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gateway/knowledge/trading/strategies/stocks/low-volatility-anomaly.md

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+---
+description: "Buys low-historical-volatility stocks and shorts high-historical-volatility stocks, exploiting the empirical anomaly that lower-risk stocks deliver higher risk-adjusted returns."
+tags: [stocks, low-volatility, anomaly]
+---
+
+# Low-Volatility Anomaly
+
+**Section**: 3.4 | **Asset Class**: Stocks | **Type**: Anomaly / Low-Volatility
+
+## Overview
+The low-volatility anomaly is based on the empirical observation that future returns of previously low-return-volatility portfolios outperform those of previously high-return-volatility portfolios. This contradicts the naive expectation that higher-risk assets should yield proportionately higher returns, and is one of the most robust anomalies in empirical finance.
+
+## Construction / Signal
+Historical volatility `sigma_i` is computed from the time series of historical returns (as in the price-momentum formula):
+
+```
+sigma_i^2 = 1/(T-1) * sum_{t=S}^{S+T-1} (R_i(t) - R_i^mean)^2   (270)
+```
+
+Stocks are sorted by `sigma_i` in ascending order. A dollar-neutral portfolio is constructed by buying stocks in the **bottom decile** (low volatility) and shorting stocks in the **top decile** (high volatility).
+
+## Entry / Exit Rules
+- **Entry**: Buy bottom-decile stocks by `sigma_i`; short top-decile stocks by `sigma_i`.
+- **Exit**: Hold for the defined holding period (similar duration to the lookback window, typically 6–12 months).
+- **No skip period required**: Unlike momentum, no skip period is needed.
+
+## Key Parameters
+- **Lookback window**: 6 months (126 trading days) to 1 year (252 trading days)
+- **Holding period**: Similar to the lookback window, typically 6 months to 1 year
+- **Volatility measure**: Historical realized volatility `sigma_i` (annualized or monthly)
+- **Portfolio construction**: Dollar-neutral (long low-vol, short high-vol)
+
+## Variations
+- **Long-only minimum variance**: Buy low-volatility stocks only; used in minimum variance portfolio construction
+- **Beta-sorted portfolios**: Sort by market beta instead of (or in addition to) realized volatility
+
+## Notes
+- This anomaly goes counter to standard asset pricing theory (CAPM) which predicts higher risk = higher return.
+- Potential explanations include leverage constraints, benchmark hugging by institutional investors, and lottery preference among retail investors.
+- The lookback and holding periods are similar in duration (no skip period needed, unlike price-momentum).
+- Strategy can be combined with value or momentum factors in a multifactor portfolio (see Section 3.6).
+- Low-volatility stocks may cluster in defensive sectors (utilities, consumer staples), creating sector concentration risk.