SystemTrader
StocksAdvancedLong-Only / Long-Short

Residual Momentum Strategy

Replace raw returns with regression residuals to capture stock-specific momentum. Removes market and factor exposure for a purer momentum signal with reduced crash risk.

Estimation
36 months
Formation
12 months
Skip Period
1 month
Holding
1-12 months

Overview

The residual momentum strategy is an enhancement of traditional price momentum. Instead of ranking stocks by raw returns, it ranks them by the residuals from a factor regression.

The idea: strip out the portion of returns explained by common factors (market, size, value) and focus on the stock-specific component. This "idiosyncratic" momentum is a distinct phenomenon from conventional momentum.

By removing systematic factor exposure, residual momentum tends to have lower crash risk than traditional momentum while maintaining strong returns. It also provides diversification when combined with other momentum strategies.

Key Insight

Factor Regression
Remove MKT, SMB, HML exposure
Reduced Crash Risk
Lower drawdowns than price momentum

Legend

Factor-explained return
Positive residual (BUY)
Negative residual (SHORT)

Formula

ε = R - β₁·MKT - β₂·SMB - β₃·HML

Residual = Raw return minus factor-explained portion

Key Insight

NVDA has high raw return (45%), but much is factor exposure. Its residual (27%) shows true stock-specific momentum. INTC has negative residual despite positive factor exposure.

Research

Research on residual (idiosyncratic) momentum and its advantages over traditional price momentum.

Recent Research

The Mathematics

In Plain English

The math behind this strategy is straightforward. Here's what you're actually doing:

  1. 1
    Run a factor regression: For each stock, regress its returns on the Fama-French factors (Market, Size, Value) over 36 months.
  2. 2
    Calculate residuals: The residual is what's left after removing factor exposure. It's the stock-specific return component.
  3. 3
    Compute risk-adjusted residual: Average the residuals over 12 months, then divide by their standard deviation.
  4. 4
    Rank and select: Buy stocks with the highest risk-adjusted residuals (top decile), short those with the lowest.

That's it. The formulas below just express this process precisely.

Technical Formulas

1
Factor Regression Model

Formula
R_i(t) = \alpha_i + \beta_{1,i} \cdot MKT(t) + \beta_{2,i} \cdot SMB(t) + \beta_{3,i} \cdot HML(t) + \varepsilon_i(t)

Stock return decomposed into factor exposures (betas) and residual. Run over 36-month estimation period.

2
Residual Calculation

Formula
\varepsilon_i(t) = R_i(t) - \beta_{1,i} \cdot MKT(t) - \beta_{2,i} \cdot SMB(t) - \beta_{3,i} \cdot HML(t)

The residual is stock return minus the factor-explained portion. Note: α is excluded from residual computation.

3
Mean Residual

Formula
\varepsilon_i^{mean} = \frac{1}{T} \sum_{t=S}^{S+T-1} \varepsilon_i(t)

Average residual over the T-month formation period (typically T=12), skipping S months (typically S=1).

4
Risk-Adjusted Residual Return

Formula
\tilde{R}_i^{risk.adj} = \frac{\varepsilon_i^{mean}}{\tilde{\sigma}_i}

The ranking signal: mean residual divided by residual volatility. Similar to a Sharpe ratio for residuals.

5
Residual Volatility

Formula
\tilde{\sigma}_i^2 = \frac{1}{T-1} \sum_{t=S}^{S+T-1} (\varepsilon_i(t) - \varepsilon_i^{mean})^2

Standard deviation of residuals over the formation period.

Why 36-Month Estimation?Note

A longer estimation period (36 months) provides more stable beta estimates. The residuals are then computed for a shorter formation period (12 months) to capture recent momentum while using reliable factor loadings.

Strategy Rules

Factor Estimation

  1. Use Fama-French 3-factor model: MKT (market excess return), SMB (small minus big), HML (high minus low)
  2. Estimate betas over 36-month rolling window
  3. Skip most recent month in estimation (1-month skip period)
  4. Require minimum 24 months of data for reliable estimates
  5. Download factor data from Ken French Data Library

Residual Calculation

  1. 1Compute residuals: ε = R - β₁·MKT - β₂·SMB - β₃·HML
  2. 2Do NOT subtract alpha (α) when computing residuals
  3. 3Calculate residuals for 12-month formation period
  4. 4Compute mean residual and residual standard deviation
  5. 5Risk-adjusted signal = mean residual / residual volatility

Portfolio Construction

  1. Rank all stocks by risk-adjusted residual return
  2. Long: Top decile (highest residual momentum)
  3. Short (optional): Bottom decile (lowest residual momentum)
  4. Equal-weight positions within each leg
  5. Dollar-neutral for long-short implementation

Rebalancing

  1. 1Rebalance monthly for strongest momentum capture
  2. 2Re-estimate betas quarterly to reduce computation
  3. 3Update residuals monthly with new beta estimates
  4. 4Holding period typically 1 month, can extend to 3-6 months
  5. 5Monitor factor exposures to ensure neutrality

Implementation Guide

Implementing residual momentum requires access to factor data and the ability to run regressions. Here's a practical approach.

1

Obtain Factor Data

Download the Fama-French factor returns from Ken French's Data Library. You'll need daily or monthly MKT-RF (market excess return), SMB (size factor), and HML (value factor). The data is free and updated regularly.

Tips
  • Use monthly factor data for simpler implementation
  • Ken French Data Library: mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
  • Factors are available for US and international markets
2

Run Factor Regressions

For each stock, regress its excess returns (stock return minus risk-free rate) on the three factors over the past 36 months. This gives you the beta coefficients. You can use Excel, Python (statsmodels), or R for regressions.

Tips
  • In Python: from statsmodels.api import OLS
  • In Excel: Use the LINEST function or Data Analysis Regression tool
  • Save the beta coefficients for residual calculation

Ensure you're using excess returns (subtract risk-free rate) for both the stock and market factor.

3

Calculate Residuals

Using the estimated betas, compute the residual for each month in the 12-month formation period. Residual = Stock Return - β₁×MKT - β₂×SMB - β₃×HML. Do NOT subtract the intercept (alpha).

Tips
  • The residual represents stock-specific return
  • Positive residual = stock outperformed its factor exposure
  • Store residuals for the formation period
4

Compute Risk-Adjusted Signal

Calculate the mean residual over 12 months and divide by the standard deviation of residuals. This risk-adjusted measure is your ranking signal. Higher values indicate stronger residual momentum.

Tips
  • Mean residual alone can work, but risk-adjusting improves results
  • This is essentially a Sharpe ratio for residuals
  • Rank all stocks by this signal
5

Construct Portfolio

Select stocks in the top decile (top 10%) by risk-adjusted residual. For long-short, also short the bottom decile. Equal-weight positions within each leg. Rebalance monthly.

Tips
  • Start with 10-20 stocks per leg for diversification
  • Consider transaction costs in your holding period decision
  • Monitor for any unintended factor tilts

Data and Tools Required

Residual momentum requires more data infrastructure than simple price momentum. You'll need: (1) Historical stock returns, (2) Fama-French factor data, (3) Regression capability. Services like Portfolio123, Quantopian (archived), or custom Python scripts can help automate this process.

Helpful Tools & Resources

Factor Data
Ken French Data Library, AQR Factor Data, WRDS
Regression Tools
Python (statsmodels), R, Excel, MATLAB
Stock Data
Yahoo Finance, Tiingo, Polygon.io, EOD Historical
Research
SSRN, Ken French Website, AQR Insights

Strategy Variations

Explore different ways to implement this strategy, each with its own trade-offs and benefits.

Three-Factor Residual

Standard approach using Fama-French MKT, SMB, HML factors. Most common implementation.

Five-Factor Residual

Add profitability (RMW) and investment (CMA) factors for more complete factor adjustment.

Industry-Adjusted

Subtract industry average return instead of running regression. Simpler but less precise.

Combined with Price Momentum

Use both residual and price momentum signals together for diversified momentum exposure.

Consider combining multiple variations or testing them against your specific investment goals and risk tolerance.

Risks & Limitations

High(1)
Medium(4)
Implementation ComplexityHigh

Requires factor data, regression analysis, and regular updates. More complex than simple price momentum.

Impact:
Data RequirementsMedium

Need reliable factor data and sufficient return history for each stock. Missing data can bias results.

Impact:
Beta Estimation ErrorMedium

Betas estimated with noise can lead to residual calculation errors. Use longer estimation periods for stability.

Impact:
Factor Model ChoiceMedium

Results depend on which factors you use. Different factor models may produce different rankings.

Impact:
Still Has DrawdownsMedium

While reduced vs. price momentum, residual momentum can still experience significant drawdowns in market stress.

Impact:
Understanding these risks is essential for proper position sizing and portfolio construction. Consider combining with other strategies to mitigate individual risk factors.

References

  • Blitz, D., Huij, J., & Martens, M. (2011). Residual Momentum. Journal of Empirical Finance, 18(3), 506-521 [Link] [PDF]
  • Gutierrez, R. C., & Pirinsky, C. A. (2007). Momentum, Reversal, and the Trading Behaviors of Institutions. Journal of Financial Markets, 10(1), 48-75 [Link] [PDF]
  • Blitz, D., Hanauer, M., & Vidojevic, M. (2020). The Idiosyncratic Momentum Anomaly. International Review of Economics & Finance, 69, 932-957 [Link] [PDF]
  • Chaves, D. B. (2016). Idiosyncratic Momentum: U.S. and International Evidence. Journal of Investing, 25(2), 64-76 [Link]
  • Fama, E. F., & French, K. R. (1993). Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33(1), 3-56 [Link]

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