- 1High-volatility stocks underperform low-volatility stocks by approximately 1% per month
- 2This contradicts the fundamental prediction of the CAPM: more risk should mean more return
- 3The anomaly persists across the U.S., developed markets, and emerging markets
- 4It survives all known risk adjustments—this is a genuine anomaly
- 5The likely explanations are behavioral (lottery preferences) and institutional (benchmark constraints)
#The Paper at a Glance
Title: The cross-section of volatility and expected returns
Authors: Andrew Ang, Robert J. Hodrick, Yuhang Xing, and Xiaoyan Zhang
Published: Journal of Finance, 2006
DOI: 10.1111/j.1540-6261.2006.00836.x
This paper documented one of the most striking anomalies in finance: the relationship between volatility and returns is negative, not positive. Stocks that bounce around the most deliver the worst returns.
#What the Paper Found
The Core Discovery
Ang et al. sorted all U.S. stocks by their idiosyncratic volatility (volatility after removing market-wide movements) and measured subsequent returns:
| Volatility Quintile | Average Monthly Return |
|---|---|
| Lowest Volatility (Q1) | 1.06% |
| Q2 | 0.97% |
| Q3 | 0.85% |
| Q4 | 0.68% |
| Highest Volatility (Q5) | 0.02% |
| Low - High Spread | 1.04% per month |
The highest-volatility stocks earned essentially zero returns—while bearing the most risk. The lowest-volatility stocks earned over 1% per month with far less volatility.
It's Not Small-Cap or Value Effects
One might suspect that high-volatility stocks are just small, cheap, distressed companies. But Ang et al. showed the effect holds after controlling for: - Size (market capitalization) - Value (book-to-market) - Momentum - Liquidity - Market beta
None of these explain the volatility anomaly. It's a standalone effect.
Global Evidence
In a follow-up paper (Ang et al., 2009), the authors confirmed the anomaly across 23 developed markets:
| Region | Volatility Spread (Monthly) |
|---|---|
| United States | -1.04% |
| Europe | -0.80% |
| Japan | -0.56% |
| Pacific ex-Japan | -0.92% |
| G7 Average | -0.83% |
The effect is weaker outside the U.S. but still economically and statistically significant everywhere.
#Why This Anomaly Exists
1. Lottery Preferences
Investors treat high-volatility stocks like lottery tickets. A stock that could double in a month is exciting—people are willing to overpay for that upside potential.
Low-volatility stocks are boring. Nobody fantasizes about owning a utility company. This lack of demand keeps their prices reasonable—and their expected returns high.
2. Leverage Constraints
Many investors can't use leverage. If you want higher expected returns without leverage, you have to buy riskier stocks. This creates artificial demand for high-beta, high-volatility stocks—pushing their prices up and returns down.
As Frazzini and Pedersen (2014) showed in their "Betting Against Beta" paper, this constraint-driven demand is a primary driver of the anomaly.
3. Institutional Benchmarking
Professional fund managers are measured against benchmark indices. To beat the benchmark, many managers load up on high-beta stocks (which move more than the market). This creates additional demand for volatile stocks.
Baker, Bradley & Wurgler (2011) showed that this benchmarking constraint is a "limit to arbitrage"—even if managers know low-volatility stocks are better, the incentive structure prevents them from acting on it.
#Risk-Return Is Flat (or Inverted)
The textbook relationship between risk and return looks like this:
Theory: Higher risk → Higher return (upward-sloping line)
Reality: Higher risk → Lower return (downward-sloping or flat)
| Portfolio | Annual Return | Annual Volatility | Sharpe Ratio |
|---|---|---|---|
| Low Vol Quintile | 12.7% | 14.5% | 0.59 |
| Medium Vol | 10.2% | 21.3% | 0.30 |
| High Vol Quintile | 0.2% | 37.8% | -0.08 |
Low-volatility stocks offer better returns, lower risk, and dramatically better risk-adjusted performance. It's the best deal in finance.
#Subsequent Research
The volatility anomaly spawned a large research literature:
- Frazzini & Pedersen (2014): "Betting Against Beta" — formal model explaining why low-beta assets outperform across 20+ asset classes
- Baker, Bradley & Wurgler (2011): Benchmark-hugging creates "limits to arbitrage" that sustain the anomaly
- Novy-Marx & Velikov (2022): Critiqued some BAB methodology but confirmed the anomaly itself is real
#How This Applies to Our Rankings
Our low volatility factor carries a 10% weight in the composite score. We measure 60-day realized volatility, annualized:
Volatility = Standard Deviation of Daily Returns × Square Root of 252
Lower volatility stocks receive higher scores (we invert the measure). Combined with our other five factors, low volatility provides a defensive tilt that helps during market drawdowns without requiring us to avoid growth sectors entirely.
See lowest-volatility stocks →
#Academic Source
Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). "The cross-section of volatility and expected returns." Journal of Finance, 61(1), 259-299.
Last updated: February 1, 2026