Profitability Premium: Risk-based or Behavioral?


When implementing quantitative investment strategies, it is generally believed that you should understand the economic rationale of why a strategy might work to minimize the probability of “overfitting.” Overfitting happens when you design a strategy that generated excess returns in your historical data, perhaps by chance or something specific to that market regime, but is unlikely to do so going forward. In this post, we go through this exercise, relying heavily on prior academic research.


Why Might These “Profitable” Firms Be Underpriced?


This is an interesting question to answer and when discussing systematic mispricing, researchers typically do so through the lens of a risk-based explanation (i.e. these firms generate higher returns because they are more risky) or a behavioral-based explanation (market participants are in aggregate underpricing these securities). I will discuss both.


Risk-Based Explanations


The risk-based explanation, supported by Fama and French (2006), is that these firms with higher profitability are pursuing more profitable, riskier projects and therefore have a higher cost of capital, leading to higher returns. Additionally, high profitability firms tend to be growth firms and therefore have a higher proportion of cash flows in the future. Because these cash flows are years away, they are considered riskier and therefore should have a higher risk premium. However, the risk-based explanation has difficulty reconciling the fact that more profitable firms are less likely to become distressed and have less operating leverage than unprofitable firms.


Additional evidence against the risk-based explanation comes from Ryan Liu’s paper “Profitability Premium: Risk or Mispricing.” He writes, “Firms with lower profitability are more volatile, suffer greater drawdowns, and are more sensitive to macroeconomic conditions. This means that the profitable firms are less risky by most measures and perform better during economic downturns. In addition, there is a monotonic relationship between profitability and forecast error. Analysts tend to be overoptimistic for low profitability firms relative to high profitability firms. Surprisingly this mis-expectation can persist even up to five years into the future” (pg 1).


He explores several risk-based explanations and finds that they do not hold up against the data. For example, if a firm has a beta or co-movement to market’s cash flow news (as opposed to discount rates news), a firm can be deemed riskier and thus require higher returns. However, when Liu investigates this possibility, he finds that unprofitable firms have higher cash flow beta than profitable firms. Another possibility revolves around the premise that investors care more about returns when times are bad, because their marginal utility of wealth is high. If a firm is very economically sensitive and cyclical, its returns will be poor at the worst possible time for an investor and thus require a higher rate of return. Liu finds that profitable firms do even better than unprofitable firms during bad times, discrediting this risk-based explanation. He writes, “I investigate the maximum drawdown, defined as the return from peak to trough, for holding periods of three months, six months, one year, and two years. In all cases, the low profitability firms tend to suffer significantly higher drawdowns and without exception, the lowest decile of profitability suffers the worst drawdown. For example, the worst three-month drawdown for the lowest decile of profitability is -51% while the next highest drawdown is suffered by Decile 3 at -37%. The worst one-year drawdown for the lowest profitability decile is -74%. This is more than 20% lower than any of the other portfolios and almost 30% lower than the most profitable decile (Table 8). This is very challenging to reconcile a risk-based explanation against.


To summarize, consistent with prior research, Liu found that profitable firms have outperformed unprofitable firms in 73% of the sample years and have done so with less volatility and higher Sharpe ratios.


Behavioral Explanations


In their 2016 paper “The Excess Returns of ‘Quality’ Stocks: A Behavioral Anomaly”, Bouchaud, Ciliberti, Landier, Simon, and Thesmar reach the same conclusion as Liu, though the way they arrive to it is different. The risk-based explanation they choose to address suggests a framework where firms can choose between two types of projects: safe and moderately profitable projects, and riskier and more profitable projects. The theory suggests that high profitability firms are engaging in these riskier projects and therefore require a higher expected return. However, the authors assert that the negative skewness associated with riskier projects does not show up in the returns of profitable firms. They write, "quality strategies are in fact found to have positive skewness and a very small propensity to crash” (pg 2). Next, they offer up a behavioral explanation, suggesting that investors underweight information contained in “quality” signals such as cash-flows, return on assets, etc. They suggest this could be driven by analysts focusing on other metrics such as earnings, momentum, and volatility. These metrics, according to the authors, do not properly capture all relevant information. Lastly, they discuss well-known cognitive biases as explanations for this phenomenon, which you can check out in the link above if interested.


The Bottom Line


The evidence presented by the authors above, especially Liu’s work on maximum peak-to-trough drawdown and macroeconomic sensitivity of low profitability firms, provide more credibility to the behavioral explanation for the historical outperformance of “profitable” firms.


Interested in learning more about Invariant's implementation? Please reach out to gary@invariantinvestments.com