That riskier assets should command higher expected returns is the most basic of asset pricing theories. Clearly, financial distress is a risk characteristic, but it presents a puzzle, as there has not been a linear relationship between it and stock returns.

For example, John Birge and Yi Zhang, authors of the April 2017 study “Risk Factors That Explain Stock Returns: A Non-Linear Factor Pricing Model,” found that when a company is not near financial distress, investors require a return premium for holding extra default risk. However, when a firm is close to or in financial distress, a negative relationship exists between default risk and return. They also found that the weakest companies tend to be small—the relationship between risk and return in these weak credit risk stocks is so negative that when the 2.5% of the weakest firms were screened out, the size premium disappeared entirely.

These results are consistent with those of  Pengjie Gao, Christopher Parsons, and Jianfeng Shen, authors of the study “The Global Relation Between Financial Distress and Equity Returns,” published in the January 2018 issue of The Review of Financial Studies. The study examined the distress risk anomaly—the tendency for stocks with high credit risk to perform poorly—across 38 countries over the period January 1992-June 2013.

Their measure of credit risk was Moody’s KMV database of monthly Expected Default Frequency (EDF). Following is a summary of their key findings:

  • There was a strong, negative relationship between default probabilities and equity returns that was concentrated among low-capitalization stocks in developed countries in North America and Europe.
  • The returns of small, distressed firms were worse by 35-50 basis points per month and persisted up through a year after portfolio formation. The results were caused by the poor performance of distressed firms rather than the good performance of the firms with the least credit risk.
  • Risk-based explanations provided a poor account of the patterns—the smaller, riskier firms had higher betas, leverage, and volatility.

Gao, Parsons, and Shen found that the anomaly was concentrated among small, illiquid stocks, where limits to arbitrage can allow mispricings to persist. They also found evidence pointing to a behavioral interpretation, suggesting that stocks of companies in financial distress are temporarily overpriced. For example, they found that the distress anomaly was concentrated in periods directly preceded by aggregate market gains, fueling investor overconfidence. They wrote: “Further underperformance is observed when up markets (price formation period) are directly followed by down markets (return measurement period). Both effects are driven by stocks with high turnover, a measure of retail trader activity.”

The authors explained: “If underreaction is responsible for the overpricing of distressed stocks, performance should be especially poor for firms having received bad news recently.”  And that is exactly what they found. They concluded that the evidence “suggests that at least in part, behavioral biases contribute to the temporary mispricing of financially distressed firms.”

Gao, Parsons, and Shen’s findings are consistent with research showing that many anomalies exist only in high-sentiment regimes, when investor overconfidence plays an important role. Their findings are also consistent with those of Doron Avramov, Tarun Chordia, Gergana Jostova, and Alexander Philipov, authors of the 2012 study “Anomalies and Financial Distress,” who found that the stocks with the worst credit ratings had more systematic risk and earned lower risk-adjusted returns than better-rated stocks.

Interestingly, Gao, Parsons, and Shen found that the anomaly in which small-cap stocks with the weakest credit have the worst returns was not present in emerging markets—only two of the 17 emerging markets they examined displayed the anomaly.

New Research

Yezhou Sha, Ziwen Bu, and Zilong Wang contribute to the financial distress literature with their study “What drives the distress risk-return puzzle? A perspective on limits of arbitrage,” published in the October 2023 issue of the International Journal of Finance & Economics, in which they examined the relationship among a firm’s distress risk, limits of arbitrage, and the cross-section of stock returns. As their measure of distress risk, they followed the failure probability from a hazard model developed by the authors of the 2005 study “In Search of Distress Risk” that predicts financial distress using accounting-based and market-based data. To measure the limits of arbitrage, they used a stock’s monthly bid-ask spread, dollar volume, and the Amihud illiquidity ratio (the daily ratio of absolute stock return to its dollar volume) as proxies of transaction costs. They then formed five-by-five portfolios that ranked stocks by distress risk and a proxy of limits of arbitrage independently. Their data covered the period 1981-2014. Following is a summary of their key findings:

  • The high-distress risk portfolio tended to have higher bid-ask spreads, illiquidity, idiosyncratic volatility, lower dollar volume and institutional ownership, and a lower short interest ratio than the low-distress risk portfolio.
  • High failure probability (FP) stocks had lower returns than low FP stocks. The spread of returns between the top 10% and the bottom 10% of stocks was 0.61% per month without risk adjusting, or 0.90%-1.42% per month with risk adjusting.
  • FP was negatively associated with a stock’s short interest ratio, suggesting that the demand for short selling was low.
  • The negative distress risk-return relation was stronger in stocks that had higher limits of arbitrage.
  • Compared to the distress risk premium among all stocks (0.61% per month), the distress risk premium in the lowest limits of arbitrage quintile was only -0.08% to 0.45% per month and was statistically insignificant from zero. However, in the highest limits of the arbitrage quintile, the distress risk premium was as high as 1.19%-1.74% per month. It was even larger when adjusted for risk. The Fama-French three-factor premium was 0.45%-1.03% per month in low limits to arbitrage stocks and 1.51%-2.27% per month in high limits to arbitrage stocks. 
  • The distress risk premium was even larger when risk adjusted. The Fama-French three-factor alpha of the above portfolio was 0.45%-1.03% per month in low limits of arbitrage stocks and 1.51%-2.27% per month in high limits of arbitrage stocks.
  • The distress risk premium came mainly from the short side of the long-short portfolio—implying short-sale constraints.
  • Investors were virtually unable to short sell mispriced, high-distress risk stocks due to the persistently low supply of lendable stocks from institutions and costly arbitrage.
  • While the average portfolio return was positively related to stocks’ monthly bid-ask spread in low-distress risk quintiles, the average portfolio return was negatively related to stocks’ monthly bid-ask spread in high-distress risk quintiles. This is inconsistent with the liquidity effect, as illiquidity should be associated with high returns.
  • While illiquidity was positively associated with high-distress risk, low liquidity stocks were associated with high returns, and high-distress stocks were associated with low returns. Thus, it is the limits of the arbitrage effect, not the liquidity effect, that drives the distress puzzle.

Their findings led Sha, Bu, and Wang to conclude: “The reversed illiquidity-return relationship in high-distress risk stocks is due to the high costs for short selling. Thus, we conclude that it is the limits of arbitrage, not the liquidity effect, that drives the distress risk premium. We observe similar patterns when using other transaction cost proxies.”

Investor Takeaway

The empirical research findings demonstrate that the return premium generated by being long low-distress risk stocks and short high-distress risk stocks is persistent and that the capital asset pricing model (CAPM) and the Fama-French three-factor models cannot explain it. Hence, we have the distress puzzle, or anomaly.

While the great debate about market efficiency continues, and whether markets are driven by risk-based explanations or behavioral ones, the evidence suggests the answer isn’t black or white. Both explanations appear to play important roles depending on market frictions. For larger companies with default risk that are not yet in financial distress, credit risk is rewarded. However, for smaller firms, where the risk of default has become heightened and more imminent, the risk relationship breaks down, and a negative relationship exists between risk and future returns. The behavioral explanation for the poor returns of the worst-rated stocks is the lottery effect: Investors have a preference for positive skewness in returns, which causes them to be willing to accept a high probability of a below-average return to have a small chance of earning an outsized return (if the company recovers from its financial distress). In other words, the explanation for the anomaly is that when a firm is exposed to high default risk, with an asset value close to or even below the company’s total obligations, equity holders have potential upside benefits but little downside risk; the call option gives them rights, but not obligations, to keep the remaining asset value. In effect, the asset becomes like a lottery ticket, a type of investment preferred by many individuals—assets with positively skewed distributions and fat tails. When designing portfolios, investors are best served by selecting funds that screen out stocks with lottery-like characteristics, specifically both small growth companies with high investment, low profitability and high leverage; and the most distressed, often value stocks (a little distress can be a good thing for returns, but too much is a very bad thing). Both ends of the spectrum seem to suffer from the lottery effect. The empirical evidence also demonstrates that to earn the higher return value, you need to be willing to hold the stocks of companies that are not exactly the strongest—you need a strong stomach and must be willing to stay disciplined during bad times when distressed stocks come under pressure.

Larry Swedroe is head of financial and economic research for Buckingham Wealth Partners, collectively Buckingham Strategic Wealth, LLC and Buckingham Strategic Partners, LLC.

For informational and educational purposes only and should not be construed as specific investment, accounting, legal, or tax advice. Certain information is based on third party data and may become outdated or otherwise superseded without notice. Third party information is deemed to be reliable, but its accuracy and completeness cannot be guaranteed. Neither the Securities and Exchange Commission (SEC) nor any other federal or state agency have approved, determined the accuracy, or confirmed the adequacy of this article. LSR-23-602

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About the Author: Larry Swedroe

Larry Swedroe
As Chief Research Officer for Buckingham Strategic Wealth and Buckingham Strategic Partners, Larry Swedroe spends his time, talent and energy educating investors on the benefits of evidence-based investing with enthusiasm few can match. Larry was among the first authors to publish a book that explained the science of investing in layman’s terms, “The Only Guide to a Winning Investment Strategy You’ll Ever Need.” He has since authored seven more books: “What Wall Street Doesn’t Want You to Know” (2001), “Rational Investing in Irrational Times” (2002), “The Successful Investor Today” (2003), “Wise Investing Made Simple” (2007), “Wise Investing Made Simpler” (2010), “The Quest for Alpha” (2011) and “Think, Act, and Invest Like Warren Buffett” (2012). He has also co-authored eight books about investing. His latest work, “Your Complete Guide to a Successful and Secure Retirement was co-authored with Kevin Grogan and published in January 2019. In his role as chief research officer and as a member of Buckingham’s Investment Policy Committee, Larry, who joined the firm in 1996, regularly reviews the findings published in dozens of peer-reviewed financial journals, evaluates the outcomes and uses the result to inform the organization’s formal investment strategy recommendations. He has had his own articles published in the Journal of Accountancy, Journal of Investing, AAII Journal, Personal Financial Planning Monthly, Journal of Indexing, and The Journal of Portfolio Management. Larry’s dedication to helping others has made him a sought-after national speaker. He has made appearances on national television shows airing on NBC, CNBC, CNN, and Bloomberg Personal Finance. Larry is a prolific writer and contributes regularly to multiple outlets, including Advisor Perspective, Evidence Based Investing, and Alpha Architect. Before joining Buckingham Wealth Partners, Larry was vice chairman of Prudential Home Mortgage. He has held positions at Citicorp as senior vice president and regional treasurer, responsible for treasury, foreign exchange and investment banking activities, including risk management strategies. Larry holds an MBA in finance and investment from New York University and a bachelor’s degree in finance from Baruch College in New York.

Important Disclosures

For informational and educational purposes only and should not be construed as specific investment, accounting, legal, or tax advice. Certain information is deemed to be reliable, but its accuracy and completeness cannot be guaranteed. Third party information may become outdated or otherwise superseded without notice.  Neither the Securities and Exchange Commission (SEC) nor any other federal or state agency has approved, determined the accuracy, or confirmed the adequacy of this article.

The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom).

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