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gateway/knowledge/trading/strategies/stocks/residual-momentum.md

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+---
+description: "Applies price-momentum to the residuals of a Fama-French factor regression rather than raw returns, isolating stock-specific momentum from common factor exposures."
+tags: [stocks, momentum, residual, fama-french]
+---
+
+# Residual Momentum
+
+**Section**: 3.7 | **Asset Class**: Stocks | **Type**: Momentum
+
+## Overview
+Residual momentum replaces raw stock returns in the price-momentum strategy with the residuals of a serial regression of stock returns on common risk factors (e.g., the 3 Fama-French factors). This isolates the stock-specific component of momentum, removing the influence of market, size, and value factor exposures. The approach is attributed to Blitz, Huij and Martens (2011).
+
+## Construction / Signal
+**Step 1 — Factor regression** (36-month estimation period, with 1-month skip):
+
+```
+R_i(t) = alpha_i + beta_{1,i} MKT(t) + beta_{2,i} SMB(t) + beta_{3,i} HML(t) + epsilon_i(t)   (278)
+```
+
+where:
+- `MKT(t)` = excess market return (market portfolio minus risk-free rate)
+- `SMB(t)` = Small Minus Big (size factor)
+- `HML(t)` = High Minus Low (book-to-market factor)
+
+Estimated over a 36-month period to get coefficients `alpha_i`, `beta_{1,i}`, `beta_{2,i}`, `beta_{3,i}`.
+
+**Step 2 — Compute residuals** for the 12-month formation period (S=1 skip):
+
+```
+epsilon_i(t) = R_i(t) - beta_{1,i} MKT(t) - beta_{2,i} SMB(t) - beta_{3,i} HML(t)   (279)
+```
+
+Note: `alpha_i` is excluded from this computation (it was estimated over the 36-month period, not the 12-month formation period).
+
+**Step 3 — Risk-adjusted residual return**:
+
+```
+epsilon_i^mean = (1/T) * sum_{t=S}^{S+T-1} epsilon_i(t)              (280)
+
+R_tilde_i^risk.adj = epsilon_i^mean / sigma_tilde_i                   (281)
+
+sigma_tilde_i^2 = 1/(T-1) * sum_{t=S}^{S+T-1} (epsilon_i(t) - epsilon_i^mean)^2   (282)
+```
+
+Construct a dollar-neutral portfolio by buying stocks in the top decile by `R_tilde_i^risk.adj` and shorting stocks in the bottom decile.
+
+## Entry / Exit Rules
+- **Entry**: At rebalance, buy top-decile stocks by risk-adjusted residual return; short bottom-decile stocks.
+- **Exit**: Hold for typically 1 month (can be longer).
+- **Skip period**: S=1 month.
+
+## Key Parameters
+- **Factor model**: 3 Fama-French factors (MKT, SMB, HML); Carhart 4-factor model (adding MOM) is an alternative
+- **Regression estimation period**: 36 months
+- **Formation period T**: 12 months
+- **Skip period S**: 1 month
+- **Holding period**: Typically 1 month
+- **Portfolio construction**: Dollar-neutral long/short decile
+
+## Variations
+- **4-factor model**: Add Carhart momentum factor MOM(t) to regression
+- **Alternative factor models**: Industry factors, principal components, other risk models
+
+## Notes
+- Alpha_i is deliberately excluded from the residual computation for the formation period, as it was estimated over the longer 36-month window.
+- Typical holding period is 1 month but can be extended.
+- The strategy removes common factor momentum (e.g., sector momentum) and isolates idiosyncratic stock momentum.
+- Risk: residual momentum can be sensitive to the choice of factor model and estimation period.