SystemTrader
StocksIntermediateMarket Neutral

Mean-Reversion Cluster Strategy

Generalize pairs trading to N > 2 correlated stocks. Short outperformers and buy underperformers within a cluster (sector, industry, or theme) while maintaining dollar neutrality.

Cluster Size
N > 2 stocks
Lookback
1-20 days
Position
Dollar-neutral
Rebalance
Daily/Weekly

Overview

The mean-reversion cluster strategy extends pairs trading from 2 stocks to N > 2 correlated stocks. Instead of trading a single pair, you trade an entire cluster of related stocks—typically from the same industry or sector.

The intuition is simple: within a group of similar stocks, relative outperformers tend to revert and underperformers tend to catch up. Short stocks with positive demeaned returns, buy stocks with negative demeaned returns.

This approach provides better diversification than pairs trading. With more stocks in the cluster, idiosyncratic noise is reduced and the mean-reversion signal becomes more reliable.

Key Insight

N-Stock Generalization
Beyond pairs to full clusters
Dollar Neutral
Longs offset shorts exactly

Position Logic

R̃ᵢ > 0 → SHORT (outperformer)
R̃ᵢ < 0 → LONG (underperformer)

Formulas

R̄ = (1/N) Σ Rᵢ
R̃ᵢ = Rᵢ - R̄
Dᵢ = -γ × R̃ᵢ

Key Insight

JPM outperformed the cluster by +2.4%, so we short it. PNC underperformed by -2.3%, so we buy it. Dollar positions are proportional to deviations.

Research

Research on statistical arbitrage, sector mean-reversion, and cluster-based trading strategies.

Recent Research

The Mathematics

In Plain English

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

  1. 1
    Define your cluster: Select N correlated stocks from the same industry or sector (e.g., all major banks, all oil companies).
  2. 2
    Calculate returns: Compute the log return for each stock over a short period (1-20 days).
  3. 3
    Compute the mean: Average the returns across all N stocks to get the cluster benchmark.
  4. 4
    Demean and trade: Subtract the mean from each stock's return. Short stocks above the mean, buy stocks below the mean.

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

Technical Formulas

1
Log Return

Formula
R_i = \ln\left(\frac{P_i(t_2)}{P_i(t_1)}\right)

Log return for stock i from time t₁ to t₂.

2
Cluster Mean Return

Formula
\bar{R} = \frac{1}{N} \sum_{i=1}^{N} R_i

Average return across all N stocks in the cluster.

3
Demeaned Return

Formula
\tilde{R}_i = R_i - \bar{R}

Stock i's return relative to cluster average. Positive = outperformer, negative = underperformer.

4
Total Investment Constraint

Formula
\sum_{i=1}^{N} P_i |Q_i| = I

Total dollar investment across all positions equals target I.

5
Dollar-Neutrality Constraint

Formula
\sum_{i=1}^{N} P_i Q_i = 0

Dollar value of longs equals dollar value of shorts. Q_i < 0 for shorts, Q_i > 0 for longs.

6
Dollar Position

Formula
D_i = -\gamma \tilde{R}_i

Position proportional to negative demeaned return. Short outperformers (R̃ > 0), buy underperformers (R̃ < 0).

7
Scaling Factor

Formula
\gamma = \frac{I}{\sum_{i=1}^{N} |\tilde{R}_i|}

Scaling factor that ensures total investment equals I while satisfying dollar-neutrality.

Why Clusters Work Better Than PairsNote

With only 2 stocks, idiosyncratic news can cause false signals. With N stocks, individual noise averages out and the mean-reversion signal becomes cleaner. The cluster mean is a more stable benchmark than a single stock.

Strategy Rules

Cluster Selection

  1. Choose stocks from same industry (e.g., banks, oil majors, tech giants)
  2. Require minimum 5-10 stocks for diversification benefit
  3. All stocks should have similar market caps and liquidity
  4. Verify high pairwise correlations (>0.60) within cluster
  5. Exclude stocks with pending corporate actions or extreme news

Signal Calculation

  1. 1Calculate log returns over lookback period (1-20 days)
  2. 2Compute cluster mean return R̄ = (1/N) Σ R_i
  3. 3Calculate demeaned returns R̃_i = R_i - R̄ for each stock
  4. 4Positive R̃_i = outperformer (short candidate)
  5. 5Negative R̃_i = underperformer (long candidate)

Position Sizing

  1. Set total investment I (e.g., $100,000)
  2. Calculate scaling factor γ = I / Σ|R̃_i|
  3. Dollar position D_i = -γ × R̃_i for each stock
  4. Convert to shares: Q_i = D_i / P_i
  5. Verify dollar-neutrality: Σ D_i should equal 0

Execution & Rebalancing

  1. 1Execute all positions simultaneously at market open or close
  2. 2Rebalance daily or weekly based on new demeaned returns
  3. 3Close positions when R̃_i reverts toward zero
  4. 4Stop-loss if cluster correlation breaks down
  5. 5Monitor for regime changes affecting the sector

Implementation Guide

Implementing cluster mean-reversion requires defining a stock cluster, calculating demeaned returns, and executing a dollar-neutral portfolio.

1

Define Your Cluster

Select 5-15 stocks from the same industry or sector. Common clusters: major banks (JPM, BAC, WFC, C, GS), big tech (AAPL, MSFT, GOOGL, META, AMZN), oil majors (XOM, CVX, COP, EOG, SLB).

Tips
  • Use sector ETF holdings as a starting point
  • Verify all stocks are liquid enough to trade
  • Check that historical correlations are high (>0.60)
2

Calculate Demeaned Returns

Each day (or week), compute the log return for each stock over your lookback period. Then calculate the cluster mean and subtract it from each stock's return. Stocks above the mean are short candidates; below the mean are long candidates.

Tips
  • Use log returns: ln(P_today / P_lookback)
  • Lookback of 5-20 days captures short-term mean reversion
  • Spreadsheet or Python makes this easy to automate
3

Calculate Position Sizes

Decide your total investment (e.g., $50,000). Calculate γ = I / Σ|R̃_i|. Then each position is D_i = -γ × R̃_i. A stock with R̃ = +2% gets a short position; one with R̃ = -2% gets an equal-sized long position.

Tips
  • The formula automatically ensures dollar-neutrality
  • Larger deviations get proportionally larger positions
  • Cap individual positions at 20-25% to limit concentration

Always verify Σ D_i ≈ 0 before executing. Rounding errors can create unintended market exposure.

4

Execute and Monitor

Execute all trades simultaneously to minimize timing risk. Monitor the cluster daily and rebalance when demeaned returns shift significantly. Exit when positions revert (R̃_i approaches zero).

Tips
  • Use market-on-close orders for cleaner execution
  • Rebalance fully each period rather than adjusting incrementally
  • Track cluster correlation—if it drops, the strategy may stop working

Execution Requirements

This strategy requires shorting multiple stocks simultaneously. Ensure your broker has shares available for all cluster members. Interactive Brokers provides good short availability and reasonable borrow rates for liquid stocks.

Helpful Tools & Resources

Cluster Data
Sector ETF holdings, Finviz sector screens, Yahoo Finance
Calculation
Excel, Google Sheets, Python (pandas)
Execution
Interactive Brokers, TD Ameritrade, TradeStation
Research
SSRN, Quantpedia, Alpha Architect

Strategy Variations

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

Industry Cluster

Use stocks from a single industry (e.g., banks, airlines). Tightest correlations.

Sector Cluster

Broader sector (e.g., all financials, all energy). More diversification but weaker signal.

Factor Cluster

Group by factor exposure (high beta, low volatility). Captures factor-based mean reversion.

Thematic Cluster

Custom themes (e.g., EV stocks, AI stocks). Can capture emerging trends.

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

Risks & Limitations

High(1)
Medium(4)
Cluster BreakdownHigh

Stocks may stop moving together due to fundamental changes. One stock's divergence may not revert.

Impact:
Sector-Wide MovesMedium

Strategy is neutral to sector direction but not to dispersion changes. Low dispersion = weak signal.

Impact:
Short AvailabilityMedium

Some cluster members may be hard to borrow, preventing full implementation.

Impact:
Execution ComplexityMedium

Managing N positions simultaneously requires more infrastructure than pairs trading.

Impact:
Regime ChangesMedium

Market regimes (e.g., crisis periods) can change correlation structures rapidly.

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

References

  • Avellaneda, M., & Lee, J.-H. (2010). Statistical Arbitrage in the US Equities Market. Quantitative Finance, 10(7), 761-782 [Link] [PDF]
  • Pole, A. (2007). Statistical Arbitrage: Algorithmic Trading Insights and Techniques. Wiley Trading Series [Link]
  • Jacobs, B. I., & Levy, K. N. (1993). Long/Short Equity Investing. Journal of Portfolio Management, 20(1), 52-63 [Link]
  • Gatev, E., Goetzmann, W. N., & Rouwenhorst, K. G. (2006). Pairs Trading: Performance of a Relative-Value Arbitrage Rule. Review of Financial Studies, 19(3), 797-827 [Link]

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