Cracking the Idiosyncratic Volatility Puzzle

Why High-Risk Stocks Don’t Always Mean High Returns

The most basic tenet of finance is that higher risk should equal higher returns. However, when it comes to idiosyncratic volatility (IVOL)—the stock-specific risk that can’t be diversified away—the real world tells a different story. The idiosyncratic volatility puzzle refers to the confounding empirical finding that stocks with higher company-specific risk often deliver lower future returns.

Zhuo Cheng, Jing Fang, and Yinglei Zhang, authors of the September 2023 study “Idiosyncratic Volatility and Return: A Finite Mixture Approach,” published in the British Accounting Review, used an innovative statistical approach to explain this puzzle: the relationship between idiosyncratic volatility and returns isn’t one-size-fits-all. It depends entirely on whether a stock is overvalued or undervalued. For investors, this means that high-volatility stocks can be either goldmines or landmines—and understanding the difference is crucial for portfolio success.

To test their hypothesis, they employed finite mixture normal regressions, a sophisticated statistical technique that identifies hidden subgroups within data without requiring researchers to specify those groups in advance. This method allowed them to discover whether the stock market actually contains distinct groups of companies with completely different IVOL-return relationships.

Key Findings: Two Hidden Groups Tell Different Stories

The researchers’ findings were striking and revealed why previous studies reached such contradictory conclusions:

Finding #1: Two Distinct Groups with Opposite Relationships

The data revealed two latent groups of stocks with fundamentally different behaviors:

• Group 1 (Negative Relationship): For one group of stocks, higher idiosyncratic volatility was associated with lower future returns

• Group 2 (Positive Relationship): For the other group, higher idiosyncratic volatility was associated with higher future returns

This discovery explained why aggregate studies had found mixed results—they were averaging together two completely different phenomena.

Finding #2: The Role of Stock Performance

The distribution of these groups wasn’t random:

• The negative IVOL-return relationship concentrated in firms with large negative realized returns (bottom two quintiles of performance)

• The positive IVOL-return relationship concentrated in firms with large positive realized returns (top two quintiles of performance)

Finding #3: Valuation Matters

The likelihood of a stock being in the negative relationship group was positively related to price-to-value ratio estimates. In other words, overvalued stocks were more likely to show the negative IVOL-return pattern.

The researchers identified a crucial mechanism: realized returns have a prominent mispricing-correction component that:

• Is negative for overvalued firms and decreases as overvaluation gets corrected.

• Is positive for undervalued firms and increases as undervaluation gets corrected.

• Creates higher volatility as prices move toward fair value.

The Big Picture: IVOL Signals Mispricing

These findings support a coherent explanation: idiosyncratic volatility is positively related to mispricing. High-volatility stocks tend to be mispriced, and the direction of future returns depends on whether they’re overvalued (leading to negative returns as prices correct downward) or undervalued (leading to positive returns as prices correct upward).

Consistent Findings

Cheng, Fang, and Zhang’s findings are consistent with those of Robert Stambaugh, Jianfeng Yu, and Yu Yuan, authors of the study “Arbitrage Asymmetry and the Idiosyncratic Volatility Puzzle,” who found:

· The IVOL effect was significantly negative among the most overpriced stocks. However, the effect was very positive among underpriced stocks.

· The negative effect among overpriced stocks was significantly stronger—the negative highest-versus-lowest difference among the most overpriced stocks was 3.7 times the magnitude of the corresponding positive difference among the most underpriced stocks.

· The IVOL effect was strongest among overpriced small stocks—consistent with small stocks being more difficult/expensive to short than large stocks. The effect held for large stocks as well, though it was no longer statistically significant at conventional levels.

· The average negative relation between IVOL and expected return was stronger in periods when there was a market-wide tendency for overpricing (when the Baker-Wurgler Sentiment Index was high) because stocks are more likely to be overpriced and arbitrage risk and costs are more likely to be high during high sentiment.

These findings are also consistent with those of the authors of the study “Dissecting the Idiosyncratic Volatility Puzzle: A Fundamental Analysis Approach” who found:

· The IVOL-return relation varied depending on the fundamental strength of stocks—the IVOL-return relation for stocks with strong (poor) fundamental strength was positive (negative).

· For stocks with poor fundamental strength, the negative IVOL effect was more pronounced following high sentiment periods.

Investor Takeaways