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

**1.5. Cash policy and the probability of default**

Another important question concerns the relationship between cash and the probability of default. In this subsection, we show that the correlation between the two depends on the horizon over which the likelihood of default is measured. Managers choose the optimal cash policy taking into account the probability of default over the long term. By contrast, in the presence of market frictions it is difficult for a distressed firm to adjust its cash balances to desired levels on a short notice. Therefore, the relationship between cash and default in the short term should be studied conditional on past cash and investment choices.

In our discrete-time model, the instantaneous probability of default is zero almost everywhere, except for the moment just before the scheduled debt repayment at *t* = 1, that is, after the random cash flow *x*_{1} is realized. Whether the firm defaults at that moment depends on the total amount of cash available at that time, which is equal to the sum of the firm’s cash reserve c chosen earlier and the realization of the random cash flow *x*_{1}. The firm defaults if the total cash amount is smaller than the required debt payment. Thus, ceteris paribus, the instantaneous probability of default is inversely related to the firm’s total cash holdings.

By contrast, for long horizons the endogeneity of cash holdings is crucial. In our model, the long-term probability of default evaluated at date 0, *q*, is given by:

To study how cash reserves are related to the probability of default at this point, consider the effect of variation in the date-1 expected cash flow, *x*_{1}. According to Proposition 1, as *x*_{1} increases, shareholders optimally decrease the cash reserve *c ^{∗}* at t = 0. Similar to the effect on credit spreads, there are two effects on the probability of default

*q*, direct and indirect. On the one hand, a higher expected cash flow results in a lower default probability (the direct effect). On the other hand, a smaller chosen cash reserve means a larger probability of default (the indirect effect). As the next proposition shows, the direct effect dominates:

Proposition 3. *The probability of default evaluated at t = *0*, q, is a decreasing function of x _{1}*.

The intuition for why the direct effect dominates is similar to that for the relationship between cash and spreads. As the expected date-1 cash flow increases by $1, optimal cash reserves decrease by less than $1 due to the concavity of the production function, so that shareholders are indifferent at the margin between higher investment returns and lower probability of realizing them due to the interim probability of default. Note that, as with the relationship between cash and credit spreads, other parameters (such as the level of debt) can induce the same result.

At the same time, exogenous variations in cash holdings are negatively correlated with the long- term probability of default. Once again, this relationship mirrors that for credit spreads, which is discussed in detail in Section 1.4.2.

**1.6. The effect of partial pledgeability**

In our base-case model, the firm has no access to external financing. In this subsection, we extend the model to consider the effect of partial pledgeability of future cash flows. Suppose that at *t* = 1 the firm can use a fraction τ of its future cash flow (which equals *f(I) + x _{2}*) as collateral for new financing, where 0 ≤ τ < 1. Here, τ = 0 corresponds to our base case of extreme financing frictions, when the firm cannot raise any external financing against its future cash flow, whereas τ = 1 implies frictionless access to external capital.

^{17}

Conditional on survival, raising new financing at *t* = 1 in this setting is value-neutral. Therefore, we can assume without loss of generality that the firm always raises the maximum available amount,
τ *f(I) + x _{2}*). Thus, cash available for debt service at date 1 is

*c + x*), which is the sum of the cash reserve c, the random cash flow x1 = x1 + u, and the newly borrowed amount τ

_{1}+ τ (f (I ) + x_{2}*f(I) + x*). The ‘default boundary,’ or the minimum cash flow shock that allows the firm to repay

_{2}*B*in full and avoid default, is:

The value of equity can be written as:

where *u − u _{B}* is the amount of cash left in the firm after

*B*is repaid, and (1 − τ ) (

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

_{2}As previously, changes in model parameters can affect spreads directly and indirectly. The following Proposition states that variations in the expected cash flow produce a positive correla- tion between equilibrium cash holdings and credit spreads, provided that financing constraints are sufficiently binding:

The first part of Proposition 4 is a generalization of the result obtained earlier for τ = 0. The second part states that there exists a minimum level of financing constraints above which the direct effect of the variation in x* _{1}* dominates, so that cash and spreads change in the same direction. Thus, Proposition 1 is a special case of Proposition 4, corresponding to τ = 0. We conclude that our main prediction holds in situations when access to external financing is possible, provided that market frictions are restrictive enough.

It is worth noting that when asset pledgeability τ is high, an increase in expected cash flow x1 may for some combinations of functions *f* and *h* result in higher credit spreads because of the following ‘asset substitution’ problem. When investment cash flows are highly pledgeable, and when investment productivity is declining only slowly, an increase in the interim cash flow by one dollar can induce an increase in investment by more than a dollar, as shareholders expect to be able to borrow more against a larger pool of collateral at *t* = 1. Thus, the composition of funds available for debt service shifts toward a lower precautionary cash reserve in combination with higher new borrowing. Even though in the new equilibrium the probability of default is lower, in default states creditors’ recovery rates are disproportionately lower, because there is less cash in the firm, and long-term investments have no value in default. Thus, under such scenarios the overall effect of the increase in the expected interim cash flow may be to increase spreads.^{18}

**2. Data description**

This section describes our data and discusses the variables that we use in the empirical tests.

**2.1. Data sources and sample composition**

Our empirical analysis focuses on credit spreads and the probability of default. We restrict our attention to firms that issue public bonds, because private-debt defaults and credit spreads are difficult to observe. Information on bonds is from the Fixed Income Securities Database (FISD) provided by Mergent. Default data are from Moody’s Default & Recovery Database (DRD), which provides comprehensive information about defaults on rated bonds, including omitted payments, bankruptcy filings, and distressed bond renegotiations. Financial data are from Compustat, exec- utive compensation data are from ExecuComp, and estimates of the expected default frequencies (EDFs) are from Moody’s/KMV (MKMV). Finally, to estimate yield spreads, we use prices of bonds included in the Merrill Lynch U.S. Investment Grade Index and High Yield Master II Index. The pricing data consists of monthly bid quotes from Merrill Lynch’s bond trading desks, and is only available for a subset of bond issuers.^{19} Our sample extends from December 1996 (the month when the indices were created) to September 2010.

We construct our sample as follows. First, we merge data on non-financial U.S. firms in Com- pustat with information on bond issuers in FISD, taking account of mergers, acquisitions, name changes, and parent-subsidiary relationships between different bond issuers, and excluding firms which we cannot merge reliably. We thus obtain 2,247 unique firms that had at least one bond outstanding between 1996 and 2010. We use quarterly Compustat data to study the probability of default for these firms. To this end, we search for these firms in the DRD, and find that 541 of them defaulted during the sample period. Overall, the sample consists of 79,932 firm-quarter observations for 2,247 bond issuers at risk of default.

Bond pricing information is available from the Merril Lynch indices for 1,595 of our firms. To be able to estimate credit spreads accurately, we eliminate non-fixed coupon bonds, asset-backed issues, bonds with embedded options (such as callable, puttable, exchangeable, and convertible securities), and bonds with sinking fund provisions. We also exclude bonds with remaining time to maturity less than one year or more than thirty years, because risk-free yields that we use to estimate spreads are not available for these maturities. This leaves us with 530 firms, 35,206 firm-months, and 103,691 bond-month observations that we use to estimate bond spreads.

Table 1 shows the composition of our sample, as well as that of the subsample for which spreads are available.^{20} As can be seen from column (1), B-rated firms are the most common in the firm- quarter sample. In total, junk firms (those rated BB+ and lower) comprise 58% of all firm-quarters. This proportion is substantially smaller for the subsample of firms for which we have spreads: In column (3), junk firms add up to 23% of the spread subsample, while 68% of it are concentrated in the two lowest investment-grade categories, A and BBB. The reason why junk firms are under- represented in the subsample of spreads is that they are more likely to issue callable bonds, which we exclude for the purposes of spread analysis. As we explain below, our main results are driven primarily by risky firms, for which the possibility of a cash shortage looms large. Thus, they would be strengthened if more junk firms issued straight bonds. Overall, the composition of spreads by rating in our subsample of spreads is similar to that documented in other corporate bond and credit default swap data sets (e.g., Collin-Dufresne, Goldstein, and Martin (2001), Davydenko and Strebulaev (2007), Schaefer and Strebulaev (2008)).

**Table 1. Sample composition by rating.**

This table shows the number of unique firms and the number of observations for the full sample (columns (1) and (2)), and for the subsample of firms with straight bonds with observed spreads (columns (3) and (4)), by the firm’s senior unsecured rating. The ratings in columns (1) and (3) are as of the first date that the firm appears in the data set, and in columns (2) and (4) as of the observation date.

**2.2. Statistics on spreads and liquidity ratios**

We measure the credit spread as the difference between the bond’s promised yield implied by its price, and the yield on a portfolio of risk-free zero-coupon securities (STRIPS) with the same promised cash flow, as suggested by Davydenko and Strebulaev (2007). This estimation method controls accurately for the shape of the term structure.^{21} Our initial data set is an unbalanced panel of monthly observations of spreads. A potential issue with this data structure is that large firms with many outstanding bonds may be overrepresented in any given month. Because we are interested in the relationship between credit risk and liquid assets, which are firm– rather than bond-specific, using all bond-month observations may bias the results toward large firms. We address this issue by computing the average spread across bonds for a given firm in a given month, and using one observation per firm-month in our analysis. We also use the average bond maturity of all bonds for which spreads are available; all other variables in our tests are measured at the firm level. Because spreads are observed at the monthly frequency, but balance sheet information is only available quarterly, in our regressions each observation of a liquidity ratio is used in three different months. This introduces correlation in regression residuals. We account for it by clustering regression residuals at the firm level (see Petersen (2009)).

Panel A of Table 2 reports descriptive statistics on credit spreads. The mean spread is 224 basis points, and the median is 153 basis points. Unsurprisingly, spreads are higher for lower-rated bonds. Untabulated comparisons suggest that for a given rating, spreads typically increase with maturity. It is interesting to note that the average BB spread (361 basis points) is almost twice as high as that for BBB bonds (196 basis points). This jump in the spread is likely attributable to not only the increase in the probability of default but also the lower liquidity of speculative-grade bonds (BB+ and below) compared with investment-grade bonds.^{22}

**Table 2. Statistics on credit spreads and liquidity ratios.**

Panel A reports the annualized bond spread, averaged over all outstanding straight bonds for each firm-month, by firm’s senior unsecured rating. The benchmark risk- free yield is the yield on a cash flow-matched portfolio of STRIPS as of the observa- tion date. Panel B reports liquidity ratios for the full sample of firm-quarters. TA is the total book assets of the issuing firm. Cash is cash and marketable securities; WC is working capital, CA is current assets, QA is current assets less inventories, and CL is current liabilities.

Panel B summarizes various measures of balance sheet liquidity. To measure liquid asset reserves, we use the Cash/Assets ratio popular in empirical corporate finance studies, as well as liquidity ratios employed in empirical default-predicting models. Among the best known models, Altman’s (1968) *z*-score includes *WC/TA*, the ratio of working capital (the difference between current assets and current liabilities) to total assets; Zmijewski’s (1984) model and the ZETA-score model of Altman, Haldeman, and Narayanan (1977) use the current ratio *CA/CL* (current assets over current liabilities); and Ohlson (1980) and Chava and Roberts (2004) use both *WC/TA* and *CL/CA* to proxy for liquidity. Davydenko (2011) uses the quick ratio, QA/CL, equal to current assets less inventories, over current liabilities. The quick ratio is similar to the current ratio, but does not consider inventories to be part of liquid asset holdings, because distressed firms may find it difficult to convert their inventories into cash. Panel B shows that our firms have lower cash reserves on average than those in the broader Compustat samples typically used in empirical studies of cash holdings. For instance, in Opler, Pinkowitz, Stulz, and Williamson (1999), the mean (median) ratio of cash to assets is 17% (6.5%), compared with 7.1% (3.1%) in our sample. These differences arise in part because our sample does not include firms with zero or near-zero leverage, which tend to hold significant amounts of cash (Strebulaev and Yang (2012)), and in part because bond issuers are likely to be less financially constrained and value cash holdings less than an average Compustat firm (which should work against our finding of any effects related to the optimally chosen cash policy). Our tests on a broad set of Compustat firms (see the discussion of Fig. 3 below) confirm that our main results are likely to be even stronger for them, as they are more financially constrained and thus more concerned about internal cash reserves.

Figure 2 summarizes cash holdings by credit rating; we obtain similar results when we use other measures of credit risk (e.g., the interest coverage ratio). The graph shows that cash is roughly U- shaped in the firm’s credit quality. Safe AAA and AA firms have higher-than-average cash holdings and low debt levels. Their high balance sheet liquidity and low net leverage are likely important reasons for why rating agencies rate them so highly in the first place. For such firms, the risk of default is unlikely to be a leading factor shaping their cash policy. However, at the other end of the ratings spectrum, speculative-grade (junk) firms (those rated below BBB–) also have higher-than- average cash holdings, and lower grades of junk generally correspond to higher cash reserves. We argue that this pattern is due to levered firms’ precautionary motives for saving cash. Despite their relatively high cash reserves, these firms remain riskier than A- or BBB-rated firms because of their much higher levels of debt relative to their cash flows. Indeed, even relatively high cash holdings of 3.6% of net assets for the median B-rated firm fade to insignificance next to its debt level, which is close to 50% of assets. Overall, in the cross-section, firms with lower credit ratings (and thus a higher probability of default) have higher cash holdings. As a result, cash turns out to be positively associated with credit spreads, with a stronger relationship for riskier firms.

**Figure 2. Cash holdings by rating: Bond issuers.**

This graph shows means and medians of the ratio of cash to total assets by the rm's senior unsecured rating. The sample consists of all firm-quarters for nonfinancial U.S. firms that had bonds outstanding between December 1996 and September 2010.

To confirm that these results are not limited to public bond issuers, we look at cash holdings of all non-financial firms in the annual Compustat file since 1950 (341,954 firm-years for 24,825 firms). Because most of these firms lack a credit rating, we use the interest coverage ratio (EBIDTA divided by the interest expense) as a proxy for credit risk. We also split the sample into firms with high and low financing constraints, depending on whether the index of constraints constructed by Hadlock and Pierce (2010) is higher or lower than its median for the year. Figure 3 plots the means of the cash-to-asset ratio for each decile of the interest coverage ratio, from the 10th (safest) to the 1st (riskiest), separately for constrained and unconstrained firms.

**Figure 3. Cash holdings by interest coverage: All Compustat firms.**

For each decile of the interest coverage ratio, this graph plots the mean of the cash-to-asset ratio among small and large firms. The sample consists of all firm-years for non-financial U.S. firms in annual Compustat between 1950 and 2011. The interest coverage ratio is the sum of Pretax Income, Depreciation & Amortization, and Interest Expense, divided by Interest Expense. In each year, firms are classified as constrained (unconstrained) if the Hadlock-Pierce index of financial constraints is above (below) its median for that year

Several results stand out. First, the U-shaped relationship between cash and credit risk holds beyond our sample of bond issuers. In particular, cash holdings are increasing sharply as firms become very risky. Second, for a given level of credit risk, constrained firms hold more cash than large firms. This finding is consistent with unconstrained firms with better access to external financing having less of an incentive for precautionary savings of cash.^{23} Third, the levels of cash for an average Compustat firm are substantially higher than those for our bond-issuing firms, consistent with lower financing constraints for bond issuers making internal cash reserves less crucial. Many corporate finance studies classify firms that issue bonds and have a credit rating as relatively unconstrained (e.g., Almeida, Campello, and Weisbach (2004)). By focusing on these firms, we are biasing ourselves against finding a role for an endogenous cash policy. Nonetheless, our results show that even for rated bond issuers the precautionary motive for saving cash is a first-order determinant of the relationship between liquid assets and credit risk.

**2.3. Control variables**

Table 3 presents descriptive statistics on the control variables used in regressions of spreads and default probabilities, which we borrow from extant empirical research.

Based on insights from structural models of credit risk, empirical studies of spreads control for leverage, volatility, debt maturity, and various macroeconomic factors, in particularly those related to the term structure of interest rates (e.g., Collin-Dufresne, Goldstein, and Martin (2001)). We estimate the (quasi-market) *leverage ratio* as the book value of total debt divided by the sum of the book value of debt and the market value of equity. Another factor featuring prominently in credit risk models is the *volatility of assets*, which we estimate as a weighted average of the 3-year volatility of equity and the volatility of debt by rating, as suggested by Schaefer and Strebulaev (2008). To further control for the effects of volatility and leverage beyond the simple linear dependence, we include the distance to default, which is a volatility-adjusted measure of leverage based on Merton’s (1974) model of credit risk. Specifically, we use the simplified (‘na¨ıve’) *distance to default* measure suggested by Bharath and Shumway (2008), which they find to outperform other, more sophisticated proxies. To control for the term premium in corporate bond yields, we use the average remaining time to maturity of all sample bonds outstanding for the firm at each observation date. We include the logarithm of total book assets to control for all influences that the firm’s size may exert on debt spreads. In some of the regressions we also use dummies for the firm’s senior unsecured credit rating (AAA, AA+, AA, AA–, . . . , C), which summarizes the credit agency’s opinion of the firm’s creditworthiness and incorporates not only its financial characteristics but also industry conditions and other, frequently soft, information.

Finally, Collin-Dufresne, Goldstein, and Martin (2001) find that a significant part of monthly changes in spreads is driven by systematic factors. We follow their study in controlling for the risk- free interest rate (using the 10-year constant-maturity Treasury rate), the slope of the yield curve (the difference between 10– and 2-year Treasury rates), the VIX index to control for market-wide volatility, the monthly S&P-500 return, and Jump, an option-implied proxy for the probability and magnitude of a large negative jump in value.^{24}

Empirical default-predicting models identify a large number of accounting- and market-based variables related to default. We re-estimate two of the best-known models, those of Altman (1968) and Zmijewski (1984), as well as one that uses the Expected Default Frequency (EDF) from MKMV. Altman’s *z*-score includes *WC/TA* (the liquidity proxy), as well as *RE/TA* (Retained Earnings over Total Assets), *EBIT/TA* (Earnings Before Interest and Tax over Total Assets), *ME/TL* (equity market capitalization over Total Liabilities), and *S/TA* (Sales over Total Assets). Zmijewski’s model includes the current ratio *CA/CL* as the liquidity proxy, *NI/TA* (net income over Total Assets), and *TL/TA* (Total Liabilities over Total Assets). Finally, we estimate a simple model that uses the quick ratio *QA/QL* as the liquidity proxy and the *EDF* from MKMV as a summary measure of credit risk. MKMV estimates the EDF based on the firm’s equity prices and liability structure using a version of the Merton (1974) model in conjunction with a proprietary data set of defaults (Crosbie and Bohn (2002)). Hillegeist *et al.* (2004) and Bharath and Shumway (2008) show that variants of this variable are strong predictors of default. As is common in such studies, we winsorize all variables at the first and 99th percentiles.

Table 3 shows that our firms are relatively large in size, with median total book assets of almost $7.7Bn. This is to be expected, given that all of them issue public bonds. They also have relatively high leverage ratios compared with broad Compustat samples not conditioned on the presence of public bonds in the capital structure. Statistics on leverage and asset volatility are similar to those in other studies of spreads (e.g., Schaefer and Strebulaev (2008)). Looking at firm characteristics by rating (not reported), we find that firms with higher ratings are larger, less levered, and more profitable; have slightly larger capital expenditures; and return substantially more cash to shareholders via dividends and repurchases than do riskier firms. Comparing the values of Altman’s and Zmijewski’s default factors with those reported in Shumway (2001), our firms appear more distressed than the average Compustat firm – again, likely because of the presence of bonds, which implies higher-than-average leverage ratios.

**Table 3. Statistics on control variables.
**

This table reports summary statistics on control variables used in regressions of spreads (Panel A) and the probability of default (Panel B). TA is the total book value of assets. Leverage is the book value of total debt divided by the sum of the book value of debt and the market value of equity. Asset volatility is the annualized standard deviation of asset returns, estimated as suggested by Schaefer and Strebulaev (2008). Distance to default is a volatility-adjusted measure of leverage computed using the simplified approach of Bharath and Shumway (2008). Bond maturity is the remaining bond maturity in years on the observation date averaged over all bonds with available spreads. Risk-free rate is the 10-year constant-maturity rate, and slope is the difference between the 10-year and the 2-year Treasury rates. Jump is the option-implied measure of market jumps, constructed as in Collin-Dufresne at al. (2001). RE is retained earnings, ME is the market value of equity, S is sales, NI is net income, TL is the book value of total liabilities, and EDF is the Expected Default Frequency provided by MKMV.

**3. Cash holdings and credit spreads**

This section studies the relationship between balance sheet liquidity and bond spreads. First, we show that standard OLS regressions used in empirical studies of spreads appear to suggest that higher cash holdings result in higher spreads. Then, we use instrumental variables suggested by the model, and demonstrate that in IV regressions, higher cash holdings correspond to lower spreads.

In these tests, the dependent variable is the bond spread relative to a cash flow-matched portfolio of Treasuries, averaged across all of the firm’s outstanding bonds for each date. To proxy for balance sheet liquidity, we use the ratio of cash to total assets, as well as working capital over total assets (as in Altman’s (1968) z-score), and the current ratio, equal to current assets over current liabilities (as in Zmijewski (1984)), although many other proxies yield similar results.

The regression results are presented in Table 4. The effect of standard credit risk factors is in line with economic intuition and corroborates evidence from other studies of spreads (e.g., Davydenko and Strebulaev (2007)): More levered, more volatile, and smaller firms are riskier and consequently have higher credit spreads. Similar to Collin-Dufresne, Goldstein, and Martin (2001), we also find the macroeconomic controls to be robustly significant and consistent with expectations. Interestingly, adding rating dummies increases the R2 noticeably even after controlling for firm-specific credit risk using leverage and volatility proxies (from 53%–55% to 63%–65%). Thus, though ratings provide an admittedly crude summary of credit risk (as evidenced by the strong significance of leverage and volatility in columns (4), (6), and (9)), they clearly have significant incremental explanatory power.

The results on the effect of liquid assets contradict the simple intuition that firms with more liquid assets are ‘safer’ and thus should have lower spreads. Both in univariate regressions and in the presence of standard credit risk controls, the correlation between credit spreads and liquidity is positive and strongly statistically significant, typically at the 1% level. The implied economic effect is also considerable: In columns (1), (4), and (7), a one standard deviation increase in the three liquidity ratios corresponds to an increase in the bond spread of 18, 15, and 20 basis points, re- spectively. The positive relationship between credit spreads and liquidity proxies persists even after controlling for the credit rating. Moreover, in untabulated tests, we estimate specification (2) sepa- rately for different ratings groups, and find that the coefficient for cash is increasing monotonically as the rating deteriorates.

These results are robust in the data and insensitive to the way the control variables are constructed. They are nearly identical if cash is measured as a fraction of assets net of cash, rather than total assets, or if, instead of Schaefer and Strebulaev’s (2008) proxy for asset volatility we use the asset volatility estimate provided by MKMV. They are strengthened if we use book instead of market leverage. One could hypothesize that cash holdings are affected by covenants restricting liq- uidity levels, which in turn are correlated with the underlying credit risk. However, such covenants are infrequent in practice (Dichev and Skinner (2002)). Using data on bank loans from DealScan, we find that only 1.6% of our firms have covenants specifying minimum liquidity ratios (current or quick ratio). In addition, for 2.9% of firms covenants restrict capital expenditures, which also may affect cash reserves. In unreported tests we find that controlling for the presence of such covenants has no impact on our results.^{25}

Our model suggests that the positive correlation of spreads with liquid assets arises as a by- product of the precautionary motive for holding cash reserves by levered firms, which results in riskier firms having both more cash and higher credit spreads. In essence, cash reserves act as another proxy for credit risk. Thus, our theory would predict that as we introduce more credit risk controls, the positive coefficient should decrease. This is what we observe in Table 4. For example, compared with column (1), the coefficient for *Cash/TA* is lower in column (2), which controls for leverage, volatility, and other factors. In column (3), which also controls for ratings, it is reduced further. Nonetheless, it retains strong statistical significance. Thus, standard OLS regressions used in empirical studies of spreads appear inadequate for studying the role of factors such as cash, which are subject to endogenous corporate financing decisions.

The model also predicts that exogenous variations in cash (those not induced by differences in credit risk factors) should be negatively related to spreads. We test this prediction using instru- mental variable regressions. Our model suggests two potential instruments. First, profitable future investment opportunities (growth options) increase the value of the firm in the absence of default, and hence strengthen the precautionary motive for saving cash. Yet once the higher cash reserve is in place, it provides a safety cushion for creditors, decreasing credit spreads. The discussion of growth options in Section 1.4.2 suggests that it is variations in non-collateralizable assets that can serve as an instrument for cash in our model. Accordingly, to proxy for growth options, we use the median ratio of intangible to total assets in the firm’s three-digit SIC industry in each calendar year.^{26}

Second, the model suggests the ratio of managerial private costs of financial distress to the fraction of the firm’s equity that the manager owns as another instrument. The higher this fraction, the higher is the manager’s incentives to hoard cash (above the level that maximizes the value of equity) to avoid default and the associated private costs. We assume that the CEO’s salary and bonus are at risk if the firm defaults. Accordingly, our agency term is the ratio of CEO’s salary, bonus, and other monetary compensation, to the market value of her shares and options, estimated using the ExecuComp database.^{27}

We employ these two instruments in IV regressions of spreads that mirror the regressions of Table 4, with the same proxies for liquid asset reserves and the same standard control variables. The results are presented in Table 5. The last row shows the p-value of the F -test of the instruments’ relevance. It shows that our two instruments are jointly strongly significant determinants of the liquidity ratios.^{28} The table shows that, as expected, exogenous variations in liquid asset reserves are negatively and significantly related to bond spreads. Moreover, the economic effect of higher liquid reserves is substantial: In fulls-specification regressions (3), (6), and (9), a one standard deviation increase in the instrumented liquidity ratios decreases spreads by between 37 and 53 basis points.

**Table 4. OLS regressions of bond spreads.**

The dependent variable is the annualized yield spread relative to a cash flow-matched portfolio of STRIPS, averaged over all outstanding bonds for each firm-month observation in the sample. TA is the book value of total assets, WC is working capital, CA is current assets, and CL is current liabilities. Leverage is the book value of total debt divided by the sum of the book value of debt and the market value of equity. Asset volatility is the annualized standard deviation of asset returns, estimated as suggested by Schaefer and Strebulaev (2008). Distance to default is a volatility-adjusted measure of leverage computed using the simplified approach of Bharath and Shumway (2008). Bond maturity is the remaining bond maturity in years on the observation date averaged over all bonds with available spreads. Risk-free rate is the 10-year constant-maturity rate, and slope is the difference between the 10-year and the 2-year Treasury rates. Jump is the option-implied measure of market jumps, constructed as in Collin-Dufresne at al. (2001). The values of t-statistics adjusted for clustering at the firm level are reported in parentheses. Coefficients marked ***, **, and * are significant at the 1%, 5%, and 10% significance levels, respectively.

**Table 5. Instrumental-variable regressions of credit spreads.
**

The dependent variable is the annualized yield spread relative to a cash flow-matched portfolio of STRIPS, averaged over all outstanding bonds for each firm-month observation in the sample. The proxies for balance sheet liquidity (Cash/TA, WC/TA, and CA/CL) are instrumented with the ratio of Intangible to Total Assets of the median firm in the same three-digit SIC industry in each quarter year, and with the Agency term, defined as the ratio of the CEO’s salary and bonus to the value of her equity holdings and options in the firm. TA is the book value of total assets, WC is working capital, CA is current assets, and CL is current liabilities. Leverage is the book value of total debt divided by the sum of the book value of debt and the market value of equity. Asset volatility is the annualized standard deviation of asset returns, estimated as suggested by Schaefer and Strebulaev (2008). Distance to default is a volatility-adjusted measure of leverage computed using the simplified approach of Bharath and Shumway (2008). Bond maturity is the remaining bond maturity in years on the observation date averaged over all bonds with available spreads. Risk-free rate is the 10-year constant-maturity rate, and slope is the difference between the 10-year and the 2-year Treasury rates. Jump is the option-implied measure of market jumps, constructed as in Collin-Dufresne at al. (2001). The values of t-statistics adjusted for clustering at the firm level are reported in parentheses. Coefficients marked ***, **, and * are significant at the 1%, 5%, and 10% significance levels, respectively. The last row reports the p-value of the F -test of the hypothesis that the instruments do not enter the first-stage regression.

Thus, the simple intuition that higher cash holdings make firms safer, implying a negative relationship between cash and spreads, is correct. However, to uncover this intuitive result, the em- piricist must overturn the effect of the endogeneity of cash, which strongly dominates in standard OLS regressions commonly used in empirical studies of credit risk. These findings show that accounting for the fact that firms can choose their cash holdings optimally is of first-order importance for understanding the role of liquid assets in credit risk.

**4. Balance sheet liquidity and the probability of default**

Most empirical default-predicting models include some proxies for balance sheet liquidity, treating them as independent variables expected to reduce the probability of default. However, despite the intuitive appeal and the widespread use of liquidity ratios in this context, Begley, Ming, and Watts (1996), Shumway (2001), and Hillegeist et al. (2004), as well as Ohlson (1980) and Zmijewski (1984) in their original work, find them unrelated to or even positively associated with default. In this section, we look at how the endogeneity of cash affects the correlation between liquid asset reserves and the probability of default.

The standard approach in the literature is to identify a set of factors expected to affect the probability of default, and, taking them as given, estimate some variant of a hazard model of default or bankruptcy. Shumway (2001) shows that discrete-time hazard regressions are equivalent to logit regressions that include all firm-quarter observations for each firm, defaulting and non-defaulting. Thus, we estimate a set of logit regressions of default for different prediction horizons using our panel of quarterly observations for the full sample of 2,247 firms. For the horizon of *m* years, the dependent variable is equal to one if the firm defaults in the *m ^{th}* year from the observation date, but not before. Under this regression design, prediction horizons for different firm-quarters overlap, which may bias conventional test statistics. Thus, to compute the standard errors in these tests, we use bootstrap, estimating each regression for 1,000 panels re-sampled from firm-level clusters.

^{29}

The results are presented in Table 6. Panel A uses the variables that enter Altman’s (1968) z- score model, including *WC/TA*, the ratio of working capital to total assets, as a proxy for liquidity. Panel B employs the specification suggested by Zmijewski (1984), which includes the current ratio to control for liquid assets. Panel C uses uses a different proxy for liquidity, the quick ratio (Davydenko (2011)), and controls for other credit risk factors by including the Expected Default Frequency (EDF) from MKMV, variations of which have been frequently used in recent empirical studies.

**Table 6. Liquid assets and the probability of default at different horizons.
**

This table reports logit regressions (columns (1)–(4)) and instrumental-variable logit regressions (columns (5)–(7)) of bond defaults at different prediction horizons. In regression (1), the dependent variable equals 1 if the firm defaults within the following year, and 0 otherwise. In regressions (2) through (7), the dependent variable equals 1 if the firm defaults within a given year from the observation date, but not before. WC is working capital, TA is the book value of total assets, CA is current assets, CL is current liabilities, QA is current assets less inventories, RE is retained earnings, ME is the market value of equity, TL is the book value of total liabilities, S is sales, NI is net income, and EDF is the Expected Default Frequency provided by MKMV. Each regression was estimated using 1,000 bootstrapped samples from firm-level clusters; the resulting z-statistics are reported in parentheses. Coefficients marked ***, **, and * are significant at the 1%, 5%, and 10% significance levels, respectively.

While the effect of most variables are consistent with expectations and prior studies (e.g, Shumway (2001)), the effect of liquidity proxies changes depending on the prediction horizon. The regressions in column (1) are for the one-year probability of default. At this horizon, in all three models liquidity ratios are negatively correlated with the probability of default. Depending on the model, a one standard deviation increase in the liquidity ratio reduces the probability of default by between one quarter (in Panels A and B) and one-third (in Panel C).^{30} These results are consistent with Davydenko (2011), who finds that, controlling for the level of economic distress, the short-term probability of default is higher when the firm’s liquid assets fall short of its current liabilities, and that the importance of illiquidity relative to insolvency in triggering default depends on the level of financing constraints.

In contrast with the short-term results, columns (2) through (4) show that liquidity is positively related to the probability of default at the two to five year horizons, and the coefficients are strongly statistically significant. The coefficients are broadly similar in magnitude to those in column (1), but have the opposite sign – implying similar economic significance, but in the wrong direction. A more detailed illustration of this sign reversal for the Zmijweski model is provided in Figure 4. It plots the coefficient for the current ratio, CA/CL, in regressions of Panel B, estimated for quarterly rather than yearly prediction intervals (i.e., predicting default within a certain quarter in the future, rather than within a certain year). The graph shows that liquidity is negatively correlated with the probability of default for horizons of up to approximately one year, but the correlation reverses its sign and becomes highly statistically significant for longer-term predictions. In our model, equilibrium cash reserves are driven by the precautionary motive for saving cash, and are larger for riskier firms with a higher probability of default. Thus, the long-term default probability is positively correlated with liquidity. This contrast with the simple intuition that traditional default-predicting studies rely on implicitly, which only holds for short horizons.^{31}

**Figure 4. Liquid assets and the probability of default at different horizons.**

This graph shows the point estimate and the 95% confidence interval for the logit regression coefficient for QA/CL in Zmijewski’s (1984) model, for different prediction horizons. For a horizon of m quarters, the dependent variable equals one if the firm defaults in the mth quarter from the observation date, and zero otherwise. The regressions also include NI/TA and TL/TA as control variables. The sample consists of 76,349 firm-quarter observations. The confidence interval is obtained by bootstrapping from firm-level clusters.

Consistent with the hypothesized effect of endogeneity, columns (5) through (7) of Table 6 show that the sign of the liquidity coefficients in long-term regressions becomes negative when we use the instrumental variables introduced in Section 3. The instrumented liquidity ratios are all negative, and statistically significant for horizons of three years or more.

Overall, these tests suggest that the effect of balance sheet liquidity on the probability of default for horizons longer than a few months cannot be captured adequately by a standard approach that treats liquid assets as given. We thus emphasize once again the importance of recognizing that firms can choose their cash policy endogenously, depending in particular on credit risk.

**5. Concluding remarks**

In this paper, we document a robust positive correlation of corporate cash holdings with credit spreads and with the long-term probability of default. These findings run contrary to the simple intuition that higher cash reserves make corporate debt ‘safer.’ We argue that they arise because of endogenous response of firms’ cash holdings to the possibility of a liquidity shortage, which in the presence of restrictions on external financing can trigger costly default. Our model shows how such effects can arise when future cash flows are only partially pledgeable and when default is costly. At the same time, exogenous variations in the firm’s cash holdings that are unrelated to credit risk factors are negatively correlated with spreads. The simple intuition that predicts that firms with high cash holdings should be safer can account only for the direct relationship between cash and spreads. It misses the indirect relationship due to the endogeneity of cash, which, as our evidence suggests, dominates in practice. An important implication is that recognizing that balance sheet liquidity is endogenous is crucial for credit risk studies, which is a key effect largely ignored in existing literature. More generally, our findings highlight the importance of adopting the corporate finance prospective in asset-pricing studies of the firm. Otherwise, using most common variables, such as corporate liquidity proxies, in some of the most standard tests, such as predictive regressions of default, may yield misleading results due to spurious correlations.

**
View the Appendix and References**

**–Viral V. Acharya*, Sergei A. Davydenko and Ilya A. Strebulaev**

*∗Viral Acharya is at New York University - Stern School of Business, and CEPR. Sergei Davydenko is at Joseph L. Rotman School of Management, University of Toronto. Ilya Strebulaev is at the Graduate School of Business, Stanford University, and NBER. We thank Heitor Almeida, Mark Carey, Darrell Duffie, Espen Eckbo, Zsuzsanna Fluck, Ron Giammarino, David Goldreich, Bruce Haslem, Jan Mahrt-Smith, Mitchell Petersen, Eric Powers, Bryan Routledge, Paola Sapienza, Tyler Shumway, Roger Stein, Michael Weisbach, Tony Whited, Youchang Wu, two anonymous referees, Andrew Karolyi (the editor), and seminar participants at McMaster University, University of Illinois at Urbana- Champaign, University of Toronto, Bank of Canada, Barclays Global Investors, Moody’s KMV, the CEPR Risk Management Conference, Gerzensee Symposium, Gutmann Symposium on Credit Risk, Moody’s Fourth Credit Risk Conference, the Moore School’s Fixed Income Conference, the Northern Finance Association Kananaskis meetings, and the Western Finance Association Waikoloa meetings for their comments and suggestions. Send correspondence to Sergei A. Davydenko, University of Toronto, Rotman School of Management, 105 St George Street, Toronto, Canada M5S 3E6; telephone: (416) 978-5528; fax: (416) 971-3048. E-mail: davydenko@rotman.utoronto.ca.*

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**NOTES**

^{17}One economic interpretation of τ is that it represents the extent to which future cash flows are verifiable at date
1. Low values of τ correspond to unverifiable cash flows that are difficult to pledge as collateral to providers of outside finance.

^{18}Note that incentives to engage in asset substitution disappear in the absence of financing frictions. Indeed, in
the limiting case of τ = 1, cash holdings and investment cash flows are perfect time substitutes, so that investment is at its first-best level, and precautionary savings play no role. In this case, higher expected interim cash flow simply enlarges the total pool of assets without affecting cash holdings, and thus results in lower credit spreads.

^{19}The indices include corporate bonds with a par amount of at least 100 million dollars ($250 million for investment-
grade bonds after December 2004) and remaining maturity of at least one year.

^{20}The number of firms in each rating class does not stay constant throughout the sample period, because ratings change over time. Statistics reported in columns (1) and (3) of Table 1 show ratings for each firm as of the date when they first appear in the sample. During our sample period, more firms were downgraded than upgraded. As a result, for junk ratings, the proportion of firm-quarters and firm-months in the sample is higher than the proportion of firms.

^{21}In robustness tests, we estimate spreads relative to the swap curve computed using the Nelson-Siegel (1987) algorithm. The spreads estimated in this way are lower, but our qualitative results are not affected in any way. Another alternative would be to use CDS spreads instead of bond spreads.

^{22}Potentially, the lower liquidity of speculative-grade bonds may be a concern in our analysis. However, if the illiquidity component in the credit spread is not highly varying within each rating group, its effect on our regression estimates should be minimal. See Schaefer and Strebulaev (2008) for a discussion of the impact of illiquidity.

^{23}In an unreported test, we also produce a version of Figure 2, separating constrained and unconstrained firms. We find that, while the cash holdings of investment-grade bond issuers are similar for both groups, they are higher for constrained speculative-grade firms than those of unconstrained firms with the same rating. This finding is consistent with the precautionary motive being stronger for constrained firms when the risk of default is relatively high.

^{24}Following Collin-Dufresne, Goldstein, and Martin (2001), we construct the variable Jump as follows. First, from the OptionMetrics database, we obtain Black-Scholes volatility estimates for at- and out-of-the-money puts and at- and in-the-money calls on S&P 500 futures with shortest maturities. Second, we estimate the regression
σ(K ) = a + bK + cK 2 , where K is the strike price. Third, for each month-end, we compute J ump = [σ(0.9F ) − σ(F )], where F is the current futures price.

^{25}See Murfin (2012) for a recent study of the determinants of bank loan covenants.

^{26}We prefer intangibles to the market-to-book ratio as a proxy for growth opportunities, because in addition to other well-known problems with market-to-book (Erickson and Whited (2000)), in our setting, it is also mechanically correlated with the market leverage ratio, which renders it unsuitable as a potential instrument. We use an industry- based measure of intangibles to avoid endogeneity concerns.

^{27}Specifically, the agency term is defined as (salary + bonus + other annual compensation + long-term incentive
plan + all other compensation)/(value of the equity stake + value of all unexercised options owned) for the CEO. As ExecuComp reports the Black-Scholes value of new option grants but not the current value of previously granted options, we employ the algorithm suggested by Himmelberg and Hubbard (2000) to estimate the market value of old options.

^{28}Staiger and Stock (1997) show that when the correlation between instruments and endogenous variables is weak,
IV regression coefficients may be biased. They suggest that the F -statistic of the hypothesis that the instruments do not enter the first-stage regression should be sufficiently large to avoid the weak-instrument bias. In our univariate regressions of Table 5 these statics range from 15 to 26, although they are smaller in multi-variate tests.

^{29}See Horowitz (2001) for a detailed discussion of bootstrap procedures. We thank Andrew Karolyi (the editor) for
alerting us to these issues, and Mitch Petersen and Tyler Shumway for their advice on statistical inference under our empirical test design.

^{30}King and Zeng (2001) show that when the event of interest is rare (as is the case in studies of default), standard
quantitative predictions in logit regressions are biased in finite samples. Thus, to compute the marginal effect of cash on the probability of default, we employ the correction for the bias proposed in their study.

^{31}In the continuous-time model that we develop in the online appendix the firm makes debt coupon payments
continuously, which allows us to study the term structure of default probabilities theoretically in more detail. The model predicts that a long-term default probability is positively correlated with cash, in a way that is qualitatively similar to our empirical findings in Fig. 4.