Campbell, John Y, Jens Hilscher and Jan Szilagyi, 2005.

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stocks are delisted and then re-enter the database, but we do not include these stocksinthesampleafterthefirst delisting. We treat firms that fail as equivalent todelisted firms, even if CRSP continues to report returns for these firms. That is, ourportfolios sell stocks of companies that fail and we use the latest available CRSP datato 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 percentagepoints, with t statistics below in parentheses, and then alphas with respect to theCAPM, the three-factor model of Fama and French (1993), and a four-factor modelproposed by Carhart (1997) that also includes a momentum factor. Panel B reportsestimated factor loadings for excess returns on the three Fama-French factors, againwith t statistics. Panel C reports some relevant characteristics for the portfolios:the annualized standard deviation and skewness of each portfolio’s excess return, thevalue-weighted mean standard deviation and skewness of the individual stock returnsin each portfolio, and value-weighted means of RSIZE, market-book, and estimatedfailure probability for each portfolio. Figures 2 and 3 graphically summarize thebehavior of factor loadings and alphas.The average excess returns reported in the first row of Table 6 are strongly andalmost monotonically declining in failure risk. The average excess returns for thelowest-risk 5% of stocks are positive at 3.4% per year, and the average excess returnsfor the highest-risk 1% of stocks are significantly negative at -17.0% per year. Along-short portfolio holding the safest decile of stocks and shorting the most distresseddecile has an average return of 10.0% per year and a standard deviation of 26%, soits Sharpe ratio is comparable to that of the aggregate stock market.There is striking variation in factor loadings across the portfolios in Table 6. Thelow-failure-risk portfolios have negative market betas for their excess returns (thatis, betas less than one for their raw returns), negative loadings on the value factorHML, and negative loadings on the small firm factor SMB. The high-failure-riskportfolios have positive market betas for their excess returns, positive loadings onHML, and extremely high loadings on SMB, reflectingtheroleofmarketcapitalizationin predicting bankruptcies at medium and long horizons.These factor loadings imply that when we correct for risk using either the CAPMor the Fama-French three-factor model, we worsen the anomalous poor performanceof distressed stocks rather than correcting it. A long-short portfolio that holds thesafest decile of stocks and shorts the decile with the highest failure risk has an average19
excess return of 10.0% with a t statistic of 1.9; it has a CAPM alpha of 12.4% witha t statistic of 2.3; and it has a Fama-French three-factor alpha of 22.7% with a tstatistic of 6.1. When we use the Fama-French model to correct for risk, all portfoliosbeyond the 60th percentile of the failure risk distribution have statistically significantnegative alphas.One of the variables that predicts failure in our model is recent past return. Thissuggests that distressed stocks have negative momentum, which might explain theirlow 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 thealpha for the long-short decile portfolio roughly in half, from 22.7% to 12.0%, but itremains strongly statistically significant.Figure 4 illustrates the performance over time of the long-short portfolios that holdthe safest decile (quintile) of stocks and short the most distressed decile (quintile).Performance is measured both by cumulative return, and by cumulative alpha or riskadjustedreturn from the Fama-French three-factor model. For comparison, we alsoplot the cumulative return on the market portfolio. Raw returns to these portfoliosare concentrated in the late 1980’s and late 1990’s, with negative returns in the lastfew years; however the alphas for these portfolios are much more consistent overtime.The bottom panel of Table 6 reports characteristics of these portfolios. There isa wide spread in failure risk across the portfolios. Stocks in the safest 5% have anaverage failure probability of about 1 basis point, while stocks in the riskiest 5% havea failure probability of 34 basis points and the 1% of riskiest stocks have a failureprobability of 80 basis points.Stocks with a high risk of failure are highly volatile, with average standard deviationsof almost 80% in the 5% most distressed stocks and 95% in the 1% mostdistressed stocks. This volatility does not fully diversify at the portfolio level. 11 Theexcess return on the portfolio containing the 5% of stocks with the lowest failure riskhas an annual standard deviation of 11%, while the excess return for the portfoliocontaining the 5% of stocks with the highest failure risk has a standard deviation of26%, and the concentrated portfolio containing the 1% most distressed stocks has a11 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 determinedprimarily by common variation in distressed stock returns.20
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Campbell, John Y, Jens Hilscher and Jan Szilagyi, 2005.

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