If you read the academic literature on the low volatility anomaly, you find they are focused on the Ang, Hodrick, Xing and Zhang papers of 2006 and 2009. This is funny for a couple reasons.

Bob Hodrick was chairman of the Northwestern Finance department when I was there back in 1994, and was completely indifferent to my dissertation on the negative relation between idiosyncratic returns and stock returns. Befitting academics, his subsequent landmark 2006 paper emphasized a new risk factor based on a stock's covariance with volatility innovations. This is standard stochastic discount function asset pricing, looking for more subtle risk factors that could save the paradigm. What they found here was obviously boring because no one mentions that angle, but rather the incidental mention that simple stock variance was hugely negatively related to returns cross-sectionally.

Consistent with my earlier experience with Hodrick, I imagine he couldn't accept the result as real or interesting except in the context of some convoluted risk factor explanation, so the seminal academic result had to be packaged as an add-on to a 'legitimate' hypothesis, one now recognized as pointless but was initially essential. Further, once a major pub mentioned it, one could address it without having people simply dismiss it as impossible because, theoretically, it doesn't happen; further, explanations could proceed unbounded, as while the introduction needed the 'risk factor' farcical explanation, secondary ones did not.

It reminds me of my favorite Darwin quote:

The fact of the negative volatility/idiosyncratic volatility/beta and returns is now legitimate, and around 2005 you had several independent institutional funds operating on the premise, so clearly the fact was in the air independent of Ang, Hodrick, Xing and Zheng. I personally had applied it as a C-corp from 1996 trying to get support, and eventually found a way to a hedge fund where I applied it at that time. Thus, I'm convinced it's not a figment of measurement error because I actually traded it and made money off it, and know people who have large funds that have outperformed their benchmarks applying this insight.

The Ang et al papers clearly show that total and idiosyncratic volatility give the same results, so all the focus on idiosyncratic makes the result seem much less robust than it is.

Anyway, I was reading a piece on explanations, and this highlighted other pieces, etc. I eventually read through this thread. Most I think are not interesting, though most are well worth reading to make sure. I'm intrigued by the assertion that stocks that have active short interest have a

1)Earnings Shocks and the Idiosyncratic Volatility Anomaly in the Cross-Section of Stock Returns

Peter Wong

Earnings momentum and post-announcement drift explains most of low vol return, in that low-returning high vol stocks have poor returns, repeatedly

2)The Information Content of Idiosyncratic Volatility

Jiang, Xu, and Yao

"Once we control for future earning shocks, there is no longer a significantly negative relation between idiosyncratic volatility and future stock returns."

3) Analyst Coverage and the Cross Sectional Relation Between Returns and Volatility

George and Hwang

"we show that the negative relations between returns and idiosyncratic volatility, and returns and turnover volatility, exist only among low coverage stocks."

4) Idiosyncratic Risk and the Cross-Section of Stock Returns: Merton (1987) Meets Miller (1977)

Boehme, Danielsen, Kumar, and Sorescu

"When short-sale constraints are absent, both idiosyncratic risk and dispersion of analyst forecasts are positively correlated with future abnormal returns for firms with low visibility, consistent with Merton. However, stocks with higher analyst dispersion and idiosyncratic volatility have negative abnormal returns when short-sale constraints are present, consistent with Miller."

See graph at right for main idea.

5) Liquidity Biases and the Pricing of Cross-Sectional Idiosyncratic Volatility Around the World

Han, Hu, and Lesmond

"Once we extract measurement errors in prices caused by the bid-ask spread we find little evidence in the pricing ability for idiosyncratic volatility."...the closing price-based idiosyncratic volatility estimate (using the three-factor model) for the developed markets (excluding the U.S.) shows a significant (at 1% level) alpha of -0.926% per month, consistent with the findings of Ang et al. (2009), while the quote midpoint return-based idiosyncratic volatility estimate demonstrates an insignificant alpha of only -0.474% per month."

6) Idiosyncratic Risk and the Cross-Section of Expected Stock Returns

Fangjian Fu

"Since idiosyncratic volatilities are time-varying, the one-month lagged idiosyncratic volatility may not be an appropriate proxy for the expected idiosyncratic volatility of this month....A zero-investment portfolio that is long in the 10% of the highest and short in the 10% of the lowest conditional idiosyncratic volatilities earns a positive return of 1.75% in a month. These findings support the theory prediction that idiosyncratic risk is positively related to expected returns."

7) Speculative Retail Trading and Asset Prices

Han and Kumar

"stocks with high idiosyncratic volatility and skewness, or lower prices are predominately held and actively traded by retail investors, while institutional investors under-weight those stocks. We also find that the characteristics of the retail clienteles of high RTP (retail trade participation) stocks are very similar to the characteristics of investors who exhibit greater propensity to speculate and gamble as documented in Kumar (2009)...Both approaches show that high RTP stocks have significantly lower average returns."

8) Maxing out: Stocks as lotteries and the cross-section of expected returns

Bali,Cakici, and Whitelaw

"When sorted first on maximum returns, the equal-weighted return difference between high and low idiosyncratic volatility portfolios is positive and both economically and statistically significant...A slightly different interpretation of our evidence is that extreme positive returns proxy for skewness, and investors exhibit a preference for skewness."

9) Default Risk, Idiosyncratic Coskewness and Equity Returns

Chabi-Yo andYang

"We find that there is a negative (positive) relation between idiosyncratic coskewness and equity returns when idiosyncratic coskewness betas are positive (negative). We construct two idiosyncratic coskewness factors to capture market-wide effect of idiosyncratic coskewness betas. When we control for these two idiosyncratic coskewness factors, the return difference for distress-sorted portfolios becomes insignificant."

10) Have we solved the idiosyncratic volatility puzzle?

Hou and Loh

"On the other hand, explanations based on expected idiosyncratic skewness, maximum daily return, retail trading proportion, one-month return reversal, pre- and post-formation earnings shocks show promise in explaining the puzzle ...Collectively, the above explanations account for roughly 60-80% of the puzzle."

11) Forecast Dispersion and the Cross Section of Expected Returns

Timothy C. Johnson

"I offer a simple explanation for this phenomenon based on the interpretation of dispersion as a proxy for unpriced information risk arising when asset values are unobservable. The relationship then follows from a general options-pricing result: For a levered firm, expected returns should always decrease with the level of idiosyncratic asset risk."

12) Anomalies and Financial Distress

Avramov, Chordia, Jostova,and Philipov

" Strategies based on price momentum, earnings momentum, credit risk, dispersion, idiosyncratic volatility, and capital investments derive their profitability from taking short positions in high credit risk firms that experience deteriorating credit conditions."

13) Can Growth Options Explain the Trend in Idiosyncratic Risk?

Cao, , Simin, and Zhao

"Empirically both the level and variance of corporate growth options are significantly related to idiosyncratic volatility. Accounting for growth options eliminates or reverses the trend in aggregate firm-specific risk. These results are robust for different measures of idiosyncratic volatility, different growth option proxies, across exchanges, and through time."

14) Does Idiosyncratic Volatility Proxy for Risk Exposure?

Chen and Petkova

"We decompose aggregate market variance into an average correlation component and an average variance component. Only the latter commands a negative price of risk in the cross section of portfolios sorted by idiosyncratic volatility. Portfolios with high (low) idiosyncratic volatility relative to the Fama-French (1993) model have positive (negative) exposures to innovations in average stock variance and therefore lower (higher) expected returns."

Bob Hodrick was chairman of the Northwestern Finance department when I was there back in 1994, and was completely indifferent to my dissertation on the negative relation between idiosyncratic returns and stock returns. Befitting academics, his subsequent landmark 2006 paper emphasized a new risk factor based on a stock's covariance with volatility innovations. This is standard stochastic discount function asset pricing, looking for more subtle risk factors that could save the paradigm. What they found here was obviously boring because no one mentions that angle, but rather the incidental mention that simple stock variance was hugely negatively related to returns cross-sectionally.

Consistent with my earlier experience with Hodrick, I imagine he couldn't accept the result as real or interesting except in the context of some convoluted risk factor explanation, so the seminal academic result had to be packaged as an add-on to a 'legitimate' hypothesis, one now recognized as pointless but was initially essential. Further, once a major pub mentioned it, one could address it without having people simply dismiss it as impossible because, theoretically, it doesn't happen; further, explanations could proceed unbounded, as while the introduction needed the 'risk factor' farcical explanation, secondary ones did not.

It reminds me of my favorite Darwin quote:

False facts are highly injurious to the progress of science, for they often long endure; but false views, if supported by some evidence, do little harm, as every one takes a salutary pleasure in proving their falseness.The fact that low volatility outperforms the average, and higher volatility greatly underperforms, was not an obvious fact in the 1990's even though I tried to explain this to people, though I wasn't working within some accepted theoretical framework, so my fact was not acknowledged.

The fact of the negative volatility/idiosyncratic volatility/beta and returns is now legitimate, and around 2005 you had several independent institutional funds operating on the premise, so clearly the fact was in the air independent of Ang, Hodrick, Xing and Zheng. I personally had applied it as a C-corp from 1996 trying to get support, and eventually found a way to a hedge fund where I applied it at that time. Thus, I'm convinced it's not a figment of measurement error because I actually traded it and made money off it, and know people who have large funds that have outperformed their benchmarks applying this insight.

The Ang et al papers clearly show that total and idiosyncratic volatility give the same results, so all the focus on idiosyncratic makes the result seem much less robust than it is.

Anyway, I was reading a piece on explanations, and this highlighted other pieces, etc. I eventually read through this thread. Most I think are not interesting, though most are well worth reading to make sure. I'm intrigued by the assertion that stocks that have active short interest have a

*positive*risk premium. Obviously, getting all that data together on short interest is non trivial so I'm not sure it's true (I like to see it myself, otherwise I generally don't believe it). These are mainly papers published around 2010 and 2011.1)Earnings Shocks and the Idiosyncratic Volatility Anomaly in the Cross-Section of Stock Returns

Peter Wong

Earnings momentum and post-announcement drift explains most of low vol return, in that low-returning high vol stocks have poor returns, repeatedly

2)The Information Content of Idiosyncratic Volatility

Jiang, Xu, and Yao

"Once we control for future earning shocks, there is no longer a significantly negative relation between idiosyncratic volatility and future stock returns."

3) Analyst Coverage and the Cross Sectional Relation Between Returns and Volatility

George and Hwang

"we show that the negative relations between returns and idiosyncratic volatility, and returns and turnover volatility, exist only among low coverage stocks."

4) Idiosyncratic Risk and the Cross-Section of Stock Returns: Merton (1987) Meets Miller (1977)

Boehme, Danielsen, Kumar, and Sorescu

"When short-sale constraints are absent, both idiosyncratic risk and dispersion of analyst forecasts are positively correlated with future abnormal returns for firms with low visibility, consistent with Merton. However, stocks with higher analyst dispersion and idiosyncratic volatility have negative abnormal returns when short-sale constraints are present, consistent with Miller."

See graph at right for main idea.

5) Liquidity Biases and the Pricing of Cross-Sectional Idiosyncratic Volatility Around the World

Han, Hu, and Lesmond

"Once we extract measurement errors in prices caused by the bid-ask spread we find little evidence in the pricing ability for idiosyncratic volatility."...the closing price-based idiosyncratic volatility estimate (using the three-factor model) for the developed markets (excluding the U.S.) shows a significant (at 1% level) alpha of -0.926% per month, consistent with the findings of Ang et al. (2009), while the quote midpoint return-based idiosyncratic volatility estimate demonstrates an insignificant alpha of only -0.474% per month."

6) Idiosyncratic Risk and the Cross-Section of Expected Stock Returns

Fangjian Fu

"Since idiosyncratic volatilities are time-varying, the one-month lagged idiosyncratic volatility may not be an appropriate proxy for the expected idiosyncratic volatility of this month....A zero-investment portfolio that is long in the 10% of the highest and short in the 10% of the lowest conditional idiosyncratic volatilities earns a positive return of 1.75% in a month. These findings support the theory prediction that idiosyncratic risk is positively related to expected returns."

7) Speculative Retail Trading and Asset Prices

Han and Kumar

"stocks with high idiosyncratic volatility and skewness, or lower prices are predominately held and actively traded by retail investors, while institutional investors under-weight those stocks. We also find that the characteristics of the retail clienteles of high RTP (retail trade participation) stocks are very similar to the characteristics of investors who exhibit greater propensity to speculate and gamble as documented in Kumar (2009)...Both approaches show that high RTP stocks have significantly lower average returns."

8) Maxing out: Stocks as lotteries and the cross-section of expected returns

Bali,Cakici, and Whitelaw

"When sorted first on maximum returns, the equal-weighted return difference between high and low idiosyncratic volatility portfolios is positive and both economically and statistically significant...A slightly different interpretation of our evidence is that extreme positive returns proxy for skewness, and investors exhibit a preference for skewness."

9) Default Risk, Idiosyncratic Coskewness and Equity Returns

Chabi-Yo andYang

"We find that there is a negative (positive) relation between idiosyncratic coskewness and equity returns when idiosyncratic coskewness betas are positive (negative). We construct two idiosyncratic coskewness factors to capture market-wide effect of idiosyncratic coskewness betas. When we control for these two idiosyncratic coskewness factors, the return difference for distress-sorted portfolios becomes insignificant."

10) Have we solved the idiosyncratic volatility puzzle?

Hou and Loh

"On the other hand, explanations based on expected idiosyncratic skewness, maximum daily return, retail trading proportion, one-month return reversal, pre- and post-formation earnings shocks show promise in explaining the puzzle ...Collectively, the above explanations account for roughly 60-80% of the puzzle."

11) Forecast Dispersion and the Cross Section of Expected Returns

Timothy C. Johnson

"I offer a simple explanation for this phenomenon based on the interpretation of dispersion as a proxy for unpriced information risk arising when asset values are unobservable. The relationship then follows from a general options-pricing result: For a levered firm, expected returns should always decrease with the level of idiosyncratic asset risk."

12) Anomalies and Financial Distress

Avramov, Chordia, Jostova,and Philipov

" Strategies based on price momentum, earnings momentum, credit risk, dispersion, idiosyncratic volatility, and capital investments derive their profitability from taking short positions in high credit risk firms that experience deteriorating credit conditions."

13) Can Growth Options Explain the Trend in Idiosyncratic Risk?

Cao, , Simin, and Zhao

"Empirically both the level and variance of corporate growth options are significantly related to idiosyncratic volatility. Accounting for growth options eliminates or reverses the trend in aggregate firm-specific risk. These results are robust for different measures of idiosyncratic volatility, different growth option proxies, across exchanges, and through time."

14) Does Idiosyncratic Volatility Proxy for Risk Exposure?

Chen and Petkova

"We decompose aggregate market variance into an average correlation component and an average variance component. Only the latter commands a negative price of risk in the cross section of portfolios sorted by idiosyncratic volatility. Portfolios with high (low) idiosyncratic volatility relative to the Fama-French (1993) model have positive (negative) exposures to innovations in average stock variance and therefore lower (higher) expected returns."