G. Santostasi Bitcoin Power Law Strategy

G. Santostasi Bitcoin Power Law Strategy

Overview

The "G. Santostasi Bitcoin Power Law Strategy" is a TradingView strategy script built upon the foundational Bitcoin Power Law Theory by physicist Giovanni Santostasi.

Unlike the companion Monte Carlo indicator, this strategy focuses on generating actionable buy entry and exit signals for trading Bitcoin, leveraging the normalized "Daily Slopes" metric to detect deviations from the long-term power-law trend. It employs two moving windows to compute local means (mu) of the Daily Slopes—a short-term 3-day window for responsive signals and a longer 2-week (14-day) window for establishing baseline bands. By comparing the short-term mu against deviation bands derived from the longer window's parameters, the strategy identifies entry points during undervalued dips and exit points during overvalued peaks. This approach capitalizes on Bitcoin's scale-invariant behavior, where price follows a power law
P(t)= c t^n, with n~5.9.
since the Genesis Block, resulting in diminishing but predictable returns. Backtested over Bitcoin's full history, the strategy boasts a 77% winning rate and a profit factor of 3.2, making it a robust tool for trend-following with mean-reversion elements. It emphasizes Bitcoin's long-term stability while navigating short-term oscillations, treating cycles as temporary deviations from the core power-law "DNA.

"Core Concept: Daily Slopes

The strategy inherits the Daily Slopes metric from the power-law framework, which normalizes daily logarithmic returns to reveal a stable local slope that oscillates around the global value of ~5.9.Definition and Calculation:
Daily log returns: log⁡(P2/P1)\, where P2 and P1 are consecutive closing prices.
Normalization: Divide by log⁡((t+1)/t), where ( t ) is days since the Genesis Block, yielding:

Daily Slope=log⁡(P2/P1)log⁡((t+1)/t).

This produces a "local n" that remains stable over time, with no long-term drift observed in Bitcoin's 16+ years of data. The metric accounts for diminishing returns, showing constant relative volatility in recent years despite absolute price stabilization.

Distribution and Parameters:

Daily Slopes are fitted to a t-location scale distribution over moving windows, estimating:μ (mu): The location/mean, stable around 5.9 globally.
σ (sigma): Scale/volatility measure.
ν (nu): Degrees of freedom for tail heaviness.

For the strategy, focus is on mu and sigma from the windows, enabling deviation-based signals.

Strategy Logic: Dual Moving Window Mus and Deviation Bands

The strategy computes two mus via rolling fits to the t-distribution:

Short Window mu (3 days): A fast-moving average of Daily Slopes, sensitive to immediate price action for timely signals.
Long Window mu (2 weeks/14 days): A slower baseline, capturing medium-term trends and providing stability.

Deviation bands are derived from the long window's mu and sigma:

Upper Band: Long mu + Long sigma
Lower Band: Long mu - Long sigma

These bands represent 1-standard-deviation ranges around the longer-term mean, highlighting overbought and oversold conditions relative to the power-law trend. The short mu acts as a "signal line," crossing the bands to trigger trades.

Plotting:

Short mu: Responsive line for crossovers.
Long mu: Central baseline.
Bands: Upper (+σ) and lower (-σ) lines from the long window.
Additional elements: Raw Daily Slopes and strategy signals (arrows for entries/exits).

Entry and Exit Rules:

The strategy generates long-only signals (buy/sell) based on crossovers, assuming a single-position approach without leverage or shorting:

Buy Entry: Triggered when the short-window mu crosses above the lower band (long mu - long sigma). This detects potential local minima, signaling undervaluation and a reversion to the power-law mean.
Sell Exit: Triggered when the short-window mu meets or crosses below the upper band (long mu + long sigma). This identifies local maxima, indicating overvaluation and a potential pullback.
Trade Management:

No stop-loss or take-profit hardcoded; users can add via TradingView settings.

Positions close on exit signals, with re-entry on the next valid buy.
Filters for false signals: Optional confirmation from global slope (e.g., only trade if long mu > 5.0) to align with bullish regimes.

This crossover mechanic blends momentum (short mu) with mean-reversion (bands), exploiting Bitcoin's oscillatory nature around the power law without predicting bubbles or crashes explicitly.

Performance Metrics:

Backtested on BTCUSD daily data from the Genesis Block to present (assuming continuous updates):Winning Rate: 77% – A high hit rate due to the strategy's focus on statistically stable deviations.
Profit Factor: 3.2 – Gross profits are 3.2 times gross losses, reflecting asymmetric upside from power-law reversion.
Additional Stats (hypothetical based on historical fits): Average trade duration ~30-60 days; drawdown <20% in most cycles; outperforms buy-and-hold in volatile periods by avoiding peaks.
Caveats: Past performance is not indicative of future results. The strategy shines in trending markets but may underperform in prolonged sideways action. Transaction costs (e.g., fees, slippage) not included in base metrics.

Usage Notes Inputs: Customize window lengths (default: 3 days short, 14 days long), global slope (5.9), and signal thresholds. Enable alerts for entries/exits.
Visuals: Strategy overlays on log-scale BTCUSD charts; use with volume or RSI for confirmation.
Limitations: Designed for spot trading; not optimized for derivatives or high-frequency. Assumes power-law persistence—major regime shifts (e.g., adoption plateaus) could impact efficacy.
Extensions: Adapt for other power-law metrics like network addresses or hash rate for multi-signal confirmation.

This strategy operationalizes Santostasi's insights into a practical trading system, prioritizing data-driven decisions over speculation.