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.FreepikFor 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:

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 ResearchYezhou 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:

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 TakeawayThe 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.More By This Author:Fifty Shades of Grey Swans: The Risks That Matter MostIs Now A Good Time To Buy Bonds? The Magnificent Seven