Shipping stocks are a trader's nightmare. Long-term returns barely beat inflation. Volatility makes crypto look stable. Timing tops and bottoms? Forget it—by the time you see the cycle turning, it's too late.
But here's the thing: what if volatility isn't the enemy? What if you could profit because shipping is chaotic?
I stumbled on Krauss's (2015) review of pairs trading strategies—market-neutral approaches that generate 7-11% excess returns by exploiting temporary mispricings between related securities. The kicker? These strategies perform best during volatile periods and market downturns. Exactly when shipping markets are most unpredictable.
Could the very chaos that makes shipping unbuyable as a directional bet make it perfect for pairs trading? This project is my attempt to find out.
What Is Pairs Trading?
Pairs trading is a market-neutral strategy. Instead of betting on whether the market goes up or down, you bet on the relationship between two securities.
Here's the core idea: find two stocks that historically move together. When they temporarily diverge—one goes up while the other goes down—you bet on them converging again. You go long the underperformer and short the outperformer.
The beauty is that market direction doesn't matter. If both stocks crash, your short position wins and offsets your long position's losses. If both rally, the opposite happens. You only profit (or lose) based on whether the spread between them narrows.
A Classic Example: Gold and Silver
The gold-to-silver ratio is a textbook pairs trade. Historically, you could exchange 1 ounce of gold for about 60-80 ounces of silver. When this ratio drops significantly—say to 50—gold is "cheap" relative to silver.
How do you bet on this? Selling silver alone is risky in a rising market. But if you also buy gold, you're hedged. If precious metals keep rising, your gold position offsets your silver short. If they crash, silver likely falls harder than gold, and you profit on the spread.
This is why pairs trading is called "market-neutral"—you're not exposed to the overall market direction.
The Academic Literature
Krauss (2015) reviewed over 90 academic papers on pairs trading and identified five distinct methodological approaches. Each has different strengths, weaknesses, and assumptions about how markets work.
1. Distance Approach (GGR)
The original method from Gatev, Goetzmann, and Rouwenhorst (2006). It's beautifully simple:
- Formation period: Calculate the Sum of Squared Distances (SSD) between normalized price series for all possible stock pairs over 12 months
- Selection: Take the 20 pairs with the lowest SSD—these are stocks that moved most similarly
- Trading period: For 6 months, when a pair's spread exceeds 2 standard deviations, enter a position betting on convergence
The original paper reported returns of 11% annually. More recent studies like Zhu (2024) still find around 6% excess returns, though profitability has declined since the strategy became widely known.
I've implemented and tested this approach. The results were underwhelming on my stock universe—but the exercise revealed important insights about pair selection.
2. Cointegration Approach
The distance method has a flaw: similar past movements don't guarantee a stable long-term relationship. Two stocks might have low SSD by coincidence.
The cointegration approach addresses this using formal statistical tests. Engle-Granger or Johansen tests identify pairs where a linear combination of the two price series is stationary—meaning they're bound together by an equilibrium relationship.
If stock A and stock B are cointegrated, any divergence must eventually correct. The spread is mean-reverting by definition.
Strengths: More theoretically grounded than distance, lower risk of divergence
Weaknesses: Computational cost explodes with universe size, and testing thousands of pairs creates false positives
3. Time Series Approach
Once you've identified a pair, how do you trade it optimally? The time series approach models the spread as a stochastic process—typically an Ornstein-Uhlenbeck process—and calculates optimal entry and exit thresholds.
Instead of using an arbitrary 2-sigma rule, you can derive thresholds that maximize expected profit given the spread's mean-reversion speed, volatility, and your transaction costs.
Some methods in this category:
- Ornstein-Uhlenbeck models: Closed-form solutions for optimal thresholds
- Kalman filtering: Dynamically estimate the hedge ratio and spread parameters
- Markov regime-switching: Allow for different market regimes with different dynamics
Strengths: Theoretically optimal trading rules, accounts for transaction costs
Weaknesses: Assumes Gaussian distributions, which financial data rarely follows
4. Stochastic Control Approach
Most pairs trading assumes a "delta-neutral" position—equal dollar amounts long and short. But is this actually optimal?
The stochastic control approach uses Hamilton-Jacobi-Bellman equations to find the optimal allocation between the long leg, short leg, and risk-free asset. Key insight: non-delta-neutral positions can be optimal depending on spread dynamics.
This is mathematically elegant but practically challenging. The optimal strategy often requires daily rebalancing, and transaction costs eat into the theoretical gains.
Strengths: Truly optimal under model assumptions
Weaknesses: High turnover, sensitive to model specification, limited empirical validation
5. Machine Learning and Other Approaches
This category includes:
- Neural networks and genetic algorithms: Learn complex patterns in spread behavior
- Copulas: Model non-linear dependencies between securities
- PCA and eigenportfolios: Create synthetic mean-reverting portfolios from principal components
Krauss (2015) suggests the future lies in combining approaches: cointegration for pair selection, time series models for trading rules, and stochastic control for position sizing.
What the Data Actually Shows
Here's what decades of research reveal:
Returns are real but declining. The GGR strategy returned 11% annually in the original 1962-2002 study. By 2004-2014, returns had fallen to around 3-5%. Markets adapt as strategies become known.
Transaction costs matter enormously. Many papers report gross returns without accounting for bid-ask spreads, short-selling costs, and commissions. Net returns are often 2-4% lower than gross.
Short-selling constraints bite. Many profitable pairs include small-cap or hard-to-borrow stocks. In practice, you often can't execute the short leg.
Market conditions matter. Pairs trading performs best in high-volatility, mean-reverting markets. During trending markets or regime changes, pairs can diverge permanently.
My Testing Approach
I'm working through the five approaches systematically:
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✅ Distance (GGR): Implemented and tested. Found that pair selection matters more than I expected—the top 5 pairs outperformed the top 100.
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⏳ Cointegration: Planned. Will implement Engle-Granger tests and compare pair selection to the distance approach.
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⏳ Time Series: Planned. Will model spreads as Ornstein-Uhlenbeck processes and derive optimal thresholds.
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⏳ Stochastic Control: Planned. The math is intimidating, but I want to understand what "truly optimal" looks like.
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⏳ Machine Learning: Planned. Will test whether modern ML can extract signal that traditional methods miss.
For each method, I'm using the same testing framework and stock universe so results are comparable. The code is open source: github.com/dhrstrijker/ggr-backtest.
References
- 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.
- Krauss, C. (2015). Statistical arbitrage pairs trading strategies: Review and outlook. IWQW Discussion Papers, No. 09/2015.
- Zhu, X. (2024). Examining pairs trading profitability. Unpublished senior essay, Yale University.