A. The Playing Fields

1. The Stock-and-Bond Sample

Our stock–bond sample investigates the common stocks (shrcd: 10 and 11) of firms traded on the NYSE, AMEX, and Nasdaq (exchcd: 1, 2, and 3). While we directly source monthly stock returns from CRSP, we replace a stock’s return with its delisting return whenever the delisting return is nonmissing. If the delisting return is missing but the delisting code available, we replace that return with −30% for NYSE and AMEX stocks and −55% for Nasdaq stocks (see Shumway (Reference Shumway1997) and Shumway and Warther (Reference Shumway and Warther1999)). We exclude stocks with a 1-month-lagged price below $5 to mitigate market microstructure issues.

We rely on data from Lehman Brothers’ Fixed Income Database, Datastream, the Intercontinental Exchange (ICE), the Trade Reporting and Compliance Engine (TRACE), and Mergent’s Fixed Income Securities (FISD) and National Association of Insurance Commissioners (NAIC) databases to compute bond returns and characteristics. While the Lehman Brothers, Datastream, ICE, TRACE, and NAIC databases contain mostly bond market data, the FISD database features bond characteristic data, including the offering amount and date; the maturity date; the coupon rate, type, and frequency; the bond type, rating, and option features; and issuer information. We retrieve Lehman Brothers data over the start-1986 to end-1997 period,Footnote ⁷ Datastream data over the start-1990 to end-2006 period, ICE data from start-1996 to end-2004, NAIC data from start-1994 to end-2020, and TRACE data from July 2002 to end-2020.Footnote ⁸ To align our stock-and-bond data, we choose the sample period from January 1986 to December 2020 for the stock–bond sample, consisting of 420 monthly observations (35 years).

While we directly source monthly bond returns from the Lehman Brothers database, we calculate the return of bond $ i $ over month $ t $ , $ {r}^B $ , from Datastream data as $ {RI}_{i,t}/{RI}_{i,t-1}-1 $ , where $ RI $ is the total return index, and $ t $ consistently indicates the entire period for flow (e.g., the return over month $ t $ ) but the end of the period for stock (e.g., the index value at the end of month $ t $ ) variables. We follow Bessembinder, Kahle, Maxwell, and Xu (Reference Bessembinder, Kahle, Maxwell and Xu2009), Choi (Reference Choi2013), and Choi and Richardson (Reference Choi and Richardson2016) in calculating that return from NAIC, ICE, and TRACE data as

(1) $$ {r}_{i,t}^B=\frac{P_{i,t}+{AI}_{i,t}+{C}_{i,t}}{P_{i,t-1}+{AI}_{i,t-1}}-1, $$

where $ P $ is the bond price, $ AI $ is the accrued interest, and $ C $ is the coupon. In case of NAIC and TRACE, we construct $ {P}_{i,t} $ ( $ {P}_{i,t-1} $ ) from the last 5 trading days of month $ t $ and, if no transactions occurred over those days, from the first 5 of month $ t+1 $ (the first 5 of month $ t $ ). See the Appendix for more details.

A downside of our main method to calculate returns from NAIC and TRACE data is that if there are no bond transactions over the periods outlined previously, the return will automatically be missing. To mitigate that issue, we also follow the alternative methodology of Bartram et al. (BGN) (Reference Bartram, Grinblatt and Nozawa2025) to create returns. Arguing that, under lenient conditions, the dirty bond price follows a martingale under the physical measure, these authors choose the earliest (latest) dirty price over month $ t $ (month $ t $ plus the first 5 trading days of month $ t+1 $ ) as proxy for the start (end) month price. They next proceed exactly as in our main methodology.

We impose standard filters on our bond return data. First, we remove non-U.S. bonds. Second, we exclude structured notes; mortgage, asset, or agency-backed bonds; and equity-linked bonds. Third, we remove convertible or putable bonds. Fourth, we keep only fixed and zero-coupon bonds. Fifth, we remove bonds with less than a single year to maturity. Sixth, we exclude bonds with a market capitalization below $25 million at the start of month $ t $ and returns outside of the −100% to 100% range over that month. Seventh, in case of the TRACE bond data, we eliminate when-issued or locked-in transactions, those with special sales conditions, and cancelled, subsequently corrected, or reversed transactions.Footnote ⁹

While the Lehman Brothers, Datastream, and ICE data contain bond quotes (first two) or matrix prices (all three), the NAIC and TRACE data contain transaction prices, with the NAIC data, however, only featuring those associated with the trades of insurance firms. As the consensus opinion is that transaction prices are more reliable than quotes, but that quotes are more reliable than matrix prices, we use the TRACE $ \succ $ NAIC $ \succ $ ICE $ \succ $ Lehman Brothers $ \succ $ Datastream preference order in our bond return calculations.Footnote ¹⁰ We finally form a value-weighted portfolio of firm $ i $ ’s outstanding bonds at the start of month $ t $ . As weight, we use either a bond’s market capitalization in case of the Lehman Brothers and Datastream data or the sum of its price and accrued interest times its outstanding number (calculated as the ratio of notional to principle amount) in case of the ICE, NAIC, and TRACE data.

In Section IA.1 of the Supplementary Material, we replicate all the exercises in the appendixes of Choi (Reference Choi2013) and Choi and Richardson (Reference Choi and Richardson2016) to confirm that our bond data are close-to-comprehensive and of a high quality. In particular, we show that although the bond sample is a relatively small (about 15%) subsample of the entire CRSP-Compustat universe featuring larger and more financially levered firms, it captures on average about 77% of the Compustat book debt of the included firms and about 85% of the outstanding balances in the entire FISD universe. Moreover, the sample contains an only small number of zero-price-change observations (1.70%); both firm- and portfolio-level returns constructed from it yield close-to-zero autocorrelations and cross-correlations with 1-month-lagged stock returns; and at least the ICE (but not necessarily Datastream) quotes are close to the corresponding NAIC and TRACE transaction prices (mean (median) difference: 0.87% (0.44%)).Footnote ¹¹ Given that all these results align with those in the two studies previously, we also conclude that our bond sample is reasonably comprehensive and features a small but not major degree of staleness.

2. The Stock, Bond, Loan, and Firm-Asset Sample

For our stock-bond-loan-asset sample, we obtain data from Creditflux CLO-i, Refinitiv LoanConnector, and Reuters Dealscan to construct loan returns and fundamentals. While CLO-i contains loan transaction data from collateralized loan obligations (CLOs) starting from 2004, LoanConnector contains the bid–ask quotes of main dealers for secondary market loans starting from 1998.Footnote ¹² Conversely, Dealscan provides loan characteristic data starting from the early 1980s. We use loan identification numbers (LINs) to merge the LoanConnector and Dealscan data. We rely on a matching algorithm based on firm and loan characteristics plus a manual verification to merge the LoanConnector/Dealscan with the CLO-i data.

Following Choi (Reference Choi2013), Choi and Richardson (Reference Choi and Richardson2016), and Beyhaghi and Ehsani (Reference Beyhaghi and Ehsani2017), we calculate the monthly return of loan $ i $ over month $ t $ , $ {r}^L $ , as

(2) $$ {r}_{i,t}^L=\frac{Par_{i,t}{P}_{i,t}+\left({Par}_{i,t}-{Par}_{i,t-1}\right)+{AI}_{i,t}+{C}_{i,t}}{Par_{i,t-1}{P}_{i,t-1}+{AI}_{i,t-1}}-1, $$

where $ Par $ is the outstanding par value, $ P $ is the loan price, $ AI $ is the loan accrued interest on a 360-day basis, and $ C $ is the coupon, so that the second summand in the numerator on the right-hand side is the principle repayment over the month.Footnote ¹³ In line with standard data sources, we set $ {P}_t $ ( $ {P}_{t-1} $ ) to the transaction price on the last (first) trading day of the month if available and else to the bid–ask midpoint. Analogous to bonds, we also use the alternative methodology of BGN to calculate loan returns. As the bid–ask midpoint is, however, almost always available in our data, this strategy only marginally raises our sample size.

Importantly, we highlight that, in contrast to several other studies, we do not impute the loan returns of firms with only nontraded loans from regressions of available loan returns on their corresponding bond returns and Treasury bond returns. We refrain from doing so since the justification for that strategy that loan values are far more stable than stock-and-bond values due to loans residing at the top of the capital structure is unlikely to hold for the loans of highly distressed firms, which are the main focus of our research.

We impose standard filters on our loan data. First, we drop non-U.S.-syndicated and non-U.S.-dollar loans. Second, we omit loans with less than 3 months to maturity. Third, we exclude loans with monthly returns outside the −100% to 100% range. We finally again form a value-weighted portfolio of all of firm $ i $ ’s outstanding loans at the start of month $ t $ , using a loan’s par value times the sum of its price ( $ Par\times P $ ) and accrued interest ( $ AI $ ) as weight. We omit loan data before August 1999 to ensure wide enough cross sections. To align our stock-and-bond (calculated as in Section II.A.1) and loan data, we choose the sample period from August 1999 to April 2020 for the stock-bond-loan-asset sample, featuring 249 monthly observations (around 21 years). Critically, however, we retain a firm-month observation in that sample only if we have stock and loan (but not necessarily bond) data.

Section IA.1 of the Supplementary Material again follows Choi (Reference Choi2013) and Choi and Richardson (Reference Choi and Richardson2016) to evaluate the coverage and quality of our sample loan data. While the loan sample is an even smaller (about 3%) subsample of the CRSP-Compustat universe than the bond sample, it captures on average about 94% of Compustat book debt and about 12% of the outstanding balances in the Dealscan universe. Compared to the bond sample, the loan sample, however, features a much greater number of zero-price-change observations (33.91% vs. 1.70%); the portfolio (but not firm) level loan returns yield a higher first-order autocorrelation (0.43 vs. 0.10); and the firm-level returns share a higher cross-correlation with 1-month-lagged stock returns (0.15 vs. 0.06). Notwithstanding, as stressed by Choi and Richardson (Reference Choi and Richardson2016), the high proportion of zero-price-change observations may not indicate price staleness but rather stable expectations about interest rates and default risk. Also, the loan quotes are close to their corresponding transaction prices (mean (median) difference: 1.85% (0.51%)), and the cross-correlation of 0.15 implies an R ² of only about 2% in a regression of loan returns on 1-month-lagged stock returns. Overall, we thus conclude that while our loan sample prices are more stale than our bond sample prices, the overall level of staleness is arguably still nonsevere.

We next follow Choi (Reference Choi2013) and Choi and Richardson (Reference Choi and Richardson2016) in appealing to Modigliani and Miller’s (Reference Modigliani and Miller1958) insight that the value of a firm’s real assets equals the value of its financial assets and approximate the firm’s (real) asset return as the value-weighted average of its stock, value-weighted bond-portfolio, and value-weighted loan-portfolio returns. To avoid bias arising from those bonds and loans excluded by our filters, we also include them in our calculations, assuming, however, that their returns equal those of their nonexcluded counterparts. In particular, let $ E $ be a firm’s stock market capitalization, $ B $ the sum of bond price plus accrued interest ( $ P+ AI $ ) times number of bonds outstanding taken over all its included and excluded bonds, and $ L $ the sum of par value times price plus accrued interest ( $ Par\times P+ AI $ ) taken over all its included and excluded loans. Letting $ MV $ be the sum of $ E $ , $ B $ , and $ L $ , we then approximate firm $ i $ ’s asset return over month $ t $ , $ {r}^A $ , as

(3) $$ {r}_{i,t}^A=\left(\frac{E_{i,t-1}}{MV_{i,t-1}}\right){r}_{i,t}^S+\left(\frac{B_{i,t-1}}{MV_{i,t-1}}\right){r}_{i,t}^{BP}+\left(\frac{L_{i,t-1}}{MV_{i,t-1}}\right){r}_{i,t}^{LP}, $$

where $ {r}^S $ and $ {r}^{BP} $ are the stock and value-weighted bond return calculated as in Section II.A.1, respectively, and $ {r}^{LP} $ is the value-weighted loan return calculated as in this section.

We acknowledge that our asset return proxy is imperfect because it ignores i) nontraded loans held by even those firms with traded loans and ii) nontraded liabilities. We later run robustness test showing that these imperfections do not greatly distort our conclusions.

B. The Pricing Variable: Corporate Distress Risk

We use Campbell et al.’s (Reference Campbell, Hilscher and Szilagyi2008) logit-hazard model to capture 12-month-ahead firm distress risk with only data available to investors at the time. To do so, we estimate a logit model of a dummy variable set to 1 if a firm defaults, files for bankruptcy, or delists for performance reasons over the month 12 months from the current, and else 0, Failure, on distress predictors at the end of the current month. We can compactly write that model as

(4) $$ \mathrm{Prob}\left({Failure}_{i,t}=1|{\mathbf{X}}_{i,t-12}\right)=\frac{1}{1+\exp \left(-\alpha -\boldsymbol{\beta} {\mathbf{X}}_{i,t-12}\right)}, $$

where $ \alpha $ is a parameter, $ \boldsymbol{\beta} $ is a vector of parameters, and $ \mathbf{X} $ is a vector encompassing the distress predictors. Consistent with Campbell et al. (Reference Campbell, Hilscher and Szilagyi2008), we estimate model (4) recursively, using data from start-January 1963 to end-December of calendar year $ t $ , where $ t $ ranges from 1980 to 2008 in unit increments. We next combine the estimates from the estimation window stretching to the end of calendar year $ t $ with the distress predictor values over calendar year $ t+1 $ . See the Appendix for more details about the default risk predictors.

We obtain the stock and accounting data required to compute the distress proxy from CRSP and Compustat. Yet, since we do not have access to Campbell et al.’s (Reference Campbell, Hilscher and Szilagyi2008) failure data, we cannot estimate logit model (4) ourselves. Fortunately, Jens Hilscher sent us the output from recursively estimating that model starting from 1980. We use the output obtained from his longest window, 1963–2008, to calculate the distress proxy for the post-2008 period. Doing so is unproblematic as his estimates strongly converge over time.Footnote ¹⁴

C. The Control Variables

We use a comprehensive set of controls in our portfolio sorts and FM regressions. In our portfolio sorts, we always start from simple factor models but then gradually expand these. In our stock sorts, we, for example, start from the Fama and French (FF3S) (Reference Fama and French1993) 3-factor model featuring the MKT, SMB, and HML. We next move to the Fama and French (FF5S) (Reference Fama and French2015) 5-factor model by adding RMW and CMA and then to the Fama and French (FF6S) (Reference Fama and French2016) 6-factor model by further adding MOM. Conversely, in our bond and loan sorts, we start from the Fama and French (FF5SB) (Reference Fama and French1993) 5-factor model featuring the MKT, SMB, HML, DEF, and TERM. We next move to an 8-factor model by adding an investment and a speculative-grade bond portfolio and bond momentum (SB8). We finally also add a parsimonious selection of bond factors chosen from recent bond pricing studies, as, for example, Dick-Nielsen et al. (Reference Dick-Nielsen, Feldhütter, Pedersen and Stolborg2025) and Dickerson et al. (Reference Dickerson, Julliard and Mueller2026), and including bond value, short- and long-term reversal, duration, and carry factors and the firm earnings announcement drift (SB14).Footnote ¹⁵ In our FM regressions, we use a comprehensive set of stock, bond, loan, and firm characteristics known to price our asset classes. See the Appendix for more details about our choice of controls and how we calculate them.

A. Descriptive Statistics

Table 1 offers descriptive statistics for our sample data. Panels A and B focus on the stock–bond and the stock-bond-loan-asset sample, respectively. The descriptive statistics include the number of observations (No. of Obs.), the mean, the standard deviation, and the first, 25th, 50th, 75th, and 99th percentiles, computed by sample month and then averaged over time. Panel A shows that the stock–bond sample contains an average of 3,480 stocks and between 764 (standard return) and 779 (BGN return) bond portfolios per month. Also, stocks attract both a higher monthly mean return (1.01% vs. 0.71%)Footnote ¹⁶ and standard deviation (12.27% vs. 2.33%) than bonds, and the average stock is larger than the average bond capitalization ($3.86 vs. $2.23 billion). Lastly, the average bond of the average sample firm has a bond market beta of 0.58, a time-to-maturity of about 10 years, and a credit rating close to BBB.

TABLE 1Descriptive Statistics on Our Stock, Bond, and Loan Data

In contrast, Panel B reveals that the stock-bond-loan-asset sample contains an average of only 179 (standard return) or 186 (BGN return) firms per month because few firms own loans traded in secondary markets.Footnote ¹⁷ Contrasting stock-and-bond capitalizations across the samples, the stock-bond-loan-asset sample is heavily tilted toward larger firms. In line with the stock–bond sample, stocks have higher mean monthly returns (0.77% vs. 0.65%) and standard deviations (14.28% vs. 4.24%) than bonds, while bonds have higher mean returns (0.65% vs. 0.30%) and standard deviations (4.24% vs. 2.13%) than loans. Next, the average bond of the average sample firm has a lower bond market beta of 0.45, a shorter time-to-maturity of about 7 years, and a lower rating around B+ relative to the stock–bond sample. Conversely, the average loan of that firm has a market size of $0.80 billion and a time-to-maturity of about 4 years. Finally, the mean monthly asset return of about 0.54% lies between the mean monthly stock, bond, and loan returns (0.77%, 0.65%, and 0.30%, respectively).

Figure 1 plots the numbers and aggregate capitalizations of the asset classes in our stock–bond (Graphs A–B) and stock-bond-loan-asset (Graphs C–D) samples, respectively. While Graph A shows that the stock–bond sample contains between about 2,300 and 5,500 stocks and between about 460 and 980 (firm-specific) bond portfolios, Graph B reveals that bonds make up between 10% and 20% of the aggregate stock-and-bond capitalization. Graph C suggests that the stock-bond-loan-asset sample contains between about 70 and 240 (40–152) firms with stocks and loans (stocks, bonds, and loans), representing only 2%–8% of the stock–bond sample. Finally, Graph D shows that the aggregate capitalization and its corresponding volatility are markedly higher for stocks than bonds, but then also markedly higher for bonds than loans.

FIGURE 1Sample Composition

Figure 1 plots the numbers and aggregate market capitalizations of the asset classes in our empirical work over our sample periods. While Graph A (B) shows the number of firms with stocks or bonds (the aggregate stock-and-bond capitalizations) in the stock–bond sample, Graph C (D) reports the number of firms with stocks and loans or stocks, bonds, and loans (the aggregate stock, bond, and loan capitalizations) in the stock-bond-loan-asset sample.

B. The Stock-and-Bond Sample

We next study the pricing of corporate distress in the stock–bond sample. We start with sorting our sample stocks or firm-specific bond portfolios into portfolios according to the decile breakpoints of Campbell et al.’s (Reference Campbell, Hilscher and Szilagyi2008) distress proxy at the end of month $ t-1 $ . We either value or equally weight the portfolios, where we use a firm’s stock capitalization or its aggregate bond capitalization to calculate the value weights. We hold the portfolios over month $ t $ . For each set of portfolios, we create three spread portfolios to identify nonlinearities in the mean return-distress relation. While the first is long the middle (i.e., fifth) distress portfolio and short the bottom (“Middle–Low”), the second is long the top and short the middle (“High–Middle”) and the third long the top and short the bottom (“High–Low”). We risk-adjust by computing the intercept (“alpha”) from regressing portfolio excess returns on the factors of the models in Section III.C.

Table 2 gives the portfolio sort results. While Panel A focuses on the stock and Panel B on the (firm-specific) bond portfolios, Panels B.1 and B.2 in Panel B report the spread portfolio results calculated from standard and BGN returns, respectively. While column 1 shows mean Campbell et al. (Reference Campbell, Hilscher and Szilagyi2008) distress risk, columns 2–5 (6–9) present the mean monthly returns and alphas of the value (equal)-weighted portfolios (all in %). Plain numbers are estimates, whereas those in square brackets are Newey and West (Reference Newey and West1987) t-statistics with a 12-month lag length. Panel A suggests that, in line with the literature, mean stock returns and alphas are hump shaped in distress risk, with them mildly rising over the first 8 deciles but sharply dropping over the last two. The value-weighted alpha of the most comprehensive factor model, the FF6S alpha, for example, rises mildly by 0.14% (t-stat: 0.89) over the first 5 deciles but then drops sharply by 1.12% (t-stat: −2.89) over the final 5 (see column 5). As a result, the drop in that alpha over the entire set of deciles is a less pronounced but still moderately significant −0.98% (t-stat: −2.25).

TABLE 2Stock-and-Bond Portfolios Sorted on Distress Risk

Panel B shows that mean bond returns and alphas decline more monotonically with distress risk, although the starkest drops again occur over the final deciles. The value-weighted standard-return alpha of the most comprehensive factor model, the SB14 alpha, for example, drops mildly by 0.06% (t-stat: −2.06) over the first 5 deciles but more sharply by 0.41% (t-stat: −6.16) over the final five (see column 5 in Panel B.1). Thus, the drop in that alpha over the entire set of deciles is an even stronger and more significant −0.47% (t-stat: −7.51). Contrasting the standard and BGN return results in Panels B.1 and B.2 reveals them to be close-to-identical, mostly due to the great overlap between the samples.

Table IA.4 and Figure IA.3 in the Supplementary Material report the mean characteristics and the factor loadings of the portfolios in Table 2, respectively. Both suggest that high-distress stocks tend to be small, unprofitable value stocks with high market betas, as also reported in prior studies. Conversely, high-distress bonds tend to be small, illiquid bonds with high speculative-grade bond market betas and coupon rates but low ratings and past returns. They also load more negatively on the earnings announcement factor than safer bonds.

In Table 3, we supplement our portfolio sorts with FM regressions explaining the month- $ t $ return. We run those regressions on the full stock sample in column 1 and the subsample of stocks with outstanding bonds in columns 2 and 3. Conversely, we run them on the full bond sample, the subsample of investment-grade bonds, and the subsample of speculative-grade bonds in columns 4 to 6, 7, and 8, respectively. We define as investment (speculative) grade bonds the value-weighted portfolio of all of a firm’s bonds with a rating equal to or above (below) BBB– at the start of month $ t $ . To capture nonlinearities, we use as main regressors two dummy variables calculated from our distress proxy, the first (second), HighDistress (LowDistress), set to 1 if the distress proxy takes on a value within the top decile (below the median) at the end of month , $ t-1 $ and else 0. In columns 3 and 5, we interact the distress dummies with a dummy variable set to 1 if the return of the other asset class is below the first quartile, and else 0, LowS/BRet. We further add the controls referred to in Section III.C. As always, plain numbers are monthly premium estimates (in %), whereas those in square brackets are Newey and West (Reference Newey and West1987) t-statistics with a 12-month lag.

TABLE 3Stock-and-Bond Regressions on Distress Risk

The FM regressions support our portfolio sorts by corroborating that mean stock returns are hump-shaped in distress risk but that mean bond returns decline more monotonically with it. Starting with the full stock sample, column 1, for example, shows that while the stocks in distress deciles 6–9 earn a 0.24% (t-stat: 2.61) higher mean return than those in deciles 1–5, the top-decile stocks earn a 0.61% (t-stat: −2.82) lower mean return than the decile 6–9 stocks. Conversely, column 4 reveals that the corresponding numbers for the full bond sample are −0.06% (t-stat: −4.10) and 0.25% (t-stat: −4.61), respectively. Noteworthily, column 2 suggests that the stocks-with-bonds subsample also produces a hump-shaped mean stock return-distress relation and columns 7 and 8 that the negative mean bond return-distress relation amplifies in the speculative-grade bond subsample.Footnote ¹⁸ In addition, the regressions featuring interactions with the other asset class in columns 3 and 5 suggest that distressed stocks (bonds) are more likely to underperform if the corresponding bonds (stocks) do so, too, refuting that one asset class exploits the other (as in the shareholder advantage theory). Finally, the standard and BGN returns again yield close-to-identical results, and the stock-and-bond controls produce premiums in agreement with the literature.Footnote ¹⁹

In Figure 2 and Table IA.5 in the Supplementary Material, we investigate the persistence in the stock-and-bond distress premiums in the stock–bond sample. Specifically, the figure plots the monthly FF6S stock (Graph A) and SB14 bond (Graph B) alphas of the value-weighted high-minus-low distress decile spread portfolios formed at the end of month $ t-1 $ plus their corresponding 95% confidence bands separately for each month from $ t $ to $ t+11 $ . The table offers the same results plus the corresponding results from the equivalent equal-weighted spread portfolios and FM regressions. The figure and table suggest that the stock-and-bond distress premiums dissipate only slowly over time, with them being statistically significant at the 95% level or better for about half a year after portfolio formation.

FIGURE 2The Longer-Horizon Stock-and-Bond Distress Premiums

Figure 2 plots the monthly FF6S stock (Graph A) and SB14 bond (Graph B) alpha of the value-weighted high-minus-low distress decile spread portfolio (sold line) and the corresponding 95% confidence bands (broken lines) separately for each of the first 12 months after portfolio formation (i.e., months $ t $ to $ t+11 $ ) in the stock–bond sample.

C. The Stock, Bond, Loan, and Firm-Asset Sample

We now study the pricing of corporate distress risk in the stock-bond-loan-asset sample. We again start with separately sorting our sample stocks, firm-specific bond portfolios, firm-specific loan portfolios, and firm-asset portfolios into portfolios according to the quintile breakpoints of Campbell et al.’s (Reference Campbell, Hilscher and Szilagyi2008) distress proxy at the end of month $ t-1 $ . We rely on quintile rather than decile breakpoints because the stock-bond-loan-asset sample is much smaller than the stock–bond sample due to it featuring only those firms with stocks and traded loans. The implication is that decile breakpoints sometimes yield ill-diversified portfolios. We again value or equally weight the portfolios and hold them over month $ t $ . Consistent with the prior section, we form three spread portfolios to identify nonlinearities in the mean return-distress relations, the first (second) [third] long the middle (top) [top] and short the bottom (middle) [bottom] portfolio (“Middle–Low,” “High–Middle,” and “High–Low,” respectively). We again risk-adjust by regressing excess portfolio returns on the factors of the same models as before.

Using a design analogous to Table 2, Table 4 gives the results from the portfolio sorts, with Panels A–C focusing on stocks, bonds, and loans, respectively. Panels A and B confirm that mean stock returns are hump-shaped in distress risk, while mean bond returns drop more monotonically with it. The value-weighted FF6S stock alpha, for example, rises by 0.46% (t-stat: 1.53) over the initial three quintiles but sharply drops by 1.58% (t-stat: −3.10) over the final three. The overall change is thus −1.12% (t-stat: −2.49). Conversely, the value-weighted standard-return SB14 bond alpha stays virtually constant over the initial three quintiles but sharply drops by 0.88% (t-stat: −3.58) over the final three. The overall change is thus −0.87% (t-stat: −3.52). Interestingly, Panel C suggests that traded loans are similar to bonds since their mean returns also drop monotonically with distress risk. The value-weighted standard-return SB14 loan alpha, for example, drops by 0.06% (t-stat: −1.88) over the initial three quintiles and 0.30% (t-stat: −2.66) over the final three. The overall change is thus −0.36% (t-stat: −2.89). The similar patterns for bonds and loans come as no surprise since both asset classes represent debt claims. Just like before, our inferences are close-to-identical across the standard and the BGN (bond or loan) return samples.

TABLE 4Stock, Bond, and Loan Portfolios Sorted on Distress Risk

Table 5 offers the results from the portfolio sorts on firm assets, calculated as the value-weighted combination of stocks, bonds, and loans (recall equation (3)). The table shows that, similar to stocks, mean firm-asset returns are hump-shaped in distress risk, although the hump is less pronounced than for stocks. The value-weighted standard-return SB17 firm-asset alpha, for example, rises by 0.11% (t-stat: 0.50) over the initial three quintiles but drops sharply by 0.91% (t-stat: −3.59) over the final three. The overall change is thus −0.80% (t-stat: −2.64). The similarity between the stock and firm-asset results is largely due to i) the greater variations in mean stock relative to mean bond or loan returns over the quintiles, and ii) the greater weights associated with stocks than bonds or loans.

TABLE 5Firm-Asset Portfolios Sorted on Distress Risk

Table IA.7 and Figure IA.4 in the Supplementary Material present the mean characteristics and factor loadings of the portfolios in Tables 4 and 5, respectively. While both corroborate that the characteristics and loadings of the stock-and-bond portfolios largely agree across the stock–bond and the stock-bond-loan-asset sample, they further reveal that high-distress loans are short-maturity loans with low (i.e., negative) loadings on the default spread, the term spread, and the earnings announcement factors. Moreover, high-distress firm assets also command low loadings on the default spread and term spread factors but, interestingly, high loadings on the speculative-grade bond market portfolio and the bond value (HML) factor.

Using a design identical to Table 3, Table 6 once again supplements our portfolio sorts with FM regressions. The table confirms the relations of mean stock, bond, and loan returns with distress risk suggested by the portfolio sorts. While the stocks in distress deciles 6–9, for example, earn a 0.11% (t-stat: 0.37) higher mean return than lower-decile stocks, the top-decile stocks earn a 1.06% (t-stat: −2.23) lower mean return than decile 6–9 stocks (see column 1). Notwithstanding, the regressions yield more monotonically negative mean firm-asset return-distress risk relations. While the firm assets in distress decile 6–9, for example, earn a 0.02% (t-stat: −0.12) lower standard mean return than lower-decile assets, the top-decile firm assets earn a 0.79% (t-stat: −3.21) lower mean return than the decile 6–9 assets (see column 9). Similar to before, distressed stocks, bonds, or loans are more likely to underperform if the other asset classes do so, too, although the modulating effect is not always significant (see columns 2, 4, and 7). Finally, the standard and BGN returns again yield close-to-identical results, whereas most controls, however, do not produce significant premiums, likely due to the stock-bond-loan-asset sample’s tilt toward larger firms.

TABLE 6Stock, Bond, Loan, and Firm-Asset Regressions on Distress Risk

Figure 3 and Table IA.8 in the Supplementary Material study the persistence of the stock, bond, loan, and firm-asset distress premiums in the stock-bond-loan-asset sample. In particular, the figure plots the monthly FF6S stock (Graph A), SB14 bond (Graph B), SB14 loan (Graph C), and SB17 firm-asset (Graph D) alphas of the value-weighted distress quintile spread portfolios plus their corresponding 95% confidence bands separately for months $ t $ to $ t+11 $ . The table offers the same results plus those from the equivalent equal-weighted portfolios and FM regressions. Both reveal that the stock and firm-asset premiums remain significant for about 2–3 months, the bond premium for about 1–4 months, and the loan premium for about 3–4 months. The weaker persistence in the stock-bond-loan-asset sample is likely due to its skew toward larger firms known to produce weaker anomalies (Fama and French (Reference Fama and French2008)).

FIGURE 3The Longer-Horizon Stock, Bond, Loan, and Firm-Asset Distress Premiums

Figure 3 plots the monthly FF6S stock (Graph A), SB14 bond (Graph B), SB14 loan (Graph C), and SB17 firm-asset (Graph D) alpha of the value-weighted high-minus-low distress quintile spread portfolio (sold line) and the corresponding 95% confidence bands (broken lines) separately for each of the first 12 months after portfolio formation (i.e., months $ t $ to $ t+11 $ ) in the stock–bond-loan-asset sample.

D. Robustness Tests

In this section, we briefly summarize the results from several robustness tests, offering more details plus the corresponding tables and figures in the Supplementary Material.

A. The Main Premise of Our Disinvestment Rationale

Our explanation starts from noting that distressed firms often sell their real assets (see Ofek (Reference Ofek1993), Asquith, Gertner, and Scharfstein (Reference Asquith, Gertner and Scharfstein1994), and Brown, James, and Mooradian (Reference Brown, James and Mooradian1994)). Yet, as the ability to sell a real asset is akin to an American put option, and since puts have negative expected excess returns (Coval and Shumway (Reference Coval and Shumway2001)), such options lower the firm’s expected asset return, especially in distress (see Hackbarth and Johnson (Reference Hackbarth and Johnson2015) and Aretz and Pope (Reference Aretz and Pope2018)). Our contribution is to show that those options are also able to lower the firm’s expected stock or debt return in distress if a sufficient amount of disinvestment proceeds flows to the appropriate claimants.

Figure 4 corroborates that our sample distressed firms also sell off their real assets. To create the figure, we select only the top-distress-decile firms from the stock–bond sample in Section IV.B and compute their quarterly asset (Graph A), property, plant, and equipment (PP&E; Graph B), and long-term asset (Graph C) growth and their sales of PP&E (Graph D) for the 16 quarters surrounding the portfolio-formation-month quarter (see the figure caption for variable definitions). To adjust for industry heterogeneity, we demean at the 49 Fama–French industry classification-quarter level. We finally take cross-sectional and then time-series averages. The figure reveals that our stock–bond sample distressed firms start selling off their real assets starting from about the portfolio formation quarter (i.e., quarter 0).

FIGURE 4The Capacity Disinvestments of Distressed Firms

Figure 4 plots the mean asset (Graph A), net property, plant, and equipment (Graph B), and net property, plant, and equipment plus long-term intangibles (Graph C) growth and the mean proceeds from sales of property, plant, and equipment scaled by assets (Graph D) of the top-distress-decile firms in our stock–bond portfolio sort over the 16 quarters surrounding the quarter containing the portfolio formation date. We first average by cross section and then over our sample period. We use Kenneth French’s 49 industry scheme to adjust for industry heterogeneity.

B. A Real Options Model of a Stock-and-Debt Financed Firm

We study a stock-and-debt financed firm operating in continuous time $ t\in \left[0,\infty \right) $ . The firm owns a continuum of incremental options to produce a unique output good (“assets-in-place”) and options to install more of those incremental options (“growth options”). Starting with the firm’s production choices, let us index the incremental options by $ k\in \left[0,\infty \right) $ , with the kth option written on the kth output increment, and assume that the firm owns the options to produce up to the Kth output increment (so $ K $ is the firm’s installed capacity). In each instant, the firm can switch on or off each option to produce, where switching on or off is cost-free. When switched on, the kth option produces one output increment per time unit at a unit cost of $ C(k)={c}_1+{c}_2k+f $ , where $ {c}_1 $ and $ {c}_2 $ are the variable cost parameters and $ f $ is the fixed cost parameter. When switched off, it does not produce output but still incurs a unit cost of $ C(k)=f $ . We finally assume that the firm instantaneously sells its output at the stochastic price $ \theta $ , which is governed by the geometric Brownian motion (GBM):

(5) $$ d\theta =\left(\mu -\delta \right)\theta d t+\sigma \theta dW, $$

where $ \mu $ is the total expected return, $ \delta $ is the dividend yield, and $ \sigma $ is the volatility of a mimicking portfolio tracking variations in the output price, and $ W $ is a Brownian motion.

Our assumptions imply that the firm optimally switches on the option to produce the kth output increment in the current instant if $ \theta \ge {c}_1+{c}_2k $ . In turn, it sets its output quantity, $ Q $ , to $ \min \left({Q}^{\ast },K\right) $ , where $ {Q}^{\ast } $ is the optimal quantity to produce if the firm’s installed capacity were infinite. Given $ Q $ , the firm’s profits per time unit, $ \Pi $ , are equal to

(6) $$ \Pi ={\int}_0^Q\left(\theta -{c}_1-{c}_2k\right) dk- fK=\theta Q-{c}_1Q-\frac{1}{2}{c}_2{Q}^2- fK, $$

and the firm immediately distributes those profits to its shareholders.

We next consider the capacity choices (i.e., investment and disinvestment options) of the firm. In each instant, the firm can spend the one-unit cost $ I $ to transform the growth option on the kth output increment into the corresponding option to produce. Conversely, it can sell off the option to produce that same increment, cashing in the one-unit disinvestment proceeds $ S $ . For simplicity, we assume that, upon disinvesting an option to produce, the firm cannot reinstall it in the future, so disinvesting does not lead to reacquiring the corresponding growth option. Crucially, while the firm funds investments through raising equity, it instantaneously distributes the share $ q $ of disinvestment proceeds to its shareholders but keeps the residual in a savings account (earning the risk-free rate) to help it honor its debt obligations. The logic is that the firm’s assets consist of easy-to-verify secured assets and hard-to-verify unsecured assets. While the firm must use the sales proceeds from secured assets to pay its debt, it can divert a share of the sales proceeds from unsecured assets to shareholders.

We finally discuss our capital structure assumptions. The firm is financed by common stock and a Merton (Reference Merton1974) zero-coupon bond. The bond obliges the firm to pay $ C $ at time $ T $ . Since the firm instantaneously pays profits to shareholders, it must pay its debt out of its remaining assets-in-place plus its saved disinvestment proceeds. If the firm cannot do so, it defaults, and debtholders receive the entire remaining firm value and saved disinvestment proceeds.

C. The Real Options Model Solution

We use standard contingent claims techniques to determine the values of the firm’s assets-in-place and growth options (see Dixit and Pindyck (Reference Dixit and Pindyck1994)). Specifically, the Supplementary Material shows that the value of the option to produce the $ {k}^{th} $ output increment, $ \Delta V\left(\theta; k\right) $ , is

(7) $$ \Delta V\left(\theta; k\right)=\left\{\begin{array}{ll}{B}_O{\theta}^{\beta_2}+\frac{\theta }{\delta }-\frac{c_1+{c}_2k+f}{r}& \hskip1.12em \mathrm{if}\;\theta \ge {c}_1+{c}_2k,\\ {}{A}_I{\theta}^{\beta_1}+{B}_I{\theta}^{\beta_2}-\frac{f}{r}& \hskip1.12em \mathrm{if}\;{\theta}^D\le \theta <{c}_1+{c}_2k,\\ {}S& \hskip1.12em \mathrm{if}\;{\theta}^D>\theta, \end{array}\right. $$

where $ r $ is the risk-free rate, and $ {B}_O $ , $ {A}_I $ , $ {B}_I $ , $ {\theta}^D $ , $ {\beta}_1 $ , and $ {\beta}_2 $ are free parameters defined in the Supplementary Material. Intuitively, $ {B}_O $ ( $ {A}_I $ ) [ $ {B}_I $ ] determines the value of the real option to switch off (switch on) [sell off] the option to produce, and $ {\theta}^D $ is the optimal disinvestment threshold (i.e., the price at or below which the firm optimally sells the option).Footnote ²²

Conversely, the value of the corresponding growth option, $ \Delta G\left(\theta; k\right) $ , is

(8) $$ \Delta G\left(\theta; k\right)=\left\{\begin{array}{ll}\Delta V\left(\theta; k\right)-I& \hskip1em \mathrm{if}\;\theta \ge {\theta}^{\ast },\\ {}G{\left({\theta}^{\ast}\right)}^{\beta_1}& \hskip1em \mathrm{if}\;\theta <{\theta}^{\ast },\end{array}\right. $$

where $ G $ and $ {\theta}^{\ast } $ are new free parameters defined in the Supplementary Material. Intuitively, $ G $ determines the pre-exercise growth option value, and $ {\theta}^{\ast } $ is the optimal investment threshold (i.e., the price threshold at or above which the firm optimally exercises the option).

We can finally compute the total value of the firm, $ V\left(\theta \right) $ , from

(9) $$ V\left(\theta \right)={\int}_0^K\Delta V\left(\theta; k\right) dk+{\int}_K^{\infty}\Delta G\left(\theta; k\right) dk, $$

which we numerically approximate through the trapezoidal method.

Unfortunately, it is impossible to determine the values of the common stock and the zero-coupon bond in closed-form. As a result, we use a Monte Carlo simulation technique to obtain them. To do so, we write the value of the zero-coupon bond, $ D\left(\theta; T\right) $ , as

(10) $$ D\left(\theta; T\right)={E}^{\unicode{x211A}}\left[{e}^{- rT}\min \Big(C,V\left({\theta}_T\right)+\left(1-q\right){S}_T\Big)\right], $$

where $ {E}^{\unicode{x211A}} $ is the expectation operator under the equivalent martingale measure, $ V\left({\theta}_T\right) $ is the value of the firm’s assets-in-place and growth options at time $ T $ , and $ {S}_T $ is the compounded-up value of the disinvestment proceeds collected by the firm until that same time. We then simulate 100,000 sample paths for the daily output price $ \theta $ from time $ t=0 $ to $ T $ under the equivalent martingale measure, derive the firm’s optimal capacity utilization, investment, and disinvestment choices at the end of each day, and calculate $ {e}^{- rT}\min \left(C,V\left({\theta}_T\right)+\left(1-q\right){S}_T\right) $ for each path. Averaging over the 100,000 $ {e}^{- rT}\min \left(C,V\left({\theta}_T\right)+\left(1-q\right){S}_T\right) $ values, we obtain $ D\left(\theta; T\right) $ . Subtracting $ D\left(\theta; T\right) $ from $ V\left(\theta \right) $ , the initial firm value, we obtain the value of the common stock, $ E\left(\theta; T\right) $ . See the Supplementary Material for more technical details.

We follow Cox and Rubinstein (Reference Cox and Rubinstein1985) in computing the instantaneous expected excess return of the assets ( $ X=V $ ), debt ( $ X=D $ ), or stocks ( $ X=E $ ), $ E\left[{R}_X^{ie}\right] $ , from

(11) $$ {\displaystyle \begin{array}{c}E\left[{R}_X^{ie}\right] dt=E\left[ dX/X\right]+\pi / Xdt- rdt=E\left[ dX/X\right]+\pi / Xdt\\ {}-\left({E}^{\unicode{x211A}}\left[ dX/X\right]+\pi / Xdt\right)\\ {}=\left(\left(\mu -\delta \right)\theta {X}_{\theta }+\frac{1}{2}{\sigma}^2{\theta}^2{X}_{\theta \theta}+{X}_t\right)/ Xdt\\ {}-\left(\left(r-\delta \right)\theta {X}_{\theta }+\frac{1}{2}{\sigma}^2{\theta}^2{X}_{\theta \theta}+{X}_t\right)/ Xdt\\ {}={X}_{\theta}\left(\theta /X\right)\left(\mu -r\right) dt,\end{array}} $$

where $ \pi $ is the claim’s payoff, $ {X}_{\theta } $ and $ {X}_t $ the first partial derivatives of the claim’s value with respect to the output price $ \theta $ and time $ t $ , respectively, and $ {X}_{\theta \theta} $ the second partial derivative of that value with respect to the output price. We rely on Itô’s lemma to derive the differential $ dX $ . Intuitively, equation (11) suggests that a claim’s expected excess return is linear in its elasticity, defined as its delta, $ {X}_{\theta } $ , times the claim value-to-output price ratio, $ \theta /X $ .

D. The Effect of Real Disinvestments on the Distress Premium

We now investigate the real-options-model-implied effect of distress risk on the expected asset, stock, and debt return of the firm. In the base case, we set the firm’s initial capacity, $ K $ , to one. We further rely on an annualized total expected return, $ \mu $ , dividend yield, $ \delta $ , and volatility, $ \sigma $ , of the output-price mimicking portfolio of 12%, 8%, and 45%, respectively, and a risk-free rate, $ r $ , of 4%. We select the variable production cost parameters, $ {c}_1 $ and $ {c}_2 $ , to be 0.00 and 0.30, respectively, and the fixed production cost parameter, $ f $ , to be 0.70. We choose a bond repayment, $ C $ , and time-to-maturity, $ T $ , of 10.00 and 2.00, respectively. Consistent with distressed firms owning few valuable growth opportunities, we select an investment cost, $ I $ , of 100, ensuring that growth options make up an only small portion of total value.

We first study the effect of distress risk on the expected asset return separately for firms varying in the ease with which they can sell their assets-in-place. To do so, we always let the initial output price, $ \theta $ , range from the lowest value at which the firm does not immediately disinvest some capacity to 2.00. To vary the firm’s ability to disinvest, we set the disinvestment proceeds, $ S $ , to 0.00, 4.00, or 8.00. In Figure 5, we then plot the expected excess asset return (equation (11)) against distress risk (the probability that $ V\left({\theta}_T\right)+\left(1-q\right){S}_T<C $ ) for each $ S $ value. The figure suggests that a greater ability to disinvest (i.e., a higher $ S $ value) lowers the expected asset returns especially for distressed firms. Specifically, while the expected asset returns of low-distress-risk firms are close to one another, those returns vividly rise (fall) with distress risk under a low (high)-disinvestment ability. The reason is that distressed firms without valuable disinvestment options have high operating leverage boosting their systematic risk (see Carlson, Fisher, and Giammarino (Reference Carlson, Fisher and Giammarino2004) and Cooper (Reference Cooper2006)). Yet, when distressed firms possess such options, the options’ negative risk can dominate the positive operating leverage risk, lowering the firms’ expected returns (see Hackbarth and Johnson (Reference Hackbarth and Johnson2015) and Aretz and Pope (Reference Aretz and Pope2018)).

FIGURE 5Disinvestments and the Default Risk-Expected Asset Return Relation

Figure 5 plots the expected excess asset return against default risk separately for a disinvestment gain, $ S $ , of 0, 4, and 8. See Section IV.D for more details about our basecase parameter value choices.

Notwithstanding, the more critical question for our purposes is whether a high-disinvestment ability can also induce expected stock or debt returns to fall with distress risk. To tackle that question, Figure 6 plots the expected excess stock (Graph A) and debt (Graph B) return against distress risk under disinvestment proceeds, $ S $ , of 8.00 and a share of proceeds going to shareholders, $ q $ , of 0.00, 0.05, 0.10, and 0.25. The figure suggests that the model can yield a negative (or, more accurately, negatively hump-shaped) relation between distress risk and expected stock (debt) returns if a sufficient amount of disinvestment proceeds flow to stock (debt) claimants. In particular, the stock (debt) relation becomes negative if at least 5% (75%) of proceeds flow to stock (debt) claimants. Strikingly, the figure also shows that the model can produce a jointly negative relation for stocks and debt if the lion’s share of proceeds flows to debtholders (e.g., 90%) but a small residual to shareholders (e.g., 10%).Footnote ²³

FIGURE 6Disinvestments and the Default Risk-Expected Stock or Debt Return Relation

Figure 6 plots the expected excess stock (Graph A) and debt (Graph B) return against default risk assuming a disinvestment gain, $ S $ , of 8 and separately for a fraction of disinvestment proceeds distributed to shareholders, $ q $ , equal to 0, 0.05, 0.10, and 0.25. See Section IV.D for details about the basecase parameter values.

All in all, this section shows that, in a real options model of a stock-and-debt financed firm with capacity utilization, investment, and disinvestment choices, the ability to disinvest real assets can not only switch the distress risk-expected asset return relation from positive to negative but also the stock and debt relations—if a sufficient amount of disinvestment proceeds flows to the appropriate claimants. More importantly, such a model can yield jointly negative relations if the lion’s share but not all of the proceeds flows to debtholders.

A. The Disinvestment Ability Proxies

We use as proxies for the ease with which a firm can disinvest its hard assets: i) Gu et al.’s (Reference Gu, Hackbarth and Johnson2018) asset inflexibility, ii) Eisfeldt and Rampini’s (Reference Eisfeldt and Rampini2006) asset reallocation, iii) Schlingemann et al.’s (Reference Schlingemann, Stulz and Walkling2002) asset liquidity, and iv) Bai et al.’s (Reference Bai, Li, Xue and Zhang2025) investment skewness.Footnote ²⁴ We calculate asset inflexibility as the range of the quarterly operating costs-to-quarterly sales ratio scaled by the volatility of the log change in the sales-to-assets ratio of a firm’s industry, where operating costs are costs of goods sold plus selling, general, and administrative costs. Asset reallocation is a firm’s annual acquisition expenses plus sales of property, plant, and equipment scaled by assets. Asset liquidity is the number of asset acquisition, firm acquisition, and merger deals in a firm’s industry over the last year. Finally, investment skewness is the sample skewness of the annual growth in the sum of net property, plant, and equipment plus depreciation and amortization of a firm’s industry. See the Appendix for more details.

The logic behind those proxies is as follows: A higher asset inflexibility signals a lower-disinvestment ability since firms waiting longer to disinvest in response to negative shocks observe greater drops in their sales than operating costs (due to fixed operating costs). In turn, they have more variable operating costs-to-sales ratios. Conversely, a higher asset reallocation signals a greater-disinvestment ability since higher-ability firms adjust their installed capacity more rapidly in response to shocks.Footnote ²⁵ A higher asset liquidity signals a greater-disinvestment ability since it indicates that firms’ real assets are traded in more active and liquid secondary markets. Finally, a more positive investment skewness signals a lower-disinvestment ability since the inability to disinvest truncates the investment distribution from the left.

In Table 7, we aim to validate the disinvestment ability proxies. To do so, we report the mean asset-sale-value-to-assets ratio for firms in the top (10), moderate (6–9), and low (1–5) distress deciles formed from the stock–bond sample in Section V.B separately for firms with an above third and below first quartile value for each disinvestment ability proxy. We obtain the asset-sale values from SDC Platinum. We compute the mean ratios by first averaging by portfolio formation date and then over our sample period. The table corroborates that firms classified by our proxies as high-disinvestment-ability markedly raise their asset sales in response to distress risk (see columns 1, 3, 5, and 7). For example, column 1 reveals that while low-distress and low-asset-inflexibility firms sell off about 7.41% of their assets, the corresponding number for high-distress firms is about 17.45%. In comparison, the asset sales of low-disinvestment-ability firms do not strongly relate to distress (see columns 2, 4, 6, and 8). Contrasting high-distress firms with a high- and low-disinvestment ability, the high-ability firms usually sell off more of their assets than their counterparts.

TABLE 7The Asset Sales of Distressed Firms

B. The Conditional Effect of Disinvestment Options

We next test whether the ability of firms to disinvest real assets helps to explain the negative stock, bond, loan, and firm-asset distress premiums in Section III. To that end, Table 8 reports the results from repeating the stock-and-bond FM regressions in columns 1, 4, and 6 of Table 3 and the loan regressions in columns 6 and 8 of Table 6 on subsamples of firms with high (above third quartile) and low (below first) values for each disinvestment ability proxy. Panels A, B, and C focus on stocks, bonds, and loans, respectively. As before, plain numbers are monthly premium estimates, while those in square brackets are Newey and West (Reference Newey and West1987) t-statistics with a 12-month lag length. To conserve space, we report estimates and t-statistics only for the distress dummy variables but not the controls.

TABLE 8Disinvestment-Ability-Specific Stock, Bond, and Loan Regressions

Starting off with our sample bonds and loans, Panels B and C suggest that their distress premiums are significantly more negative in the subsamples of firms with a higher-disinvestment ability, in line with firms owning easy-to-disinvest hard assets selling those in distress and distributing most of the proceeds to debtholders. Columns 1 and 2 in Panel B, for example, show that while the monthly standard-return bond distress premium is an insignificant −0.09% (t-stat: −0.74) in the high asset inflexibility (low-disinvestment ability) subsample, the corresponding number is a significant −0.29% (t-stat: −3.24) in the low inflexibility (high ability) subsample (contrast the coefficients on the HighDistress variable). As another example, columns 7 and 8 in Panel C reveal that while the standard-return loan distress premium is an insignificant −0.14% (t-stat: −0.94) in the high investment skewness (low-disinvestment ability) subsample, the corresponding number is a significant −0.69% (t-stat: −2.94) in the low skewness (high ability) subsample. Overall, the bond premium is significantly negative at the 95% level in eight (out of eight) cases in the high but in only two in the low disinvestment-ability subsample. Conversely, the loan premium is significantly negative in six cases in the high but only in two in the low disinvestment-ability subsample.

Reverting to our sample stocks, Panel A shows that their distress premium tends to be significantly more negative in the lower-disinvestment-ability subsamples. Columns 3 and 4, for example, suggest that while the monthly stock distress premium is an insignificant −0.15% (t-stat: −0.30) in the high asset reallocation (high-disinvestment ability) subsample, it is a significant −1.30% (t-stat: −2.70) in the low reallocation (low ability) subsample. Overall, the stock distress premium is significantly negative at the 95% level in two (out of four) cases in the low but in none in the high-disinvestment ability subsamples.

While it could be seen as puzzling that the ability to disinvest hard assets conditions the stock distress premium with the opposite sign compared to the bond and loan premiums, we note that easier-to-disinvest hard assets are likely attractive as collateral in debt contracts due to, for example, their high fire-sale values. As a result, it is likely that the proceeds from disinvesting them flow to debtholders, and not shareholders. In contrast, hard-to-disinvest hard assets are likely less attractive as collateral, allowing firms to channel some of the proceeds from disinvesting them to shareholders. Yet, as we demonstrate in Section IV, assigning an only small fraction of disinvestment proceeds to shareholders can already switch the distress risk-expected stock return relation from positive to negative.

C. The Conditional Effect of Volatility

We now offer further evidence that the modulating effect of the disinvestment ability proxies on the stock, bond, and loan distress premiums in Section V.B can be attributed to variations in the ease with which firms are able to sell their hard assets. To that end, we recall that the value of real options (such as the disinvestment option) rises with uncertainty. The upshot is that the modulating effect of the disinvestment ability proxies should be stronger for firms exposed to more uncertainty (see Grullon, Lyandres, and Zhdanov (Reference Grullon, Lyandres and Zhdanov2012) and our comparative statics on the effect of output-price volatility on the stock and debt distress premiums in Section IA.7.3 of the Supplementary Material). To test that conjecture, we choose those subsamples from Table 8 generating a stronger distress anomaly (i.e., the hard-to-disinvest stock and easy-to-disinvest bond and loan subsamples) and further split them according to the median of historical stock volatility. We estimate historical volatility from firm-specific regressions of the monthly stock return on the Fama and French (Reference Fama and French1993) 3-factor model factors over the last 2 years of data and computing the annualized volatility of the residual. We finally repeat the relevant regressions from Table 8 separately on the subsamples with a high versus low historical stock volatility.

Using a design similar to Table 8, Table 9 offers the subsample regression results. As always, plain numbers are monthly premium estimates, whereas those in square brackets are Newey and West (Reference Newey and West1987) t-statistics. The table supports the conjecture that the modulating effect of the disinvestment ability proxies is stronger in the higher-volatility subsamples. For example, while a high-distress risk lowers the monthly mean stock return of high-volatility, low inflexible-asset firms by a significant 0.73% (t-stat: −2.04), the corresponding change is an insignificant −0.24% (t-stat: −0.54) for low-volatility firms (contrast the HighDistress coefficient across columns 1 and 2 in Panel A). In the same vein, while a high-distress risk lowers the monthly mean standard loan return of high-volatility, high asset-liquidity firms by a significant 0.55% (t-stat: −2.29), the corresponding change is an insignificant 0.00% (t-stat: 0.03) for low-volatility firms (contrast the same coefficient across columns 5 and 6 in Panel C.1). Overall, the modulating effect of the disinvestment ability proxies is stronger in the high versus the low-volatility sample in all but two cases.

TABLE 9Volatility-Specific Stock, Bond, and Loan Regressions