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