Da and Gao (2010) find that the distress premium is mainly driven by stocks among high distress risk stocks with poor return performance in recent months. They conclude that for a one-year holding period portfolio, highest 10% distress risk stocks earn an average return at 2.10% in the first month and drop to 1.52% per month in the second holding month, and then vanishes in subsequent months of the entire holding period. They also find that distress risk thus loses its predictive power for expected returns when the previous one-month return and illiquidity ratio enters the Fama-MacBeth regression. To test if the distress puzzle is related to the short-term reversal effect, the monthly excess return is then regressed on two short-term reversal variables as presented below:
Short-term Return Reversal (𝑹𝒊,𝒕−𝟏): The monthly return one month prior to the formation of a portfolio. According to Da and Gao (2010), this is negatively priced in the cross-sectional returns and overrules the pricing power of firm’s distress risk.
Two-month Short-term Return Reversal (𝑹𝒊,𝒕−𝟐): The monthly return two months prior to the formation of a portfolio. According to Da and Gao (2010), this is negatively priced in the cross-sectional returns and reduces the coefficient of distress risk controlling for stock’s illiquidity.
However, the results in Table 13 suggest that the Turn-of-Month effect does not account for the distress puzzle, as Da and Gao (2010) argue. In line with their argument, the Amihud illiquidity ratio (𝐼𝐿𝐿𝐼𝑄) is included alongside 𝑙𝑛𝐵𝑀, 𝑙𝑛𝑀𝐸 , 𝑀𝑂𝑀12 , and remains significant considering the short-term reversal
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effect (Model 1 and Model 2). The 𝑅𝑖,𝑡−1 (t=-9.22) and 𝐼𝐿𝐿𝐼𝑄 (t=5.73) show strong predictive power in terms of each stock’s expected return, but the pricing power of distress risk remains strong and stable that 𝐹𝑃 in all three models has a t-stat over 3.0. The previous month’s return, 𝑅𝑡−1, does not subsume the predictive power of 𝐹𝑃, and 𝐹𝑃 still retains a negative sign. Checking whether monthly returns from two months before the formation of the portfolio may provide additional information is also relevant in judging the conclusions drawn by Da and Gao (2010). The relevant results from Model 2 show that even returns from two-months (=-0.367, t=-1.20) prior to portfolio formation cannot explain the significance of the distress puzzle (=-0.319, t=-3.62), though the coefficient of 𝐹𝑃 is slightly reduced compared to the Model 1 (-0.319 against -0.325).
One possible explanation for the divergence of Da and Gao (2010) and the current results is that they use the default likelihood ratio to represent distress risk, a method taken directly from Vassalou and Xing (2004). This is used based on information from U.S. stocks from 1971 to 1999. However, here, the proxy of distress risk is the failure probability, in line with Campbell et al. (2008), and the data comes from U.S. stocks from 1981 to 2014. Campbell et al. (2008) prove that failure probability and DLI are generally negatively related to equity returns in the 1981 to 2003 period, which contradicts Da and Gao (2010). Furthermore, the current research suggests that the distress premium exists within longer holding periods and, as such, it is unlikely that a short-term return reversal could cause abnormal returns over a period of months.
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Table 13 Fama-MacBeth regression on distress risk and turn-of-month effect Each month 𝑡, stocks monthly excess return is regressed on lagged characteristics based on distress risk (𝐹𝑃), Amihud (2002) illiquidity ratio (𝐼𝐿𝐿𝐼𝑄), and control variables including firm’s size (𝑙𝑛𝑀𝐸), book-to-market ratio (𝑙𝑛𝐵𝑀), momentum (𝑀𝑂𝑀12) using all NYSE, AMEX and NASDAQ common stocks as benchmark, and Model 1 and Model 2 adds short- term reversal variable (see section 4.5.5.1 for detail). T-statistics adjusted by the Newey- West standard error, are reported in parentheses. This dataset covers January 1981 to December 2014. *denotes p<0.10, ** denotes p<0.05 and *** denotes p<0.01.
Benchmark Model 1 Model 2
𝑙𝑛𝐵𝑀 0.491*** 0.490*** 0.492*** (4.64) (4.61) (4.83) 𝑙𝑛𝑀𝐸 -0.089* -0.085* -0.079* (-1.87) (-1.81) (-1.68) 𝑀𝑂𝑀12 0.381*** 0.369*** 0.361** (2.83) (2.61) (2.49) 𝐹𝑃 -0.294*** -0.325*** -0.319*** (-3.30) (-3.54) (-3.62) 𝐼𝐿𝐿𝐼𝑄 0.046*** 0.048*** 0.045*** (5.73) (6.00) (6.40) 𝑅𝑡−1 -3.683*** (-9.22) 𝑅𝑡−2 -0.367 (-1.20) Constant -0.565 -0.825 -0.863 (-0.56) (-0.80) (-0.86) Observations 1347785 1347785 1347785 Adj R2 0.031 0.037 0.032
130 4.5.3.2Robustness: Do penny stocks matter?
Untabulated regression results also show that the pricing power of distress risk is not merely a tautology of penny stock effect. When penny stocks are removed from the dataset, that is, any firm-month observation that has a stock price below $1 is removed, the t-statistic of 𝐹𝑃 in the cross-sectional regression is ranging - 3.46 and -3.53, a significant increase of t-statistics from the value range of -1.45 and -1.92 found in the previous sample where penny stocks were included. This strongly rejects the hypothesis that the penny stocks effect is a major contributor to the distress puzzle. In addition, the 𝐵𝐴 variable showed significant explanatory power in terms of explaining the pricing power of distress risk. When penny stocks are included, the results from the portfolio-level analysis and stock-level analysis are consistent. The coefficient sign of 𝐼𝑉𝑂𝐿 also changes. In the analysis in Section 4.5.3, 𝐼𝑉𝑂𝐿 is negatively related to stock returns, but in the new sample it is negatively related to stock returns, a result that is consistent with Ang et al. (2006). Thus, robustness analysis supports the hypothesis of the arbitrage limit playing a major role in explaining the distress risk anomaly, and it rejects the alternative explanation where penny stock effects drives most of the distress puzzle.
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