Low-Volatility Anomaly

The foundational paper that challenged the efficiency of market-cap weighted portfolios. Haugen and Baker showed that minimum variance portfolios constructed from the 1,000 largest U.S. stocks had lower volatility AND higher returns than the Wilshire 5000 index from 1972-1989. They concluded that "matching the market is an inefficient investment strategy, even in an informationally efficient market." The paper was one of the first to demonstrate that stock returns are not well explained by beta, laying the groundwork for decades of low-volatility research.

Extended Haugen and Baker's work with more sophisticated methodology. Using the 1,000 largest U.S. stocks from 1968-2005, they achieved a volatility reduction of about 25% while delivering comparable or higher average returns than the market portfolio. The paper demonstrated that minimum-variance portfolios can be constructed using only the estimated covariance matrix, without reference to expected returns. They also analyzed the factor characteristics of low-volatility portfolios, finding persistent tilts toward value and quality.

The landmark study that documented the idiosyncratic volatility puzzle. Analyzing all NYSE, AMEX, and NASDAQ stocks from 1963-2000, the authors found that stocks with high idiosyncratic volatility earn abnormally low returns. The effect was economically large and statistically significant. Importantly, this held even after controlling for size, book-to-market, momentum, and liquidity. The paper sparked intense debate: why would investors accept lower returns for taking more firm-specific risk? With over 4,000 citations, it remains one of the most influential papers in asset pricing.

Documented the volatility effect using simple historical volatility (rather than idiosyncratic volatility). The annual alpha spread between global low and high volatility decile portfolios was 12% over the 1986-2006 period. The effect appeared independently in U.S., European, and Japanese markets. Crucially, it could not be explained by value, size, or momentum factors. The authors proposed three explanations: leverage restrictions, inefficient investment processes, and behavioral biases. Their methodology of sorting on 36-month historical volatility became a standard approach.

Extended their 2006 findings to 23 developed markets around the world. The negative relationship between idiosyncratic volatility and future returns held in virtually every market examined. The effect was not driven by small stocks, illiquidity, or transaction costs. The paper also addressed concerns about their U.S. findings, showing the effect persisted out-of-sample and was not due to reversals or microstructure issues. This global evidence made it harder to dismiss the anomaly as a statistical artifact.

Provided the definitive explanation for why the anomaly persists. Over 41 years (1968-2008), low volatility portfolios outperformed high volatility portfolios regardless of how risk was measured. The authors argued the anomaly survives because of limits to arbitrage: institutional investors are mandated to maximize information ratios relative to benchmarks, which discourages buying low-beta stocks (underweighting them creates tracking error). Individual investors, meanwhile, treat high-volatility stocks as lottery tickets. Baker et al. called low-volatility "perhaps the greatest anomaly in finance."

Documented the "MAX effect": stocks with extreme positive daily returns (lottery-like payoffs) subsequently underperform by about 1% per month. The MAX variable (highest daily return in the prior month) captured much of the idiosyncratic volatility anomaly. The interpretation: investors with lottery preferences overpay for stocks that have recently had extreme positive returns, expecting that lightning will strike twice. This behavioral explanation helped reconcile the low-volatility anomaly with investor irrationality rather than risk-based theories.

Presented a model explaining why high-beta assets are overpriced. Because many investors cannot use leverage, they tilt toward high-beta stocks instead. This demand pushes up high-beta prices and compresses their returns. The "Betting Against Beta" (BAB) factor (long low-beta, short high-beta) delivered significant positive alpha across U.S. equities, 20 international equity markets, Treasury bonds, corporate bonds, and futures. The return rivaled value, momentum, and size factors in magnitude. AQR now publishes updated BAB factor returns, making this one of the most practical academic contributions.