The Idiosyncratic Volatility Puzzle

CAPM makes a clean prediction: only market risk (beta) should be priced, because company-specific risk can be diversified away for free just by holding many stocks, so no rational investor should demand extra compensation for bearing it. If that's true, sorting stocks by their idiosyncratic volatility — the part of their return variance not explained by common factors — should show no relationship with average returns. Ang, Hodrick, Xing and Zhang (2006) sorted stocks exactly this way and found the opposite of "no relationship": stocks in the highest idiosyncratic-volatility quintile earned dramatically lower average returns than the lowest quintile, by roughly 1% per month. High company-specific risk was being paid a negative premium, not zero.

Measuring idiosyncratic volatility

Idiosyncratic volatility is what's left of a stock's return variance after removing the part explained by common factors. Regress a stock's daily returns on the Fama-French factors (market, size, value) over a trailing window, and the standard deviation of the regression's residuals is the idiosyncratic volatility measure:

$\sigma_{idio} = \text{std}(\epsilon_t), \quad r_t = \alpha + \beta_{MKT} MKT_t + \beta_{SMB} SMB_t + \beta_{HML} HML_t + \epsilon_t$

In words: strip out how much of the stock's daily wiggle is explained by the market, size, and value factors, and measure the leftover noise. A stock whose price is driven mostly by idiosyncratic news (a biotech awaiting a single trial result) has high $\sigma_{idio}$; a stable utility with returns that track the market closely has low $\sigma_{idio}$.

Worked example. Sort 2,000 stocks into quintiles by trailing-month $\sigma_{idio}$. In the Ang et al. sample, the lowest quintile earned an average monthly return around 1.10%, while the highest quintile earned around 0.02% — a spread of roughly 1.08% per month, or well over 12% annualized, in the "wrong" direction from what compensation-for-risk would predict. A long-short portfolio buying the low-idio-vol decile and shorting the high-idio-vol decile would have captured that spread directly, and this observation is a direct ancestor of the modern "low-volatility" and "low-risk" factor strategies now run by large systematic funds.

What this means in practice, and why it's debated

No single explanation has fully settled the debate. Leading candidates include lottery-preference demand (retail investors overpay for stocks with small odds of a huge payoff, bidding up exactly the high-idio-vol names and depressing their forward returns), that the effect is partly a max-return or short-term reversal effect in disguise once controls are added, and that some of the original spread has weakened since publication as funds traded against it. Low-volatility equity strategies at firms managing tens of billions of dollars are a direct commercial descendant of this finding.