, (3) constant cash-carrying costs, tion in the financing conditions leads to stronger cash (4) risk premia for productivity and financing shocks, and hoarding incentives. With a higher probability of a crisis (5) dynamic hedging opportunities. The firm optimally occurring, firms invest more conservatively, issue equity manages its cash reserves, financing, and payout decisions sooner, and delay payouts to shareholders in good times. by following a state-dependent optimal double-barrier Consequently, firms’ cash inventories rise, investment policy for issuance and payout, combined with continuous becomes less sensitive to changes in cash holdings, and adjustments of investment, cash accumulation, and hed- the ex post impact of financing shocks on investment is ging between the issuance and payout barriers. much weaker. This effect is quantitatively significant. The main results of our analysis are as follows. First, When we raise the probability of a financial crisis within during a financial crisis, to avoid extremely high external a year from 1% to 10%, the average reduction in a firm’s financing costs, the firm optimally cuts back on invest- investment-capital ratio following the realization of the ment, delays payout, and, if needed, engages in asset shock drops from 6.6% to 1.8%. Furthermore, this reduced sales, even if the productivity of its capital remains investment response is in large part due to the firm unaffected. This is especially true when the firm enters cutting back investment in the good state in preparation the crisis with low cash reserves. These predictions are for the crisis. These findings provide important new consistent with the stylized facts about firm behavior insights on the transmission mechanism of financial during the recent financial crisis. shocks to the real sector and helps us interpret empirical Second, during favorable market conditions (a period measures of the real effects of financing shocks. In of low external financing costs), the firm could time the particular, it shows that judging the real effect of financial market and issue equity even when no immediate need crisis by measuring the changes of investment following exists for external funds. Such behavior is consistent with the crisis can be misguided. the findings in Baker and Wurgler (2002), DeAngelo, Fifth, due to the presence of aggregate financing DeAngelo, and Stulz (2010), Fama and French (2005), shocks, the firm’s risk premium in our model has two and Huang and Ritter (2009). We thus explain firms’ components: a productivity risk premium and a financing investment, saving, and financing decisions through a risk premium. Both risk premia change substantially with combination of stochastic variations in the supply of the firm’s cash holdings, especially when external finan- external financing and firms’ precautionary demand for cing conditions are poor. Quantitatively, the financing risk liquidity. We also show that, due to market timing, premium is significant for firms with low cash holdings, investment can be decreasing in the firm’s cash reserves. especially in a financial crisis, or when the probability of a The reason is that the market timing option together with financial crisis is high. However, due to firms’ precau- the fixed external financing costs can cause firm value to tionary savings, the financing risk premium is low for the become locally convex in financial slack. This local majority of firms as they are able to avoid falling into a low cash trap. Moreover, our model predicts that idiosyn- cratic cashflow risk affects a firm’s cost of capital. Firms 1 See Almeida, Campello, and Weisbach (2004), Dittmar and Mahrt- facing higher idiosyncratic risk optimally hold more cash Smith (2007), Dittmar and Dittmar (2008), Bates, Kahle, and Stulz (2009), Riddick and Whited (2009), among many others, on the empirical rele- on average, which lowers their and expected returns. vance and potential explanations of corporate cash holding policies. This result highlights that the endogeneity of cash 42 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 holdings is key to understanding the cross-sectional Finally, in contemporaneous work, Hugonnier, Malamud, relation between cash holdings and returns. and Morellec (2012) also develop a dynamic model with Our analysis reveals that first-generation static models stochastic financing conditions. They model investment as a of financial constraints are inadequate to explain how growth option, while we model investment as in Hayashi’s corporate investment responds to changing financing q-theory framework. In addition, they model the window of opportunities. Static models, such as Fazzari, Hubbard, financing opportunities via a Poisson process. When such an and Petersen (1988), Froot, Scharfstein, and Stein (1993), opportunity arrives, the firm has to decide immediately and Kaplan and Zingales (1997), cannot explain the effects whether to raise funds or not. Thus, the duration of the of market timing on corporate investment, because these financing opportunity in their model is instantaneous. In our effects cannot be captured by a permanent exogenous model, the finite duration of financing states is important for change in the cost of external financing or an exogenous generating market timing. The two papers share the same change in the firm’s cash holdings in the static setting. overall focus but differ significantly in their modeling Market timing effects can only appear when there is a approaches, thus complementing each other. finitely lived window of opportunity of getting access to The remainder of the paper proceeds as follows. cheaper equity financing. More recent dynamic models of Section 2 sets up the model. Section 3 presents the model investment with financial constraints include Gomes solution. Section 4 investigates the quantitative results. (2001), Hennessy and Whited (2005, 2007), Riddick and We then study the impact of market timing in a good Whited (2009), and BCW, among others. However, all state on investment, financing, and payout (Section 5), these models assume that financing conditions are time- risk and return (Section 6), and hedging (Section 7). invariant. Section 8 concludes. Our work is also related to two other sets of dynamic models of financing. First, DeMarzo, Fishman, He, and 2. The model Wang (2012) develop a dynamic contracting model of corporate investment and financing with managerial We consider a financially constrained firm facing agency, by building on Bolton and Scharfstein (1990) stochastic investment and external financing conditions. and using the dynamic contracting framework of Specifically, we assume that the firm can be in one of two DeMarzo and Sannikov (2006) and DeMarzo and (observable) states of the world, denoted by st ¼ G,B.In 2 Fishman (2007b). These models derive optimal dynamic the two states, the firm faces potentially different finan- contracts and corporate investment with capital adjust- cing and investment opportunities. Over a time ment costs. Second, Rampini and Viswanathan (2010, interval D, the state switches from G to B (or from B to 2011) develop dynamic models of collateralized financing, G) with a constant probability zGD (or zBD). in which the firm has access to complete markets but is subject to endogenous collateral constraints induced by 2.1. Production technology limited enforcement. Our paper is one of the first dynamic models of The firm employs capital and cash as the only factors corporate investment with stochastic financing condi- of production. We normalize the price of capital to one tions. We echo the view expressed in Baker (2010) that and denote by K and I the firm’s capital stock and gross equity supply effects are important for corporate finance. investment, respectively. As is standard in capital accu- While we treat changes in financing conditions as exo- mulation models, the capital stock K evolves according to genous in this paper, the cause of these variations could ¼ð Þ Z ð Þ be changes in financial intermediation costs, changes in dKt It dKt dt, t 0, 1 ’ risk attitudes, changes in , or where dZ0 is the rate of depreciation. changes in aggregate uncertainty and information asym- The firm’s operating revenue is proportional to its metry. Stein (1996) develops a static model of market capital stock Kt and is given by Kt dAt, where dAt is the timing and Baker, Stein, and Wurgler (2003) empirically firm’s productivity shock over time increment dt.We 3 test this model. To some extent, our model can be viewed assume that as a dynamic formulation of Stein (1996), in which a ¼ ð Þ þ ð Þ A ð Þ rational manager behaves in the interest of existing dAt m st dt s st dZt , 2 shareholders in the face of a market that is subject to A where Zt is a standard Brownian motion and mðsÞms and potentially irrational changes of sentiment. The sðsÞss denote the drift and in state s, respec- manager then times the market optimally and issues tively. In the remainder of this paper, we use the notation equity when financing conditions are favorable. This xs to denote a state-dependent variable x(s) whenever interpretation assumes that markets underreact to the there is no ambiguity. manager’s timing behavior, causing favorable financing The firm’s operating profit dYt over time increment dt conditions to persist. is then given by

dYt ¼ Kt dAtIt dtGðIt,Kt,stÞ dt, t Z0, ð3Þ 2 DeMarzo and Fishman (2007a) study optimal investment where Kt dAt is the firm’s operating revenue, It dt is dynamics with managerial agency in a discrete time setting. the investment cost over time dt, and GðI ,K ,s Þ dt is the 3 Using a panel of international data, Birru (2012) finds that market- t t t wide mispricing can mitigate underinvestment through its effect on the additional adjustment cost that the firm incurs in the cost of capital, and links market-wide mispricing to the macroeconomy. investment process. P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 43

Following the neoclassical investment literature financing costs to raise net proceeds dHt from external (Hayashi, 1982), we assume that the firm’s adjustment cost financing), and by U the firm’s cumulative nondecreasing is homogeneous of degree one in I and K.Inotherwords, payout process to shareholders (so that dUt is the payout the adjustment cost takes the form GðI,K,sÞ¼ gsðiÞK,where over time dt). i is the firm’s investment capital ratio (i¼I/K)andgs(i)isa The financing cost to raise net proceeds dHt under our state-dependent function that is increasing and convex in i. assumptions is given by dX ¼ K 1 þ dH . If the t fst t fdHt 4 0g gst t We further assume that gs(i) is quadratic: firm runs out of cash (Wt ¼ 0), it needs to raise external funds to continue operating, or its assets will be liqui- y ðin Þ2 g ðiÞ¼ s s , ð4Þ dated. If the firm chooses to raise external funds to s 2 continue operating, it must pay the financing costs spe- where ys is the adjustment cost parameter and ns is a cified above. The firm could prefer liquidation if the cost constant.4 This assumption makes the analysis more tract- of financing is too high relative to the continuation value. able, but our main results do not depend on the specific We denote by t the firm’s stochastic liquidation time. functional form of gs(i). Our model allows for state- Distributing cash to shareholders could take the form dependent adjustment costs of investment. For example, of a special or a .6 The benefit of in bad times, assets are often sold at a deep discount (see a payout is that shareholders can invest the proceeds at Shleifer and Vishny, 1992; Acharya and Viswanathan, the market and avoid paying a carry cost on

2011), which can be captured in this model by making ys the firm’s retained cash holdings. We capture this carry large when financing conditions are tough. cost by assuming that cash inside the firm earns a below- Finally, the firm can liquidate its assets at any time and market riskless return, with the difference denoted by 7 obtain a liquidation value Lt that is also proportional to l40. the firm’s capital stock Kt. Specifically, the liquidation We can then write the dynamics for the firm’s cash W value is Lt ¼ lsKt, where ls denotes the recovery value per as follows: unit of capital in state s. dW ¼ðK dA ðI þGðI ,K ,s ÞÞ dtÞþðrðs ÞlÞW dtþdH dU , The production technology in our model is essentially t t t t t t t t t t t the same as the ones used in BCW, DeMarzo, Fishman, He, ð5Þ and Wang (2012) in an optimal dynamic contracting where rðsÞrs is the risk-free interest rate in state s. setting, and Wang, Wang, and Yang (2012) for a model The first term in (5) is the firm’s cash flow from opera- of entrepreneurship dynamics. Our model also allows for tions dYt given in (3); the second term is the return on Wt the drift, the volatility, and the adjustment cost functions (net of the carry cost l); the third term dHt is the net to be regime dependent. As in these papers, the homo- proceeds from external financing; and the last term dUt is geneity property in our model allows us to study the the payout to investors. Note that (5) is a general financial impact of stochastic financing conditions on corporate accounting equation, in which dHt and dUt are endogen- investment, external financing, and liquidity hoarding in ously determined by the firm. an analytically tractable framework. The homogeneity assumptions embedded in the pro- duction technology, the adjustment cost, and the finan- 2.2. Stochastic financing opportunities cing costs allow us to deliver our key results in a parsimonious and analytically tractable framework. The firm may choose to raise external equity financing Adjustment costs might not always be convex and the at any time.5 When doing so, it incurs a fixed as well as a production technology could exhibit -run decreasing variable cost of issuing stock. The fixed cost is given by returns to scale in practice, but these functional forms substantially complicate the formal analysis.8 fsK, where fs is the fixed cost parameter in state s.We take the fixed cost to be proportional to the firm’s capital stock K, which ensures that the firm does not grow out of 2.3. Systematic risk and the pricing of risk its fixed costs of issuing equity. This assumption is also analytically convenient, as it preserves the homogeneity Our model has two different sources of systematic of the model in the firm’s capital stock K. Besides the fixed risk: (1) a small diffusion shock to productivity, and (2) a cost fsK, the firm incurs a variable cost gs 40 for each incremental dollar it raises. We denote by H the process for the firm’s cumulative 6 We cannot distinguish between a and a share external financing (so that dH denotes the net proceeds repurchase, as we do not model taxes. However, a commitment to t regular dividend payments is suboptimal in our model. We also exclude from external financing over time dt), by X the firm’s any fixed or variable payout costs so as not to overburden the model. 7 cumulative issuance costs (so that dXt denotes the The cost of carrying cash could arise from an agency problem or from tax distortions. Cash retentions are tax disadvantaged because the associated tax rates generally exceed those on interest income (Graham, 4 In the literature, common choices of ns are either zero or the rate 2000). If l ¼ 0, the firm has no incentives to pay out cash because of deprecation d. While the former choice implies zero adjustment cost keeping cash inside the firm does not have any disadvantages but still for zero gross investment, the latter choice implies a zero adjustment has the benefit of relaxing financial constraints. We could also let the cost when net investment is zero. cash-carrying cost vary with the state. For the sake of brevity, we do not 5 For simplicity, we only consider external equity financing as the pursue this generalization in this paper. source of external funds for the firm. We leave the generalization to 8 See Riddick and Whited (2009) for an intertemporal model of a include debt financing for future research. financially constrained firm with decreasing returns to scale. 44 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 large shock when the state of the economy changes. The the risk-neutral measure): Z R R small productivity shocks in any given state s can be t t t Q ru du ru du correlated with the aggregate market, and we denote the E0 e 0 ðdUtdHtdXtÞþe 0 ðLt þWtÞ , ð9Þ 0 correlation coefficient by rs. The large shock can affect the conditional moments of the firm’s productivity or its where ru denotes the interest rate at time u. The first term external financing costs, or both. is the discounted value of net payouts to shareholders, How are these sources of systematic risk priced? Our and the second term is the discounted value upon model can allow for either risk-neutral or risk-averse liquidation. Optimality could imply that the firm never investors. If investors are risk neutral, then the prices of liquidates. In that case we have t ¼1. risk are zero and the physical probability distribution coincides with the risk-neutral probability distribution. 3. Model solution If investors are risk averse, we need to distinguish between physical and risk-neutral measures. We do so Given that the firm faces external financing costs 9 Z as follows. (fs 40, gs 0), its value depends on both its capital stock For the diffusion risk, we assume that there is a K and its cash holdings W. Thus, let PðK,W,sÞ denote the value of the firm in state s. Since the firm incurs a carry constant market price of risk Zs in state s. The firm’s risk-adjusted productivity shock (under the risk-neutral cost l on its stock of cash, one would expect that it would probability measure Q) is then given by choose to pay out some of its cash once its stock grows sufficiently large. Accordingly, let W s denote the (upper) b bA dAt ¼ ms dtþss dZ t , ð6Þ payout boundary. Similarly, if the firm’s cash holdings are low, it could choose to issue equity. We therefore let W where the mean of productivity shock accounts for the s denote the (lower) issuance boundary. firm’s exposure to the systematic diffusion risk: The interior regions: W 2ðW ,W Þ for s ¼ G,B. When a b s s ms ¼ msrsssZs, ð7Þ firm’s cash holdings W are in the interior regions, PðK,W,sÞ bA satisfies the following system of Hamilton-Jacobi-Bellman and Z t is a standard Brownian motion under the risk- neutral probability measure Q. (HJB) equations under the risk-neutral measure: b A risk-averse investor also requires a risk premium to rsPðK,W,sÞ¼max½ðrslÞW þmsKIGðI,K,sÞPW ðK,W,sÞ I compensate for the risk of the economy switching states. 2 2 ss K We capture this risk premium through the wedge þ PWW ðK,W,sÞþðIdKÞPK ðK,W,sÞ between the transition intensity under the physical prob- 2 b ability measure and under the risk-neutral probability þzsðPðK,W,s ÞPðK,W,sÞÞ: ð10Þ b b measure Q. Let zG and zB denote the risk-neutral transi- The first and second term on the right side of Eq. (10) tion intensities from state G to state B and from state B to represent the effects of the expected change in the firm’s state G, respectively. Then, cash holdings W and volatility of W on firm value, respec- b kG b kB tively. Notice that the firm’s cash grows at the net return zG ¼ e zG and zB ¼ e zB, ð8Þ ðrslÞ and is augmented by the firm’s expected cash flow where the parameters kG and kB capture the risk adjust- b from operations (under the risk-neutral measure) msK ment for the change of state. In our calibrated model, minus the firm’s capital expenditure IþGðI,K,sÞ.Also,the state G (B) is the state with good (bad) external financing firm’s cash stock is volatile only to the extent that cash conditions. We set kG ¼kB 40, which implies that the flows from operations are volatile, and the volatility of the transition intensity out of state G (B) is higher (lower) firm’srevenuesisproportionaltothefirm’ssizeasmea- under the risk-neutral probability measure than under suredbyitscapitalstockK. The third term represents the the physical measure. Intuitively, this reflects the idea effect of capital stock changes on firm value, and the last that an investor’s towards a bad state is term captures the expected change of firm value when the captured by making it more likely to transition into the state changes from s to s, where we use the notation s to bad state and less likely to leave it. In sum, it is as if a risk- denote the state that is different from s. averse investor were uniformly more ‘pessimistic’ than a Because firm value is homogeneous of degree one in W risk-neutral investor: she thinks ‘good times’ are likely to and K in each state, we can write PðK,W,sÞ¼psðwÞK, be shorter and ‘bad times’ longer. where w W=K is the cash-capital ratio. Substituting this expression into Eq. (10) and simplifying, we obtain the 2.4. Firm optimality following system of ordinary differential equations

(ODEs) for ps(w): The firm chooses its investment I, cumulative payout 2 b 0 ss 00 policy U, cumulative external financing H, and liquidation rspsðwÞ¼max½ðrslÞwþmsisgsðisÞpsðwÞþ ps ðwÞ i 2 time t to maximize firm value defined as follows (under s 0 b þðisdÞðpsðwÞwpsðwÞÞþzsðps ðwÞpsðwÞÞ: ð11Þ

9 In Appendix A, we provide a more detailed discussion of systema- The first-order condition for the investment-capital ratio tic risk premia. The key observation is that the adjustment from the i (w)is s physical to the risk-neutral probability measure reflects a representative 1 p ðwÞ risk-averse investor’s stochastic discount factor in a dynamic asset s isðwÞ¼ 0 w1 þns, ð12Þ pricing model. ys psðwÞ P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 45

0 where psðwÞ¼PW ðK,W,sÞ is the marginal value of cash in that state s. 0 psðwsÞ¼1þgs: ð19Þ Payout boundary W s and payout region (W ZW s): The firm starts paying out cash when the marginal value of cash Intuitively, if the firm chooses to issue equity before it held by the firm is less than the marginal value of cash held runs out of cash, it must be the case that the marginal by shareholders. The payout boundary ws ¼ W s=K thus value of cash at the issuance boundary ws 40 is equal to satisfies the following value matching condition: the marginal issuance cost 1þgs.If(19) fails to hold, the 0 firm does not issue equity until it exhausts its cash psðwsÞ¼1: ð13Þ holdings, i.e., ws ¼ 0. That is, when the firm chooses to pay out, the marginal We also need to determine whether equity issuance or value of cash p0ðwÞ must be one. Otherwise, the firm can liquidation is optimal, as the firm always has the option to always do better by changing ws. Moreover, payout optim- liquidate. Under our assumptions, the firm’s capital is ality implies that the following super contact condition productive and, thus, its going-concern value is higher (Dumas, 1991)holds: than its liquidation value. Therefore, the firm never 00 voluntarily liquidates itself before it runs out of cash. p ðwsÞ¼0: ð14Þ s However, when it runs out of cash, liquidation could We specify next the value function outside the payout be preferred if the alternative of accessing external boundary. If the marginal value of cash in state s is such financing is too costly. If the firm liquidates, then 0 that psðwÞo1, the firm is better off reducing its cash psð0Þ¼ls: ð20Þ holdings to ws by making a lump-sum payout. Therefore, we have The firm prefers equity issuance to liquidation as long as ð Þ psðwÞ¼psðwsÞþðwwsÞ, w4ws: ð15Þ the equilibrium value ps 0 under external financing arrangement is greater than the liquidation value ls. This situation could arise when the firm starts off with too For our later discussion it is helpful to introduce the much cash or when the firm’s cash holding in state s is following concepts. First, the enterprise value is often such that ws owows and the state of the economy defined as firm value net of the value of short-term liquid suddenly changes from s into s. assets. This measure is meant to capture the value created The equity issuance boundary W s and region (W rW s): from productive illiquid capital. In our model, it equals Similarly, we must specify the value function outside the PðK,W,sÞW. Second, we define average q as the ratio issuance boundary. The firm could suddenly transition between the enterprise value and the capital stock, from the state s with the financing boundary ws into PðK,W,sÞW the other state s with a higher financing boundary q ðwÞ¼ ¼ p ðwÞw: ð21Þ s K s (ws 4ws ) and its cash holdings could lie between the two lower financing boundaries (ws owows). In that Third, the sensitivity of average q to changes in the cash- case, if the firm is sufficiently valuable it then chooses to capital ratio measures how much the enterprise value raise external funds through an equity issuance so as to changes with an extra dollar of cash inside the firm. It is bring its cash stock back into the interior region. But how given by much should the firm raise in this situation? Let M s q0 ðwÞ¼p0 ðwÞ1: ð22Þ denote the firm’s cash level after equity issuance, which s s 0 we refer to as the target level, and define ms ¼ Ms=K. We also refer to qsðwÞ as the net marginal value of cash. As 0 Similarly, define ws ¼ W s=K. Firm value per unit of capital w approaches the optimal payout boundary ws, qsðwÞ in state s, ps(w), when wrws then satisfies goes to 0. psðwÞ¼psðmsÞfsð1þgsÞðmswÞ, wrws: ð16Þ 4. Quantitative results We thus have the following value matching and smooth pasting conditions for w : s Having characterized the conditions that the solution psðwsÞ¼psðmsÞfsð1þgsÞðmswsÞ, ð17Þ to the firm’s dynamic optimization problem must satisfy, we can now illustrate the numerical solutions for given p0 ðm Þ¼1þg : ð18Þ s s s parameter choices of the model. We begin by motivating our choice of parameters and then illustrate the model’s With fixed issuance costs (fs 40), equity issuance is solutions in the good and bad states of the world. lumpy. The firm first pays the issuance cost fs per unit of capital and then incurs the marginal cost gs for each unit raised. Eq. (17) states that firm value is continuous around the issuance boundary. In addition, the firm optimally 4.1. Parameter choice and calibration selects the target ms so that the marginal benefit of 0 issuance psðmsÞ is equal to the marginal cost 1þgs, which In our choice of parameters, we select plausible num- yields Eq. (18). bers based on existing empirical evidence to the extent How does the firm determine its equity issuance that it is available. For those parameters on which there boundary ws? We use the following two-step procedure. is no empirical evidence we make an educated guess First, suppose that the issuance boundary ws is interior to reflect the situation we are seeking to capture in (ws 40). Then, the standard optimality condition implies our model. 46 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62

The capital liquidation value is set to lG ¼ 1:0 in state G, take a firm stand on the precise interpretation of the cash- in line with the estimates provided by Hennessy and carrying cost, it can be due to a tax disadvantage of cash Whited (2007).10 In the bad state, the capital liquidation or to agency frictions. Although in reality these parameter value is set to lB ¼ 0:3 to reflect the severe costs of asset values can also change with the aggregate state, we keep fire sales during a financial crisis, when few investors them fixed in this model so as to isolate the effects of have sufficiently deep pockets or the risk appetite to changes in external financing conditions. acquire assets.11 The model solution depends on these We calibrate the expected productivity m and the adjust- liquidation values only when the firm finds it optimal to ment cost parameter y to match the median cash-capital liquidate instead of raising external funds. ratio and investment-capital ratio for US public firms during We set the marginal cost of issuance in both states to the period from 1981 to 2010. For the median firm, the be g ¼ 6% based on the estimates reported in Altinkilic average cash-capital ratio is 0.29, and the average and Hansen (2000). We keep this parameter constant investment-capital ratio is 0.17. The details of the data across the two states for simplicity and focus only on construction are given in Appendix B.Wethenobtain changes in the fixed cost of equity issuance to capture m ¼ 22:7% and y ¼ 1:8, both of which are within the range changes in the firm’s financing opportunities. The fixed of empirical estimates found in previous studies (see for cost of equity issuance in the good state is set at example Eberly, Rebelo, and Vincent, 2010; Whited, 1992). fG ¼ 0:5%. In the benchmark model, this value implies Finally, Table 1 summarizes all the parameter values. that the average cost per unit of external equity raised in state G is around 10%. This is in the ballpark with the 4.2. Market timing in good times estimates for seasoned offers in Eckbo, Masulis and Norli (2007).12 As for the issuance costs in state B, we chose When the firm is in state G, it can enter the crisis state fB ¼ 50%. No empirical study exists on which we can rely B with a 10% probability per year. Since the firm faces for the estimates of issuance costs in a financial crisis for substantially higher external financing costs in state B,we the obvious reason that there are virtually no initial show that the option to time the equity market in good public offerings or secondary equity offerings in a crisis. times has significant value and generates rich implica-

Our choice for the parameter of fB reflects the fact that tions for investment dynamics. raising external financing becomes extremely costly in a Fig. 1 plots average q and investment-capital ratio for financial crisis and only firms that are desperate for cash state G as well as their sensitivities with respect to the are forced to raise new funds. We later show that even cash-capital ratio w. Panel A shows as expected that the with fB ¼ 50%, firms that run out of cash in the crisis average q increases with w and is relatively stable in state state still prefer raising equity to liquidation. G. The optimal external financing boundary is wG ¼ 0:027. The transition intensity out of state G is set at zG ¼ 0:1, At this point, the firm still has sufficient cash to continue which implies an average duration of ten years for good operating. Further deferring external financing would times. The transition intensity out of state B is zB ¼ 0:5, with help the firm save on the time value of money for an implied average length of a financial crisis of two years. financing costs and also on subsequent cash-carrying We choose the price of risk with respect to financing shocks costs. However, doing so would mean taking the risk that in state G to be kG ¼ ln 3, which implies that the risk- the favorable financing opportunities disappear and that adjusted transition intensity out of state G is the state of nature switches to the bad state when b kG zG ¼ e zG ¼ 0:3. Due to symmetry, the risk-adjusted transi- financing costs are much higher. The firm trades off these b kG tion intensity out of state B is then zB ¼ e zB ¼ 0:167. two margins and optimally exercises the equity issuance These risk adjustments are clearly significant. While we take option by tapping securities markets when w hits the these risk adjustments as exogenous in this paper, they can lower barrier wG. be generated in general equilibrium when the same finan- Should the firm start in state G with wrwG, or should cing shocks also affect aggregate output (see Chen, 2010). its cash stock shrink to wG, it immediately raises external The other parameters remain the same in the two funds of an amount ðmGwÞ per unit of its capital stock. states: the risk-free rate is r ¼ 5%, the volatility of the The lumpy size of the issue reflects the fact that it is productivity shock is s ¼ 12%, the rate of depreciation of efficient to economize on the fixed cost of issuance fG. capital is d ¼ 15%, and the adjustment cost parameter n is Similarly, should the firm start in state G with set to equal the depreciation rate, so that n ¼ d ¼ 15%.We wZwG ¼ 0:371, or should its cash stock grow to wG,it rely on the technology parameters estimated by Eberly, responds by paying out the excess cash ðwwGÞ because Rebelo, and Vincent (2009) for these parameter choices. the net marginal value of cash (that is, the difference The cash-carrying cost is set to l ¼ 1:5%. While we do not between the value of a dollar inside the firm and the value of a dollar in the hands of investors) would drop below zero if the firm holds onto the excessive cash reserve (see

10 They suggest an average value for l of 0.9, so that the liquidation Panel B of Fig. 1). value in the good state should be somewhat higher. When firms face external financing costs, it is optimal 11 See Shleifer and Vishny (1992), Acharya and Viswanathan (2011), for them to hoard cash for precautionary reasons. This is and Campello, Graham, and Harvey (2010). why firm value is increasing and concave in financial slack 12 Eckbo, Masulis, and Norli (2007) report total costs of 6.09% for in most models of financially constrained firms. In our firm commitment offers, excluding the cost of the offer price discount and the value of Green Shoe options. They also report a negative average model, while the precautionary motive for hoarding cash price reaction to a secondary equity offering announcement of 2.22%. is still a key reason that firms save, stochastic financing P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 47

Table 1 Summary of key variables and parameters. This table summarizes the symbols for the key variables used in the model and the parameter values in the benchmark case. For each upper-case variable in the left column (except K, A, and F), we use its lower case to denote the ratio of this variable to capital. Whenever a variable or parameter depends on the state s, we denote the dependence with a subscript s. All the boundary variables are in terms of the cash-capital ratio wt. All the parameter values are annualized when applicable.

Variable Symbol Parameters Symbol State G State B

A. Baseline model

Capital stock K Riskfree rate r 5.0% Cash holding W Rate of depreciation d 15% Investment I Mean productivity shock m 22:7% Cumulative productivity shock A Volatility of productivity shock s 12% Investment adjustment cost G Adjustment cost parameter y 1.8 Cumulative operating profit Y Center of adjustment cost parameter n 15% Cumulative external financing H Proportional cash-carrying cost l 1.5% Cumulative external financing cost X Proportional financing cost g 6% A M Cumulative payout U Correlation between Zt and Zt r 0.4 Firm value P Price of risk for technology shocks Z 0.4 Average qq 0 Net marginal value of cash q State transition intensity zs 0.1 0.5 Payout boundary w Capitalliquidation value ls 1.0 0.3

Financing boundary w Fixed financing cost fs 0:5% 50% Target cash-capital ratio m Price of risk for financing shocks ks lnð3Þlnð3Þ Conditional risk premium mR

B. Hedging

Hedge ratio c Market volatility sm 20% Fraction of cash in account a Futures price F Margin requirement ps 52 Maximum-hedging boundary wb Speculation boundary w~ opportunities introduce an additional motive for the firm implications for investment, as can be seen from the 0 to issue equity: timing equity markets in good times. This expression for the cash-sensitivity of investment isðwÞ market timing option is more in the money near the obtained by differentiating the optimal investment policy equity issuance boundary, which causes firm value to is(w) in Eq. (12) with respect to w: become locally convex in w. In other words, the firm 1 p ðwÞp00ðwÞ becomes endogenously risk-loving when w is close to the i0 ðwÞ¼ s s : ð24Þ s y p0 ðwÞ2 lower barrier wG. s Panel B clearly shows that firm value is not globally As Eq. (24) highlights, investment increases with w if and concave in w. For sufficiently high w, wZ0:061, q (w)is G only if firm value is concave in w. For 0:061 w 0:371, concave. This is because when the firm already has a r r q (w) is concave and corporate investment increases with considerable amount of cash, the benefits from timing the G w. In contrast, in the region where w 0:061, q (w)is market are outweighed by the cash-carrying costs it o G convex in w, which implies that investment decreases with would incur, so that the market timing option is out of w, contrary to conventional wisdom. This surprising result is the money. Corporate savings are then driven only by due to the interaction between stochastic external financing precautionary considerations, so that the firm behaves in conditions and the fixed equity issuance costs. a risk-averse manner. In contrast, for low values of w, Panels C and D of Fig. 1 highlight this non-monotonicity wr0:061, the firm is more concerned about the risk that of investment in cash. Our model is thus able to account for financing costs could increase in the future when the state the seemingly paradoxical behavior that the prospect of switches to B. A firm with low cash holding might want to higher financing costs in the future can cause investment to issue equity while it still has access to relatively cheap respond negatively to an increase in cash today. financing opportunities, even before it runs out of cash. Another interesting observation from Panel C is that Because the issuance boundary w and the target cash G investment at the financing boundary w and the target balance m are optimally chosen, the marginal values of G G m are almost the same. That is, in a situation of equity cash at these two points must be equal: G issuance driven by market timing, the firm holds onto the 0 0 qGðwGÞ¼qGðmGÞ¼g: ð23Þ cash raised and leaves its investment outlays more or less unchanged. By combining Eq. (12) and the boundary The dash-dotted line in Panel B gives the (net) marginal conditions one can show that we must have cost of equity issuance: g ¼ 0:06. One immediate conse- f quence of condition (23) is that qG(w) [or equivalently i ðm Þi ðw Þ¼ G , ð25Þ G G G G ð þ Þ pG(w))] is not globally concave in w, which in turn has y 1 g 48 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62

1.06 0.15

1.055

1.05 0.1

1.045

1.04 0.05

1.035

1.03 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

0.2 1

0.18 0

0.16 −1 0.14

−2 0.12

0.1 −3 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

Fig. 1. Firm value and investment in the normal state, state G. The parameter values are given in Table 1. (A) Average q, qG(W), (B) Net marginal value of 0 0 cash, q G (W), (C) Investment-capital ratio iG(W), and (D) Investment-cash sensitivity i G(W).

which is a small difference when the fixed cost of productivity shock and therefore leads to higher invest- financing in the good state is low. This explains why most ment and lower cash savings. They find empirical support of the new cash raised in a market timing situation is for the possibility that the corporate propensity to save hoarded. out of cash flow could be negative. They suggest that the Although considerable debate exists in the literature contrasting findings of their analysis and Almeida, on corporate investment about the sensitivity of investment Campello, and Weisbach (2004) could be due to differ- to cash flow (see, e.g., Fazzari, Hubbard, and Petersen, 1988; ences in the measurement of Tobin’s q. Our analysis above Kaplan and Zingales, 1997), a general consensus is that shows that, even when it faces constant investment investment is monotonically increasing with cash reserves opportunities, a firm with low cash holding might not or financial slack. In this context, our result that when firms necessarily save more out of cash flow if financing con- face market-timing options, the monotonic relation between ditions are uncertain. investment and cash holds only in the precautionary saving Finally, because productivity shocks are i:i:d: in our region is noteworthy, for it points to the fragility of see- model, this implies that the firms that tend to time equity mingly plausible but misleading predictions derived from markets are those with low cash holdings, as opposed to simple static models about how corporate investment is those having better investment opportunities.13 In reality affected by financial constraints proxied by firms’ cash there is likely to be a mix of firms with low cash or high holdings. investment opportunities, or both, timing the market. Another example of a potentially misleading proxy for We turn next to the investment and firm value in bad financial constraints in our dynamic model relates to the times (state B) and compare them with the results in good cash flow sensitivity of cash of Almeida, Campello, and times (state G). Weisbach (2004). They argue that constrained firms will tend to save more cash in periods of higher cash flows, but 13 Time-varying investment opportunities could also play a signifi- unconstrained firms will not. In a dynamic model, Riddick cant role on cash accumulation and external financing. Eisfeldt and Muir and Whited (2009) argue that an increase in the realized (2011) empirically document that liquidity accumulation and external cash flow is correlated with a positive and persistent financing are positively correlated, and they argue that a pure precau- tionary savings model can account for the empirical evidence. P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 49

1.1 25

1 20 0.9

0.8 15

0.7 10 0.6 5 0.5

0.4 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

0.3 6

0.2 4 0.1

0 2

−0.1 0 −0.2 −2 −0.3

−0.4 −4 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

Fig. 2. Firm value and investment: Comparing states B with state G. The parameter values are given in Table 1. For both s ¼ G and s ¼ B, we have panels 0 0 (A) Average q, qs(w), (B) Net marginal value of cash qs (w), (C) Investment-capital ratio is(w) and (D) Investment-cash sensitivity is (W).

4.3. High financing costs in bad times bad times if we were to specify a proportional issuance

cost gB that is much higher than the cost gG in good times. Fig. 2 plots average q and investment for both states Also, because no market timing opportunity exists in state and their sensitivities with respect to w. As expected, B, firm value is globally concave in bad times. The firm’s average q in state G is higher than in state B. More precautionary motive is stronger in bad times, so that we remarkable is the fact that the difference between qG should expect to see more cash hoarding by the firm. This and qB is very large for low levels of cash holdings w. is reflected in the lower levels of investment and the

Because productivity shocks in our calibration are higher payout boundary wB ¼ 0:408, which is significantly the same in both states, this wedge in the average q is larger than wG ¼ 0:371. solely due to the differences in financial constraints. Panel B underscores the significant impact of financing An important implication of this observation for the empiri- constraints on the marginal value of cash in bad times, cal literature on corporate investment is that using average even though state B is not permanent. In our model, when q to control for investment opportunities and then testing the firm runs out of cash (w approaches zero) the net for the presence of financing constraints by using variables 0 marginal value of cash qBðwÞ reaches 23. Strikingly, the such as cash-flow or cash is not generally valid. Panel C of firm also engages in large asset sales and divestment to Fig. 2 shows that investment in state G is higher than in avoid incurring very costly external financing in bad state B for a given w, and again the difference is especially times. Despite the fact that there is a steeply increasing large when w is low. Also, investment is much less variable marginal cost of asset sales, the firm chooses to sell its with respect to w in state G than in state B. capital at up to a 40% annual rate near w¼0 in bad times

In state B there is no market timing and, hence, the [iBð0Þ¼0:4]. Finally, unlike in good times, investment is firm issues equity only when it runs out of cash: wB ¼ 0. monotonic in w because the firm behaves in a risk-averse The amount of equity issuance is then mB ¼ 0:219, which manner and qB(w) is globally concave in w. is much larger than mGwG ¼ 0:128, the amount of Conceptually, the firm’s investment behavior and firm issuance in good times. The significant fixed issuance cost value are different in bad and good times. Quantitatively, in bad times (fB ¼ 0:5) causes the firm to be more the variation of the investment and firm value in bad aggressive should it decide to tap equity markets. The times dwarfs the variation in good times. In particular, amount of issuance would be significantly decreased in firm value at low levels of cash holdings is much more 50 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62

Table 2 Panel C reports the net marginal value of cash q0ðwÞ in Conditional distributions of cash-capital ratio w, investment-capital states G and B. As one might expect, the marginal value of ratio i (w), and net marginal value of cash q0 ðwÞ. s s cash is higher in state B than in G on average. Quantita- The conditional distributions of the investment-capital ratio and the net marginal value of cash are computed based on the conditional tively, the firm on average values a dollar of cash margin- distributions of the cash-capital ratio in state G and B, respectively. All ally at 1.015 in state G and 1.03 in state B, implying a the parameter values are reported in Table 1. difference of 1.6 cents on the dollar between the two states. Remarkably, firms are able to optimally manage Mean 1% 25% 50% 75% 99% their cash reserves in anticipation of unfavorable market Panel A. Cash-capital ratio: w¼W/K conditions and, therefore, end up spending very little time in regions of high marginal value of cash. For low cash G 0.283 0.088 0.240 0.300 0.341 0.370 holdings, the difference between the marginal value B 0.312 0.114 0.266 0.325 0.371 0.408 of cash in states G and B are larger. For example, at the

Panel B. Investment-capital ratio: is(w) 99th percentile, the firm values a dollar of cash marginally at 1.35 in state B and 1.11 in state G, implying a difference G 0.170 0.112 0.166 0.176 0.179 0.180 of 22 cents on the dollar. This is a sizable difference, but it B 0.161 0.003 0.159 0.173 0.178 0.180 is still much less than the extreme cases illustrated in Panel C. Net marginal value of cash: q0 ðwÞ s Panel B of Fig. 2. G 0.015 0.000 0.001 0.005 0.019 0.111 B 0.031 0.000 0.001 0.008 0.028 0.351 4.5. Equity issuance waves and stock repurchase waves volatile in state B than in state G, as can be seen from One can see from Panel A in Fig. 2 that the payout

Panel A. This could be an important reason why stock boundary is higher in state B than in state G: wB ¼ price volatility tends to rise sharply in downturns. 0:4084wG ¼ 0:371. This implies that any firm in state B with cash holding w 2ð0:371,0:408Þ will time the favor- 4.4. The stationary distribution able market conditions by paying out a lump sum amount

of ðwwGÞ as the state switches from B to G. To the extent Table 2 reports the conditional stationary distributions that the payout is performed through a stock repurchase for w, i(w), and q0ðwÞ in both states G and B. Panel A shows (as is common for non-recurrent corporate payouts), our that the average cash holding in state B (0.312) is higher model then provides a simple explanation for why stock than in state G (0.283) by about 10%. Understandably, repurchase waves tend to occur in favorable market firms on average hold more cash for precautionary conditions. reasons under unfavorable financial market conditions. Similarly, the issuance boundary is lower in state B

In addition, for a given percentile in the distribution, the than in state G: wB ¼ 0 o wG ¼ 0.0277, which implies that cutoff cash reserve level is higher in state B than in state any firm in state B with cash holding w 2ð0,0:027Þ will G, meaning that the precautionary motive is unambigu- time the favorable market conditions by issuing external ously stronger in state B than state G. Finally, it is striking equity of an amount ðmGwÞ per unit of capital as the that even at the bottom 1% of cash holdings the firm’s state switches from B to G. In other words, our model also cash-capital ratio is still reasonably high, 0.088 for state G generates equity issuance waves in good times. and 0.114 for state B, which reflects the firm’s strong Taken together, these two results provide a plausible incentive to avoid running out of cash. explanation for the Dittmar and Dittmar (2008) finding Panel B describes the conditional distribution of that equity issuance waves coincide with stock repurch- investment in states G and B. The average investment- ase waves. As financing conditions improve, firms’ pre- capital ratio i(w) is lower in state B (16.1%) than in state G cautionary demand for cash is reduced, which translates (17%), as cash is more valuable on average in state B than into stock repurchases by cash-rich firms. Note that our in state G. Naturally, the underinvestment problem is model does not predict repurchases when firms are more significant for firms with low cash holdings in state undervalued, the standard explanation for repurchases B than state G. For example, the firm that ranks at the in the literature. As Dittmar and Dittmar (2008) point out, bottom 1% in state B invests at the rate of only 0.3% of its this theory of stock repurchases is inconsistent with the capital stock, while the firm that ranks at the bottom 1% evidence on repurchase waves. They further suggest that in state G invests at the rate of 11.2% of its capital stock. the market timing explanations by Loughran and Ritter Thus, firms substantially cut investment to decrease the (1995) and Baker and Wurgler (2000) are rejected by their likelihood of expensive external equity issuance in bad evidence on repurchase waves. However, as our model times. As soon as the firm piles up a moderate amount of shows, this is not the case. It is possible to have at the cash, the underinvestment wedge between the two states same time market timing through equity issues by cash- disappears. In fact, the top half of the distributions of poor firms and market timing through repurchases by investments in the two states are almost identical. This cash-rich firms. These two very different market timing result is in sharp contrast to the large gap between the behaviors can be driven by the same change in external investment-capital ratios iG(w) and iB(w) in Panel C of financing conditions. The difference in behavior is driven Fig. 2. It again illustrates the firm’s ability to smooth out only by differences in internal financing conditions, the the impact of financing constraints on investment. amount of cash held by firms. P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 51

0.14 0.22

0.12 0.2

0.1 0.18

0.08 0.16

0.06 0.14

0.04 0.12

0.02 0.1

0 0.08 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

0 0 Fig. 3. The effect of duration in state G on qGðwÞ and iG(w). This figure plots (A) the net marginal value of cash qGðwÞ and (B) investment-capital ratio iG(w) for three values of transition intensity, zG ¼ 0:01,0:1,0:5. All other parameter values are given in Table 1.

4.6. Comparative analysis Table 3 Fixed cost of equity issuance. Next, we study the effect of changes in the duration of This table reports the amount of equity issuance relative to capital, m w , the average issuance cost, the equity issuance boundary, w , state G and then analyze the effect of changes in the G G G and the payout boundary, wG, for different fixed cost of equity issuance issuance cost . fG fG in state G. All the parameter values are reported in Table 1.

4.6.1. Effect of changes in the duration of state G fG mG wG Average cost wG wG How does the transition intensity z out of state G G 0 0.000 0.060 0.092 0.357 (or, equivalently, the duration 1=zG of state G) affect firms’ 0.5% 0.128 0.099 0.027 0.370 market timing behavior? Consider the case in which state 1.0% 0.153 0.126 0.013 0.375 G has a very high average duration of one hundred years 2.0% 0.176 0.174 0.000 0.380 5.0% 0.189 0.324 0.000 0.388 (zG ¼ 0:01). Not surprisingly, in this case the firm taps 10.0% 0.199 0.563 0.000 0.394 equity markets only when it runs out of cash (wG ¼ 0). Firm value qG(w) is then globally concave in w and iG(w) increases with w everywhere. Essentially, the expected afirmfacinganarrowerwindowofgoodfinancingcondi- duration of favorable market conditions is so long that the tions and its investment is higher, as Panel B illustrates. market timing option has no value for the firm. Both investment and the net marginal value of cash are

With a sufficiently high transition intensity zG (say highly nonlinear and non-monotonic in cash despite the zG ¼ 0:1), however, the firm could time the market by fact that the real side of our model is time invariant. Our selecting an interior equity issuance boundary wG 40. The model thus suggests that the typical empirical practice of firm then equates the net marginal value of cash at wG with detecting financial constraints is conceptually flawed. 0 the proportional financing cost g : qGðwGÞ¼ g ¼ 6%,ascan Using average q to control for investment opportunities be seen from Panel A of Fig. 3. Because the net marginal and then testing for the presence of financing constraints value of cash at the target cash-capital ratio, mG,alsosatisfies by using variables such as cash flow or cash (which 0 qGðmGÞ¼6%,itfollowsthat,forw 2½wG,mG, the net is often done in the empirical literature) would be mis- 0 marginal value of cash qGðwÞ first increases with w and then leading and miss the rich dynamic adjustment involved to decreases, as Panel A again illustrates. balance the firm’s market timing and precautionary sav-

When zG increases from 0.1 to 0.5, the firm taps the ing motives. equity market even earlier (wG increases from 0.027 to 0.071) and holds onto cash longer (the payout boundary wG increases from 0.370 to 0.400) for fear that favorable 4.6.2. The effect of changes in issuance cost fG financial market conditions could be disappearing faster. Table 3 reports the effects of changes in the issuance

For sufficiently high w, the firm facing a shorter duration cost parameter fG on the issuance boundary wG, the of favorable market conditions (higher zG) values cash issuance amount ðmGwGÞ, the average issuance cost, more at the margin [higher qG(w)] and invests less [lower and the payout boundary wG. iG(w)]. However, for sufficiently low w, the opposite holds Consistent with basic economic intuition, when the because the firm with a shorter lived market timing fixed issuance cost fG increases, the firm becomes less option taps equity markets sooner so that the net willing to issue equity, holds onto its cash longer, and marginal value of cash is lower. Consequently and somewhat issues more equity whenever it taps the equity market. surprisingly, the underinvestment problem can be smaller for These responses are reflected in a lower issuance 52 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62

boundary wG, a higher payout boundary wG, and a larger have high cash holdings could pay out cash but would amount of issuance ðmGwGÞ. While a firm with a larger hold even more cash after a negative financing shock. fixed cost fG issues more, the average issuance cost is still Another empirical prediction that differentiates our 14 higher. Without any fixed cost (fG ¼ 0), the firm issues model from other market timing models concerns the link just enough equity to stay away from its optimally chosen between equity issuance and corporate investment. Our

financing boundary wG ¼ 0:092, and the net marginal model predicts that underinvestment is substantially 0 value of cash at issuance equals qGðwÞ¼g ¼ 6%, so that mitigated when the firm is close to the equity financing the average issuance cost is precisely 6%. In this extreme boundary. Moreover, the positive correlation between 0 case, the marginal value of cash qGðwÞ is monotonically investment and equity issuance in our model is not driven decreasing in w, and firm value is again globally concave by better investment opportunities (as the real side of the in w even under market timing. economy is held constant across the two states). It is When the fixed cost of issuing equity is positive but driven solely by the market timing and precautionary not very high (consider fG ¼ 1%), the firm times equity demand for cash. markets at the optimally chosen issuance boundary of 5. Real effects of financing shocks wG ¼ 0:013 and issues the amount ðmGwGÞ¼0:153. Neither the marginal value of cash nor investment is then Several empirical studies have attempted to measure monotonic in w in the region where w 2½wG,mG. More- over, higher fixed costs lead firms to choose larger the impact of financing shocks on corporate investment by exploiting the recent financial crisis as a natural issuance sizes ðmGwGÞ. Also, wG ¼ 0 when fG ¼ 2%. This 16 result shows that market timing does not necessarily lead experiment. A central challenge for any such study is to a violation of the pecking order between internal cash to determine the degree to which the financial crisis has been anticipated by corporations. As long as corporations and external equity financing and that wG 40 is not necessary for the convexity of the value function. Finally, put a nonzero probability on a financial crisis occurring, when the fixed cost of issuing equity is very high, the the real effects of the financing shock would already be market timing effect is so weak that the precautionary present before the realization of the shock. Any real motive dominates again, so that the net marginal value of response following the shock would merely be a residual cash is monotonically decreasing in w. response. Our model is naturally suited to contrast the Having determined why the value function could be impact of more versus less anticipated financing shocks locally convex, we next explore the implications of con- on investment and firm value. vexity for investment. Recall from Eq. (24) that the sign of The fact that shocks are anticipated does not necessa- 0 00 rily mean that the firm knows exactly when a financial the investment-cash sensitivity isðwÞ depends on ps ðwÞ. Thus, in the region where pG(w) is convex, investment is crisis will occur. It simply means that the firm (and decreasing in cash holdings w. everyone else in the economy) attaches a certain prob- There are other ways to generate a negative correlation ability to the crisis. In our benchmark model the firm between changes in investment and cash holdings. First, solves the value maximization problem in the good state when the firm moves from state G to B, this not only assuming that zG ¼ 0:1. This is a scenario in which a results in a drop in investment, especially when w is low negative financing shock is thought to be likely, at least (see Panel C in Fig. 2), but also in an increase in the payout compared with a scenario in which the firm assumes that boundary, which could explain why firms during the zG ¼ 0:01. What are the real effects of an increase in zG recent financial crisis have increased their cash reserves from 0.01 to 0.1 both before and after the economy and cut back on capital expenditures, as Acharya, switches from state G to state B? We explore this question Almeida, and Campello (forthcoming) show. Second, in a below while keeping the transition intensity in the bad model with persistent productivity shocks (as in Riddick state fixed at zB ¼ 0:5. and Whited, 2009), when expected future productivity A higher probability of a crisis leads firms to respond falls, the firm cuts investment and the cash saved could by holding more cash, adopting more conservative invest- also result in a rise in its cash holding.15 ment policies, and raising external financing sooner, etc. Is it possible to distinguish empirically between these As a result, the ex post impact of the financing shock on two mechanisms? In the case of a negative productivity investment and other real decisions can appear to be shock, the firm has no incentive to significantly raise its small due to the fact that the shock has already been cash holding. In fact, reduced investment might lead the partially smoothed out through precautionary savings. firm to hold less cash. This prediction is opposite to the Fig. 4 illustrates this idea. A comparison of the two prediction related to a negative financing shock. Thus, scenarios with different probabilities of a negative finan- following a negative technology shock firms that already cing shock demonstrates that the firm smoothes out financing shocks in two ways. First, a heightened concern about the incidence of a financial crisis pushes firms to invest more conservatively in state G most of the time. 14 The case with low (close to zero) financing costs is empirically Second, a firm anticipating a higher probability of crisis relevant. Baker and Wurgler (2000) claim that financing costs can be precipitously close to zero in market conditions that can be identified (in sample) by econometricians. 16 See Campello, Graham, and Harvey (2010), Campello, Giambona, 15 This mechanism is captured in our model with the two states Graham, and Harvey (2011), Duchin, Ozbas, and Sensoy (2010), and corresponding to two different values for the return on capital ms. Almeida, Campello, Laranjeira, and Weisbenner (2012), among others. P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 53

0.22

0.2

0.18

0.16

0.14

0.12

0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Fig. 4. Impact of financing shocks on investment. This figure illustrates the response in investment when the financing shock occurs. The two solid lines plot the investment-capital ratio in the case of more anticipated shocks, with zG ¼ 0:1. The two dotted lines are for the case of less anticipated shocks, where zG ¼ 0:01.

Table 4 1% to 10%, which is a main contributor to the overall Distribution of investment responses. reduction in the firm’s investment response. The ex ante This table reports the distributions of instantaneous investment responses of the firm in state G such as lower levels of responses when firms in state G (good state) experience a negative financing shock. The distributions of investment responses are com- investment, higher (costly) cash holdings, and earlier use puted based on the stationary distributions of the cash-capital ratio W of costly external financing are all reflections of the conditional on being in state G. For example, the column 25% gives the impending threat of a negative financing shock and investment response by a firm whose cash holding is at 25th-percentile all of them contribute to the real costs of financing of the stationary distribution in state G. The mean responses are shocks. integrated over the conditional stationary distribution in state G. Panel A of Table 4 provides information about the Mean 1% 5% 25% 50% 75% entire distribution of investment responses to financing

shocks for zG ¼ 1% and 10%. The average investment Panel A. Financing shock reduction following a negative financing shock is 1.78%

when zG ¼ 10%, compared with 6.59% when the shock zG ¼ 1% 6.59 43.17 23.66 7.06 3.66 2.23 zG ¼ 10% 1.78 18.11 6.49 1.67 0.76 0.39 was perceived to be less likely (zG ¼ 1%). The median investment decline is 0:76% for z ¼ 10%, which is again Panel B. Shock to expected productivity G lower than 3.66%, the median investment drop when

zG ¼ 1% 6.59 6.84 6.84 6.81 6.67 6.40 zG ¼ 1%. Moreover, in the scenario in which the financing zG ¼ 10% 3.15 3.17 3.17 3.17 3.16 3.15 shock was seen to be less likely, the distribution of investment responses also has significantly fatter left tails. For example, at the 5th percentile, the investment also holds more cash on average, which further reduces decline is 23.66% when zG ¼ 1%, which is much larger the impact of financial shocks on investment. than the drop of 6.49% when zG ¼ 10%. In other words, We specify in Fig. 4 the size of the investment response when a financial crisis strikes, only those firms that to a financing shock at the average cash holdings in state happen to have low cash holdings will be forced to cut G. With a lower probability of a financing shock investment dramatically.

(zG ¼ 0:01), the average cash holding in state G is 0.224, This result is consistent with the survey evidence of at which point investment drops by 4.03% following the Campello, Graham, and Harvey (2010). They report that shock. In contrast, with a higher probability (zG ¼ 0:1), the during the financial crisis in 2008 the chief financial average cash holding in state G rises to 0.283, and the officers they surveyed planned to cut capital expenditures drop in investment reduces to 0.96% at this level of cash by 9.1% on average when their firm was financially holding. constrained, while the unconstrained firms planned to This analysis reveals that a small observed investment keep capital expenditures essentially unchanged (on response to a financing shock does not imply that finan- average, CFOs of these firms reported a cutback of cing shocks are unimportant for the real economy. investment of only 0.6%). Our model further demonstrates As Fig. 4 shows, with a higher risk of a crisis, the firm that the fraction of firms that have to significantly cut responds by taking actions ahead of the realization of the investment (e.g., by over 5%) following a severe financing shock. Thus, the firm substantially scales back its invest- shock decreases significantly as firms assign higher prob- ment in state G when the transition intensity zG rises from abilities to a financial crisis shock. 54 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62

Furthermore, the average investment response in our which in turn leads to small average investment responses scenario of more anticipated shocks quantitatively to financing shocks ex post. matches the empirical findings from the recent financial Second, the heterogeneity in investment responses crisis. Duchin, Ozbass, and Sensoy (2010) find that corpo- across firms with different cash holdings can help us rate investment on average declined by 6.4% from its distinguish between financing shocks and productivity unconditional mean level before the crisis. Based on the shocks empirically. There will be significant variation in average investment-capital ratio of 17%, this number the investment responses across firms with different cash translates into a 1% decline in the investment-capital holdings following a financing shock, but little such ratio, which is between the mean and median investment variation following a shock to expected productivity. response for zG ¼ 10% in Panel A of Table 4. While firms can effectively shield investment from 6. Financial constraints and the risk premium financing shocks by hoarding more cash, changes in cash reserves have almost no effect on firms’ investment In this section, we explore how aggregate financing responses when they are hit by a shock to expected shocks affect the risk premium for a financially constrained productivity. To compare the effects of shocks to expected firm.18 Without external financing constraints, the firm in productivity against the effects of financing shocks, we our model has a constant risk premium. When the firm’s carry out the following experiment. Holding the financing financing conditions remain the same over time, a condi- cost constant (fG ¼ fB ¼ 0:5% and g ¼ 6%), we instead tional CAPM (capital asset pricing model) holds in our assume that the conditional mean return on capital (ms)is model, in which the conditional beta is monotonically higher in state G than B. Specifically, we hold mG at 22.7% decreasing in the firm’s cash-capital ratio. In the presence as in the benchmark model but calibrate mB ¼ 19:25% of aggregate financing shocks, however, the conditional risk such that the average drop in investment following a premium is determined by a two-factor model, which prices productivity shock is 6.59% when zG ¼ 1%, the same as in both the aggregate shocks to profitability and the shocks to the scenario with financing shocks (see Panel A of financing conditions.19 Table 4). Again, we consider the two scenarios with A heuristic derivation of the firm’s (risk-adjusted) zG ¼ 1% and 10% respectively, while holding zB ¼ 0:5. expected return involves a comparison of the HJB equa- The results for the distribution of investment responses tions under the physical and risk-neutral measures P and immediately following a productivity shock are reported Q. Let the firm’s conditional risk premium in state s be in Panel B of Table 4. R ms ðwÞ. We can then write the HJB equation under the A higher transition intensity zG means that the high- physical measure as productivity state is expected to end sooner on average, R 0 ðrs þms ðwÞÞpsðwÞ¼max½ðrslÞwþmsisgsðisÞpsðwÞ and the firm invests less aggressively in state G as a result. is This is why the average decline in investment following a 2 ss 00 0 productivity shock is smaller when z ¼ 10% than when þ p ðwÞþðisdÞðp ðwÞwp ðwÞÞ G 2 s s s zG ¼ 1%. More interestingly, unlike the effects of financing þzsðp ðwÞp ðwÞÞ, ð26Þ shocks for which there is significant heterogeneity in s s investment responses across firms with different levels where ms and zs, respectively, denote the expected return of cash-capital ratios, the investment responses following on capital and the transition intensity from state s to s a productivity shock are essentially the same across all under the physical probability measure. By matching firms. The contrast of investment responses to financing terms in the HJB equations (11) and (26), and using the shocks and shocks to expected productivity in our cali- risk adjustments specified in (7) and (8), we then obtain brated model suggests that financing and productivity the following expression for the conditional risk pre- shocks can have significantly different implications for mium: investment responses among firms with different amount of financial slack.17 18 Livdan, Sapriza, and Zhang (2009) also study the effect of In summary, our model provides two new insights financing constraints on stock returns. Their model, however, does not about the real effects of financing shocks. First, it will be allow for stochastic financing conditions or cash accumulation. wrong to conclude that financing shocks have small effect 19 One interpretation of the pricing model in this section is that all on the real economy just because the ex post investment investors are rational risk-averse investors who anticipate shocks to a firm’s financing opportunities, which could be driven by (unmodeled) responses to financing shocks are small. The effects of shocks to financial intermediation costs or changes in the opaqueness of financing shocks on a firm’s investment policy crucially the firm’s balance sheets. An alternative interpretation is that the firm’s depend on two variables: (1) the probability that the firm external financing costs are driven by (unmodeled) changes in market attaches to the financing shock, and (2) the firm’s cash sentiment. This behavioral interpretation is still consistent with the holding. A relatively small rise in the probability of a view that investors require compensation for the risk with respect to changes in the firm’s financing opportunities if one takes the approach financing shock can already cause firms to underinvest based on differences of opinion a la Scheinkman and Xiong (2003). The significantly and hold onto excess cash in good times, point is that, in the differences of opinion model, investors are aware that at any moment there could be other more optimistic or pessimistic investors. Each investor is not always the marginal investor, and to the 17 Fixed capital adjustment costs can also generate heterogenous extent that each investor is aware of this (as is assumed in the investment responses to shocks to expected productivity. However, the differences of opinion model) he faces risk with respect to other response will depend more on how close the firm is to the adjustment investors’ optimism (which here takes the form of risk with respect to boundary rather than on the firm’s cash holding. the firm’s financing opportunities) for which he requires compensation. P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 55

0 p ðwÞ ðp ðwÞp ðwÞÞ R s ks s s ðps ðwÞpsðwÞÞ=psðwÞ gives the percentage change of firm ms ðwÞ¼Zsrsss ðe 1Þzs : ð27Þ psðwÞ psðwÞ value if financing conditions change. Intuitively, the finan- cing risk premium is larger the bigger the relative change in The first term in Eq. (27) is the productivity risk firm value due to a change in external financing conditions. premium, which is the product of the firm’s exposure to Fig. 5, Panel A, plots the productivity risk premium 0 aggregate (Brownian) productivity shocks rssspsðwÞ=psðwÞ [the first term in Eq. (27)] in state G as a function of the and the price of Brownian risk Zs (where rs is the cash-capital ratio w. This premium is generally decreasing in conditional correlation between the firm’s productivity the cash-capital ratio, except near the financing boundary. shock dAt and the stochastic discount factor in state s). In the benchmark case (zG ¼ 0:1), the risk with respect to This term is positive for firms whose productivity shocks higher future financing costs generates market timing are positively correlated with the aggregate market. behavior and non-monotonicity in the marginal value of The second term is the financing risk premium, which cash (Fig. 1, Panel B), which in turn can cause the produc- compensates risk-averse investors for the firm’s exposure tivity risk premium to be locally increasing in w for low to aggregate financing shocks. Financing shocks are priced levels of w. As the non-monotonicity in the marginal value when their arrival corresponds to changes in the stochas- of cash is partially offset by the asset composition effect, the tic discount factor. As seems empirically plausible, we non-monotonicity in the productivity risk premium is suppose that the stochastic discount factor jumps up relatively weak. Similarly, holding w fixed at a low level, when aggregate financing conditions deteriorate, that is, 0 market timing can lower pGðwÞ as the transition intensity zG kG ¼kB 40 in our two state model. In other words, increases. This explains why the productivity risk premium investors demand an extra premium for investing in firms may be decreasing in the transition intensity for low w. whose values drop during times when external financing When the transition intensity is sufficiently low (e.g., conditions worsen [p ðwÞ4p ðwÞ]. G B zG ¼ 0:01), the non-monotonicity in the productivity risk In the first-best setting where a firm has free access to premium disappears. external financing, its risk premium is constant and can Second, Panel B plots the financing risk premium. The be recovered from Eq. (27) by setting Zs, rs, and ss to size of this premium depends on the relative change in constants and dropping the second term. We then obtain firm value when external financing conditions change. It the standard CAPM formula: is increasing in the transition intensity zG, but decreasing 1 in w. Intuitively, when the cash holding is low, a sudden mFB ¼ Zrs : ð28Þ qFB worsening in external financing conditions is particularly costly to the firm as it leads deep cuts in investment, asset R FB The comparison between ms ðwÞ and m highlights the fire sales, and costly equity issuance. However, when the impact of external financing frictions on the firm’s cost of cash holding is high, the firm can still maintain relatively capital. high levels of investment using the internal funds. When financing opportunities are constant over time, In Panels C and D, both the productivity risk premium financial constraints affect only the cost of capital by and financing risk premium in state B are monotonically amplifying (or dampening) a firm’s exposure to produc- and rapidly decreasing in the firm’s cash holding. When w tivity shocks. This effect is captured by the productivity is close to zero, the annualized conditional productivity (diffusion) risk premium in Eq. (27). As the cash-capital risk premium can exceed 80%. The high premium and ratio w increases, the firm tends to become less risky for sharp decline with w mirror the rapid decline in the two reasons. First, if a greater fraction of its assets is in marginal value of cash (see Fig. 2, Panel B). High marginal cash, the firm beta is automatically lower due to a simple value of cash in the low w region can dramatically amplify portfolio composition effect. As a financially constrained the firm’s sensitivity to productivity shocks. The produc- firm hoards more cash to reduce its dependence on costly tivity risk premium eventually falls below 2% when the external financing, the firm beta becomes a weighted firm is near the payout boundary. Similarly, the condi- average of its asset beta and the beta of cash, which is tional financing premium can exceed 30% when w is close equal to zero. In particular, with a large enough buffer to zero, this is due to the large jump in firm value when stock of cash relative to its assets, this firm could be even the financing state changes (see Fig. 2, Panel A). safer than a firm facing no external financing costs and Quantitatively, the level and variation of the conditional therefore holding no cash. Second, an increase in w risk premium generated by financing constraint should be relaxes the firm’s financing constraint and therefore interpreted in conjunction with the stationary distributions reduces the sensitivity of firm value to cash flow, which of cash holdings in Section 4.4. Because the firm’s cash also tends to reduce the risk of the firm. holdings rarely drop to very low levels, its risk premium is Time-varying external financing costs affect the cost of small and smooth most of the time in our model. capital for a financially constrained firm in two ways. First, Our model has several implications for the expected the firm’s exposure to productivity shocks changes as returns of financially constrained firms. Controlling for financing conditions change, because the marginal value of productivity and financing costs, the model predicts an 0 cash psðwÞ and firm value ps(w) both depend on the state s. inverse relation between the expected returns and corpo- Second, when external financing shocks are priced, investors rate cash holdings, which has been shown by Dittmar and demand an extra premium for investing in firms that do Mahrt-Smith (2007) and others. Our analysis points out poorly when financing conditions worsen. This effect is that this negative relation might not be due to agency captured by the second term in Eq. (27).Notethat problems, as they emphasize, but could be driven by 56 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62

0.022 0.03

0.025 0.02 0.02 0.018 0.015 0.016 0.01

0.014 0.005

0.012 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

1 0.35

0.3 0.8 0.25

0.6 0.2

0.4 0.15 0.1 0.2 0.05

0 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5

Fig. 5. The effects of stochastic financing conditions on the cost of capital. This figure plots firm risk premium in state G and B. We consider three levels of transition intensity from G (good state) to B (bad state): zG ¼ 0:01, 0.1, 0.5. All other parameter values are given in Table 1. (A) Productivity risk premium in state G, (B) Financing risk premium in state G, (C) Productivity risk premium in state B and (D) Financing risk premium in state B.

relaxed financing constraints and a changing asset com- shows how a firm’s conditional beta depends on the firm’s of the firm. When heterogeneity in productivity cash holdings. and financing costs is difficult to measure, it is important to take into account the endogeneity of cash holdings 7. Market timing and dynamic hedging when comparing firms with different cash holdings empirically. A firm with higher external financing costs We have thus far restricted the firm’s financing choices tends to hold more cash. However its risk premium could to internal funds and external equity financing. In this still be higher than for a firm with lower financing costs section, we extend the model to allow the firm to engage and consequently lower cash holdings. Thus, a positive in dynamic hedging via derivatives such as market-index relation between returns and corporate cash holdings futures. How does market timing behavior interact with across firms could still be consistent with our model dynamic hedging? This is the question we address in this [see Palazzo, 2012 for a related model and supporting section. We denote by F the index futures price for a market empirical evidence]. portfolio that is already completely hedged against finan- With time-varying financing conditions, our model can cing shocks. Under the risk-neutral probability measure, the be seen as a conditional two-factor model to explain the futures price F then evolves according to cross section of returns (we provide details of the derivation bM in Appendix C). A firm’s risk premium is determined by its dFt ¼ smFt dZ t , ð29Þ productivity beta and its financing beta. Other things equal, where s is the volatility of the market index portfolio and a firm whose financing costs move closely with aggregate m bM financing conditions has a larger financing beta and earns fZ t : tZ0g is a standard Brownian motion under Q that is A higher returns than one with financing costs independent of correlated with the firm’s productivity shock fZt : tZ0g aggregate conditions. Empirically, this two-factor model can with a constant correlation coefficient r. be implemented using the standard market beta plus a beta Futures contracts require that investors hold cash in a with respect to a portfolio that is sensitive to financing margin account. We denote the notional amount of the shocks (e.g., a banking portfolio). This model, in particular, futures contract by ctWt, and denote the fraction of the P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 57

1 firm’s total cash Wt held in the margin account by hedge ratio that achieves this objective is rsBsm =w. at 2½0,1. Cash held in this margin account incurs a flow However, this hedge ratio might not be attainable due to unit cost EZ0. Futures market regulations typically the margin requirement. In that case, the firm chooses the n require that an investor’s futures position (in absolute maximally admissible hedge ratio cBðwÞ¼pB.Eq.(31) value) cannot exceed a multiple p of the amount of cash captures the effect of margin constraints on hedging. Because atWt held in the margin account. We let this multiple be there is no (i.e., E ¼ 0), the hedge ratio c given in (31) state dependent and denote it by pðstÞ. The margin is independent of firm value and depends only on w.Wenext requirement in state s then imposes the following limit turn to the focus of this section: hedging in state G. 9 9 on the firm’s futures position: ct rpðstÞat. As the firm can costlessly reallocate cash between the margin account 7.2. In state G and its regular interest-bearing account, it optimally holds the minimum amount of cash necessary in the Before entering the crisis state, the firm has external margin account when E40. For simplicity, we shall ignore financing opportunities. Moreover, the margin require- this haircut on the margin account and assume that E ¼ 0. ment could be different (i.e., pG 4pB). In state G, the firm Under this assumption, we do not need to keep track chooses its investment policy I and its index futures of cash allocations in the margin account and outside the position cW to maximize firm value PðK,W,GÞ by solving account. We can then simply set at ¼ 1. the following HJB equation: The firm’s cash holdings evolve as rGPðK,W,GÞ¼max½ðrGlÞW þmGKIGðI,K,GÞPW I,c dWt ¼ Kt½mðstÞ dtþsðstÞ dZtðIt þGtÞ dt þdHtdUt 1 M 2 2 2 2 2 þ½ ð Þ þ ð Þ þðIdKÞPK þ ðsGK þc smW r st l Wt dt ctWtsm dZt , 30 2 9 9 þ2rsmsGcWKÞPWW where ct rpðstÞ. To avoid unnecessary repetition, we consider only the case with positive correlation, i.e., r40. þz½PðK,W,GÞPðK,W,BÞ, ð32Þ Next, we examine the crisis state. subject to 9c9rpG. When firm value is concave in cash, we have the same 7.1. In state B solution as in state B, but with margin p . That is, G n rsG Given that firm value is always concave in cash in state cGðwÞ¼max ,pG : ð33Þ wsm B (PWW ðK,W,GÞo0), the firm in state B faces the same decision problem as the firm in BCW. BCW show that the However, market timing opportunities combined with optimal hedge ratio (with time-invariant opportunities) is fixed costs of equity issuance imply that firm value could given by be convex in cash, i.e., PWW ðK,W,GÞ40 for certain regions of w¼W/K. With convexity, the firm naturally speculates n rs c ðwÞ¼max B ,p : ð31Þ in derivatives markets. Given the margin requirement, B ws B m the firm takes the maximally allowed futures position,

Intuitively, the firm chooses the hedge ratio c so that i.e., the corner solution cGðwÞ¼pG. The firm is long in the firm faces only idiosyncratic volatility after hedging. The futures despite positive correlation between its

n Fig. 6. Optimal hedge ratios c ðwÞ in states G (good states) and B (bad states) when state B is absorbing. The parameter values are: market volatility sm ¼ 20%, correlation coefficient r ¼ 0:4, and margin requirements pG ¼ 5 and pB ¼ 2. All other parameter values are given in Table 1. 58 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62

b productivity shock and the index futures. Let wG denote exposure to systemic volatility. However, when the firm’s the endogenously chosen point at which PWW ðK,W,GÞ¼0, cash holdings are sufficiently low, the firm optimally engages 00 b or pGðwGÞ¼0. We now summarize the firm’s futures in speculation to take advantage of its market timing option. position in state G as Rampini and Viswanathan (2010) arguethatmorefinan- 8 > rs cially constrained firms hedge less because the firm’s < G Z b n max ,pG for w wG, financing needs for investment override hedging concerns. c ðwÞ¼ wsm ð34Þ G :> An important link then exists between financing and risk p for w w wb : G G r r G management, both of which involve promises to pay by the n firm that are limited by collateral. Like Rampini and Note the discontinuity of the hedge ratio c ðwÞ in w. The G Viswanathan (2010), our model for corporate risk manage- firm switches from a hedger to a speculator when its ment is also consistent with the evidence that smaller firms cash-capital ratio w falls below wb . G hedge less. These firms are likely to be more financially For numerical illustration, we choose the correlation constrained and would have limited hedging capacity due to between index futures and the firm’s productivity shock the difficulty in meeting the margin requirements. to be r ¼ 0:4 and a market return volatility of sm ¼ 20%. The margin requirements in states G and B are set at 8. Conclusion pG ¼ 5 and pB ¼ 2, respectively. All other parameter values are the same as in the previous sections. Mounting evidence show large market-wide swings in the financing conditions. What is more, in rare episodes of n 7.3. Optimal hedge ratios cs ðwÞ financial crises, primary markets essentially shut down. Firms have also become increasingly aware of the risks Fig. 6 plots the optimal hedge ratios in the two states: and opportunities they face with respect to these external n n cGðwÞ and cBðwÞ. First, for sufficiently high w, the firm financing costs, and they appear to time equity markets as hedges the same way in both states. Hedging is then suggested by Baker and Wurgler (2002). However, despite unconstrained by the firm’s cash holding. The firm the rapid growth in empirical research on the effects of 1 chooses its hedge ratio to be equal to rssm =w so as shocks to the supply of capital on firms’ corporate policies to eliminate its exposure to systematic volatility of the (see Baker and Wurgler, 2011 for a survey of the literature), productivity shock. This explains the concave and over- very few theoretical analyses are available on the implica- lapping parts of the hedging policies in Fig. 6. tions of stochastic external financing costs for the dynamics Second, for low w, hedging strategies differ in the of corporate investment and financing. This paper aims to two states. In state B the hedge ratio hits the constraint close this gap by taking the perspective of a rational firm n cBðwÞ¼pB ¼2forwr0:12. In state G, the firm issues manager maximizing shareholder value by timing favorable equity at wG ¼ 0:0219 and firm value is convex in w (due to equity market conditions and shielding the firm against 00 market timing) for wrw~ G ¼ 0:0593 [where p ðw~ GÞ¼0]. In crisis episodes through precautionary cash holdings. other words, for w 2ðwG,w~ GÞ firm value is convex in w and We show that firms optimally hoard cash and issue the firm engages in maximally allowed speculation by equity in favorable market conditions even when they do n setting cGðwÞ¼pG ¼ 5forw 2ð0:0219,0:0593Þ. not have immediate funding needs. As simple as this Hedging lowers the firm’s precautionary holding of market timing behavior by the firm appears to be, we cash and, hence, lowers its payout boundary from 0.371 show that it has subtle implications for the dynamics of (no hedging benchmark) to 0.355 in state G and from corporate investment, risk management, and stock 0.408 to 0.385 in state B. Intuitively, because both cash returns. The key driver of these surprising implications hoarding and risk management mitigate financial con- is the finite duration of favorable financing conditions straints, they act as substitutes for each other. Leland combined with the fixed issuance costs firms incur when (1998) studies the effect of agency costs on leverage and they tap equity markets. Finally, we highlight how much a risk management and finds that risk management allows firm that optimally times equity markets and holds the firm to choose a higher leverage. We find that risk optimal precautionary cash buffers is able to shield itself management allows the firm to lower its cash holding, against large shocks to external financing conditions. although the mechanism is different from Leland (1998). A firm entering a crisis state with an optimally replen- For sufficiently low cash holdings, the ability to spec- ished cash buffer in good times is able to maintain its ulate lowers the firm’s issuance boundary wG because the investment policy almost unaltered and, thus, substan- marginal value of cash for a firm with speculation or tially smooth out adverse external financing shocks. hedging opportunity is higher. The ability to increase the One natural question for future research is how would volatility of the cash accumulation process makes the time-varying financing conditions interact with time-varying equity issuance option more valuable and hence causes investment opportunities to affect firms’ financing con- the issuance boundary wG to be lowered from 0.0268 (no straints. Our analysis in Appendix D shows that a firm with hedging or speculation benchmark) to 0.0219. positively correlated financing and investment opportunities Froot, Scharfstein, and Stein (1993) argue that hedging in- can sometimes be more financially constrained than when creases firm value by mitigating its underinvestment pro- the two are negatively correlated. Another interesting ques- blem. We show that this result does not hold generally in a tion is how time-varying uncertainty about the financing dynamic setting. For sufficiently high cash holdings, hedging conditions could affect corporate decisions. Bloom (2009) mitigates the firm’s underinvestment problem by reducing studies uncertainty shocks about productivity for financially P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 59 unconstrained firms. The recent financial crisis suggests that A.2. Solution of the n-state model uncertainty shocks about external financing conditions can potentially have first-order effects on investment and output Under the first best, the HJB equation for the n-state as well. model is X FB b FB 1 FB 2 FB FB b FB FB r q ¼ m i y ði n Þ þq ði dÞþ z 0 ðq 0 q Þ, s s s s 2 s s s s s ss s s Appendix A. General model setup s0as ð38Þ Our analysis in the paper focuses on the special case of where for each state s ¼ 1, ...,n the average q is given by two states of the world. It is straightforward to generalize FB FB our model to a setting with more than two states, denoted qs ¼ 1þysðis nsÞ: ð39Þ by st ¼ 1, ...,n. The transition matrix in the n-state Markov While there are no closed form solutions for n42, it is chain is then given by f ¼½zij.Then-state Markov chain can straightforward to solve the system of nonlinear equa- capture aggregate and firm-specific shocks, as well as tions numerically. productivity and financing shocks. In sum, the firm’s With financial frictions, the HJB equation is general- expected return on capital, volatility, and financing costs ized from Eq. (11) as follows: could all change over time under the general formulation. b rsPðK,W,sÞ¼max½ðrslÞW þmsKIGðI,K,sÞPW ðK,W,sÞ I 2 2 ss K A.1. Risk adjustments þ PWW ðK,W,sÞþðIdKÞPK ðK,W,sÞ X2 b 0 To determine the adjustments for systematic risk in þ zss0 ðPðK,W,s ÞPðK,W,sÞÞ, ð40Þ s0as the model, we assume that the economy is characterized by a stochastic discount factor (SDF) Lt, which evolves as for each state s ¼ 1, ...,n, and W s rW rW s. As before, X firm value is homogeneous of degree one in W and K in d Lt M kðst ,st Þ ðst ,st Þ ¼rðst Þ dtZðst Þ dZt þ ðe 1Þ dMt , each state, so that Lt st ast PðK,W,sÞ¼psðwÞK, ð41Þ ð35Þ where ps(w) solves the following system of ODE: where r(s) is the risk-free rate in state s, ZðsÞ is the price of 2 M b 0 ss 00 risk for systematic Brownian shocks Zt , kði,jÞ is the rspsðwÞ¼max½ðrslÞwþmsisgsðisÞpsðwÞþ ps ðwÞ i 2 relative jump size of the discount factor when the Markov s X ði,jÞ 0 b þðisdÞðp ðwÞwp ðwÞÞþ z 0 ðp 0 ðwÞp ðwÞÞ: chain switches from state i to state j, and Mt is a s s ss s s s0as compensated Poisson process with intensity zij, ð42Þ dMði,jÞ ¼ dNði,jÞz dt, iaj: ð36Þ t t ij The boundary conditions in each state s are then defined In Eq. (35),wehavemadeuseoftheresultthatann-state in similar ways as in Eqs. (13)–(16). continuous-time Markov chain with generator ½zij can be equivalently expressed as a sum of independent Poisson Appendix B. Calibration ði,jÞ a processes Nt (i j) with intensity parameters zij (see e.g., Chen, 2010).20 The above SDF captures two different types of We use annual data from COMPUSTAT to calculate the risk in the market: small systematic shocks generated by the moments of the investment-capital ratio and cash-capital Brownian motion, and large systematic shocks from the ratio for our model calibration. The sample is from 1981 M to 2010 and excludes utilities (Standard Industrial Classi- Markov chain. We assume that dZt is partially correlated A fication (SIC) codes 4900-4999) and financial firms (SIC with the firm’s productivity shock dZt , with instantaneous correlation r dt. Chen (2010) shows that the SDF in codes 6000-6999). We require firms to be incorporated in Eq. (35) can be generated from a consumption-based asset the United States and have positive assets and positive net pricing model. PPE (property, plant, and equipment). In addition, because The SDF defines a risk-neutral probability measure Q, our model does not allow for lumpy investment, mergers under which the process for the firm’s productivity shocks and acquisitions, or dramatic changes in profitability, we becomes Eq. (6). In addition, if a change of state in the eliminate firm-years for which total assets or sales grew Markov chain corresponds to a jump in the SDF, then the by more than 100% or investments exceeded 50% of corresponding large shock carries a risk premium, which capital stock from the previous year. leads to an adjustment of the transition intensity under Q Capital investment is measured using capital expendi- as follows: ture (CAPXt). Because our calibrated model does not allow for short-term debt, we measure cash holdings as the b kði,jÞ a zij ¼ e zij, i j: ð37Þ difference between cash and short-term investments

(CHEt) and average short-term borrowing (BASTt). Capital stock is the total net PPE (PPENTt). Then, the cash-capital ratio for year t is defined as ðCHEtBASTtÞ=PPENTt, and the 20 investment-capital ratio for year t is CAPX =PPENT .We More specifically, theP process s solves the following stochastic t t1 ðst ,kÞ differential equation: ds ¼ d ðs Þ dN , where d ðÞ¼j ji. t kast k t t k first compute moments for the cash-capital ratio and the 60 P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 investment-capital ratio at the firm level and then cali- the firm in state s. The technology beta is large when the brate the model parameters to match the moments of the marginal value of cash relative to firm value is high. The median across firms. financing beta is large when the probability that financing conditions will change is high or when the change in Appendix C. Beta representation financing conditions has a large impact on firm value.

Because this model has two sources of aggregate risk, the CAPM does not hold. Instead, expected returns reflect Appendix D. Correlated investment and financing aggregate risk driven by a two-factor model. We, thus, opportunities assume that there are two diversified portfolios T and F, each subject only to one type of aggregate shock, the To focus on the effects of stochastic financing shocks, technology shock or financing shock. Suppose their return we set the productivity shocks to be i:i:d in the paper. dynamics are given as In this appendix, we relax this restriction and explore the implications of correlation between investment and dRT ¼ðr þ T Þ dt þ T dZM ð43Þ t s ms ss t financing opportunities. and We conduct the following thought experiment. Sup- pose two firms face identical financing conditions as in F F kF 1 kF 2 ¼ð þ Þ þð 1 Þ þð 2 Þ ð Þ dRt rs ms dt e 1 dMt e 1 dMt : 44 the benchmark model (determined by the states G and B). Then, the stochastic discount factor in Eq. (35) implies To make the two states symmetric, we assume the risk- that neutral transition intensities are the same in the two states. Firm 1’s investment opportunities are positively T ¼ T ð45Þ ms ss Zs correlated with financing opportunities. That is, its and expected return on capital (i.e., expected productivity

F shock ms) is higher when the financing cost (fs) is lower. F ks ks ms ¼ zsðe 1Þðe 1Þ: ð46Þ The opposite is true for Firm 2, in that ms is higher when We can now rewrite the risk premium in Eqs. (43) and the financing cost (fs) is higher. (44) using betas as follows: Fig. D1 plots the investment-capital ratio for the two firms in state G (with low financing costs) and B (high R T T F F ms ðwÞ¼bs ðwÞms þbs ðwÞms , ð47Þ financing costs). Not surprisingly, Firm 1 has higher where return on capital in state G and, thus, invests more in this state, while the opposite is true in state B,espe- r s p0 ðwÞ bT ðwÞ¼ s s s ð48Þ cially when cash holdings are high. Firm 1 on average s sT p ðwÞ s s holds onto more cash in state G than Firm 2, but less in and state B (as indicated by the payout boundaries on the right ends of the curves). These results indicate that F ps ðwÞpsðwÞ bs ðwÞ¼ F ð49Þ Firm 1 can sometimes have a stronger precautionary p ðwÞðeks 1Þ s motive than Firm 2 due to the fact that better invest- are the technology beta (beta with respect to portfolio T) ment opportunities call for more cash holding to reduce and financing beta (beta with respect to portfolio F) for underinvestment.

0.2 0.2

0 0

−0.2 −0.2

positive correlation negative correlation −0.4 −0.4 0 0.05 0.1 0.15 0.2 0.25 0 0.1 0.2 0.3 0.5

Fig. D1. Investment-capital ratio for firms with different correlation between investment and financing opportunities. The financing costs are the same as in our benchmark model (see Table 1 in the paper). We assume Firm 1 has m ¼ 22:7% and m ¼ 19:7%. Firm 2 has m ¼ 19:7% and m ¼ 22:7%. Finally, b b G B G B we set the risk-neutral transition intensities zG ¼ zB ¼ 0:1. (A) State G and (B) State B. P. Bolton et al. / Journal of Financial Economics 109 (2013) 40–62 61

0.01 0.5

0.005 0

0 −0.5 −0.005 −1 −0.01

−1.5 −0.015

−0.02 −2 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4

Fig. D2. Differences in the marginal value of cash for two firms with different correlation between investment and financing opportunities. Panels A and B plot the differences in the marginal value of cash in states (A) G and (B) B, respectively. See Fig. 1 caption for details of the setup.

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