How does the low-volatility anomaly contradict CAPM, and why hasn't it been arbitraged away?

You've identified one of the most fascinating contradictions in modern finance. The low-volatility anomaly is real, persistent, and genuinely challenging for the CAPM framework.

What the Data Shows: Portfolios of low-volatility stocks have historically delivered:

• Similar or slightly lower absolute returns than high-volatility stocks
• Significantly higher risk-adjusted returns (Sharpe ratios)
• Much smaller drawdowns during market crashes

This means you give up very little return for a massive reduction in risk — the opposite of what CAPM predicts.

Why It Persists (Explanations):

1. Lottery Preference Investors are drawn to high-volatility stocks the same way people buy lottery tickets — the small chance of a huge payoff is psychologically attractive. This 'demand for lottery-like payoffs' pushes volatile stocks above fair value and depresses their subsequent returns.

2. Leverage Constraints Many institutional investors cannot use leverage. If you want higher returns and can't lever up a low-vol portfolio, you're forced to buy high-beta stocks instead. This excess demand for high-beta stocks pushes their prices up and future returns down.

3. Benchmarking and Career Risk Professional fund managers are judged against benchmarks. Holding a portfolio of low-vol utility stocks when the market is rallying leads to career risk — 'why is your fund underperforming the S&P?' This behavioral pressure pushes managers toward high-beta stocks.

4. Agency Problems Asset managers are often rewarded for high absolute returns, not risk-adjusted returns. A 15% return on a high-vol portfolio looks better in marketing materials than a 10% return on a low-vol portfolio, even if the Sharpe ratio favors the latter.

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Example: Consider two portfolios over a 15-year period. The Steadfast Low-Vol Portfolio (utilities, consumer staples, healthcare) returns 9.2% annualized with 10% volatility. The High-Octane Portfolio (biotech, crypto-adjacent, speculative growth) returns 9.8% with 25% volatility. The Sharpe ratio of the low-vol portfolio (0.62) crushes the high-vol portfolio (0.27).

Exam Tip: Know that the low-volatility anomaly challenges CAPM's prediction that beta is the sole determinant of expected return, and be able to cite behavioral and structural explanations for its persistence.

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