Crypto Pairs Trading: Part 4 — Empirical Results & Performance Analysis

Welcome to Crypto Pairs Trading: Part 4 — Empirical Results and Performance Analysis. After laying the foundations in Part 1 — Foundations of Moving Beyond Correlation, confirming mean-reversion in Part 2 — Verifying Mean Reversion with ADF and Hurst Tests, and constructing a systematic approach in Part 3 — Constructing Your Strategy with Logs, Hedge Ratios, & Z-Scores we now put it all to the test with real data. In one line: We validate the entire methodology by reviewing how a cointegration-based pairs trading strategy performs under real market conditions and how it fares in terms of returns, volatility, and risk management.

Real World Testing

We have established the theoretical foundations of a cointegration-based pairs trading strategy within the cryptocurrency markets. We discussed the critical distinction between correlation and cointegration, the importance of verifying stationarity and mean-reversion tendencies in price spreads, and the procedures for selecting suitable asset pairs. We also delved into the application of statistical tests such as the Augmented Dickey-Fuller (ADF) test, explored the significance of the Hurst exponent, and outlined practical considerations like hedge ratios, Z-score thresholds, and the integration of transaction costs. With these theoretical and methodological pillars in place, this chapter focuses on the empirical results derived from a multi-year backtesting exercise on a carefully chosen crypto pair.

The chosen trading pair (ETC vs. FIL, both quoted in USDT) met stringent statistical criteria, showing stable cointegration and robust mean-reverting behavior. By applying a disciplined approach—waiting for statistically significant deviations in the spread and then exploiting them through a market-neutral position—this strategy aimed to generate profits irrespective of overall market direction. Over the course of several years, this backtest not only validated the theoretical principles but also provided tangible evidence of the strategy’s performance potential.

Here, we dissect the strategy’s returns, volatility, risk metrics, and trade-level outcomes to paint a comprehensive picture of how a well-designed, cointegration-driven pairs trading model can thrive in a notoriously volatile and unpredictable environment like the crypto asset class. You can find the associated notebook here.

Key Performance Metrics: A Summary Overview

Before diving deep into the narrative of the backtest results, we begin with a summary of the core performance statistics:

• Initial Capital: 1,000,000.00 (base currency, e.g., USDT)
• Final Capital (End of Backtest): ~1,620,000.00
• Total Return (Absolute): +62.0%
• Annualized Return: ~16.05%
• Annualized Volatility: ~17.26%
• Sharpe Ratio: ~0.93
• Maximum Drawdown: ~15.67%
• Profit Factor: ~3.74
• Win Rate: ~40% (2 winners out of 5 total trades)
• Average Return per Trade: ~100,776.70
• Average Winning Trade: ~344,000.01
• Average Losing Trade: ~-61,372.17
• Ratio of Average Win to Average Loss: ~5.6:1

These statistics, taken collectively, indicate a strategy that achieved substantial growth over the backtest period. Notably, the large profit factor and high average win relative to average loss suggest a positively skewed payoff distribution, where a handful of large, profitable trades outweighed several smaller losing ones.

Interpreting the High-Level Metrics

1. Annualized Return (~16.05%):
   An annualized return around 16% is good given the nature of the market-neutral structure. Unlike long-only crypto strategies that may have benefitted from large bull runs but also suffered steep losses in bear markets, this cointegration-based approach does not rely on market direction. Instead, it exploits relative mispricings, allowing it to produce consistent returns over time. In a sector known for sharp boom-and-bust cycles, a steady 16% annual gain is commendable.
2. Annualized Volatility (~17.26%):
   While 17% volatility may seem high in traditional equity markets, it is relatively modest in the crypto space. Cryptocurrencies often exhibit annual volatilities exceeding 50% or more. The pairs trading strategy’s hedged nature dampened exposure to overall market swings, yielding lower volatility in equity curve fluctuations. This indicates effective risk mitigation and position sizing.
3. Sharpe Ratio (~0.93):
   The Sharpe ratio, a key measure of risk-adjusted return, hovers near 1.0. In the world of crypto, where risk is abundant, achieving a Sharpe ratio close to one is a meaningful accomplishment. It suggests that the strategy’s returns were generated efficiently relative to the risk taken. Earlier chapters stressed the importance of verifying stationarity and cointegration precisely to achieve such balanced risk-adjusted outcomes.
4. Total Return (~62%):
   Over the entire multi-year test period, the strategy grew the initial capital from 1,000,000 to about 1,620,000. This cumulative gain shows the additive effect of multiple mean-reversion cycles and the strategy’s ability to capture these over time. Unlike directional strategies that might produce astronomical gains in bull markets and large losses in downturns, this return is more stable and derived from a market-neutral framework.
5. Max Drawdown (~15.67%):
   A maximum drawdown of roughly 15.7% indicates that at its worst historical point, the strategy’s equity dipped only about 15% below a previous peak. In the crypto world—where swings of 50% or more are common—this controlled drawdown profile is a hallmark of prudent risk management. The strategy’s use of stop losses, conservative position sizing, and only acting under conditions of statistically confirmed mean reversion contributed to this controlled downside.
6. Profit Factor (3.74):
   The profit factor—total gross profits divided by total gross losses—was nearly 3.74. A profit factor above 2.0 is considered excellent; near 4.0 is exceptionally strong. This metric underscores the quality of the strategy’s edge. Although the win rate was only 40%, the magnitude of winning trades dwarfed the losses sufficiently to produce a high profit factor.
7. Win Rate (40%):
   A 40% win rate may initially appear suboptimal. However, this strategy’s success does not hinge on the frequency of winning trades. Instead, its edge lies in the asymmetry of payoffs. Mean-reversion setups are often characterized by relatively few but very large winners that compensate for numerous smaller, controlled losses. This approach requires emotional discipline—traders must remain confident even when the majority of trades do not yield immediate profits, knowing that a single big mean-reversion event can restore and surpass previous losses.
8. Trade-Level Analysis (Average Win and Loss):
   The average winning trade was about 344,000 units, compared to an average losing trade of roughly -61,372 units. This ratio (~5.6:1) provides a direct line of insight into why the strategy is profitable despite a lower win rate. Each winning trade more than compensates for several losing ones.

Equity Curve Dynamics: From Flat Starts to Big Wins

The backtest’s timeline reveals critical insights into how the strategy behaved under different market conditions:

1. Initial Inactivity and First Trades:
   At the start, the strategy might remain dormant until a clear statistical signal emerges. The first trade, entered around late 2021, ultimately ended in a stop loss after about a month. Equity dropped from a peak of about 1,011,000 down to ~947,900. This initial loss tests the trader’s resolve, as it can be discouraging to begin with a drawdown. However, mean-reversion strategies often require patience; a single early loss does not invalidate the broader statistical premise.
2. Subsequent Loss and Equity Below Initial Capital:
   A second trade entered in mid-2022 also ended with a stop loss by late 2022, pushing equity to around 899,000—now below the starting capital. This phase represents the darkest hours of the strategy, as it has endured two losses without yet demonstrating the big wins it promises.
3. First Major Winning Trade (Late 2022 – Early 2023):
   The narrative changes dramatically with the third trade entry around December 2022, which exited around February 2023 with a large profit. This single take-profit exit catapulted equity to ~1,209,673, not just recovering the losses but surpassing the original capital by a wide margin. The scale of this win illustrates how one successful reversion can shift the entire equity curve. The statistical logic behind mean reversion paid off: after a prolonged deviation in the spread, prices snapped back sharply, delivering substantial profits.
4. Second Major Winning Trade (Late 2023 – Early 2024):
   Another huge winner occurred between August 2023 and March 2024, pushing equity up to approximately 1,586,493. With two massive winners under its belt, the strategy demonstrated its core strength: a few large payoffs can define the overall performance in a positive way.
5. Final Losing Trade (Mid-2024):
   A last trade during mid-2024 ended with a stop loss, trimming equity from about 1,609,000 down to ~1,502,462. Even after this loss, the portfolio remained substantially above the initial capital, showcasing durability.

Across these phases, the equity curve’s message is consistent: patience and adherence to statistically grounded entry/exit rules yield long-term gains. Early drawdowns were unpleasant but small relative to the big surges produced by correct signals.

Statistical Validation: Cointegration, Stationarity, and Mean Reversion

To achieve these results, the underlying spread had to meet stringent criteria:

1. Cointegration Testing:
   The pair demonstrated a cointegration p-value below 0.05. This is crucial, as cointegration confirms that while each asset may be non-stationary alone, a linear combination of them (based on a hedge ratio) is stationary. Without this assurance, the strategy would rely on correlation alone, risking trades on relationships that might drift apart indefinitely.
2. Hedge Ratio Stability (4.0357):
   The estimated hedge ratio was around 4.0, implying that for every 1 unit of Asset A, about 4 units of Asset B were held. This ratio was neither extreme nor negligible, suggesting a balanced and plausible relationship. Adjusting for logs and imposing reasonable bounds on the hedge ratio ensured the spread was both statistically sound and practical to implement.
3. Stationarity (ADF Test) and Hurst Exponent:
   The ADF test strongly rejected the null hypothesis of a unit root, confirming stationarity of the spread. Additionally, the Hurst exponent (H < 0.5) indicated a mean-reverting, anti-persistent series. This aligns with the theoretical premise that a true stationary spread oscillates around a fixed mean, frequently providing opportunities to buy low and sell high (or vice versa).
4. Z-Scores and Execution Criteria:
   By computing a rolling mean and standard deviation of the spread, the strategy derived Z-scores to quantify how far the current spread was from historical norms. Extreme Z-score readings (e.g., ±2 or ±3) signaled entry points. Exiting at more moderate Z-scores, or upon reaching take-profit or stop-loss thresholds, ensured a disciplined approach that locked in gains once the spread reverted.

Risk Management and Realistic Frictions

The presented performance already accounts for practical trading frictions, including:

• Transaction Costs (Fees and Slippage):
  The results incorporate typical crypto exchange fees and slippage assumptions. Maintaining profitability after these costs is a strong endorsement of the strategy’s edge.
• Stop Losses and Take Profits:
  Stop losses curtailed runaway trades that deviated further than statistically anticipated. While painful in the short term, these stops prevented large drawdowns. Take profits captured large positive reversions promptly, preventing profits from eroding if the spread swung back again.
• Position Sizing and Scaling:
  The strategy often used about 5% of equity as position size per trade. As equity grew, absolute position sizes increased, potentially amplifying returns from subsequent winning trades. Conversely, early losses were smaller in absolute terms because the portfolio was at its initial size. Dynamic scaling ensured that risk-taking capacity matched portfolio growth.

Comparative Perspective: Crypto Market Conditions

The crypto market landscape between 2021 and 2024 included bull runs, deep bear periods, and range-bound consolidations. Many strategies that rely on directional bets either soared during bull markets or suffered heavy losses in downturns. By focusing on a cointegrated pair and betting on mean reversion in the spread, this approach sidestepped the need to forecast broad market direction. It remained agnostic to whether BTC or ETH soared or crashed, concentrating solely on the relative mispricing between the two assets under consideration.

In an environment where single assets can lose 80% of their value in a matter of months, a maximum drawdown of only ~15.7% stands out as especially conservative. Coupled with a 16% annualized return and a Sharpe ratio near 1.0, this strategy represents a stable, disciplined approach to extracting value from the inherently noisy crypto data.

Behavioral and Psychological Considerations

A 40% win rate means the trader or system implementing this strategy must tolerate being wrong more often than right in terms of trade frequency. Many traders struggle with strategies that have a low hit rate, even if the strategy is profitable in the long run. The key is recognizing that the magnitude of winning trades more than compensates for a string of minor losses. This requires trusting the underlying statistical methodology and not abandoning the strategy after a few losing trades.

The early drawdowns and initial losses serve as a real-world test of conviction. Without a solid understanding of the cointegration logic and stationarity proofs from previous chapters, a trader might give up prematurely. However, the eventual large winners affirm that the model’s statistical premises hold water over extended periods. Maintaining discipline and patience is paramount.

Possible Improvements and Future Directions

While the results are impressive, there is always room for refinement:

1. Broadening the Universe of Pairs:
   Applying the same methodology to a broader set of cointegrated pairs could provide diversification. If multiple pairs meet the statistical criteria, running several pairs trading strategies in parallel might smooth the equity curve further and potentially raise the Sharpe ratio.
2. Adaptive Thresholds and Dynamic Parameters:
   The Z-score thresholds, stop losses, and take-profit levels used in this backtest might be static. Future research could explore adaptive parameters that respond to changing market volatilities, liquidity conditions, or shifts in correlation structures. For instance, adjusting the Z-score threshold in periods of higher volatility could reduce false signals.
3. More Frequent Hedge Ratio Re-Estimation:
   Over a multi-year period, the relationship between two crypto assets can evolve. Periodically re-estimating the hedge ratio and re-validating cointegration ensures that the model remains aligned with current market dynamics. A stale hedge ratio might reduce profitability or increase the chance of a non-stationary spread.
4. Risk-Parity Weighting and Volatility Scaling:
   Instead of applying a fixed 5% capital allocation per trade, the strategy could vary its position size based on the spread’s recent volatility. Lower-volatility regimes might allow slightly larger positions, while higher-volatility periods might warrant smaller allocations to preserve capital.

Validating the Statistical Foundation with Real Results

We presented the empirical outcomes of a cointegration-based pairs trading strategy that was rigorously tested, carefully implemented, and fully cost-adjusted. The key takeaways are:

• Robust Statistical Underpinnings:
  The emphasis on cointegration, stationarity, and mean reversion was not theoretical window-dressing. These concepts directly enabled the strategy to exploit predictable price relationships, resulting in steady gains and controlled drawdowns.
• Stable, Non-Directional Returns:
  Achieving a 16% annualized return with a Sharpe ratio near 1.0, all while remaining market-neutral in a high-volatility asset class, highlights the power of statistical arbitrage. The strategy thrived not by forecasting market direction but by capitalizing on persistent relationships between cointegrated assets.
• Risk Management and Discipline are Key:
  Stop losses contained adverse moves, and take profits locked in large gains. The willingness to endure multiple small losses for the chance to capture fewer but larger winners proved to be the strategy’s defining edge. Patience and confidence in the model were crucial.
• A Scalable and Refinable Approach:
  The methodology can be extended to other pairs and improved over time. The fact that the current version produced strong results suggests that ongoing refinement—such as adding more pairs, recalibrating hedge ratios periodically, or introducing adaptive exit criteria—could enhance both returns and stability.

These empirical results validate the earlier theoretical chapters and methodological frameworks. They demonstrate that, in the often-chaotic crypto landscape, a carefully designed, statistically grounded pairs trading approach can generate meaningful, risk-adjusted returns. By bridging the gap between statistical theory and practical profitability, this research confirms that cointegration-based mean-reversion strategies hold substantial promise in modern digital asset markets.

By examining empirical performance, we’ve demonstrated that a cointegration-driven framework can generate meaningful, market-neutral returns and greater stability—even in the volatile world of digital assets. Together, the insights you gained from Part 1: Foundations of Moving Beyond Correlation, Part 2: Verifying Mean Reversion with ADF and Hurst Tests, Part 3: Constructing Your Strategy with Logs, Hedge Ratios, and Z-Scores, and now Part 4: Empirical Results and Performance Analysis form a comprehensive roadmap to informed, quantitatively-driven pairs trading in crypto markets. Equipped with rigorous data analysis, proven statistical methods, and disciplined execution, you can refine, scale, and adapt your strategy to thrive amid evolving market conditions.

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