Results
Last updated
Last updated
The performance analysis evaluates the empirical performance of three distinct cryptocurrency trading strategies under a base case scenario incorporating standard exchange taker fees (fbase) plus a 25 basis point execution cost buffer (fextra = 0.25%) to account for market impact and slippage-related transaction cost externalities. Table 1 presents the performance metrics for a pure machine learning-driven algorithmic strategy ("AI Strategy"), demonstrating key risk-adjusted return characteristics across the 2022-2024 observation period. Table 2 quantifies the performance distribution of the composite implementation ("Hybrid Strategy") described above. Table 3 establishes the benchmark performance of a passive Bitcoin allocation strategy ("BTC Buy-and-Hold"), providing the null hypothesis comparison set for statistical outperformance evaluation. The tabulated metrics encompass the canonical risk-adjusted performance ratios (Sharpe, Sortino, Calmar), compound annual growth rate (CAGR), absolute return, annualized volatility, and market exposure duration expressed as percentage of total available trading intervals.
The backtest results demonstrate statistically significant outperformance of both AI and Hybrid strategies versus the traditional BTC Buy-and-Hold approach across multiple risk-adjusted return metrics. The AI strategy generated superior Sharpe ratios of 1.45, 2.21, and 3.14 for 2022-2024 respectively, compared to the Buy-and-Hold ratios of -1.3, 2.2, and 1.8. This alpha generation is particularly pronounced in the 2022 bear market, where the AI strategy delivered +151% total return against -65% for the passive approach, highlighting its ability to extract value through volatility regime identification.
The Sortino ratio differential is even more pronounced, with the AI strategy achieving 2.58, 6.95, and 11.19 across the three years compared to -1.82, 3.22, and 2.56 for Buy-and-Hold. This indicates substantially improved downside risk management capabilities. The Calmar ratio, measuring return relative to maximum drawdown, further validates this hypothesis, with the AI strategy's 2022-2024 aggregate ratio of 1.83 versus Buy-and-Hold's 0.25, representing a 7.32x improvement in drawdown-adjusted return.
The Hybrid approach demonstrates significant performance enhancement over both baseline strategies. Its cumulative 2022-2024 CAGR of 122% exceeds both the AI strategy's 99% and dramatically outperforms Buy-and-Hold's 17%. The most compelling evidence lies in the total return figures, where the Hybrid approach generated 2628% cumulative return versus 1620% for the AI strategy and 91% for Buy-and-Hold. This 62.2% increase in return over the pure AI implementation suggests effective utilization of market exposure timing.
Analysis of the Time in Market parameter reveals a key differentiator: the AI strategy's selective exposure (21% average) versus the Hybrid approach's higher but still discriminating exposure (64% average). This strategic participation appears to optimize the volatility-adjusted return profile, as evidenced by the Hybrid strategy's superior Sharpe ratio in 2023 (2.7 vs 2.21) and 2024 (3.16 vs 3.14), despite marginally higher annualized volatility (69% vs 64% for the full period).
Table 4 quantifies the performance degradation function f(τ), where τ represents execution delay in minutes for the AI trading strategy. The empirical results demonstrate monotonically decreasing performance across all risk-adjusted metrics as τ increases from τ=1 to τ=15, with Sharpe ratio declining by 18.2% (1.37→1.12) and CAGR diminishing by 28.6% (56%→40%).
Despite this latency-induced performance decay, the results confirm persistent alpha generation relative to the passive benchmark. When comparing against the Buy-and-Hold strategy's metrics from Table 3 (CAGR=17% Total Return=91%, SR=0.69), even the maximum latency implementation (Ï„=15) delivers:
CAGR outperformance: ΔCAGR=+23% (absolute), representing a +135.3% relative improvement
Total return differential: ΔTotal Return=+211% (absolute), a +231.9% relative enhancement
Sharpe ratio superiority: ΔSR=+0.43, indicating a +62.3% improvement in risk-adjusted performance
The Sortino ratio demonstrates even stronger statistical resilience to execution latency, with the Ï„=15 implementation maintaining a 1.96 value versus the Buy-and-Hold's 0.97, representing a +102.1% improvement in downside deviation-adjusted returns. Most notably, the Calmar ratio at maximum tested latency (0.77) still exhibits a +208.0% enhancement over the passive benchmark (0.25).
The consistent Time in Market parameter (21%) across all latency scenarios confirms that the alpha generation persists through selective market participation rather than changing exposure duration, validating the signal quality's robustness to reasonable execution delays encountered in practical implementation environments.
The performance data in Table 5 documents statistically significant alpha generation across both algorithmic implementations relative to the passive Bitcoin allocation strategy. The Hybrid approach exhibits superior performance across all risk-adjusted metrics, with a Sharpe ratio of 2.0 versus 1.86 for PAM and 0.69 for BTC Hold, representing a 189.9% enhancement over the passive benchmark. This alpha generation extends to downside risk measures, with the Hybrid strategy's Sortino ratio (3.74) and Calmar ratio (2.08) demonstrating 285.6% and 732.0% improvements respectively over the BTC Hold baseline. Most notable is the 28.9x increase in cumulative return for the Hybrid approach (2628%) versus the passive implementation (91%), achieved with only a Δσ = +15% increment in annualized volatility (69% vs 54%).
The time series decomposition of excess returns in Figures 2 and 3 reveals systematic outperformance across most observation periods, with 8/12 quarters showing positive excess returns for the AI strategy and 9/12 quarters for the Hybrid implementation. Figure 1 illustrates the compounding effect of this persistent alpha, with significant performance divergence beginning in Q3 2023 and accelerating through 2024.
The distributional characteristics of the leverage utilization function L displayed in Figure 4 reveal a strategically conservative risk management framework employed by the AI strategy. The probability mass function exhibits strong positive skewness with 51% of all trading intervals utilizing the minimum leverage parameter (L=1.0). Additionally, the distribution indicates that around 86% of all position entries maintain leverage below or equal to 2.0x. This pronounced left-truncated distribution with minimal density in the upper tail (only 2% of positions employ maximum leverage L=5.0) demonstrates a systematic variance-minimization approach consistent with an optimal criterion for long-term capital growth.
The capital utilization profile C depicted in Figure 5 further reinforces this risk-controlled allocation methodology. The highly concentrated mass in the first decile bin (≤0.10) representing 60% of all trading intervals suggests substantial risk dispersion across temporal periods. The bimodal structure with secondary density at ≈0.70 (11% of observations) likely represents conditional sizing increases during periods of maximum statistical advantage identification, while maintaining an expected capital utilization ≈17% across the entire sample period.
The joint probability distribution f(L,C) visualized in Figure 6 provides granular empirical evidence of the algorithmic risk management framework's implementation characteristics. The conditional probability mass exhibits strong concentration in the region defined by {(L,C):L=1.0,C∈[0,10%]} with P(L=1.0,C∈[0,10%])=0.362, indicating that 36.2% of all trading intervals utilize minimum leverage with minimal capital deployment. The cumulative density function reveals that P(L≤2.0,C≤10%)=0.533, demonstrating that the majority of position entries maintain both conservative leverage and capital utilization parameters simultaneously.
The empirical covariance structure between L and C displays notable heteroscedasticity, with increasing capital utilization variance at higher leverage levels. Specifically, the conditional distribution f(C∣L=5.0) exhibits a bimodal characteristic with local maxima at C≈70% while maintaining zero probability mass in lower capital utilization bins. This conditional dependency structure implements an implicit risk parity framework that allocates capital proportionally to signal conviction, with the maximum combined risk exposure (L=5.0,C≈70%) representing only 1.7% of trading events.
The joint moments of the bivariate distribution yield an expected leverage-capital product
confirming approximately 28.6% average portfolio risk utilization. This empirically optimized risk allocation framework mathematically ensures sufficient margin buffer capacity during market regime transitions while systematically limiting the value at risk to levels that prevent path-dependent performance degradation through forced liquidations.
