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Thus, workers with specialized human capital in distressed ﬁrms have an incentive to avoid holding their ﬁrms’ stocks. If variation in distress is correlated across ﬁrms, workers in distressed ﬁrms have an incentive to avoid the stocks of all distressed ﬁrms. The result can be a state-variable risk premium in the expected returns of distressed stocks.” (p.77).

An alternative possibility is that investors have not understood the relation between our predictive variables and failure risk, and so have not discounted the prices of high-risk stocks enough to oﬀset their failure probability. In this case we will ﬁnd that failure risk appears to command a negative risk premium during our sample period. This expectation is consistent with the high failure risk of volatile stocks, since Ang, Hodrick, Xing, and Zhang (2005) have recently found negative average returns for stocks with high idiosyncratic volatility.

We measure the premium for ﬁnancial distress by sorting stocks according to their failure probabilities, estimated using the 12-month-ahead model of Table 4. Each January from 1981 through 2003, the model is reestimated using only historically available data to eliminate look-ahead bias. We then form ten value-weighted portfolios of stocks that fall in diﬀerent regions of the failure risk distribution. We minimize turnover costs and the eﬀects of bid-ask bounce by eliminating stocks with prices less than $1 at the portfolio construction date, and by holding the portfolios for a year, allowing the weights to drift with returns within the year rather than rebalancing monthly in response to updated failure probabilities.9 Our portfolios contain stocks in percentiles 0—5, 5—10, 10—20, 20—40, 40—60, 60—80, 80—90, 90—95, 95—99, and 99—100 of the failure risk distribution. This portfolio construction procedure pays greater attention to the tails of the distribution, where the distress premium is likely to be more relevant, and particularly to the most distressed ﬁrms. We also construct long-short portfolios that go long the 10% or 20% of stocks with the lowest failure risk, and short the 10% or 20% of stocks with the highest failure risk.

Because we are studying the returns to distressed stocks, it is important to handle carefully the returns to stocks that are delisted and thus disappear from the CRSP database. In many cases CRSP reports a delisting return for the ﬁnal month of the ﬁrm’s life; we have 6,481 such delisting returns in our sample and we use them where they are available. Otherwise, we use the last available full-month return in CRSP. In some cases this eﬀectively assumes that our portfolios sell distressed stocks at the end of the month before delisting, which imparts an upward bias to the returns on distressed-stock portfolios (Shumway 1997, Shumway and Warther 1999).10 We assume that the proceeds from sales of delisted stocks are reinvested in each portfolio in proportion to the weights of the remaining stocks in the portfolio. In a few cases, In the ﬁrst version of this paper we calculated returns on portfolios rebalanced monthly, and obtained similar results to those reported here.

In the ﬁrst version of this paper we did not use CRSP delisting returns. The portfolio results were similar to those reported here.

stocks are delisted and then re-enter the database, but we do not include these stocks in the sample after the ﬁrst delisting. We treat ﬁrms that fail as equivalent to delisted ﬁrms, even if CRSP continues to report returns for these ﬁrms. That is, our portfolios sell stocks of companies that fail and we use the latest available CRSP data to calculate a ﬁnal return on such stocks.

Table 6 reports the results. Each portfolio corresponds to one column of the table.

Panel A reports average returns in excess of the market, in annualized percentage points, with t statistics below in parentheses, and then alphas with respect to the CAPM, the three-factor model of Fama and French (1993), and a four-factor model proposed by Carhart (1997) that also includes a momentum factor. Panel B reports estimated factor loadings for excess returns on the three Fama-French factors, again

**with t statistics. Panel C reports some relevant characteristics for the portfolios:**

the annualized standard deviation and skewness of each portfolio’s excess return, the value-weighted mean standard deviation and skewness of the individual stock returns in each portfolio, and value-weighted means of RSIZE, market-book, and estimated failure probability for each portfolio. Figures 2 and 3 graphically summarize the behavior of factor loadings and alphas.

The average excess returns reported in the ﬁrst row of Table 6 are strongly and almost monotonically declining in failure risk. The average excess returns for the lowest-risk 5% of stocks are positive at 3.4% per year, and the average excess returns for the highest-risk 1% of stocks are signiﬁcantly negative at -17.0% per year. A long-short portfolio holding the safest decile of stocks and shorting the most distressed decile has an average return of 10.0% per year and a standard deviation of 26%, so its Sharpe ratio is comparable to that of the aggregate stock market.

There is striking variation in factor loadings across the portfolios in Table 6. The low-failure-risk portfolios have negative market betas for their excess returns (that is, betas less than one for their raw returns), negative loadings on the value factor HML, and negative loadings on the small ﬁrm factor SMB. The high-failure-risk portfolios have positive market betas for their excess returns, positive loadings on HML, and extremely high loadings on SMB, reﬂecting the role of market capitalization in predicting bankruptcies at medium and long horizons.

These factor loadings imply that when we correct for risk using either the CAPM or the Fama-French three-factor model, we worsen the anomalous poor performance of distressed stocks rather than correcting it. A long-short portfolio that holds the safest decile of stocks and shorts the decile with the highest failure risk has an average excess return of 10.0% with a t statistic of 1.9; it has a CAPM alpha of 12.4% with a t statistic of 2.3; and it has a Fama-French three-factor alpha of 22.7% with a t statistic of 6.1. When we use the Fama-French model to correct for risk, all portfolios beyond the 60th percentile of the failure risk distribution have statistically signiﬁcant negative alphas.

One of the variables that predicts failure in our model is recent past return. This suggests that distressed stocks have negative momentum, which might explain their low average returns. To control for this, Table 6 also reports alphas from the Carhart (1997) four-factor model including a momentum factor. This adjustment cuts the alpha for the long-short decile portfolio roughly in half, from 22.7% to 12.0%, but it remains strongly statistically signiﬁcant.

Figure 4 illustrates the performance over time of the long-short portfolios that hold the safest decile (quintile) of stocks and short the most distressed decile (quintile).

Performance is measured both by cumulative return, and by cumulative alpha or riskadjusted return from the Fama-French three-factor model. For comparison, we also plot the cumulative return on the market portfolio. Raw returns to these portfolios are concentrated in the late 1980’s and late 1990’s, with negative returns in the last few years; however the alphas for these portfolios are much more consistent over time.

The bottom panel of Table 6 reports characteristics of these portfolios. There is a wide spread in failure risk across the portfolios. Stocks in the safest 5% have an average failure probability of about 1 basis point, while stocks in the riskiest 5% have a failure probability of 34 basis points and the 1% of riskiest stocks have a failure probability of 80 basis points.

Stocks with a high risk of failure are highly volatile, with average standard deviations of almost 80% in the 5% most distressed stocks and 95% in the 1% most distressed stocks. This volatility does not fully diversify at the portfolio level.11 The excess return on the portfolio containing the 5% of stocks with the lowest failure risk has an annual standard deviation of 11%, while the excess return for the portfolio containing the 5% of stocks with the highest failure risk has a standard deviation of 26%, and the concentrated portfolio containing the 1% most distressed stocks has a On average there are slightly under 500 stocks for each 10% of the failure risk distribution, so purely idiosyncratic ﬁrm-level risk should diversify well, leaving portfolio risk to be determined primarily by common variation in distressed stock returns.

standard deviation of almost 40%. The returns on distressed stocks are also positively skewed, both at the portfolio level and particularly at the individual stock level.

Distressed stocks are much smaller than safe stocks. The value-weighted average size of the 5% safest stocks, reported in the table, is over 16 times larger than the value-weighted average size of the 5% most distressed stocks, and the equal-weighted size is about 9 times larger. Market-book ratios are high at both extremes of the failure risk distribution, and lower in the middle. This implies that distressed stocks have the market-book ratios of growth stocks, but the factor loadings of value stocks, since they load positively on the Fama-French value factor.

The wide spread in ﬁrm characteristics across the failure risk distribution suggests the possibility that the apparent underperformance of distressed stocks results from their characteristics rather than from ﬁnancial distress per se. For example, it could be the case that extremely small stocks underperform in a manner that is not captured by the Fama-French three-factor model. To explore this possibility, in Table 7 we double-sort stocks, ﬁrst on size using NYSE quintile breakpoints, and then on failure risk. In Table 8 we double-sort, ﬁrst on the book-market ratio using NYSE quintile breakpoints, and then on failure risk.

Table 7 shows that distressed stocks underperform whether they are small stocks or large stocks. The underperformance is, however, considerably stronger among small stocks. The average return diﬀerence between the safest and most distressed quintiles is three times larger when the stocks are in the smallest quintile as opposed to the largest quintile. If we correct for risk using the Fama-French three-factor model, the alpha diﬀerence between the safest and most distressed quintiles is about 50% greater in the smallest quintile than in the largest quintile. The table also shows that in this sample period, there is only a weak size eﬀect among safe stocks, and among distressed stocks large stocks outperform small stocks.

Table 8 shows that distressed stocks underperform whether they are growth stocks or value stocks. The raw underperformance is more extreme and statistically significant among growth stocks, but this diﬀerence disappears when we correct for risk using the Fama-French three-factor model. The value eﬀect is absent in the safest stocks, similar to a result reported by Griﬃn and Lemmon (2002) using Ohlson’s Oscore to proxy for ﬁnancial distress. However this result may result from diﬀerences in three-factor loadings, as it largely disappears when we correct for risk using the three-factor model.

As a ﬁnal speciﬁcation check, we have sorted stocks on our measure of distance to default. Contrary to the ﬁndings of Vassalou and Xing (2004), this sort also generates low returns for distressed stocks, particularly after correction for risk using the Fama-French three-factor model.

Overall, these results are discouraging for the view that distress risk is positively priced in the US stock market. We ﬁnd that stocks with a high risk of failure have low average returns, despite their high loadings on small-cap and value risk factors.

5 Conclusion This paper makes two main contributions to the literature on ﬁnancial distress. First, we carefully implement a reduced-form econometric model to predict corporate bankruptcies and failures at short and long horizons. Our best model has greater explanatory power than the existing state-of-the-art models estimated by Shumway (2001) and Chava and Jarrow (2004), and includes additional variables with sensible economic motivation. We believe that models of the sort estimated here have meaningful empirical advantages over the bankruptcy risk scores proposed by Altman (1968) and Ohlson (1980). While Altman’s Z-score and Ohlson’s O-score were seminal early contributions, better measures of bankruptcy risk are available today. We have also presented evidence that failure risk cannot be adequately summarized by a measure of distance to default inspired by Merton’s (1974) pioneering structural model. While our distance to default measure is not exactly the same as those used by Crosbie and Bohn (2001) and Vassalou and Xing (2004), we believe that this result, similar to that reported independently by Bharath and Shumway (2004), is robust to alternative measures of distance to default.

Second, we show that stocks with a high risk of failure tend to deliver anomalously low average returns. We sort stocks by our 12-month-ahead estimate of failure risk, calculated from a model that uses only historically available data at each point in time. We calculate returns and risks on portfolios sorted by failure risk over the period 1981-2003. Distressed portfolios have low average returns, but high standard deviations, market betas, and loadings on Fama and French’s (1993) small-cap and value risk factors. Thus, from the perspective of any of the leading empirical asset pricing models, these stocks have negative alphas. This result is a signiﬁcant challenge to the conjecture that the value and size eﬀects are proxies for a ﬁnancial distress premium. More generally, it is a challenge to standard models of rational asset pricing in which the structure of the economy is stable and well understood by investors.