### Cash Holdings and Credit Risk (1 of 2)

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**ABSTRACT**

Intuition suggests that firms with higher cash holdings should be ‘safer’ and have lower credit spreads. Yet empirically, the correlation between cash and spreads is robustly positive. This puzzling finding can be explained by the precautionary motive for saving cash, which in our model causes riskier firms to accumulate higher cash reserves. In contrast, spreads are negatively related to the part of cash holdings that is not determined by credit risk factors. Similarly, although firms with higher cash reserves are less likely to default in the short term, endogenously determined liquidity may be related positively to the longer-term probability of default. Our empirical analysis confirms these predictions, suggesting that precautionary savings are central to understanding the effects of cash on credit risk.

**INTRODUCTION**

Common intuition suggests that firms that have larger cash holdings in their asset and investment portfolio should be ‘safer.’ In particular, cash-rich firms should have a lower probability of default and lower credit spreads, other things equal. In this paper, we argue that, in general, other things are not equal, and that the intuitive, but na¨ıve, prediction falls prey to the confounding effects of endogeneity. We show empirically that a conservative cash policy is more likely to be pursued by a firm that finds itself close to distress. As a result, larger cash holdings are empirically associated with higher, not lower, levels of credit risk.

Our theoretical argument can be summarized as follows: The firm is a portfolio of assets, of which cash is one, and the composition of assets in the portfolio depends on the firm’s liability structure. In particular, when the risk of default increases, the firm increases its holdings of liquid assets in response. This adjustment offsets the change in risk, but only partially. As a result, a higher level of cash reflects changes across the firm’s assets and liabilities, but does not necessarily imply a safer firm overall.

We take predictions from this simple argument to the data to explore complex interactions between cash policy and credit risk. Two of our empirical results are particularly striking and counter-intuitive. First, when we replicate the reduced-form approach commonly used in empirical studies of credit spreads, we find that a one standard deviation increase in the cash-to-asset ratio is associated with an economically significant 20 basis point increase in credit spreads, after controlling for firm-specific characteristics such as leverage, volatility, and credit rating. Thus, it may appear that higher cash holdings increase credit spreads. The effect is robust and persistent.

Second, we explore the role of
liquid assets in empirical default-predicting models, such as Altman’s (1968) z-score.^{1} While almost all such studies control for
balance sheet liquidity, their findings concerning the effect of liquidity on the
probability of default are inconclusive and often puzzling.^{2} When we re-estimate such models, we find that the correlation
of liquidity with default depends crucially on the time horizon over which default is
being considered. The short-term probability of default is lower when liquid asset
reserves are large, consistent with the common intuition. However, for horizons over one
year, the correlation between cash and default reverses sign and becomes positive and
strongly statistically significant. It would appear that higher cash holdings increase the
long-term probability of default.

What can explain these puzzling empirical findings? We propose a theory based on the endo- geneity of a levered firm’s cash policy. In the presence of financing constraints, riskier firms (for example, those with lower expected cash flows) optimally choose to maintain higher cash reserves as a buffer against the possible cash flow shortfall in the future. In the model, the firm firm can either invest its cash long term, or retain it as a cash buffer until the firm’s debt comes due. Market frictions restrict the firm’s access to external capital, and default is costly. The firm faces a trade-off between investing more (and getting higher cash flows in the future, conditional on not defaulting) and keeping more cash in a reserve (implying a lower probability of a cash shortage and thus a higher chance of survival).

In this model, a change in factors that affect the firm’s credit risk influences spreads and default probabilities through two channels: directly (the ‘direct’ channel), and through the adjustment in the level of cash holdings (the ‘indirect’ channel). For example, a decline in expected future cash flows leads to an increase in default probability and a corresponding rise in credit spreads. At the same time, the firm responds by optimally increasing its cash holdings, which reduces the probability of a cash shortfall and leads to lower spreads. The model’s main insight is that the direct channel dominates as long as constraints on external financing are binding. As a result, riskier firms have both higher optimal cash reserves and higher credit spreads and long-term default probability. Consistent with this prediction, we find empirically that for speculative-grade firms cash holdings increase in credit risk, as do credit spreads.

The model also implies that variations in cash holdings that are unrelated to credit risk factors (so that there is no direct effect on spreads) should be negatively related to spreads, in line with the standard intuition. Indeed, we find empirically that the correlation between cash and spreads, as well as that between cash and longer-term default probability, turns negative when we ‘instrument’ the variations in cash by such variables as proxies for managerial self-interest and firm’s long-term investment opportunities. Finally, the model also predicts that over a short horizon, higher cash reserves reduce the prob- ability of default (consistent with the findings of Davydenko (2011)), but may increase it over a longer period, reconciling the seemingly conflicting evidence of the effect of cash holdings in default- predicting studies.

Our findings highlight the importance of
adopting the corporate finance prospective in asset pricing studies. For instance, extant
credit risk models typically assume that should the firm find itself in a temporary cash
shortage, it avoids default by costlessly selling new equity, as long as the share price
remains positive, rendering cash policy irrelevant.^{3} This approach is mirrored in empirical credit risk studies,
which also do not consider the role of cash holdings.^{4} Our results suggest that theoretical and empirical studies of
credit risk (and likely other areas of asset pricing) should account for the endogeneity
of corporate financial and investment policies.^{5} Otherwise, employing the most common balance-sheet ‘control’
variables (such as proxies for corporate liquidity) in standard tests (such as predictive
regressions of default) may yield economically misleading conclusions.

Our paper is related to the stream of papers in corporate finance on the endogenous determination of corporate cash holdings, such as Opler, Pinkowitz, Stulz, and Williamson (1999), Almeida, Campello, and Weisbach (2004), and Bates, Kahle, and Stulz (2009). In this literature, the precau- tionary motive for hoarding cash arises because of financing frictions that restrict firms’ access to external financing. Recently, studies such as Eisfeldt and Muir (2012) have extended this approach to look into the implications of financial constraints for the dynamics of financing and cash holdings. However, extant research does not explicitly link cash holdings to credit risk or credit spreads, as we do. Moreover, we show that precautionary motives for saving cash are of first-order importance even for rated public bond issuers, suggesting that these firms exhibit behavior qualitatively similar to that of more financially constrained firms.

**1. The model**

This section develops a model of a firm’s optimal cash policy in the presence of costly default and restricted access to external financing. Our main goal is to show that cash holdings in equilibrium can be positively correlated with credit spreads and default risk, and to discuss the economic mechanisms behind this counter-intuitive relationship. We disentangle the intuitive, but na¨ıve, prediction that cash-rich firms should be ‘safer’ from the confounding effects of endogeneity. As discussed in Section 1.2, although the model is stylized, our conclusions are quite general. In an online appendix we develop a continuous-time model of endogenous cash policy, which delivers the same main results as outlined in this section.

**1.1. Model setup**

The model features a
single levered firm in a three-period investment economy. The firm has both assets in
place and growth opportunities. In each period t from 0 to 2, its assets in place produce
a cash flow xt . For our purposes, it is important that the interim-period cash flow x1 is
random and unknown at date 0. We can write x1 as x1 = x1 + u, where x1 is a known constant
and u is a zero-mean random cash flow shock. The probability distribution of u is
described by the density function* g(u)* with support [u, ∞),^{6} and with the associated cumulative distribution function *G(u)*
and the hazard rate *h(u)*, defined as:

We assume the hazard rate *h(u)* to
be weakly monotonically increasing.^{7} For our
purposes, it is sufficient that the cash-flow shock u is the only source of randomness in
the model, and hence we assume that the cash flows at dates 0 and 2 are known. As will
become clear below, the timing in the model is such that allowing for a random component
in these cash flows would neither alter shareholders’ incentives nor affect our results in
any way.

At date *t = 0*, the assets in place generate a positive cash flow *x*_{0} > 0. At
this time, the firm has access to a long-term project, which in return for investment
* I* at

*t*= 0 yields a deterministic cash flow of f

*(I )*at

*t*= 2, where

*f*(I ) is a standard increasing concave production function. Market frictions preclude the firm from accessing outside financing, so that the firm’s disposable cash comes entirely from its internal cash flow, x0. This cash can be invested, either partially or fully, in the long-term project, or retained within the firm as a cash reserve, carried over from date 0 to date 1. We denote the cash reserve as

*c*

_{,}_{ }so that

*c = x*.

_{0}− I
At date *t* = 1, the firm must make a debt payment of *B*, which is assumed to be
predetermined (a legacy of the past).^{8} We also assume that debt cannot be
renegotiated due to high bargaining costs; for example, it might be held by
dispersed bondholders prone to co-ordination problems. Failure to repay the debt
in full at t = 1 results in default and liquidation, in which future cash flows both
from the long-term investment, *f (I )*, and from the assets in place, *x _{2}* , are lost.
As the period-1 cash flow, x1 , is random, there is no assurance that it will be
sufficient to repay the debt in full. Moreover, due to market frictions, external
financing is unavailable, and hence the debt payment must be made out of the firm’s
internal funds. This gives rise to incentives for the firm to retain part of its cash
between periods 0 and 1 as a buffer against a possible future cash shortfall, to reduce
the probability of default.

The firm’s equityholders maximize the final-period payoff. The risk-free rate of interest is nor- malized to zero, and, in the base case, managers act in the best interests of shareholders. Figure 1 illustrates the model’s timeline.

**FIgure 1**

The timeline of the model.

Before proceeding further, we want to stress that the exact specification of the model can vary widely without affecting the results qualitatively, as long as two assumptions are satisfied. First, default involves deadweight costs. (Although we assume that all future cash flows are lost in default, an extension to a partial loss is straightforward.) Second, external financing cannot be raised against the full value of future cash flows, meaning that there are some financing frictions at date 1. If the firm can pledge a large enough fraction of its future cash flows as collateral, then current and future cash holdings can be viewed as time substitutes, and there is no role for precautionary savings of cash. In reality, the condition of partial pledgeability is likely to be universally met. While the base-case model assumes that external financing is prohibited altogether, Subsection 1.6 extends the model by allowing the firm to borrow up to a certain fraction of its future cash flows at t = 1, and shows that our main results hold as long as financing constraints are sufficiently binding.

A related feature in our model is that a non-trivial part of the cash flow from the current investment will be realized only after a portion of the outstanding debt is due, giving rise to a time mismatch between cash flows and liabilities. Effectively, the expected long-term cash flow can neither be pledged nor used as cash to cover debt obligations. In practice, most capital expenditure items are likely to satisfy this requirement, because they usually generate cash flows after some non- trivial debt payments. In the base-case model, we assume that the investment outcome is realized in full only at date 2. This assumption can be relaxed so that the investment also can generate a cash flow at date 1. What is needed is a non-trivial fraction of cash flows expected after the debt payment is due, so that firm survival at the intermediate stage is a worthy option.

In general, in addition to saving and investing, firms can
also distribute some of the cash to their shareholders. Fixed, pre-committed dividends at
*t* = 0 amount to a reduction in the net cash flow *x _{0}*, and can
be easily incorporated in the model. Although modeling an optimal dividend policy at

*t*= 0 would complicate the analysis considerably by introducing a second choice variable, the intuition is straightforward. Most firms in the model would choose not to pay any dividend, because the cash can be profitably invested in the long-term project. However, if the firm is very risky, the precautionary motive for saving cash can be dominated by the incentives to engage in ‘asset substitution’, i.e., to pay out a large immediate dividend at the expense of making the firm even riskier. In our base-case model, we assume that in order to prevent such behavior, discretionary dividends are prohibited by covenants.

If the firm has access to external capital at *t* = 0, it can
choose to raise additional capital at that time to increase its investment and/or cash
holdings. Selling equity can be viewed as making a negative dividend payment. By the same
logic as above, in our model a firm should normally find it desirable to raise equity, as
long as the marginal value of an additional dollar of investment is greater than one.
However, if the firm is very risky, instead of investing, shareholders would have
incentives to pay themselves a dividend rather than contribute additional equity. By
contrast, raising debt maturing at *t* = 1 that is more senior than the existing
debt solely in order to increase the cash reserve is value-neutral in this setting, as the
increase in cash is exactly offset by the increase in the required debt repayment (i.e.,
cash is negative debt in our model). In our base-case model, we assume that financing
constraints at *t* = 0 preclude the firm from accessing any additional financing.
Allowing for optimally chosen financing ex ante could be an interesting extension of our
model.

To assert the generality of our main results, we have constructed a fully dynamic continuous-time model that relaxes some of the assumptions of the base-case model. In the model, the firm is financed by equity and infinite-maturity debt with continuously paid coupon. In contrast with the base-case model, investment is fixed, but dividends are endogenously determined. The firm’s cash flow is first used for debt service. The remainder can be paid out as dividends or retained within the firm as a buffer against a possible cash flow shortage. The firm faces a trade-off between higher dividends and higher cash reserves that reduce the probability of default. Although this setting is very different from the base-case model, its main predictions regarding the relationship between cash and credit risk are very similar. A full description of this model can be found in the online appendix, also available from the authors upon request.

Returning to the base-case model, note that cash reserves are costly to the firm because they are financed by reductions in long-term investment. This way of modeling the cost of cash holdings is convenient, but by no means unique. For example, Kim, Mauer, and Sherman (1998), Anderson and Carverhill (2007), and Asvanunt, Broadie, and Sundaresan (2007) assume that cash has a convenience yield because of taxes or agency issues. In our model, forgone investment should be understood more broadly as the opportunity cost of cash. For example, in our continuous model outline above, investment is fixed but the dividend policy is optimally determined. In that model, the opportunity cost of retaining cash is represented by the value of unpaid dividends.

**1.3. Optimal cash policy**

At date 0, the firm faces the following trade-off between investing its cash in the
long-term project and retaining it until the next period. On the one hand, larger retained
cash holdings imply lower investment. This results in lower future cash flows generated by
the long-term investment conditional on survival in the interim period. On the other
hand, an increase in cash holdings reduces the probability of a cash shortage at date 1,
and thus increases the likelihood that the firm survives until date 2 to reap the benefits
of the long-term investment. The firm’s optimal cash and investment policies balance these
costs and benefits of cash.^{9}

The amount
of cash available for debt service at date 1 is c + x1 , where c = x0 − I is the cash
reserve and *x _{1}* =

*x*

_{1}+

*u*is the interim-period cash flow from assets. The ‘default boundary,’ or the minimum cash flow shock that allows the firm to repay

*B*in full and avoid default, is:

^{10}

The default boundary
increases in the level of debt and sunk investment, and decreases in realized date-0 and
expected date-1 cash flows. For all realizations of u between u and uB , the firm
defaults and equityholders are left with nothing. The total payoff to equityholders
is the sum of the cash flows from assets in place and the payoff from the long-term
investment, less the invested amount and the debt repayment, provided that the firm
does not default on its debt in the interim. The market value of equity is
therefore:

which can also be rewritten intuitively as:

Here, *u − u _{B}* is the amount of cash left in the firm after B
is repaid, and

*f (I ) + x*is shareholders’ claim on period-2 cash flow, conditional on the firm not defaulting in the interim.

_{2}
Managers maximize the value of equity by choosing the optimal level of
investment. From Equation (3), equityholders’ optimization problem yields the following first-order
condition:^{11}

Substituting the expression for xB from Equation (2) and rearranging, we can rewrite
this first-order condition as:

In the first-best case of
unrestricted investment, the standard maximization solution would yield *f(I)* =
1. In the presence of costly default and restricted access to outside financing,
investment is below its first-best level. This follows from Equation (6), given that
the right-hand side is greater than one. To understand the intuition behind the optimal
investment and cash policies, notice that the first-order condition (5) can be re-written
as follows:

The left-hand side in Equation (7) is the net value gain
from increasing investment by d*I* , which is equal to *(f(I)*− 1) d*I* , multiplied by
1 − *G(u _{B})* to condition on the probability of survival. The right-hand side gives
shareholders’ marginal expected loss from default, equal to the value of equity at the
default boundary,

*f(I ) + x*, multiplied by the marginal increase in the probability of default due to the shift in the default boundary,

_{2}*g(u*d

_{B})*u*.

_{B}
The market value of the firm’s debt, *D*, is:

which equals the face value of debt *B* adjusted for the loss that creditors expect to
incur in default states [*u, u _{B}*]. (Note that creditors recover

*c + x*in case of default.)

_{1}With the riskless interest rate at zero, the credit spread, denoted *s*, coincides with
the total debt yield, given by:

**1.4. Cash holdings and credit spreads**

In this subsection, we study the correlation between credit spreads and cash reserves, which arises when they both adjust in response to changes in model parameters.

The effect of any variable *y* on the credit spread can be decomposed into two components,
which we call direct and indirect effects. First, the spread may depend on y directly,
for example, because *y*affects the default boundary and hence the likelihood of default.
Second, a change in *y* may induce a change in the optimal cash reserve *c*, which in turn
alters the default boundary and thus affects spreads (an indirect effect through
cash).

It is convenient to introduce a special term for variations in cash not induced
by changes in credit risk factors. Formally, suppose that cash holdings depend on a
variable y that does not affect spreads directly, so that *∂s/∂y* = 0. In particular,
within our model this condition implies that *y* does not enter the expression for
the default boundary *u _{B}* , nor does it affect the distribution of the time-1 cash flow,
g(u). When all other variables are fixed,

*y*can affect spreads only indirectly, through its effect on cash. We will refer to changes in cash holdings induced by changes in variables that do not affect spreads directly as ‘exogenous’ (to credit risk). By contrast, variations in cash are ‘endogenous’ (to credit risk) if they are induced by changes in credit risk factors. It should be emphasized that an ‘exogenous’ variation in cash need not be due to factors outside the firm’s control. Instead, it can arise as the firm optimally adjusts its cash policy in response to changes in firm characteristics that have no direct effect on credit spreads.

**1.4.1. Endogenous variations in cash**

A change in many variables that affect spreads directly may also cause cash to adjust in the same direction, so as to undo the direct effect partially. For example, a direct effect of a drop in the expected cash flow is to raise the yield spread. However, optimal cash holdings also increase, which in turn decreases the spread (the indirect effect of the drop in cash flow). Other variables, such as the level of debt and the volatility of cash flow, may produce similar effects. This subsection shows that such adjustments in cash can result in a positive correlation between cash holdings and credit spreads in the cross-section.

Let ‘^{∗}’ denote the equilibrium values of the variables, so that *I*^{∗}
and *c ^{∗} = x_{0} − I^{∗}* are the
equilibrium levels of investment and cash holdings, and

*s*

^{∗}= s(c

^{∗}) is the credit spread when

*I = I*. The following Proposition summarizes the effect of changes in the expected date-1 cash flow,

^{∗}*x1*on cash holdings and spreads (see Appendix for all proofs):

When the expected cash flow decreases, the probability of a cash flow shortage at the time of debt repayment increases, so that the direct effect is to make the firm riskier and to raise the credit spread. The first part of Proposition 1 states that the firm’s optimal response is to alleviate the increase in risk by increasing its precautionary savings. This gives rise to the indirect effect of the decrease in cash flow, which is to reduce spreads. The second part of Proposition 1 states that the direct effect dominates, so that despite their larger cash holdings, firms with lower expected cash flows have higher credit spreads. In practice, this means that when cash flow levels are allowed to vary over time or in the cross-section, this variation can induce a positive correlation between endogenously chosen cash reserves and credit spreads.

To understand why the direct effect dominates, notice that for each dollar of decline in the expected cash flow, the firm increases its cash reserves by less than a dollar. This can be seen from the first-order condition (6), which balances the marginal cost of cash due to lower investment with its marginal benefit due to lower probability of default. Suppose that the expected cash flow decreases by $1, so that without any adjustments, the default boundary would drop by $1. In response, the firm reduces investment and increases the cash reserve, so that the boundary does not drop as much. However, since the production function is concave and the hazard function h(·) is non-decreasing, for the Equation (6) to be satisfied again, investment has to drop by less than
$1. Thus, the concavity of the production function makes one-for-one reductions in investment prohibitively costly. As a result, cash holdings increase by less than $1, so that the net effect of the drop in the expected cash flow is to reduce the default boundary and thus to increase the credit spread. The intuition behind this economic mechanism is quite general: If the cost of increasing cash levels to offset higher default risk is convex, the firm offsets default risk only partially, and the direct effect on spreads dominates.^{12}

As noted above, similar effects can arise due to variations in firm characteristics other than the cash flow, if they affect both spreads and optimal cash holdings. For example, suppose that the firm’s debt level increases. The direct effect of this increase is to raise spreads. However, optimal cash holdings also rise, which dampens the effect of higher debt levels on spreads. It can be shown that the direct effect dominates, much as in the case of varying expected cash flow in Proposition 1. As a result, more indebted firms have both higher cash levels and higher spreads, implying a positive cross-sectional correlation between the two. Similar effects may also arise when the initial cash flow, x0, is allowed to vary, or when the firm pays a fixed dividend that reduces its net cash flow (see Subsection 1.2).

**1.4.2. Exogenous variations in cash**

This subsection considers the effect of ‘exogenous’ variations in cash, which are not induced by changes in credit risk factors. It is easy to show that such cash variations are negatively correlated with credit spreads, consistent with the simple intuition that firms with more cash should be ‘safer’ and have lower spreads.

This Proposition states that when a factor that is unrelated to credit risk causes cash holdings to increase, credit spreads fall in response. In other words, spreads are negatively related to ‘exogenous’ (to credit risk) changes in cash.

In our empirical analysis, we refer to factors *y* that induce an exogenous variation in cash as instruments. To be an instrument, a variable must affect cash holdings without altering creditors’ payoffs or the probability of default other than through changes in cash. Put differently, an instru- ment would not affect spreads if cash were held constant. Formally, instruments in our model are variables that enter the first-order condition (Equation (6)), but not the expression for the value of debt (Equation (8)). Assuming that external financing cannot be raised against any part of period-2 cash flow, both the cash flow from assets in place, x2, and the parameters of the production function, ** f(·)**, satisfy these requirements. Variations in cash induced by changes in these variables would be negatively correlated with spreads.

**Example 1: Growth options.** The long-term cash flow from assets in place, x2, can be inter- preted as the value of the firm’s growth options. An increase in the growth option increases the value of equity conditional on survival, and hence enhances shareholders’ incentives to conserve cash to avoid default. At the same time, as this cash flow is not collateralizable, it does not benefit short-term creditors directly. Since the growth option does not enter the expression for the value of debt, it affects spreads only indirectly, through the induced variation in cash holdings. It follows from Proposition 2 that the resulting cross-sectional variation in cash is negatively correlated with credit spreads.

More generally, when external financing is not fully prohibited, a fraction of the long-term cash flow can be used as collateral in order to raise external financing. Anticipating this at *t* = 0, the firm would substitute some of its cash reserve with future external financing, which would enter the expression for the default boundary and thus affect the probability of default directly. Thus, not every long-term cash flow can provide an instrument. Only variations in the levels of those assets that the firm does not anticipate using as collateral at the time when it chooses its cash holdings (i.e., at *t* = 0) can play this role.1^{13} One example of an instrument would be any unanticipated shock to the firm’s cash that occurs between *t* = 0 and debt maturity.^{14} As discussed above, non-collateralizable long-term growth options also induce exogenous variations in cash. Other non-collateralizable assets, such as human capital, can play the same role.

It is worth emphasizing that in more general settings with multiple classes of debt, some variables can be used as an instrument for some debt obligations, but not for others. For example, if at time t a firm has two outstanding bonds with different maturities, *T _{1} < T_{2}*, then non-collateralizable assets that produce a cash flow between

*T*do not affect the value of the short-term debt but can affect the cash reserve at

_{1}and T_{2}*t*, and hence can be used as an instrument for analyzing the relationship between cash and the short-term credit risk. However, the cash flow from the same assets affects the value of the long-term debt directly (by increasing the amount of cash available at

*T*), and hence cannot be used as a long-term instrument.

_{2}^{15}

**Example 2: Managerial losses in distress. ** Another example of a non-collateralizable ‘asset’ is the private benefit that managers derive from avoiding default. Gilson (1989), Baird and Rasmussen (2007), and Ozelge and Saunders (2008) find that upon distress, there is a significantly higher probability of top-management dismissal, especially due to direct intervention by lending banks, and that managers dismissed in distress suffer a significant private cost in the form of diminished future employment opportunities. Eckbo and Thorburn (2003) find that in Sweden, where creditor rights include automatic firing of the manager in default, managers of bankrupt companies suffer a median (abnormal) income loss of 47%. Managers’ private costs of distress likely depend on the structure of their compensation contracts.^{16} Differences in managerial compensation across firms should thus result in different incentives for managers to save cash in order to avoid default, because the private costs differ. As a result, differences in compensation can induce an exogenous variation in cash holdings.

Consider the following extension of the base-case model. Assume that the firm’s risk-neutral manager owns a share *θ* > 0 of the equity *E* and incurs a fixed, private cost *γ* > 0 if the firm defaults. For a given ownership level θ, the manager’s incentives to retain cash increase with the private cost of distress *γ*. Conversely, given γ*γ*, they decline with her ownership of the firm θ. The overall effect on the manager’s chosen cash policy depends on the ratio of managerial cost to equity stake,*γ*, which can be interpreted as a measure of agency problems between the manager and equityholders. The higher the manager’s private cost of default and the lower her equity stake, the more conservative the firm’s cash policy (relative to one that maximizes the overall value of equity), resulting in lower credit spreads for the same underlying level of credit risk. Formally,the manager’s objective is to choose investment *I* to maximize:

As shown in the Appendix, this case is technically very similar to that of the variation in x_{2}, and the cross-sectional correlation between cash holdings and spreads induced by variations in the agency factor *γ* is thus negative.

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**NOTES**

1 Other prominent studies include Ohlson (1980), Zmijewski (1984), Shumway (2001), and Chava and Jarrow (2004)

2For example, the correlation of the probability of default with the current ratio is positive in Zmijewski (1984) and negative in Shumway (2001), whereas that with the ratio of working capital to total assets is negative in Ohlson (1980) and positive in Hillegeist et al. (2004).

3This assumption is made in most prominent credit risk models, such as Black and Cox (1976), Leland (1994), Longstaff and Schwartz (1995), Collin-Dufresne and Goldstein (2001), and others. Notable exceptions include recently developed models by Acharya, Huang, Subrahmanyam, and Sundaram (2006), Anderson and Carverhill (2007), Gamba and Triantis (2008), Asvanunt, Broadie, and Sundaresan (2010), and Gryglewicz (2011), which allow for optimal cash holdings in the presence of costly external financing.

4E.g., Collin-Dufresne, Goldstein, and Martin (2001), Duffee (1998), and Schaefer and Strebulaev (2008).

5Although the endogeneity of firm characteristics is recognized as a major issue in empirical corporate finance and many other areas of economic research (Roberts and Whited (2012)), it appears to have attracted less attention in asset pricing studies.

6Although the firm’s cash flow can be negative, it is bounded from below by investors’ limited liability. We assume that the minimum cash flow shock, u, is large enough for the limited liability to be satisfied.

7This assumption is unrestrictive and often appears in economic applications, such as game theory and auctions (e.g., Fudenberg and Tirole (1991, p.267)). Bagnoli and Bergstrom (2005) show that the hazard rate is weakly monotonic if the function (1 − G(u)) is log-concave, which holds for uniform, normal, logistic, exponential, and many other probability distributions.

8Although firms can choose not only cash holdings but also debt levels, variations in cash holdings are likely to be much larger than those in leverage ratios. To test this conjecture, we use annual Compustat data between 1980 and 2006, focusing on non-financial firms with non-trivial debt amounts (book leverage above 5%). We find that for the median firm, the coefficient of variation (standard deviation divided by the mean) for cash as a proportion of total assets is 0.80, compared with 0.36 for total debt over total assets and only 0.27 for book equity over total assets, with differences significant at the 1% level. Thus, cash holdings are likely to be more easily adjusted than debt levels. Therefore, in our analysis of the optimal cash policy we treat debt as exogenous.

9Covenant restrictions may prevent the firm from investing at the optimum. Should this be
the case, the firm may end up with excessive cash reserves (from equityholders’ point of
view) and our results are likely to be strengthened.
10Without loss of generality, we
assume that u_{B} ≥ u.

11It is easy to show that the second-order condition for maximization is satisfied. We also assume that initial cash holdings are high enough for the first-order condition to yield an interior solution.

12This discussion underscores the importance of financing constraints. If the firm can pledge a sufficiently high proportion of its long-term cash flow to creditors as collateral, long-term income can play only a secondary role as a cash substitute. The marginal cost of cash holdings is then effectively reduced and Proposition 1 may not hold. We discuss the case of partially pledgeability in Subsection 1.6.

13We would like to thank the referee for pointing out this property of instruments.

14For example, if the firm obtains an unexpected settlement in a lawsuit (see Blanchard et al (1994)), its cash reserve increases exogenously and its debt becomes safer as a result of the change in cash.

15Simutin (2010) also finds that firms with growth options hold more cash. He suggests that if growth options are risky, then cash holdings might be positively related to firm riskiness. Our model clarifies that firm riskiness induced by growth options may not necessarily be related to credit risk, if on average growth options arrive beyond the maturity of the firm’s debt. Thus, whether cash holdings induced by growth options are independent of the firm’s credit risk depends on the debt’s maturity structure, and is ultimately an empirical question, which we examine in Section 3 below.

16Managerial incentives have also been shown to be important in studies of capital structure (Carlson and Lazrak (2010)) and corporate takeovers (Pinkowitz, Sturgess, and Williamson (2011)).

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